8.3: The Impact of News of Expected Returns

8.3.1: Surprises and Returns

Learning Objective

Describe how a surprise announcement can influence a stock’s price

Key Points

• Surprise announcements that come from a company, its competition, or a supplier or customer can affect the long run value of a stocks and bonds related to that company.
• These announcements will often concern earnings, stages in a product development cycle (FDA approval of a drug) or corporate structure changes (the acquisition of a competitor) and can move a company’s outlook positively or negatively.
• When the news is generally seen as positive, a company’s equity and debt become more valuable on the secondary market, and its stock price will rise and the effective yield on its debt instruments will fall.

Key Term

mergers and acquisitions

Mergers and acquisitions (M&A) is an aspect of corporate strategy, corporate finance, and management dealing with the buying, selling, dividing, and combining of different companies and similar entities that can help an enterprise grow rapidly in its sector or location of origin, or a new field or new location, without creating a subsidiary, other child entity, or using a joint venture.

Surprise announcements can trigger a chain of events that affect the stock price of a particular company, competitors and other companies that might be suppliers to or customers of the primary company.

Announcements of Mergers and acquisitions (M&A) are a frequent type of surprise announcements. Mergers and acquisition is a category of announcement that deals with corporate structure. When the announcement is publicly made, analysts use that information to factor into the company’s long run market outlook. A merger or an acquisition could signal to an analyst that one particular company is financially weak, and it could downgrade its long run outlook for that company. Alternatively, an M&A announcement could also signal to analysts that a company has a chance to increase its market share and henceforth its profits. These announcements typically make the biggest splash in a top-heavy industry, such as automobiles, pharmaceuticals, or healthcare, with a few strong players dominating a market that is researching, developing, and innovating new products.

Other announcements that can have a variety of impacts on asset valuation can come in the form of a major court decision, news of development of new research, and innovation, FDA approval of a new drug or a new cheap source of raw materials. Any of this news has the potential to impact a particular company and, in some cases, competition, suppliers, and customers of that company. In many cases, there will be signals that analysts pick up on ahead of time. Investors who are actively making investment decisions based on a particular company or within a particular industry need to be aware of how a surprise announcement might affect their investment.

Fixed-income market participants also make forecasts on the long-run health of a company to project the likelihood an issuer of debt might default. A company’s instruments are subject to move in the event of an aforementioned announcement or if a private rating agency (Standard and Poors or Moody’s) changes its outlook on their debt. If a news announcement is seen as positive for a company, its fixed-income instruments might seem more creditworthy, its bonds will rise in price, and its yield will decline. The inverse is also true.

Take a look at the creditworthiness ratings of different countries by Standard and Poors.

World countries Standard & Poor’s ratings

An example of the credit ratings prescribed by Standard & Poor’s as a result of their respective long-term liability analysis for debt issued at the national government level. Countries issue debt to build national infrastructure. Look how expensive it is to raise capital for such projects based on geographic region.

8.3.2: Announcements, News, and Returns

Learning Objective

Describe how analysts use announcements, news, and returns to evaluate stock

Key Points

• A company that is publicly traded must announce its earnings reports quarterly. When the report matches analysts’ expectations, the stock’s price will not be greatly affected. When it announces a report that is unexpected, it can affect the stock price of a competitor or supplier as well.
• Beta is a metric used to signal the risk in a particular stock. Stocks with high beta values fluctuate more on a day-to-day basis than those with lower beta values.
• Analysts constantly assess the health of public companies to assess the value of its equity and debt instruments, and their outlook affects stock and bond prices in secondary markets.

Key Term

beta

In finance, the Beta (β) of a stock or portfolio is a number describing the correlated volatility of an asset in relation to the volatility of the benchmark that said asset is being compared to.

The words stock and equity are used interchangeably, because a stock is reflective of a piece of ownership in a company. In general, investors buy stocks for two reasons: because they expect the company to grow its product and market share over time (growth) or because they feel that the company is undervalued based on its current stock price. Analysts may research a stock from a fundamental or a technical lens.

Fundamental analysis involves analyzing a company’s financial statements and health, its management and competitive advantages, and its competitors and markets . Technical analysts study the patterns and price fluctuations and attempt to forecast the direction of prices through the study of past market data, primarily price, and volume. A stock’s price is essentially determined by the buying and selling decisions of fundamental and technical analysts, who often manage large sums of money and have access to broad pools of data. Some stocks tend to fluctuate more than others on a day-to-day basis, and the metric called Beta describe’s the variance of a stocks day to day price. Stocks that tend to experience larger swings have higher beta values and expose owners to more specific risk.

In order for a company to be publicly traded on an exchange, it must comply with the regulations of that exchange board (NYSE or NASDAQ). Public investors are entitled to complete, accurate, and timely financial information about their investments. Companies generally announce updated financial figures on a quarterly basis. These figures include their current revenues, expenses and profits, and investors use this information to assess the company’s financial health. For most established companies, these reports are consistent and predictable and barely affect a stock’s price. Macy’s may announce higher profits in quarter 4 than quarter 3, but its price might not move, because analysts expected that Christmas would bring additional sales based on past data.

When a company announces its earnings as higher or lower than expected, the stock may experience a sudden shift in value. A higher than expected profit may come from increased revenues or decreased expenses. If a growing company announces higher than expected profits because of decreased expenses, it signals to investors that the company has found a cheaper way to produce its good. That could in turn affect the expected returns of a competitor’s stock, either positively or negatively, depending on how analysts forecast the effect. The announcement of higher than expected sales from Ford could affect its stock price significantly, and it could set into motion a chain of events. If analysts believe that the trend is based on a shift away from public transportation, it could raise the price of GM, Toyota, and maybe even Chevron. If Nvidia, a company who produces micro-processors for smart phones, announces higher than expected profits on reduced production costs, it might not only cause their stock to spike, but it could lead to a decrease in the price of the stock of their primary competition, Intel.

In general, fluctuations in one stock will often lead to fluctuations in another stock. There are times when the markets are relatively stable and those when it is relatively volatile. Consider the image below. The correlation of 0.769 suggests that the volatility of the stock market in one month is very highly correlated to that in the previous month.

Volatility begets volatility

Data shown is from the period of Jan. 1990-Sep. 2009. Volatility is measured as the standard deviation of S&P 500 one-day returns over a month’s period.

8.4: Risk

8.4.1: Types of Risk

There are many types of financial risk, including asset-backed, prepayment, interest rate, credit, liquidity, market, operational, foreign, and model risk.

Learning Objective

Classify different securities by the types of financial risk associated with the investment opportunity

Key Points

• Financial risk is associated to the chances that an investor might lose value in an investment. It is separated into different sources of decline.
• Often the risks interact with each other and ultimately shock causes panic. Many of the worst market crashes have been a result of widespread speculation and not the devaluation of that asset itself.
• In the market crash of 2008, investors feared that some home owners would default. It triggered a chain of events that shocked the whole world and left many people in bad financial situations.

Key Term

Variable Rate Mortgage

A variable-rate mortgage, adjustable-rate mortgage (ARM), or tracker mortgage is a mortgage loan with the interest rate on the note periodically adjusted based on an index which reflects the cost to the lender of borrowing on the credit markets.

The term “financial risk” is broad, but can be broken different categories to understand it better.

Types of Financial Risk

Asset-backed risk affects investments in asset-backed securities such as home loans. In order to finance home sales, banks issue bonds that serve as a debt obligation to its buyer. The buyer of the debt is essentially receiving the interest from the bank that the home-buyer is paying to it.

Prepayment risk is the risk that the buyer goes ahead and pays off the mortgage. Therefore, the buyer of the bond loses the right to the buyer’s interest payments over time.

Interest rate risk refers an asset whose terms can change over time, such as a Variable Rate Mortgage payment.

Credit risk or default risk, is the risk that a borrower will default (or stop making payments).

Liquidity risk is the risk that an asset or security cannot be converted into cash in a timely manner. Some investments (i.e. stocks) can be sold immediately at the current market rate and others (i.e. houses) are subject to a much higher degree of liquidity risk.

Market risk is the term associated with the risk of losing value in an investment will lose value because of a decline in the market.

Operational risk is another type of risk that deals with the operations of a particular business. If you are invested in the Boston Red Sox, your operational risk might include the chance that starting pitchers and recent acquisitions won’t perform, that your manager will turn the clubhouse into a mess, or that ownership will not be able to execute a long term strategy. Any of these risks might result in decreased revenues from ticket sales.

Foreign investment risk involves the risk associated with investments in foreign markets.

Model risk involves the chances that past models, which have been used to diversify away risk, will not accurately predict future models.

Example

A recent phenomenon that applies the concepts of these risks and how they interact with each other happened in 2008 when the housing market crashed. Can you find an example of each form of risk here?

Leading up to the crisis, many people received loans to buy houses which they really couldn’t afford. The mortgages often featured variable rate annuities, meaning that the interest rate terms of the mortgage started low and increased over time. Over the past 20 year period, house prices had risen constantly and investors assumed the trend would continue. Buyers worried about an adjustment to their interest rate, and all of a sudden a 1500 monthly payment became 2000. When interest rates climbed 2 percentage points and the mortgage climbed to $2000, some owners had to default (stop making payments) . They were promised that their investment would appreciate in value and they would be able to refinance it. The home loans were packaged and shipped off to investors all over the world in the form of complex investment vehicles. They seemed rewarding and highly safe at first, but then a few started breaking down. By now, these vehicles had made their way all the way around the world. When some investors defaulted, the world realized there were no mechanics around to fix these vehicles. After a few vehicles broke down, no one wanted to buy them, leading to the worst crash across world markets since 1929.

8.4.2: Measuring Risk

The higher the risk undertaken, the more ample the expected return and the lower the risk, the more modest the expected return.

Learning Objective

Calculate the risk of a portfolio using computational methods

Key Points

• The general progression in the risk-return spectrum is: short-term debt, long-term debt, property, high-yield debt, and equity.
• When a firm makes a capital budgeting decision, they will wish, as a bare minimum, to recover enough to pay the increased cost of goods due to inflation.
• Risk aversion is a concept based on the behavior of firms and investors while exposed to uncertainty to attempt to reduce that uncertainty.
• Beta is a measure firms can use in order to determine an investment’s return sensitivity in relation to overall market risk.

Key Terms

systematic risk

The risk associated with an asset that is correlated with the risk of asset markets generally, often measured as its beta.

inflation

An increase in the general level of prices or in the cost of living.

Risk and Return Considerations

Risk refers to the variability of possible returns associated with a given investment. Risk, along with the return, is a major consideration in capital budgeting decisions. The firm must compare the expected return from a given investment with the risk associated with it. Higher levels of return are required to compensate for increased levels of risk. In other words, the higher the risk undertaken, the more ample the return – and conversely, the lower the risk, the more modest the return.

This risk and return tradeoff is also known as the risk-return spectrum. There are various classes of possible investments, each with their own positions on the overall risk-return spectrum. The general progression is: short-term debt, long-term debt, property, high-yield debt, and equity. The existence of risk causes the need to incur a number of expenses. For example, the more risky the investment the more time and effort is usually required to obtain information about it and monitor its progress. Moreover, the importance of a loss of X amount of value can be greater than the importance of a gain of X amount of value, so a riskier investment will attract a higher risk premium even if the forecast return is the same as upon a less risky investment. Risk is therefore something that must be compensated for, and the more risk the more compensation is required.

When a firm makes a capital budgeting decision, they will wish, as a bare minimum, to recover enough to pay the increased cost of investment due to inflation. Thus, inflation is a pivotal input in a firm’s cost of capital. However, since interest rates are set by the market, it happens frequently that they are insufficient to compensate for inflation.

Inflation

Inflation is a rise in the general level of prices of goods and services in an economy over a period of time.

Risk aversion also plays an important role in determining a firm’s required return on an investment. Risk aversion is a concept based on the behavior of firms and investors while exposed to uncertainty to attempt to reduce that uncertainty. Risk aversion is the reluctance to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff. For example, a risk-averse investor might choose to put his or her money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value. Risk aversion can be thought of as having three levels:

1. Risk-averse or risk-avoiding
2. Risk-neutral
3. Risk-loving or risk-seeking

Beta is a measure firms can use in order to determine an investment’s return sensitivity in relation to overall market risk. Beta describes the correlated volatility of an asset in relation to the volatility of the benchmark that said asset is being compared to. This benchmark is generally the overall financial market and is often estimated via the use of representative indices, such as the S&P 500. Beta is also referred to as financial elasticity or correlated relative volatility, and can be referred to as a measure of the sensitivity of the asset’s returns to market returns, its non-diversifiable risk, its systematic risk, or market risk. Higher-beta investments tend to be more volatile and therefore riskier, but provide the potential for higher returns. Lower-beta investments pose less risk, but generally offer lower returns.

8.5: Implications Across Portfolios

8.5.1: Calculating Expected Portfolio Returns

A portfolio’s expected return is the sum of the weighted average of each asset’s expected return.

Learning Objective

Calculate a portfolio’s expected return

Key Points

• To calculate the expected return of a portfolio, you need to know the expected return and weight of each asset in a portfolio.
• The figure is found by multiplying each asset’s weight with its expected return, and then adding up all those figures at the end.
• These estimates are based on the assumption that what we have seen in the past is what we can expect in the future, and ignores a structural view on the market.

Key Term

weighted average

In statistics, a weighted average is an average that takes each object and calculates the product of its weight and its figure and sums all of these products to produce one average. It is implied that all the individual weights add to 1.

Let’s say that we have a portfolio that consists of three assets, and we’ll call them Apples, Bananas, and Cherries. We decided to invest in all three, because the previous chapters on diversification had a profound impact on our investment strategy, and we now understand that diversifiable risk doesn’t pay a risk premium, so we try to eliminate it.

A Fruitful Portfolio

How would you calculate the expected return on this portfolio?

The return of our fruit portfolio could be modeled as a sum of the weighted average of each fruit’s expected return. In math, that means:

Where A stands for apple, B is banana, C is cherry and FMP is farmer’s market portfolio. W is weight and E(R_X) is the expected return of X. A good exercise would be to calculate this figure on your own, then look below to see if you completed it accurately.

Here’s what you should get:

In reality, a portfolio is not a fruit basket, and neither is the formula. A math-heavy formula for calculating the expected return on a portfolio, Q, of n assets would be:

What does this equal?

Remember that we are making the assumption that we can accurately measure these outcomes based on what we have seen in the past. If you were playing roulette at a casino, you may not know if red or black (or green) is coming on the next spin, but you could reasonably expect that if you bet on black 4000 times in a row, you’re likely to get paid on about 1900 of those spins. If you go to Wikipedia, you can review a wide variety of challenges to this model that have very valid points. Remember, the market is random: it is not a roulette wheel, but that might be the best thing we have to compare it to.

8.5.2: Portfolio Risk

The risk in a portfolio is measured as the amount of variance that investors can expect based on historical data.

Learning Objective

Calculate a portfolio’s variance

Key Points

• Portfolios that are efficient investments are those that effectively diversify the underlying risk away and price their investment efficiently.
• Portfolio risk takes into account the risk and weight of each individual position and also the co-variances across different positions.
• To calculate the risk of a portfolio, you need each asset’s variance along with a matrix of cross-asset correlations.

Key Terms

portfolio

The group of investments and other assets held by an investor.

Co-Variance

In probability theory and statistics, co-variance is a measure of how much two random variables change together.

risk

The potential (conventionally negative) impact of an event, determined by combining the likelihood of the event occurring with the impact, should it occur.

Portfolio Risk

An investor can reduce portfolio risk by holding combinations of instruments which are not perfectly positively correlated (correlation coefficient). In other words, investors can reduce their exposure to individual asset risk by holding a diversified portfolio of assets. Diversification may allow for the same portfolio expected return with reduced risk.

Three assets (apples, bananas, and cherries) can be thought of as a bowl of fruit. The index is a a fruit basket. A full fruit basket probably has 10 or 15 different fruits, but my bowl will be efficient as much as its statistical parameters (risk and return) mimic those of the whole basket. In this unit, we are talking about calculating the risk of a portfolio. In addition, we can extend the implications made by the security market line theory from individual assets to portfolios. How does my bowl of fruit compare to the whole basket and how does that compare to other bowls out there?

Calculating Portfolio Risk

To calculate the risk in my bowl, we need a little more background information on fruit markets. First, we are going to need the variance for each fruit. Remember that the standard deviation answers the question of how far do I expect one individual outcome to deviate from the overall mean. And variance is that number squared. Mathematically, the formula is:

It is the expected value of the difference between the individual return in a given day (R) and the average outcome average return over a year (E(R)).

In order to calculate the variance of a portfolio of three assets, we need to know that figure for apples, bananas, and cherries, and we also need to know the co-variance of each. Co-variances can be thought of as correlations. If every time bananas have a bad day, so do apples, their co-variance will be large. If bananas do great half of the time when cherries do bad and bananas do terrible the other half, their co-variance is zero. If there is zero correlation among all three fruits, we have cut our risk in thirds by owning all three, but if they are perfectly correlated, we haven’t diversified away any of our risk.

In reality, they are probably positively correlated, since they are all fruits, but not at all perfectly. Apples and bananas grow in different climates so their performance may be a result of weather patterns in either region. Apples may be a substitute for cherries when cherries are expensive. The overall risk of the portfolio would take into account three individual variances and three co-variances (apples-bananas, apples-cherries, and bananas-cherries) and it would reduce the overall portfolio to the degree that they are uncorrelated.

The formula to compute the co-variance between returns on X and Y:

This means what do I expect to see, in a given time period, when I multiply how much X returned off its average performance from how much Y returned off its average. But notice how it could be positive or negative. And if X tends to be up when Y is down, that would make them two good hedges. And it can be shown that:

From co-variance, we get correlation coefficients:

In finance and statistics, the greek letter rho squared represents variance.

So now that we have figures to help us measure the risk and reward of our individual fruit bowl, we can go look at historical figures to determine the expected returns and the risk of the index that comprises the entire fruit basket industry. If our portfolio of investments has diversified away as much risk as is possible given the costs of diversifying, our portfolio will be attractive to investors. If our bowl does not diversify away enough risk, it will not lie on the Security Market Line for those who we are trying to recruit into buying our portfolio.

The same principles that were applied to individual investments in the Understanding the SML section can be applied to the market for portfolio investments. If an institutional investor, such as a city pension fund, looked at two portfolios with identical returns and different risks, they would choose the portfolio that minimized its risk. Thus the only portfolios that are efficient investments are those that effectively diversify the underlying risk away and price their investment efficiently .

Variance of any portfolio

The formula shows that the overall variance in a portfolio is the sum of each individual variance along with the cross-asset correlations.

8.5.3: Beta Coefficient for Portfolios

A portfolio’s Beta is the volatility correlated to an underlying index.

Learning Objective

Calculate a portfolio’s beta

Key Points

• In individual stocks, a beta coefficient compares how much a particular stock fluctuates in value on a day-to-day basis.
• A beta coefficient for a portfolio of assets measures how that portfolio value changes compared to a benchmark, like the S&P 500. A value of 1 suggests that it fluctuates as much as the index and in the same direction.
• A beta coefficient of less than 1 suggests a portfolio that fluctuates less than the benchmark. A negative beta is an indication that a portfolio moves in the opposite direction of its benchmark.

Key Term

Normalized variable

In statistics, a normalized variable is one that is calculated using a ratio of itself and some benchmark figure. Normalized figures tend to be smaller than the original values.

In this section, we will discuss the idea of calculating a Beta coefficient to help investors measure the risk-reward trade-off for a blended pool of investments.

In this case, it is important to remember that a portfolio may represent the seller side of the market and the buyer can be thought of an institutional investor or a mutual fund. A portfolio’s Beta is the volatility correlated to an underlying index. If we think of the S&P 500 as the index, a portfolio that fluctuates identically to the market has a Beta of 1. What would the following portfolios have for Beta values?

Calculating Beta

Two hypothetical portfolios; what do you think each Beta value is?

Do you have an answer? Beta is a normalized variable, which means that it is a ratio of two variances, so you have to compare the volatility of returns to the benchmark volatility. Portfolio A has a direct relationship with the S&P 500 – it is scaled by three times each day. When the market is up 2%, it is up 6%. Thus, the portfolio would have a Beta value of 3. Portfolio B is a different situation; it is also directly proportional, but in the negative direction. Every time the market is up 1%, the portfolio is down half a percent. The Beta for this portfolio, when compared with the S&P 500 benchmark, would be -0.5. A Beta of zero in this situation doesn’t necessarily mean a risk free asset, it simply means that it is not correlated with the benchmark.

In reality, the numbers would rarely work out this cleanly, but this is a good model to demonstrate some key concepts. A pension fund that seeks to maximize its reward and limit its risk might be interested in each of these portfolios. If you invested equal amounts in each portfolio, it would leave you over-exposed to the market because it would have a Beta of 1.5. But let’s say you have $300,000 to invest; you could put that in a fund that is indexed to the S&P 500 and is perfectly correlated with it.

Every time the S&P gains 1%, your fund nets you 100,000 in fund A and S Misplaced &3,000 and your position in fund B pays you 2,000, which is less damage than you would have suffered on your position in the S&P index fund. On days when the S 3,000 and your fund A position loses 2,000 and your upside is limited by the same amount, your downside is reduced.

A pension fund is a good example of an institutional client that could extend the principles of diversification to a pool of blended portfolios. A city with an aging workforce needs to be protected from downside risk. It is the same principle as an employee approaching retirement; it can afford to have a heavier position in the S&P 500 if it has a position in portfolio B.

8.6: Diversification

8.6.1: Impact of Diversification on Risk and Return: Unsystematic Risk

In general, diversification can reduce risk without negatively impacting expected return.

Learning Objective

Describe unsystemic risk

Key Points

• Diversification is not putting all your eggs in one basket.
• Diversification relies on the lack of a tight positive relationship among the assets’ returns, and works even when correlations are near zero or somewhat positive.
• The debate over active vs passive management is one that takes on the limits to diversification.

Key Term

Unsystematic risk

Unsystematic or diversifiable risk is a term given to the portion of risk in a portfolio that can be diversified away by holding a pool of individual assets.

Did your grandmother ever warn you not to put all your eggs in one basket? Did you know what she was talking about? The implication is obvious. If you put all your eggs in one basket, and that basket breaks, you are stuck with nothing to fry up into an omelet.

Grandma wasn’t telling you to grow up and be an omelet chef, she was actually giving you some sage advice that applies to your future as a portfolio manager. We have talked about diversification previously, and this section will follow from that. Remember, we talked about every particular investment having an expected return and a variance. If you are managing a pool of assets, you want to get positive returns without being in danger of “losing your shirt. ” The probability that one stock goes belly up is much higher than that the whole stock market does. In finance, systematic risk is the term associated with risk that can be diversified away by investing in a broader pool of assets.

Diversification relies on the lack of a tight positive relationship among the assets’ returns, and works even when correlations are near zero or somewhat positive. On the flip-side, hedging is the tactic that relies on negative correlations among assets. Diversification comes with a cost associated with it, and some might point out that it is possible to over-diversify. The idea is that you can only diversify away so much risk, that the marginal returns on each new asset are decreasing, and each transaction has a cost in terms of a transaction fee and also research costs. At some point, it just isn’t worth it anymore. The risk that can be diversified away is called “unsystematic risk” or “diversifiable risk. “

Some investors like to call themselves fans of active or passive management. In fact, two of the biggest mutual fund managers–Fidelity and Vanguard–take opposite stances on this issue and use it as a selling point to customers. Proponents of passive management say the market knows best, and they seek a portfolio that has an underlying pool that mimics a benchmark index (think S&P 500). The other guys–active managers–believe that their fundamental analysis yields them a competitive advantage. They might decide Microsoft’s stock is underpriced based on changing demographics to the labor supply in Seattle, or they might decide that political stability has improved emerging markets in Sub-Saharan Africa but the yield on their bonds hasn’t taken that into account. This debate is all held on the margins. Research has shown that there is a clear advantage in any portfolio to hold at least 30 different positions.

An empirical example relating diversification to risk reduction

In 1977 Elton and Gruber worked out an empirical example of the gains from diversification. Their approach was to consider a population of 3,290 securities available for possible inclusion in a portfolio, and to consider the average risk over all possible randomly chosen n-asset portfolios with equal amounts held in each included asset, for various values of n. Their results are summarized in the following table. It can be seen that most of the gains from diversification come for n≤30.

8.6.2: Impact of Diversification on Risk and Return: Systematic Risk

Systematic risk is intrinsic to the market, and thusly diversification has no effect on its presence in investments.

Learning Objective

Describe how systemic risk influences the stock market

Key Points

• Diversification is a technique for reducing risk that relies on the lack of a tight positive relationship among the returns of various types of assets.
• The role of diversification is to narrow the range of possible outcomes.
• Unsystematic risk does not factor into an investment’s risk premium, since this type of risk can be diversified away.

Key Term

systematic risk

systematic or non-diversifiable risk is a term given to the portion of risk in a portfolio that cannot be diversified away by holding a pool of individual assets and therefore commands a return in excess of the risk-free-rate.

Recall that previously we talked about the security market line and the implication that investors require more compensation for extra risk. One might pay the same amount for a safe investment as for an investment carrying more risk; however, the riskier investment will, in theory, provide a higher return. This is the principle behind the security market line . Diversification is a technique for reducing risk that relies on the lack of a tight positive relationship among the returns of various types of assets. By diversifying a portfolio of assets, an investor loses the chance to experience a return associated with having invested solely in a single asset with the highest return. On the other hand, the investor also avoids experiencing a return associated with having invested solely in the asset with the lowest return — sometimes even becoming a negative return. Thus, the role of diversification is to narrow the range of possible outcomes.

The Security Market Line

Diversification theory says that the only risk that earns a risk premium is that which can’t be diversified away.

As a result, the portion of risk that is unsystematic — or risk that can be diversified away — does not require additional compensation in terms of expected return. For example, consider the case of an individual who buys 50 corporate bonds from a single company. The individual receives a certain yield based on the purchase price. However, if unexpected business risks lead to liquidity problems, the company might go bankrupt and default on its loans. In such a case, the investor will lose the entirety of the investment. Conversely, if the investor buys a single bond from 50 different corporations who have similar credit ratings, then one instance of insolvency will have a far less drastic effect on the investor’s portfolio.

Now, imagine that these 50 corporations are all given a lesser credit rating because of the risk of their overall market segment. In this case, the individual is still at risk to lose some or all of the initial investment. This type of risk cannot be diversified away, and is referred to as systematic risk. This is the portion of risk that pays the risk premium, because the risk associated with this particular segment of the market is more tightly linked to the risk of the market as a whole. This risk is present regardless of the amount of diversification undertaken by an investor.

8.7: Understanding the Security Market Line

8.7.1: Expected Risk and Risk Premium

Overall riskiness of an asset is composed of its own individual risk (beta) along with its risk in relation to the market as a whole.

Learning Objective

Use a stock’s beta to estimate a stock’s daily growth or decline.

Key Points

• In return for undertaking risk, investors expect to be compensated in such as a way as to reasonably reward them.
• Systemic risk is the risk associated with an entire financial system or entire market. It cannot be diversified away.
• Unsystematic risk is risk to which only specific classes of securities or industries are vulnerable, and with proper grouping of assets it can be reduced or even eliminated.
• Beta is a number describing the correlated volatility of an asset in relation to the volatility of the benchmark that said asset is being compared to — usually the market as expressed in an index.
• The term risk premium refers to the amount by which an asset’s expected rate of return exceeds the risk-free interest rate.

Key Terms

Risk free rate

Risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss.

treasury bill

Treasury bills (or T-Bills) mature in one year or less. They do not pay interest prior to maturity; instead they are sold at a discount of the par value to create a positive yield to maturity.

A certain amount of risk is inherent in any investment. Risk can be defined, generally, as the potential that a chosen action or activity (including the choice of inaction) will lead to a loss or an undesirable outcome. The notion of risk implies that a choice having an influence on the outcome exists. More specifically to finance, risk can be seen as relating to the probability of uncertain future events. In return for undertaking risk, investors expect to be compensated in such as a way as to reasonably reward them. This is a central them in the subject of finance. In the financial realm, two types of risk exist: systematic and unsystematic.

Systemic risk is the risk associated with an entire financial system or entire market. This type of risk is inherent in all marketable securities and cannot be diversified away. On the other hand, unsystematic risk is risk to which only specific classes of securities or industries are vulnerable. This type of risk is uncorrelated with broad market returns, and with proper grouping of assets can be reduced or even eliminated. Because of this characteristic, investors are not rewarded for taking on unsystematic risk.

Systematic risk can be understood further using the measure of Beta. This is a number describing the correlated volatility of an asset in relation to the volatility of the benchmark that said asset is being compared to — usually the market as expressed in an index.

Beta

Beta is a measure that relates the rate of return of an asset, ra, with the rate of return of a benchmark, rb.

Values of Beta can be interpreted using the following information:

• Betas less than 0: Asset generally moves in the opposite direction as compared to the index.
• Betas equal to 0: Movement of the asset is uncorrelated with the movement of the benchmark.
• Beta between 0 and 1: Movement of the asset is generally in the same direction as, but less than the movement of the benchmark.
• Beta equal to 1: Movement of the asset is generally in the same direction as, and about the same amount as, the movement of the benchmark.
• Beta greater than 1: Movement of the asset is generally in the same direction as, but more than, the movement of the benchmark.

Risk Premium

The term risk premium refers to the amount by which an asset’s expected rate of return exceeds the risk free rate. The difference between the return of an asset in question and that of a risk-free asset — for instance, a US Treasury bill — can be interpreted as a measure of the excess return required by an investor on the risky asset. The risk premium, along with the risk-free rate and the asset’s Beta, is used as an input in popular asset valuation techniques, such as the Capital Asset Pricing Model.

8.7.2: Defining the Security Market Line

The security market line displays the expected rate of return of a security as a function of systematic, non-diversifiable risk.

Learning Objective

Describe the Security Market Line

Key Points

• The security market line is the theoretical line on which all capital investments lie. Investors want higher expected returns for more risk.
• On a graph, the line has risk on its horizontal axis (independent variable) and expected return on the vertical axis (dependent variable).
• Assuming a linear relationship between risk and return, the assumption is that the y-intercept is the return on a risk-free investment (the risk free rate), and the slope is the premium on risk in terms of expected returns.
• Given two investments with the same expected return, investors would always choose less risk. Someone with opposite preferences might better be called a gambler.

Key Terms

market risk premium

the amount by which expected rate of return of the exchange system exceeds the risk-free interest rate

market risk

the potential for loss due to movements in prices in a system of exchange

line of credit

source of debt extended to a government, business or individual by a bank or other financial institution

diversifiable risk

the potential for loss which can be removed by investing in a variety of assets

security market line

Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of return of an individual security as a function of systematic, non-diversifiable risk (its beta).

beta

Average sensitivity of a security’s price to overall securities market prices.

The security market line, also known as the “characteristic line”, is the graphical representation of the capital asset pricing model. It is a hypothetical construct based on a world of perfect information. In the absence of perfect information, we can more or less assume historical data will give us an accurate expectation of what kind of returns and risk to expect with a particular investment of capital. The security market line graphs the systematic, non-diversifiable risk (stated in terms of beta) versus the return of the whole market at a particular time, and shows all risky marketable securities. The security market line is defined by the equation:

The equation that defines the security market line.

Look at the equation and remember that old formula of a line: y = mx + b. In this case it looks rearranged, like y = b + mx, but the real question is what do the slope and y-intercept actually represent?

The Y-intercept of the SML is equal to the risk-free interest rate. Recall that the risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss. When used in portfolio management, the SML represents the investment’s opportunity cost — i.e., investing in a combination of the market portfolio and the risk-free asset. All the correctly priced securities are plotted on the SML. The assets that lie above the line are undervalued because for a given amount of risk, they yield a higher return. The assets below the line are overvalued because for a given amount of risk, they yield a lower return.

The slope of the SML is equal to the market risk premium and reflects the risk return trade off at a given time. The idea of a security market line follows from the ideas asserted in the last section, which is that investors are naturally risk averse, and a premium is expected to offset the volatility of a risky investment. In a perfect world, with perfect information, any capital investment is on the security market line. The idea of a security market line is important for understanding the capital asset pricing model. Let’s look at the line again:

The Security Market Line

This is an example of a security market line graphed. The y-intercept of this line is the risk-free rate (the ROI of an investment with beta value of 0), and the slope is the premium that the market charges for risk.

8.7.3: Impact of the SML on the Cost of Capital

The plotted location of an instrument on the SML has consequences on its price, return, and cost of capital it contributes to a firm.

Learning Objective

Describe the impact of the SML on determining the cost of capital

Key Points

• The security market line is a hypothetical concept that suggests that investors require compensation in the form of expected returns for the risk the investment exposes them to.
• A capital investment below the security market wouldn’t be efficiently priced to the buyer of the investment. A higher return or lower price would be required, both increasing the cost of capital.
• A capital investment above the security market line wouldn’t be efficiently priced for the seller or whomever raises the capital. A lower return or higher price would be necessary to justify this cost of capital for the company.

Key Term

capital asset pricing model

In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset’s non-diversifiable risk.

The Security Market Line

The location of a financial instrument above, below, or on the security market line will lead to consequences for a company’s cost of capital.

The security market line is a graphical representation of the capital asset pricing model that illustrates the idea that investments are priced efficiently based on the expected return and beta-value (risk). Companies often turn to capital markets in order to generate funds — using the issuance of either debt or equity. The cost of obtaining funds in such a manner is known as a company’s cost of capital. There is a tradeoff between a security’s price and its expected return. If the price of the instrument goes up, its expected returns go down, and vice versa. A firm that is raising capital would like to sell these instruments for a high price, and investors want to buy them for a low price.

An instrument plotted below the SML would have a low expected return and a high price. This market situation would be quite attractive from the perspective of a company raising capital; however, such an investment wouldn’t make sense for a rational buyer. The rational investor will require either a higher return or lower price, which will both result in a higher cost of capital for the company.

An instrument plotted above the line has a high expected return and a low price. This would not be an attractive market situation for a company looking to raise capital. Such a firm wants to raise as much money as possible, which means getting investors to pay the highest price possible.

An instrument plotted on the SML can be thought of to be fairly priced for the amount of expected return. Such an instrument would be a fair investment from an individual’s perspective, and would lead to a fair cost of capital from a company’s perspective.

7.3: Rules and Rights of Common and Preferred Stock

7.3.1: Claim to Income

Learning Objective

Describe the rights preferred stock has to a company’s income

Key Points

• Common stock and preferred stock are both forms of equity ownership but carry different rights and claims to income.
• Preferred stock shareholders will have claim to assets over common stock shareholders in the case of company liquidation.
• Preferred stock also has first right to dividends.

Key Terms

Common stock

Common stock is a form of equity and type of security. Common stock shareholders are at the bottom of the line when it comes to dividends and receiving compensation in the case of bankruptcy.

Preferred Stock

Preferred stock is an equity security that has the properties of both an equity and debt instrument and is higher ranking than common stock.

Preferred and common stock have varying claims to income which will change from one equity issuer to another. In general, preferred stock will be given some preference in assets to common assets in the case of company liquidation, but both will fall behind bondholders when asset distribution takes place. In the event of bankruptcy, common stock investors receive any remaining funds after bondholders, creditors (including employees), and preferred stock holders are paid. As such, these investors often receive nothing after a bankruptcy. Preferred stock also has the first right to receive dividends. In general, common stock shareholders will not receive dividends until it is paid out to preferred shareholders. Access to dividends and other rights vary from firm to firm.

1903 stock certificate of the Baltimore and Ohio Railroad

Preferred and common stock both carry rights of ownership, but represent different classes of equity ownership.

Preferred stock may or may not have a fixed liquidation value (or par value) associated with it. This represents the amount of capital that was contributed to the corporation when the shares were first issued. Preferred stock has a claim on liquidation proceeds of a stock corporation equal to its par (or liquidation) value, unless otherwise negotiated. This claim is senior to that of common stock, which has only a residual claim.

Both types of stock can have a claim to income in the form of capital appreciation as well. As company value increases based on market determinants, the value of equity held in this company also will increase. This translates to a return on investment to shareholders. This will be different to common stock shareholders and preferred stock shareholders because of the different prices and rewards based on holding these different kinds of shares. In turn, should market forces decrease, the value of equity held will decrease as well, reflecting a loss on investment and, therefore, a decrease on the value of any claims to income for shareholders.

7.3.2: Voting Right

Learning Objective

Summarize the voting rights associated with common and preferred stock

Key Points

• Common stock shareholders can generally vote on issues, such as members of the board of directors, stock splits, and the establishment of corporate objectives and policy.
• While having superior rights to dividends and assets over common stock, generally preferred stock does not carry voting rights.
• Many of the voting rights of a shareholder can be exercised at annual general body meetings of companies. An annual general meeting is a meeting that official bodies, and associations involving the general public, are often required by law to hold.

Key Terms

Voting rights

Rights which are generally associated with common stock shareholders in regards to business entity matters ( such as electing the board of directors or establishing corporate policy)

Preferred Stock

Preferred stock is an equity security that has the properties of both an equity and debt instrument and is higher ranking than common stock.

Common stock

Common stock is a form of equity and type of security. Common stock shareholders are at the bottom of the line when it comes to dividends and receiving compensation in the case of bankruptcy.

Voting Rights

Common stock can also be referred to as a “voting share. ” Common stock usually carries with it the right to vote on business entity matters, such as electing the board of directors, establishing corporate objectives and policy, and stock splits. However, common stock can be broken into voting and non-voting classes. While having superior rights to dividends and assets over common stock, generally preferred stock does not carry voting rights.

The matters that a stockholder gets to vote on vary from company to company. In many cases, the shareholder will be able to vote for members of a company board of directors and, in general, each share gets a vote as opposed to each shareholder. Therefore, a single investor who owns 300 shares will have more say in a voting matter than a single shareholder that owns 30.

Exercising Voting Rights

Many of the voting rights of a shareholder can be exercised at annual general body meetings of companies. An annual general meeting is a meeting that official bodies and associations involving the general public (including companies with shareholders) are often required by law (or the constitution, charter, by-laws, etc., governing the body) to hold. An AGM is held every year to elect the board of directors and inform their members of previous and future activities. It is an opportunity for the shareholders and partners to receive copies of the company’s accounts, as well as reviewing fiscal information for the past year and asking any questions regarding the directions the business will take in the future. Shareholders also have the option to mail their votes in if they cannot attend the shareholder meetings. In 2007, the Securities and Exchange Commission voted to require all public companies to make their annual meeting materials available online. Shareholders with the right to vote will have numerous options in how to make their voice heard with regards to voting matters should they choose to.

Shareholder Meeting

This scene from “The Office” humorously illustrates a shareholder meeting, where the shareholder can exercise their right to vote on company issues or question company directors.

7.3.3: Purchasing New Shares

Learning Objective

Discuss the process and implication of purchasing new shares by a shareholder that already holds shares in a company

Key Points

• New share purchase is an important indicator of current shareholder belief in the health of the company and long term prospects for growth.
• Current Shareholders will often have preemptive rights that give them the right to purchase newly issued company shares before they go on sale to the general public.
• New shares can be purchased on exchanges, which offer a platform for the financial marketplace.

Key Terms

Stock Exchange

A form of exchange that provides services for stock brokers and traders to trade stocks, bonds and other securities.

Preemption

The right of a shareholder to purchase newly issued shares of a business entity before they are available to the general public so as to protect individual ownership from dilution.

New share purchases are an important action by share shareholders, since it requires a further investment in a business entity and is a reflection of a shareholder’s decision to maintain an ownership position in a company, or a potential investor’s belief that purchasing equity in a company will be an investment that grows in value.

Current shareholders may have preemptive rights over new shares offered by the company. In practice, the most common form of preemption right is the right of existing shareholders to acquire new shares issued by a company in a rights issue, a usually but not always public offering. In this context, the pre-emptive right is also called “subscription right” or “subscription privilege. ” This is the right, but not the obligation, of existing shareholders to buy the new shares before they are offered to the public. In this way, existing shareholders can maintain their proportional ownership of the company, preventing stock dilution.

New shares may be purchased over the same exchange mechanisms that previous stock was acquired. A stock exchange is a form of exchange which provides services for stock brokers and traders to trade stocks, bonds, and other securities. Stock exchanges also provide facilities for issue and redemption of securities and other financial instruments, and capital events, including the payment of income and dividends. The initial offering of stocks and bonds to investors is by definition done in the primary market and subsequent trading is done in the secondary market. A stock exchange is often the most important component of a stock market. Supply and demand in stock markets are driven by various factors that, as in all free markets, affect the price of stocks.

Exchanges

New shares can be traded on exchanges such as the Nasdaq, but will usually be offered to current shareholders before being put on sale to the general public.

7.3.4: Preferred Stock Rules and Rights

Learning Objective

List the rights that preferred stock generally has

Key Points

• Preferred stock generally does not carry voting rights, but this may vary from company to company.
• Preferred stock can gain cumulative dividends, convertibility to common stock, and callability.
• The rights that come with ownership of preferred stock are detailed in a “Certificate of Designation”.

Key Terms

liquidation

liquidation is the process by which a company (or part of a company) is brought to an end, and the assets and property of the company redistributed

Preferred Stock

Preferred stock is an equity security that has the properties of both an equity and debt instrument and is higher ranking than common stock.

Preferred stock usually carries no voting rights, but may carry a dividend and may have priority over common stock in the payment of dividends and upon liquidation. Terms of the preferred stock are stated in a “Certificate of Designation. “

VOC stock

Preferred stock is a security ( a little more modern that this stock from the VOC or Dutch East India Company) that carries certain rights which designate it from common stock or debt.

Preferred stock is a special class of shares that may have any combination of features not possessed by common stock. The following features are usually associated with preferred stock: Preference in dividends preference in assets, in the event of liquidation, convertibility to common stock, callability, and at the option of the corporation. Some preferred shares have special voting rights to approve extraordinary events (such as the issuance of new shares or approval of the acquisition of a company) or to elect directors, but, once again, most preferred shares have no voting rights associated with them. Some preferred shares gain voting rights when the preferred dividends are in arrears for a substantial time.

Preferred stock may or may not have a fixed liquidation value (or par value) associated with it. This represents the amount of capital which was contributed to the corporation when the shares were first issued. Preferred stock has a claim on liquidation proceeds of a stock corporation equal to its par (or liquidation) value, unless otherwise negotiated. This claim is senior to that of common stock, which has only a residual claim.Almost all preferred shares have a negotiated, fixed-dividend amount. The dividend is usually specified as a percentage of the par value, or as a fixed amount. Sometimes, dividends on preferred shares may be negotiated as floating; they may change according to a benchmark interest-rate index. Preferred stock may also have rights to cumulative dividends.

7.3.5: Provisions of Preferred Stock

Learning Objective

Describe in detail the different types of provisions for preferred stock

Key Points

• If a preferred share has cumulative dividends, then it contains the provision that should a company fail to pay out dividends at any time at the stated rate, then the issuer will have to make up for it as time goes on.
• Convertible preferred stock can be exchanged for a predetermined number of company common stock shares.
• Often times companies will keep the right to call or buy back preferred shares at a predetermined price.
• Participating preferred issues offer holders the opportunity to receive extra dividends if the company achieves predetermined financial goals.
• Sometimes, dividends on preferred shares may be negotiated as floating; they may change according to a benchmark interest-rate index.

Key Terms

Callable shares

Shares which can be bought back by the issuer at a predetermined price.

Convertible preferred stock

Convertible preferred stock can be exchanged for a predetermined number of company common stock shares.

Cumulative Dividends

Condition where owners of certain shares will receive accumulated dividends in the case a company cannot pay out dividends at the stated rate at the stated time.

Preferred stock may be entitled to numerous rights, depending on what is designated by the issuer. One of these rights may be the right to cumulative dividends. Preferred stock shareholders already have rights to dividends before common stock shareholders, but cumulative preferred shares contain the provision that should a company fail to pay out dividends at any time at the stated rate, then the issuer will have to make up for it as time goes on.

Historical dividend information for Franklin Automobile Company

Dividends are one of the privileges of stock ownership, and preferred shares get more rights to them than common shares do.

Convertible preferred stock can be exchanged for a predetermined number of company common stock shares. Generally, this can occur at the discretion of the investor, and he or she may pick any time to do so and, therefore, take advantage of fluctuations in the price of common stock. Once converted, the common stock cannot be converted back to preferred status.

Often times companies will keep the right to call or buy back preferred shares at a predetermined price. These shares are callable shares.

There is a class of preferred shares known as “participating preferred stock. ” These preferred issues offer holders the opportunity to receive extra dividends if the company achieves predetermined financial goals. Investors who purchased these stocks receive their regular dividend regardless of company performance (assuming the company does well enough to make its annual dividend payments). If the company achieves predetermined sales, earnings, or profitability goals, the investors receive an additional dividend.

Almost all preferred shares have a negotiated, fixed-dividend amount. The dividend is usually specified as a percentage of the par value, or as a fixed amount. Sometimes, dividends on preferred shares may be negotiated as floating; they may change according to a benchmark interest-rate index or floating rate. An example of this would be tying the dividend rate to LIBOR.

7.3.6: Comparing Common Stock, Preferred Stock, and Debt

Learning Objective

Differentiate between the rights of common shareholders, preferred shareholders, and bond holders

Key Points

• Common stock and preferred stock fall behind debt holders as creditors that would receive assets in the case of company liquidation.
• Common stock and preferred stock are both types of equity ownership. They receive rights of ownership in the company, such as voting and dividends.
• Debt holders often receive a bond for lending and while this does not give the ownership rights of being a stockholder, it does create a superior claim to a company’s assets in the case of liquidation.

Key Terms

Common stock

Common stock is a form of corporate equity ownership, a type of security.

bond

A bond is an instrument of indebtness of the bond issuers toward the bond holders.

Preferred Stock

Preferred stock is an equity security that has the properties of both an equity and debt instrument and is higher ranking than common stock.

Equity

Common Stock and Preferred Stock are both methods of purchasing equity in a business entity.

Common stock generally carries voting rights along with it, while preferred shares generally do not.

Preferred shares act like a hybrid security, in between common stock and holding debt. Preferred stock can (depending on the issue) be converted to common stock and have access to accumulated dividends and multiple other rights. Preferred stock also has access to dividends and assets in the case of liquidation before common stock does.

However, both common and preferred stock fall behind debt holders when it comes to claims to assets of a business entity should bankruptcy occur. Common shareholders often do not receive any assets after bankruptcy as a result of this principle. However, common stock shareholders can theoretically use their votes to affect company decision making and direction in a way they believe will help the company avoid liquidation in the first place.

Debt

Debt can be “purchased” from a company in the form of a bond.

A bond from the Dutch East India Company

A bond is a financial security that represents a promise by a company or government to repay a certain amount, with interest, to the bondholder.

In finance, a bond is an instrument of indebtedness of the bond issuer to the holders. It is a debt security, under which the issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest and/or to repay the principal at a later date, termed the maturity. Therefore, a bond is a form of loan or IOU: the holder of the bond is the lender (creditor), the issuer of the bond is the borrower (debtor), and the coupon is the interest. Bonds provide the borrower with external funds to finance long-term investments, or, in the case of government bonds, to finance current expenditure.

Bonds and stocks are both securities, but the major difference between the two is that (capital) stockholders have an equity stake in the company (i.e., they are owners), whereas, bondholders have a creditor stake in the company (i.e., they are lenders). Another difference is that bonds usually have a defined term, or maturity, after which the bond is redeemed, whereas stocks may be outstanding indefinitely.

7.4: Stock Markets

7.4.1: Market Actors

Market actors include individual retail investors, mutual funds, banks, insurance companies, hedge funds, and corporations.

Learning Objective

Identify the different actors that participate in a stock market

Key Points

• Pension funds are important shareholders of listed and private companies.
• Insurance companies are generally classified as either mutual or proprietary companies.
• A mutual fund is a type of professionally-managed collective investment vehicle that pools money from many investors to purchase securities.
• An index fund or index tracker is a collective investment scheme (usually a mutual fund or exchange-traded fund) that aims to replicate the movements of an index of a specific financial market, or a set of rules of ownership that are held constant, regardless of market conditions.
• An exchange-traded fund (ETF) is an investment fund traded on stock exchanges, much like stocks.
• A hedge fund is an fund that can undertake a wider range of investment and trading activities than other funds. It is generally only open to certain types of investors specified by regulators.

Key Terms

open-end

An open-end(ed) fund is a collective investment scheme which can issue and redeem shares at any time.

closed-end

Closed-end funds (or closed-ended funds) are mutual funds with a fixed number of shares (or units). Unlike open-end funds, new shares/units are not created by managers, to meet demand from investors, but the shares can only be purchased (and sold) in the market.

The individual actors in the financial markets can be broken down into three main categories: investors, intermediaries, and issuers. Specifically, market actors include individual retail investors, institutional investors such as mutual funds, banks, insurance companies and hedge funds, and also publicly traded corporations trading in their own shares. The value of a stock is derived from buying and selling decisions of these actors. Some studies have suggested that institutional investors and corporations trading in their own shares generally receive higher risk-adjusted returns than retail investors .

Stock Market

Different kinds of investors are active in stock market.

Investors

An investor is someone who allocates capital with the expectation of a financial return. The types of investments include, — equity, debt securities, real estate, currency, commodity, derivatives such as put and call options, etc. A few decades ago, worldwide, buyers and sellers were individual investors, such as wealthy businessmen, usually with long family histories to particular corporations. Over time, markets have become more “institutionalized. ” Buyers and sellers are largely institutions. Investors can include: pension funds, insurance companies, mutual funds, index funds, exchange-traded funds, and hedge funds.

Issuers

The issuer is a legal entity that develops, registers, and sells securities for the purpose of financing its operations. Issuers may be domestic or foreign governments, corporations, or investment trusts.

Intermediaries

Financial institutions (intermediaries) perform the vital role of bringing together those economic agents with surplus funds who want to lend, with those with a shortage of funds who want to borrow. The classic example of a financial intermediary is a bank that consolidates bank deposits and uses the funds to transform them into bank loans. Other classes of intermediaries include: credit unions, financial advisers or brokers, collective investment schemes, and pension funds.

Pension funds

A pension fund is any plan, fund, or scheme that provides retirement income.

Pension funds are important shareholders of listed and private companies. They are especially important to the stock market where large institutional investors dominate. The largest 300 pension funds collectively hold about $6 trillion in assets. In January 2008, The Economist reported that Morgan Stanley estimates that pension funds worldwide hold over $20 trillion in assets, the largest for any category of investor ahead of mutual funds, insurance companies, currency reserves, sovereign wealth funds, hedge funds, or private equity.

Insurance companies

Insurance companies are generally classified as either mutual or proprietary companies. Mutual companies are owned by the policyholders, while shareholders (who may or may not own policies) own proprietary insurance companies.

Mutual funds

A mutual fund is a type of professionally-managed collective investment vehicle that pools money from many investors to purchase securities. While there is no legal definition of mutual fund, the term is most commonly applied only to those collective investment vehicles that are regulated, available to the general public, and open-ended in nature. Hedge funds are not considered a type of mutual fund.

There are three types of U.S. mutual funds: open-end, unit investment trust, and closed-end. The most common type, the open-end mutual fund, must be willing to buy back its shares from its investors at the end of every business day. Exchange-traded funds are open-end funds or unit investment trusts that trade on an exchange. Open-end funds are most common, but exchange-traded funds have been gaining in popularity.

Index fund

An index fund or index tracker is a collective investment scheme (usually a mutual fund or exchange-traded fund) that aims to replicate the movements of an index of a specific financial market, or a set of rules of ownership that are held constant, regardless of market conditions. As of 2007, index funds made up over 11% of equity mutual fund assets in the United States.

Exchange-traded fund (ETF)

An exchange-traded fund (ETF) is an investment fund traded on stock exchanges, much like stocks. An ETF holds assets such as stocks, commodities, or bonds, and trades close to its net asset value over the course of the trading day. Most ETFs track an index, such as a stock index or bond index. ETFs may be attractive as investments because of their low costs, tax efficiency, and stock-like features. ETFs are the most popular type of exchange-traded product.

Hedge fund

A hedge fund is an fund that can undertake a wider range of investment and trading activities than other funds. It is generally only open to certain types of investors specified by regulators. These investors are typically institutions, such as pension funds, university endowments and foundations, or high-net-worth individuals, who are considered to have the knowledge or resources to understand the nature of the funds. As a class, hedge funds invest in a diverse range of assets, but they most commonly trade liquid securities on public markets. They also employ a wide variety of investment strategies, and make use of techniques such as short selling and leverage.

7.4.2: NYSE

The New York Stock Exchange is the world’s largest stock exchange by market capitalization at $14.242 trillion as of December 2011.

Learning Objective

Distinguish the New York Stock Exchange from other stock exchanges

Key Points

• The origin of the NYSE can be traced to May 17, 1792, when the Buttonwood Agreement was signed by 24 stockbrokers outside of 68 Wall Street in New York under a buttonwood tree on Wall Street.
• The New York Stock Exchange (sometimes referred to as “the Big Board”) provides a means for buyers and sellers to trade shares of stock in companies registered for public trading.
• The New York Stock Exchange is open for trading Monday through Friday from 9:30 am to 4:00 pm ET, with the exception of holidays declared by the NYSE in advance.
• Traders can gather around the appropriate post. There, a specialist broker acts as an auctioneer in an open outcry auction market environment to bring buyers and sellers together and to manage the actual auction.
• To be listed on the New York Stock Exchange, a company must have issued at least a million shares of stock worth $100 million and must have earned more than $10 million over the last three years.

Key Terms

Dutch auction

an event to buy or sell that starts at a high price that is gradually reduced by the auctioneer until someone is willing to buy

secondary market

The financial market in which previously issued financial instruments such as stock, bonds, options, and futures are bought and sold.

NASDAQ

The National Association of Securities Dealers Automated Quotations; this is an electronic stock market.

New York Stock Exchange

The New York Stock Exchange, commonly referred to as the NYSE, is a stock exchange, or a secondary market. With primary issuances of securities or financial instruments, or the primary market, investors purchase these securities directly from issuers such as corporations issuing shares in an IPO or private placement, or directly from the federal government in the case of treasuries.

After the initial issuance, investors can purchase from other investors in secondary markets like the NYSE. If an investor wished to buy a stock from Apple, for example, the actual company is not directly involved. Secondary markets can be further subdivided into auction or dealer markets, typified by the mode of transactions. The NYSE is an auction market. Buyers and sellers meet at a physical location (in this case, Wall Street) and announce their bid or ask prices.

At the NYSE, traders gather around a specialist broker, who acts as an auctioneer in an open outcry auction market environment to bring buyers and sellers together and to manage the actual auction. The auction market format aims to bring together the parties with mutually agreeing prices in an efficient manner. The auction process moved toward automation in 1995 through the use of wireless hand held computers (HHC). The system enabled traders to receive and execute orders electronically via wireless transmission .

NYSE Trading Floor

Buyers and sellers meet and engage in face-to-face transactions at the NYSE, which is an auction-style secondary market.

The NYSE is by far the world’s largest stock exchange by market capitalization of its listed companies at $14.242 trillion as of December 2011, and most of the largest US companies are listed on the NYSE. The NYSE’s biggest competitor is NASDAQ; both are major secondary markets vying for large and profitable companies to list on their exchange.

Secondary markets like the NYSE serve a vital function as a setting where companies can raise capital for expansion through selling shares to the investing public. They also gain advertising and a boost in prestige, which likely increases their stock value. To be able to trade a security on the NYSE, it must be listed. To be listed on the New York Stock Exchange, a company must have issued at least a million shares of stock worth $100 million and must have earned more than $10 million over the last three years. They must also disclose certain information to the exchange, providing a measure of transparency that prevents insider manipulation of the stock prices.

7.4.3: NASDAQ

The NASDAQ is an American dealer-based stock market in which the dealers sell electronically to investors or firms.

Learning Objective

Distinguish the NASDAQ from other stock exchanges

Key Points

• NASDAQ was founded in 1971 by the National Association of Securities Dealers (NASD), who divested themselves of it in a series of sales in 2000 and 2001.
• NASDAQ quotes are available at three levels: Level 1 shows the highest bid and lowest offer; Level 2 shows all public quotes of market makers; Level 3 is used by the market makers and allows them to enter their quotes and execute orders.
• NASDAQ has a pre-market session from 7:00am to 9:30am, a normal trading session from 9:30am to 4:00pm, and a post-market session from 4:00pm to 8:00pm (all times in ET).
• Three market tiers are NASDAQ Capital Market – Small Cap, NASDAQ Global Market – Mid Cap, NASDAQ Global Select Market – Large Cap.

Key Term

FINRA

In the United States, the Financial Industry Regulatory Authority, Inc., or FINRA, is a private corporation that acts as a self-regulatory organization (SRO). FINRA is the successor to the National Association of Securities Dealers, Inc. (NASD). Though sometimes mistaken for a government agency, it is a non-governmental organization that performs financial regulation of member brokerage firms and exchange markets. The government organization which acts as the ultimate regulator of the securities industry, including FINRA, is the Securities and Exchange Commission.

NASDAQ Stock Market

The NASDAQ Stock Market, also known simply as the NASDAQ, is an American stock exchange. “NASDAQ” originally stood for “National Association of Securities Dealers Automated Quotations. ” It is one of the largest stock exchanges in the world along with the New York Stock Exchange.

NASDAQ

NASDAQ is the second-largest stock exchange market in the world, as of 2012.

The NASDAQ is a dealer-based market in which stock dealers sell directly to investors or firms electronically via phone or Internet. The New York Stock Exchange conducts its trading in person.

History

NASDAQ was founded in 1971 by the National Association of Securities Dealers (NASD), who divested themselves of it in a series of sales in 2000 and 2001. It is owned and operated by the NASDAQ OMX Group and regulated by the Financial Industry Regulatory Authority (FINRA), the successor to the NASD.

When the NASDAQ stock exchange began trading on February 8, 1971, it was the world’s first electronic stock market. At first, it was merely a computer bulletin board system and did not actually connect buyers and sellers. The NASDAQ helped lower the spread (the difference between the bid price and the ask price of the stock), but paradoxically was unpopular among brokerages because they made much of their money on the spread.

Firms including Microsoft began doing business through NASDAQ early in their history, and remained with this exchange as the technology industry boomed. NASDAQ became known for its concentration of tech and high-growth firms, making it the primary tech market and an indicator for industry trends.

Indices

A stock index or stock market index is a method of measuring the value of a section of the stock market. It is computed from the prices of selected stocks, which vary depending on the index. Investors and financial managers can use it as a “snapshot” to describe the market conditions, and also as a tool to compare the return on specific investments. NASDAQ’s major indices include:

• NASDAQ-100
• NASDAQ Bank
• NASDAQ Biotechnology Index
• NASDAQ Transportation Index
• NASDAQ Composite

The NASDAQ Composite is often referred to as the NASDAQ. It is calculated from weighting common stocks and similar securities listed on the NASDAQ stock market. Thus “NASDAQ” can mean two things: either the stock exchange itself, or the index.

7.4.4: Market Reporting

Market indices provide valuable information for stock valuation.

Learning Objective

Explain how a market index works and its purpose

Key Points

• The is a tool used by investors and financial managers to describe the market and to compare the return on specific investments.
• An index is a mathematical construct, so it may not be invested in directly.
• A ‘world’ or ‘global’ stock market index includes (typically large) companies without regard for where they are domiciled or traded.
• A ‘national’ index represents the performance of the stock market of a given nation—and by proxy, reflects investor sentiment on the state of its economy.
• Stock market indices provide invaluable information for investors and accountants.

Key Terms

market capitalization

The total market value of the equity in a publicly traded entity.

weighted average

An arithmetic mean of values biased according to agreed weightings.

Common stock

Shares of an ownership interest in the equity of a corporation or other entity with limited liability. Holders of this type of stock are entitled to dividends. Importantly, the financial rights for holders of this type of stock are junior to preferred stock and liabilities.

Market Reporting

A stock index or stock market index is a method of measuring the value of a section of the stock market. It is computed from the prices of selected stocks (sometimes a weighted average). It is a tool used by investors and financial managers to describe the market and to compare the return on specific investments.

Historical Graph of the Dow Jones Industrial Average

This graph shows the general increase in the DJIA over the last century. Particularly notable is the growth from around 1,000 points in the late 1980s to around 10,000 points in 2005.

An index is a mathematical construct, so it may not be invested in directly. Many mutual funds and exchange-traded funds attempt to “track” an index. The funds that do may not be judged against those that do.

Stock market indices may be classed in many ways. A ‘world’ or ‘global’ stock market index includes (typically large) companies without regard for where they are domiciled or traded. Two examples are MSCI World and S&P Global 100.

A ‘national’ index represents the performance of the stock market of a given nation—and by proxy, reflects investor sentiment on the state of its economy. The most regularly quoted market indices are national indices composed of the stocks of large companies listed on a nation’s largest stock exchanges, such as the American S&P 500, the Japanese Nikkei 225, the Brazilian Ibovespa, the Russian RTSI, the Indian SENSEX, and the British FTSE 100.

Stock market indices provide invaluable information for investors and accountants. For example, the current market price per share, market capitalization, and trading volume are all readily available. With this information, along with a company’s consolidated financial statements, the following ratios and calculations can be performed:

• Dividend yield on common stock ratio=Dividend per share of common stock
• Payout ratio on common stock = Dividend per share of common stock
• Earnings per share (EPS)

By comparing the above ratios with those of other companies, investors, accountants, and forecasters can determine the position and health of their respective company’s stock.

7.5: Stock Valuation

7.5.1: Expected Dividends, No Growth

A no-growth company would be expected to return high dividends under traditional finance theory.

Learning Objective

Describe how a company should make a dividend decision when it expect no growth

Key Points

• Companies generally either retain earnings for investment, or distribute them as dividend, according to their growth strategy.
• Clientele effects suggests that different dividend levels attract different types of investors.
• Value investors look for indications that a stock is undervalued. High dividends are one indication of undervaluation.
• Knowing a firm’s cost of capital is needed in order to make better decisions. Managers make capital budgeting decisions while capital providers make decisions about lending and investment.

Key Term

clientele

The body or class of people who frequent an establishment or purchase a service, especially when considered as forming a more-or-less homogeneous group of clients in terms of values or habits.

The Dividend Decision

Whether to issue dividends and what amount is calculated mainly on the basis of the company’s unappropriated profit and its earning prospects for the coming year. The amount is also often calculated based on expected free cash flows, which means cash remaining after all business expenses, and capital investment needs have been met.

If there are no favorable investment opportunities–projects where return exceed the hurdle rate–finance theory suggests that management will return excess cash to shareholders as dividends. However, there are exceptions. For example, shareholders of a “growth stock,” expect that the company will, almost by definition, retain earnings so as to fund growth internally.

At the other end of the spectrum, investors of a “no growth,” or value stock will expect the firm to retain little cash for investment, and to distribute a comparatively greater proportion to investors as a dividend.

Clientele Effects

This suggests that a particular pattern of dividend payments may suit one type of stock holder more than another; this is sometimes called the “clientele effect. ” A retiree may prefer to invest in a firm that provides a consistently high dividend yield, whereas a person with a high income from employment may prefer to avoid dividends due to their high marginal tax rate on income. If clienteles exist for particular patterns of dividend payments, a firm may be able to maximize its stock price and minimize its cost of capital by catering to a particular clientele. This model may help to explain the relatively consistent dividend policies followed by mostlisted companies.

Value Investors

No growth, high dividend stocks may appeal to value investors. Value investing involves buying securities with shares that appear underpriced by some form of fundamental analysis. As examples, such securities may be stock in public companies that have high dividend yields, low price-to-earning multiples, or have low price-to-book ratios. Thus, high dividends and low reinvestment of retained earnings can signal an appealing value stock to an investor.

Investing trade-offs

Value investors trade growth for dividends.

7.5.2: Expected Dividends and Constant Growth

Valuations rely heavily on the expected growth rate of a company; past growth rate of sales and income provide insight into future growth.

Learning Objective

Calculate a company’s stock price using the Constant Growth Approximation

Key Points

• Companies are constantly changing, as well as the economy. Solely using historical growth rates to predict the future is not an acceptable form of valuation. Calculating the future growth rate requires personal investment research.
• A generalized version of the Walter model (1956), SPM considers the effects of dividends, earnings growth, as well as the risk profile of a firm on a stock’s value.
• The Gordon model or Gordon’s growth model is the best known of a class of discounted dividend models. It assumes that dividends will increase at a constant growth rate (less than the discount rate) forever.

Key Term

Gordon Growth Model

Gordon Growth Model is also called the dividend discount model (DDM), which is a way of valuing a company based on the theory that a stock is worth the discounted sum of all of its future dividend payments.

Growth Rate

Valuations rely very heavily on the expected growth rate of a company. One must look at the historical growth rate of both sales and income to get a feeling for the type of future growth expected. However, companies are constantly changing, as well as the economy, so solely using historical growth rates to predict the future is not an acceptable form of valuation. Instead, they are used as guidelines for what future growth could look like if similar circumstances are encountered by the company. Calculating the future growth rate requires personal investment research. This may take form in listening to the company’s quarterly conference call or reading a press release or other another company article that discusses the company’s growth guidance. However, although companies are in the best position to forecast their own growth, they are far from accurate. Unforeseen events could cause rapid changes in the economy and in the company’s industry.

And for any valuation technique, it’s important to look at a range of forecast values.

• For example, if the company being valued has been growing earnings between 5 and 10% each year for the last five years, but believes that it will grow 15 – 20% this year, a more conservative growth rate of 10 – 15% would be appropriate in valuations.
• Another example would be for a company that has been going through restructuring. They may have been growing earnings at 10 – 15% over the past several quarters / years because of cost cutting, but their sales growth could be only 0 – 5%. This would signal that their earnings growth will probably slow when the cost cutting has fully taken effect. Therefore, forecasting an earnings growth closer to the 0 – 5% rate would be more appropriate rather than the 15 – 20%. Nonetheless, the growth rate method of valuations relies heavily on gut feel to make a forecast. This is why analysts often make inaccurate forecasts. It is also why familiarity with a company is essential before making a forecast.

Sum of Perpetuities Method

The PEG ratio is a special case in the Sum of Perpetuities Method (SPM) equation. A generalized version of the Walter model (1956), SPM considers the effects of dividends, earnings growth, as well as the risk profile of a firm on a stock’s value. Derived from the compound interest formula using the present value of a perpetuity equation, SPM is an alternative to the Gordon Growth Model. The variables are:

• P is the value of the stock or business
• E is a company’s earnings
• G is the company’s constant growth rate
• K is the company’s risk adjusted discount rate
• D is the company’s dividend payment

Constant Growth Approximation

The Gordon model or Gordon’s growth model is the best known of a class of discounted dividend models . It assumes that dividends will increase at a constant growth rate (less than the discount rate) forever. The valuation is given by the formula:

Your Dividend

DDM can be used to calculate a constant growth company.

7.5.3: Relationship Between Dividend Payments and the Growth Rate

The portion of the earnings not paid to investors is, ideally, left for investment in order to provide for future earnings growth.

Learning Objective

Describe the relationship between dividend payments and a company’s growth

Key Points

• Investors take into account how much capital is distributed to investors, and conversely how much capital is kept from investors.
• Investors hope that firms will use retained earnings to either maximize their current operations or invest in such as a way as to lead to higher profits.
• Some firms are unable to distribute earnings, since their funds are tied up in maintenance, repairs, et cetera.
• On the other hand, some companies can retain earnings and put that money back to work – i.e., invest in growth opportunities.

Key Term

capital gains

Profit that results from a disposition of a capital asset, such as stock, bond, or real estate due to arbitrage.

From an investor’s point of view, the fundamentals of a company are of the utmost importance. One such fundamental that that investors take into account is how much capital is distributed to investors, and conversely how much capital is kept from investors. Capital is distributed to investors via dividend payments and, indirectly, through capital gains. Capital that is kept from investors is known as retained earnings. Investors hope that firms will use retained earnings to either maximize their current operations or invest in such as a way as to lead to higher profits. In other words, the portion of profits not paid out to investors via dividends is, ideally, left for investment in order to provide for future earnings growth.

Some companies require large amounts of new capital just to continue operations. Such firms are usually unable to distribute earnings, since their funds are tied up in maintenance, repairs, et cetera. These companies also provide limited growth opportunities, since earnings are not reinvested for the purpose of growth. On the other hand, some companies can retain earnings and put that money back to work – i.e., invest in growth opportunities. Firms that can do this tend to retain more of their earnings. These firms are attractive to investors, even though there is relatively low distribution of profits.

Put succinctly, investors seeking high current income and limited capital growth prefer companies with a high dividend payout ratio. However, investors seeking higher capital growth may prefer a lower payout ratio because capital gains are taxed at a lower rate. High growth firms in early life generally have low or zero payout ratios in order to reinvest as much of their earnings as possible. As they mature, they tend to return more of the earnings back to investors. Note that dividend payout ratio is calculated as dividend per share divided by earnings per share.

7.5.4: Understanding Future Stock Value

There are many different ways to appraise the future value of stocks, including fundamental criteria and stock valuation methods.

Learning Objective

Describe different ways of valuing stock

Key Points

• Earnings Per Share is the total net income of the company divided by the number of shares outstanding; the Profits/Earnings ratio is the stock price divided by the annual EPS figure.
• Return on Invested Capital measures how much money the company makes each year per dollar of invested capital and approximates the expected level of growth; Return on Assets measures the company’s ability to make money from its assets.
• To measure Market Capitalization (the value of all of a company’s stock), multiply the current stock price by the fully diluted shares outstanding; Enterprise Value is equal to the total value the company is trading for on the stock market.
• Enterprise Value (EV) to earnings before interest, taxes, depreciation and amortization (EBITDA) is one of the best measurements of whether or not a company should be valued as cheap or expensive.

Key Terms

GAAP

Generally Accepted Accounting Principles refer to the standard framework of guidelines, conventions, and rules accountants are expected to follow in recording, summarizing, and preparing financial statements in any given jurisdiction.

risk premium

A risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the known return on a risk-free asset, or the expected return on a less risky asset, in order to induce an individual to hold the risky asset rather than the risk-free asset.

Example

• P/E Ratio: For example, if the stock is trading at 10 and the EPS is 0.50, the P/E is 20 times. To get a good feeling of what P/E multiple a stock trades at, be sure to look at both the historical and forward ratios.

In financial markets, stock valuation involves calculating theoretical values of companies and their stocks. The main use of stock valuation is to predict future market prices and profit from price changes. Stocks that are judged as undervalued (with respect to their theoretical value) are bought, while stocks that are perceived to be overvalued are sold, in the expectation that undervalued stocks will, on the whole, rise, while overvalued stocks will, on the whole, fall .

Stock Valuation

Stock valuation involves many methods.

Fundamental Criteria (Fair Value)

The soundest stock valuation method, the discounted cash flow (DCF) method of income valuation, involves discounting the profits (dividends, earnings, or cash flows) the stock will bring to stockholders in the foreseeable future, and calculating a final value on disposal. The discounted rate normally includes a risk premium which is often based on the capital asset pricing model.

Stock Valuation Methods

There are many different ways to value stocks. The key is to take each approach into account while formulating an overall opinion of the stock. If the valuation of a company is lower or higher than other similar stocks, then the next step would be to determine the reasons for the discrepancy.

1. Earnings Per Share (EPS)

EPS is the total net income of the company divided by the number of shares outstanding. Numbers are usually reported as a GAAP EPS number (which means it is computed using mutually agreed upon accounting rules) and a Pro Forma EPS figure (income is adjusted to exclude any one time items as well as some non-cash items like amortization of goodwill or stock option expenses).

2. Price to Earnings (P/E)

Once one has several EPS figures (historical and forecasts), the most common valuation technique used by analysts is the price to earnings ratio, or P/E. To compute this figure, the stock price is divided by the annual EPS figure.

3. Price Earnings to Growth (PEG) Ratio

This valuation technique has become more popular over the past decade or so. It is better than just looking at a P/E because it takes three factors into account: the price, earnings, and earnings growth rates. To compute the PEG ratio, divide the Forward P/E by the expected earnings growth rate (historical P/E and historical growth rate are also used to see where the stock has traded in the past).

4. Return on Invested Capital (ROIC)

This valuation technique measures how much money the company makes each year per dollar of invested capital. Invested capital is the amount of money invested in the company by both stockholders and debtors. The ratio is expressed as a percent and Return on Invested Capital ratio should have a percent that approximates the expected level of growth. In its simplest definition, this ratio measures the investment return that management is able to get for its capital. The higher the number, the better the return.

5. Return on Assets (ROA)

Similar to ROIC, ROA, expressed as a percent, measures the company’s ability to make money from its assets. To measure the ROA, take the pro forma net income divided by the total assets. However, because of very common irregularities in balance sheets (due to things like goodwill, write-offs, discontinuations, etc. ) this ratio is not always a good indicator of the company’s potential. If the ratio is higher or lower than expected, be sure to look closely at the assets to see what could be overstating or understating the figure.

6. Price to Sales (P/S)

This figure is useful because it compares the current stock price to the annual sales. In other words, it tells you how much the stock costs per dollar of sales earned.

7. Market Cap

Market Cap, which is short for Market Capitalization, is the value of all of the company’s stock. To measure it, multiply the current stock price by the fully diluted shares outstanding.

8. Enterprise Value (EV)

Enterprise Value is equal to the total value of the company, as trading on the stock market. To compute it, add the Market Cap (see above) and the total net debt of the company.

9. EBITDA

EBITDA stands for earnings before interest, taxes, depreciation and amortization. It is one of the best measures of a company’s cash flow and is used for valuing both public and private companies.

10. EV to EBITDA

This is perhaps one of the best measurements of whether or not a company should be valued as cheap or expensive. To compute, divide the EV by EBITDA (see above for calculations). The higher the number, the more expensive the company is.

7.5.5: Valuing Nonconstant Growth Dividends

Limited high-growth approximation, implied growth models, and the imputed growth acceleration ratio are used to value nonconstant growth dividends.

Learning Objective

Describe the limitations of valuing a company with dividends that have a nonconstant growth rate

Key Points

• Limited high-growth approximation: When a stock has a significantly higher growth rate than its peers, it is sometimes assumed that the earnings growth rate will be sustained for a short time (say, 5 years), and then the growth rate will revert to the mean.
• Implied Growth Models: One can use the Gordon model or the limited high-growth period approximation model to impute an implied growth estimate.
• Imputed growth acceleration ratio: Subsequently, one can divide this imputed growth estimate by recent historical growth rates.

Key Terms

DCF models

Valuation using discounted cash flows is a method for determining the current value of a company using future cash flows adjusted for time value. The future cash flow set is made up of the cash flows within the determined forecast period and a continuing value that represents the cash flow stream after the forecast period.

break-even

Break-even (or break even) is the point of balance between making either a profit or a loss.

Limited high-growth period approximation

When a stock has a significantly higher growth rate than its peers, it is sometimes assumed that the earnings growth rate will be sustained for a short time (say, 5 years), and then the growth rate will revert to the mean. This is probably the most rigorous approximation that is practical.

While these DCF models are commonly used, the uncertainty in these values is hardly ever discussed. Note that the models diverge for and hence are extremely sensitive to the difference of dividend growth to discount factor. One might argue that an analyst can justify any value (and that would usually be one close to the current price supporting his call) by fine-tuning the growth/discount assumptions.

Implied Growth Models

One can use the Gordon model or the limited high-growth period approximation model to impute an implied growth estimate. To do this, one takes the average P/E and average growth for a comparison index, uses the current (or forward) P/E of the stock in question, and calculates what growth rate would be needed for the two valuation equations to be equal. This gives you an estimate of the “break-even” growth rate for the stock’s current P/E ratio. (Note: we are using earnings not dividends here because dividend policies vary and may be influenced by many factors including tax treatment).

Imputed growth acceleration ratio

Subsequently, one can divide this imputed growth estimate by recent historical growth rates. If the resulting ratio is greater than one, it implies that the stock would need to experience accelerated growth relative to its prior recent historical growth to justify its current P/E (higher values suggest potential overvaluation). If the resulting ratio is less than one, it implies that either the market expects growth to slow for this stock or that the stock could sustain its current P/E with lower than historical growth (lower values suggest potential undervaluation). Comparison of the IGAR across stocks in the same industry may give estimates of relative value. IGAR averages across an industry may give estimates of relative expected changes in industry growth (e.g. the market’s imputed expectation that an industry is about to “take-off” or stagnate). Naturally, any differences in IGAR between stocks in the same industry may be due to differences in fundamentals, and would require further specific analysis.

7.6: Valuing the Corporation

7.6.1: Valuing the Corporation

Three approaches are commonly used in corporation valuation: the income approach, the asset-based approach, and the market approach.

Learning Objective

Distinguish between the income, asset-based, and market approaches for corporate valuation

Key Points

• Income approaches include Discount or capitalization rates, Capital Asset Pricing Model (CAPM), Modified Capital Asset Pricing Model, and Weighted average cost of capital (“WACC”).
• The asset approach to business valuation is based on the principle of substitution: no rational investor will pay more for the business assets than the cost of procuring assets of similar economic utility.
• The market approach to business valuation is rooted in the economic principle of competition: in a free market the supply and demand forces will drive the price of business assets to a certain equilibrium.

Key Terms

net asset value

Net asset value (NAV) is the value of an entity’s assets less the value of its liabilities, often in relation to open-end or mutual funds, since shares of such funds registered with the U.S.

corporation

a group of individuals, created by law or under authority of law, having a continuous existence independent of the existences of its members, and powers and liabilities distinct from those of its members

discounted cash flow

In finance, discounted cash flow (DCF) analysis is a method of valuing a project, company, or asset using the concepts of the time value of money. All future cash flows are estimated and discounted to give their present values (PVs)–the sum of all future cash flows, both incoming and outgoing, is the net present value (NPV), which is taken as the value or price of the cash flows in question.

Corporation valuation is a process and a set of procedures used to estimate the economic value of an owner’s interest in a business. Valuation is used by financial market participants to determine the price they are willing to pay or receive to perfect the sale of a business. In addition to estimating the selling price of a business, the same valuation tools are often used by business appraisers to resolve disputes related to estate and gift taxation, divorce litigation, allocate business purchase price among business assets, establish a formula for estimating the value of partners’ ownership interest for buy-sell agreements, and many other business and legal purposes.

Three different approaches are commonly used in business valuation: the income approach, the asset-based approach, and the market approach. Within each of these approaches, there are various techniques for determining the value of a business using the definition of value appropriate for the appraisal assignment. Generally, the income approach determines value by calculating the net present value of the benefit stream generated by the business (discounted cash flow); the asset-based approach determines value by adding the sum of the parts of the business (net asset value); and the market approach determines value by comparing the subject company to other companies in the same industry, of the same size, and/or within the same region.

1. Income approaches

• Discount or Capitalization Rates

A discount rate or capitalization rate is used to determine the present value of the expected returns of a business. The discount rate and capitalization rate are closely related to each other, but are distinguishable. Generally speaking, the discount rate or capitalization rate may be defined as the yield necessary to attract investors to a particular investment, given the risks associated with that investment.

• Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is one method of determining the appropriate discount rate in business valuations. The CAPM method originated from the Nobel Prize winning studies of Harry Markowitz, James Tobin, and William Sharpe. The CAPM method derives the discount rate by adding a risk premium to the risk-free rate. In this instance, however, the risk premium is derived by multiplying the equity risk premium times “beta,” which is a measure of stock price volatility. Beta is published by various sources for particular industries and companies. Beta is associated with the systematic risks of an investment.

• Modified Capital Asset Pricing Model

The Cost of Equity (Ke) is computed by using the Modified Capital Asset Pricing Model

CAPM Model ke = Rf + B ( Rm-Rf) + SCRP + CSRP Where: Rf = Risk free rate of return (Generally taken as 10-year Government Bond Yield) B = Beta Value (Sensitivity of the stock returns to market returns) Ke = Cost of Equity Rm= Market Rate of Return SCRP = Small Company Risk Premium, CSRP= Company specific Risk premium

• Weighted Average Cost of Capital (“WACC”)

The weighted average cost of capital is an approach used to determine a discount rate. The WACC method determines the subject company’s actual cost of capital by calculating the weighted average of the company’s cost of debt and cost of equity. The WACC must be applied to the subject company’s net cash flow to total invested capital.

2. Asset-Based Approaches

The value of asset-based analysis of a business is equal to the sum of its parts. That is the theory underlying the asset-based approaches to business valuation. The asset approach to business valuation is based on the principle of substitution: no rational investor will pay more for the business assets than the cost of procuring assets of similar economic utility. In contrast to the income-based approaches, which require the valuation professional to make subjective judgments about capitalization or discount rates, the adjusted net book value method is relatively objective.

3. Market Approaches

The market approach to business valuation is rooted in the economic principle of competition: that in a free market the supply and demand forces will drive the price of business assets to a certain equilibrium. Buyers would not pay more for the business, and the sellers will not accept less than the price of a comparable business enterprise. It is similar in many respects to the “comparable sales” method that is commonly used in real estate appraisal. The market price of the stocks of publicly traded companies engaged in the same or a similar line of business, whose shares are actively traded in a free and open market, can be a valid indicator of value when the transactions in which stocks are traded are sufficiently similar to permit meaningful comparison.

7.6.2: Discounted Dividend vs. Corporate Valuation

The dividend discount model values a firm at the discounted sum of all of its future dividends, and does not factor in income or assets.

Learning Objective

Calculate a company’s stock price using the discounted dividend formula

Key Points

• P = D1 / ( r – g ). P is the current stock price, g is the constant growth rate in perpetuity expected for the dividends, r is the constant cost of equity for that company, and D1 is the value of the next year’s dividends.
• The equation can also be understood to generate the value of a stock such that the sum of its dividend yield (income) plus its growth (capital gains) equals the investor’s required total return.
• There are also problems with the model, such as the presumption of a steady and perpetual growth rate less than the cost of capital may not be reasonable.

Key Term

Miller-Modigliani hypothesis

The Modigliani–Miller theorem (of Franco Modigliani, Merton Miller) forms the basis for modern thinking on capital structure. The basic theorem states that, under a certain market price process (the classical random walk), in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed.

The dividend discount model (DDM) is a way of valuing a company based on the theory that a stock is worth the discounted sum of all of its future dividend payments. In other words, it is used to value stocks based on the net present value of the future dividends. The equation most always used is called the “Gordon Growth Model. ” It is named after Myron J. Gordon who originally published it in 1959, although the theoretical underpin was provided by John Burr Williams in his 1938 text The Theory of Investment Value.

The variables and equation are:

• P is the current stock price.
• g is the constant growth rate in perpetuity expected for the dividends.
• r is the constant cost of equity for that company.
• D1 is the value of the next year’s dividends.
• There is no reason to use a calculation of next year’s dividend using the current dividend and the growth rate, when management commonly disclose the future year’s dividend, and websites post it.

Income plus capital gains equals total return:

The equation can also be understood to generate the value of a stock such that the sum of its dividend yield (income) plus its growth (capital gains) equals the investor’s required total return. Consider the dividend growth rate as a proxy for the growth of earnings and by extension the stock price and capital gains. Consider the company’s cost of equity capital as a proxy for the investor’s required total return.

Income + Capital Gain = Total Return

Dividend Yield + Growth = Cost of Equity

Problems with the Model

• a) The presumption of a steady and perpetual growth rate less than the cost of capital may not be reasonable.
• b) If the stock does not currently pay a dividend, like many growth stocks, more general versions of the discounted dividend model must be used to value the stock. One common technique is to assume that the Miller-Modigliani hypothesis of dividend irrelevance is true and, therefore, replace the stocks’s dividend D with E earnings per share. However, this requires the use of earnings growth rather than dividend growth, which might be different.
• c) The stock price resulting from the Gordon model is hypersensitive to the growth rate chosen.

6.3: Key Characteristics of Bonds

6.3.1: Par Value

Learning Objective

Assess when a bond should be sold at its par value

Key Points

• When a bond trades at a price above the face value, it is said to be selling at a premium. When a bond sells below face value, it is said to be selling at a discount.
• A bond’s price fluctuates throughout its life in response to a number of variables, including interest rates and time to maturity.
• Pull to par is the effect in which the price of a bond converges to par value as time passes. At maturity, the price of a debt instrument in good standing should equal its par (or face value).

Key Terms

resale market

The resale market, also called “secondary market” or “aftermarket,” is the financial market in which previously issued financial instruments, such as stock, bonds, options, and futures, are bought and sold.

par value

the stated value or amount of a bill or a note

Par value/face value (also known as the principal) is the amount of money a holder will get back once a bond matures. Par value means stated value or face value in finance and accounting. From this comes the expressions at par (at the par value), over par (over par value) and under par (under par value).

A newly issued bond usually sells at the par value. Corporate bonds normally have a par value of $1,000, but this amount can be much greater for government bonds. What confuses many people is that the par value is not the price of the bond. A bond’s price fluctuates throughout its life in response to a number of variables, including interest rates and time to maturity. When a bond trades at a price above the face value, it is said to be selling at a premium. When a bond sells below face value, it is said to be selling at a discount.

Temporary bonds for the state of Kansas issued in 1922

Par values of these bonds were $50, $100, $10000, and $3000.

Pull to par is the effect in which the price of a bond converges to par value as time passes. At maturity, the price of a debt instrument in good standing should equal its par (or face value). Another name for this effect is “reduction of maturity. ” It results from the difference between market interest rate and the nominal yield on the bond.

A bond selling at par has a coupon rate such that the bond is worth an amount equivalent to its original issue value or its value upon redemption at maturity. In other words, if you buy a bond at face value, or par, when it is issued and hold it until it matures, you’ll earn interest at the stated, or coupon, rate. For example, if you buy a 20-year $1,000 bond paying $550 a year for 20 years. The yield, or your return on investment, will also be 5%. You will get your $1,000 back when the 20 years are up. You can also buy and sell bonds through a broker after their date of issue. This is known as the “secondary market” or “resale market. “

6.3.2: Coupon Interest Rate

Learning Objective

Classify bonds based on coupon rate

Key Points

• Coupon interest rate is usually fixed throughout the life of the bond. It can also vary with a money market index.
• Not all bonds have coupons. Zero-coupon bonds are those that pay no coupons and thus have a coupon rate of 0%.
• Based on different coupon rates, there are fixed rate bonds, floating rate bonds, and inflation linked bonds.

Key Term

time value of money

The value of money, figuring in a given amount of interest, earned over a given amount of time.

The coupon rate is the amount of interest that the bondholder will receive expressed as a percentage of the par value. Thus, if a bond has a par value of 1,000 and a coupon rate of 10,100 a year during the time between when the bond is issued and when it matures. Usually this rate is fixed throughout the life of the bond. It can also vary with a money market index, such as LIBOR, or it can be even more exotic. The bond will also specify when the interest is to be paid, whether monthly, quarterly, semi-annually, or annually.

Mecca Temple 1922 Bond Coupons

A coupon payment on a bond is a periodic interest payment that the bond holder receives during the time between when the bond is issued and when it matures.

The name “coupon” arose because in the past, paper bond certificates were issued that had coupons attached to them, one for each interest payment. On the due dates, the bondholder would hand in the coupon to a bank in exchange for the interest payment.

Not all bonds have coupons. Zero-coupon bonds are those that pay no coupons and thus have a coupon rate of 0%. Such bonds make only one payment–the payment of the face value on the maturity date. Normally, to compensate the bondholder for the time value of money, the price of a zero-coupon bond will always be less than its face value on any date before the maturity date. The bondholder receives the full principal amount on the redemption date. An example of zero coupon bonds is Series E savings bonds issued by the U.S. government.

Based on different coupon rates, bonds are classified into many types. Fixed-rate bonds have a coupon that remains constant throughout the life of the bond. A variation are stepped-coupon bonds, with a coupon that increases during the life of the bond.

Floating rate notes (FRNs, floaters) have a variable coupon that is linked to a reference rate of interest, such as LIBOR or Euribor. For example, the coupon may be defined as three month USD LIBOR + 0.20%. The coupon rate is recalculated periodically, typically every one or three months.

Inflation linked bonds (linkers), in which the principal amount and the interest payments are indexed to inflation. The interest rate is normally lower than for fixed rate bonds with a comparable maturity. However, as the principal amount grows, the payments increase with inflation. The United Kingdom was the first sovereign issuer to issue inflation linked Gilts in the 1980s. Treasury Inflation-Protected Securities (TIPS) and I-bonds are examples of inflation linked bonds issued by the U.S. government.

6.3.3: Maturity Date

Learning Objective

Define a US security based on its maturity date

Key Points

• As long as all due payments have been made, the issuer has no further obligations to the bond holders after the maturity date.
• The length of time until the maturity date is often referred to as the term or tenor or maturity of a bond.
• In the market for United States Treasury securities, there are three categories of bond maturities: short term, medium term, and long term.

Key Terms

callable

A callable bond (also called “redeemable bond”) is a type of bond (debt security) that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches its date of maturity.

puttable

Puttable bond (put bond, putable, or retractable bond) is a bond with an embedded put option. The holder of the puttable bond has the right, but not the obligation, to demand early repayment of the principal.

In finance, maturity date or redemption date, refers to the final payment date of a loan or other financial instrument, at which point the principal (and all remaining interest) is due to be paid.

Austrian war bond

The first Austrian bonds had 5% rates of return and a five-year maturity.

The issuer has to repay the nominal amount on the maturity date. As long as all due payments have been made, the issuer has no further obligations to the bond holders after the maturity date. The length of time until the maturity date is often referred to as the term or tenor or maturity of a bond. The maturity can be any length of time, although debt securities with a term of less than one year are generally designated money market instruments rather than bonds. Most bonds have a term of up to 30 years. Some bonds have been issued with terms of 50 years or more and, historically, there have been some issues with no maturity date (irredeemables).

In the market for United States Treasury securities, there are three categories of bond maturities:

• short term (bills): maturities between 1 to 5 years (instruments with maturities less than one year are called “Money Market Instruments”);
• medium term (notes): maturities between 6 to 12 years; and
• long term (bonds): maturities greater than 12 years.

Normally the maturity of a bond is fixed. However, it is important to note that bonds are sometimes “callable,”which means that the issuer of the debt is able to pay back the principal at any time. In this case, the maturity date is the day when the bond is called. Thus, investors should inquire, before buying any fixed-income securities, whether the bond is callable or not. Bonds can also be puttable, meaning that the holder has the right, but not the obligation, to demand early repayment of the principal. Similarly, the maturity date, if applicable, is the date as the bond is redeemed.

6.3.4: Call Provisions

Learning Objective

Classify a bond based on its call provision

Key Points

• A callable bond is a type of bond that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches its date of maturity.
• If interest rates in the market have gone down by the time of the call date, the issuer will be able to refinance its debt at a cheaper level and so will be incentivized to call the bonds it originally issued.
• Most callable bonds allow the issuer to repay the bond at par. With some bonds, the issuer has to pay a premium, known as the call premium.
• Price of callable bond = Price of straight bond – Price of call option. Price of a callable bond is always lower than the price of a straight bond because the call option adds value to an issuer.

Key Terms

par

Equal value; equality of nominal and actual value; the value expressed on the face or in the words of a certificate of value, as a bond or other commercial paper.

straight bond

A straight bond is a bond with no embedded options (call or put options).

Occasionally a bond may contain an embedded option. That is, it grants option-like features to the holder or the issuer. A callable bond (also called redeemable bond) is a type of bond that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches its date of maturity. In other words, on the call date, the issuer has the right, but not the obligation, to buy back the bonds from the bond holders at a defined call price. Technically speaking, the bonds are not really bought and held by the issuer. They are instead cancelled immediately.

Call dates are the dates on which callable bonds can be redeemed early.

There are three main categories.

1. A Bermudan callable has several call dates, usually coinciding with coupon dates.
2. A European callable has only one call date. This is a special case of a Bermudan callable.
3. An American callable can be called at any time until the maturity date.

Redeemed Bonds

This Bond is one of the 400 issued to the Central Pacific Rail Road Company of California and 200 to the Western Pacific Rail Road Company in 1865 under the Act of the California Legislature passed on April 22, 1863. Coupon #1 was redeemed and cancelled on November 2, 1865, and coupon #35 on November 2, 1882, at which time the principal of $1,000.00 in gold coin was also paid from the Treasury of the City and County of San Francisco and the Bond was cancelled.

Most callable bonds allow the issuer to repay the bond at par. With some bonds, the issuer has to pay a premium, known as the call premium. This is mainly the case for high-yield bonds. These have very strict covenants, restricting the issuer in its operations. To be free from these covenants, the issuer can repay the bonds early, but only at a high cost.

The issuer has an option, for which it pays in the form of a higher coupon rate. If interest rates in the market have gone down by the time of the call date, the issuer will be able to refinance its debt at a cheaper level. The issuer will be incentivized to call the bonds it originally issued. Another way to look at this interplay is that as interest rates go down, the price of the bonds goes up. Therefore, it is advantageous to buy the bonds back at par value. With a callable bond, investors have the benefit of a higher coupon than they would have had with a straight, non-callable bond. On the other hand, if interest rates fall, the bonds will likely be called, and they can only invest at the lower rate.

The price behavior of a callable bond is the opposite of that of puttable bond. Since call option and put option are not mutually exclusive, a bond may have both options embedded.

Price of callable bond = Price of straight bond – Price of call option

Price of a callable bond is always lower than the price of a straight bond because the call option adds value to an issuer. Similarly, yield on a callable bond is higher than the yield on a straight bond.

6.3.5: Sinking Funds

Learning Objective

Describe how a sinking fund operates in regards to a bond issue

Key Points

• Sinking fund provision of the corporate bond indenture requires a certain portion of the issue to be retired periodically.
• A sinking fund reduces credit risk but presents reinvestment risk to bondholders.
• For the creditors, the fund reduces the risk the organization will default when the principal is due: it reduces credit risk. However, if the bonds are callable, this comes at a cost to creditors, because the organization has an option on the bonds.

Key Terms

debentures

A debenture is a document that either creates a debt or acknowledges it, and it is a debt without collateral.

Preferred Stock

Stock with a dividend, usually fixed, that is paid out of profits before any dividend can be paid on common stock. It also has priority to common stock in liquidation.

call provision

the right for the issuer to buy back the bond at a predetermined price at a certain time in future

In modern finance, a sinking fund is a method by which an organization sets aside money over time to retire its indebtedness by repaying or purchasing outstanding loans and securities held against the entity. More specifically, it is a fund into which money can be deposited, so that over time preferred stock, debentures or stocks can be retired. Sinking funds can also be used to set aside money for purposes of replacing capital equipment as it becomes obsolete .

Farm bond

One purpose of a sinking fund is to repurchase outstanding bonds.

Sinking fund provision of the corporate bond indenture requires a certain portion of the issue to be retired periodically. The entire bond issue can be liquidated by the maturity date. Issuers may either pay to trustees, which in turn call randomly selected bonds in the issue, or, alternatively, purchase bonds in open market, then return them to trustees.

A sinking fund may operate in one or more of the following ways:

• The firm may repurchase a fraction of the outstanding bonds in the open market each year.
• The firm may repurchase a fraction of outstanding bonds at a special call price associated with the sinking fund provision (they are callable bonds).
• The firm has the option to repurchase the bonds at either the market price or the sinking fund price, whichever is lower. The firm can only repurchase a limited fraction of the bond issue at the sinking fund price. At best some indentures allow firms to use a doubling option, which allows repurchase of double the required number of bonds at the sinking fund price.
• A less common provision is to call for periodic payments to a trustee, with the payments invested so that the accumulated sum can be used for retirement of the entire issue at maturity: instead of the debt amortizing over the life, the debt remains outstanding and a matching asset accrues. Thus the balance sheet consists of Asset = Sinking fund, Liability = Bonds

For the creditors, the fund reduces the risk the organization will default when the principal is due: it reduces credit risk. However, if the bonds are callable, this comes at a cost to creditors, because the organization has an option on the bonds: The firm will choose to buy back discount bonds (selling below par) at their market price,while exercising its option to buy back premium bonds (selling above par) at par. Therefore, if interest rates fall and bond prices rise, a firm will benefit from the sinking fund provision that enables it to repurchase its bonds at below-market prices. In this case, the firm’s gain is the bondholder’s loss–thus callable bonds will typically be issued at a higher coupon rate, reflecting the value of the option.

6.3.6: Other Features

Learning Objective

Describe the effect a bond’s market price has on its yield

Key Points

• The yield is the rate of return received from investing in the bond. It usually refers either to the current yield, or to the yield to maturity or redemption yield.
• The market price of a tradeable bond will be influenced by the amounts, currency and timing of the interest payments and capital repayment due, the quality of the bond, and the available redemption yield of other comparable bonds which can be traded in the markets.
• Some bonds give the holder the right to force the issuer to repay the bond before the maturity date on the put dates. These are referred to as retractable or putable bonds.

Key Terms

Yield to maturity

The internal rate of return on a bond held to maturity, assuming scheduled payment of principal and interest.

clean price

the price of a bond excluding any interest that has accrued since issue or the most recent coupon payment.

Some other important features of bonds are presented below, namely the yield, market price and putability of a bond. “”

San Francisco Pacific Railroad Bond

$1,000 (30 year, 7%) “Pacific Railroad Bond” (#93 of 200) issued by the City and County of San Francisco under “An Act to Authorize the Board of Supervisors of the City and County of San Francisco to take and subscribe One Million Dollars to the Capital Stock of the Western Pacific Rail Road Company and the Central Pacific Rail Road Company of California and to provide for the payment of the same and other matters relating thereto” approved on April 22, 1863, as amended by section Five of the “Compromise Act” approved on April 4, 1864, to fund the construction of the Western Pacific Railroad between San Francisco Bay (at Alameda) and the CPRR of Cal. at Sacramento, dated May 1, 1865.

Yield

The yield is the rate of return received from investing in the bond. It usually refers either to the current yield, which is simply the annual interest payment divided by the current market price of the bond (often the clean price), or to the yield to maturity or redemption yield. Yield to maturity is a more useful measure of the return of the bond, taking into account the current market price, the amount and timing of all remaining coupon payments, and of the repayment due on maturity.

Eurozone Government Bonds Yield

Development of yield to maturity of bonds of 2019 maturity of a number of Eurozone governments.

Market Price

The market price of a tradeable bond will be influenced – amongst other things – by the amounts, currency and timing of the interest payments and capital repayment due; the quality of the bond; and the available redemption yield of other comparable bonds which can be traded in the markets. The price can be quoted as clean or dirty. “Dirty” refers to the actual price to be paid; while “clean” includes an adjustment for accrued interest. The issue price at which investors buy the bonds when they are first issued will typically be approximately equal to the nominal amount. The net proceeds that the issuer receives are thus the issue price, less issuance fees. The market price of the bond will vary over its life: it may trade at a premium (above par, usually because market interest rates have fallen since issue), or at a discount (below par, if market rates have risen or there is a high probability of default on the bond).

Putability

Some bonds give the holder the right to force the issuer to repay the bond before the maturity date on the put dates. These are referred to as retractable or putable bonds. Put dates are the dates on which putable bonds can be redeemed early. This type of bond protects investors: if interest rates rise after bond purchase, the future value of coupon payments will become less valuable. Therefore, investors sell bonds back to the issuer and may lend proceeds elsewhere at a higher rate. Bondholders are ready to pay for such protection by accepting a lower yield relative to that of a straight bond. A death put is an optional redemption feature on a debt instrument allowing the beneficiary of the estate of a deceased bondholder to put (sell) the bond (back to the issuer) at face value in the event of the bondholder’s death or legal incapacitation.

Price of puttable bond = Price of straight bond + Price of put option

Price of a puttable bond is always higher than the price of a straight bond because the put option adds value to an investor. Yield on a puttable bond is lower than the yield on a straight bond.

6.4: Understanding Bonds

6.4.1: The Nature of Bonds

A bond is an instrument of indebtedness of the bond issuer to the holders.

Learning Objective

Distinguish the various types of bonds from other types of securities

Key Points

• A bond is an instrument of indebtedness of the bond issuer to the holders. The issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest (the coupon) and/or to repay the principal at a later date, termed the maturity.
• Bonds provide the borrower with external funds to finance long-term investments, or, in the case of government bonds, to finance current expenditure.
• Bonds and stocks are both securities, but the major difference between the two is that (capital) stockholders have an equity stake in the company (i.e. they are owners), whereas bondholders have a creditor stake in the company (i.e. they are lenders).

Key Terms

municipal bonds

A municipal bond is a bond issued by an American city or other local government, or their agencies.

Treasury bonds

A United States Treasury bond is a government debt issued by the United States Department of the Treasury through the Bureau of the Public Debt, with a maturity of 20 years to 30 years.

corporate bonds

A corporate bond is a bond issue by a corporation. It is a bond that a corporation issues to raise money effectively in order to expand its business.

Nature of Bonds

A bond is an instrument of indebtedness of the bond issuer to the holders, as such it is often referred to as a debt instrument. A bond is a debt security, under which the issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest (the coupon) and/or repay the principal at a later date, termed the maturity. Interest is usually payable at fixed intervals (semiannual, annual, sometimes monthly).

Bonds are issued by public authorities, credit institutions, companies, and supranational institutions in the primary market. Both individuals and companies can purchase bonds.

However, very often the bond is negotiable, i.e. the ownership of the instrument can be transferred in the secondary market .

A bond from the Dutch East India Company

A bond is a financial security that represents a promise by a company or government to repay a certain amount, with interest, to the bondholder.

Types of Bonds

The main categories of bonds are corporate bonds, municipal bonds, and U.S. Treasury bonds, notes, and bills, which are collectively referred to simply as “Treasuries. ” Two features of a bond – credit quality and duration – are the principal determinants of a bond’s interest rate. Bond maturities range from a 90-day Treasury bill to a 30-year government bond. Corporate and municipal bonds are typically in the three to 10-year range.

Overview of the Instrument

A bond is a form of loan: the holder of the bond is the lender (creditor), the issuer of the bond is the borrower (debtor), and the coupon is the interest. Bonds provide the borrower with external funds to finance long-term investments, or, in the case of government bonds, to finance current expenditure. Certificates of deposits (CDs), or short term commercial papers, are considered to be money market instruments and not bonds: the main difference is in the instruments length of term.

Bonds and stocks are both securities, but the major difference between the two is that (capital) stockholders have an equity stake in the company (they are owners), whereas bondholders have a creditor stake in the company (they are lenders). Another difference is that bonds usually have a defined term, or maturity, after which the bond is redeemed, whereas stocks may be outstanding indefinitely. An exception is an irredeemable bond, such as Consols, which is a perpetuity, that is, a bond with no maturity.

6.4.2: Duration

Duration is the weighted average of the times until fixed cash flows of a financial asset are received.

Learning Objective

Define the different types of duration

Key Points

• A good approximation for bond price changes due to yield is the duration, a measure for interest rate risk.
• The Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years. It really makes sense only for an instrument with fixed cash flows.
• The modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield. It really makes sense only for an instrument with fixed cash flows.
• The modified duration is a derivative (rate of change) or price sensitivity and measures the percentage rate of change of price with respect to yield. The concept of modified duration can be applied to interest-rate sensitive instruments with non-fixed cash flows.

Key Terms

Convexity

As interest rates change, the price does not change linearly, but rather is a convex function of interest rates. Convexity is a measure of the curvature of how the price of a bond changes as the interest rate changes. Specifically, duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question, and the convexity as the second derivative.

Yield to maturity

The yield to maturity (YTM) of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity and that all coupon and principal payments will be made on schedule.

Duration

In finance, the duration of a financial asset that consists of fixed cash flows, for example a bond, is the weighted average of the times until those fixed cash flows are received. When an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields. Since cash flows for bonds are usually fixed, a price change can come from two sources: The passage of time (convergence towards par) which is predictable and a change in the yield.

The yield-price relationship is inverse and investors would ideally wish to have a measure of how sensitive the bond price is to yield changes. A good approximation for bond price changes due to yield is the duration, a measure for interest rate risk. For large yield changes convexity can be added to improve the performance of the duration. A more important use of convexity is that it measures the sensitivity of duration to yield changes.

Types of Durations

The dual use of the word “duration” in the Macaulay duration and the modified duration, as both the weighted average time until repayment and as the percentage change in price, often causes confusion. The Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years.

Macaulay duration

The Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years.

Where: i indexes the cash flows, PV_i is the present value of the cash payment from an asset, t_i is the time in years until the payment will be received, and V is the present value of all cash payments from the asset.

The Modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield.

Modified duration

The modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield.

Where: k is the compounding frequency per year (1 for annual, 2 for semi-annual, 12 for monthly, 52 for weekly, and so on), y is the is the yield to maturity for an asset.

When yields are continuously-compounded the Macaulay duration and the modified duration will be numerically equal. When yields are periodically-compounded the Macaulay duration and the modified duration will differ slightly and in this case there is a simple relation between the two. The modified duration is used more than the Macaulay duration.

The Macaulay duration and the modified duration are both termed “duration” and have the same (or close to the same) numerical value, but it is important to keep in mind the conceptual distinctions between them. The Macaulay duration is a time measure with units in years and really makes sense only for an instrument with fixed cash flows. For a standard bond, the Macaulay duration will be between 0 and the maturity of the bond. It is equal to the maturity if and only if the bond is a zero-coupon bond.

The modified duration, on the other hand, is a derivative (rate of change) or price sensitivity and measures the percentage rate of change of price with respect to yield. The concept of modified duration can be applied to interest-rate sensitive instruments with non-fixed cash flows and can thus be applied to a wider range of instruments than can the Macaulay duration. For everyday use, the equality (or near-equality) of the values for the Macaulay duration and the modified duration can be a useful aid to intuition.

6.4.3: Indenture

A bond indenture is a legal contract issued to lenders that defines commitments and responsibilities of the seller and the buyer.

Learning Objective

Review the rights and responsibilities of parties to a bond

Key Points

• Terms of indentures include the interest rate, maturity date, repayment dates, convertibility, pledge, promises, representations, covenants, and other terms of the bond offering.
• A bond indenture is held by a trustee. If the company fails to live up to the terms of the bond indenture, the trustee may bring legal action against the company on behalf of the bondholders.
• The offering memorandum, also known as a prospectus, is a document that describes a financial security for potential buyers.

Key Terms

convertibility

Quality of a bond that allows the holder to convert into shares of common stock in the issuing company or cash of equal value, at an agreed-upon price.

indenture

a document, written as duplicates separated by indentations, specifying such a contract

public debt offerings

A public debt offering is the offering of debt securities of a government, a company or a similar corporation to the public.

A bond indenture (also called a trust indenture or deed of trust) is a legal contract issued to lenders. The specifications given within the bond indenture define the responsibilities and commitments of the seller as well as those of the buyer by describing key terms such as the interest rate, maturity date, repayment dates, convertibility, pledge, promises, representations, covenants, and other terms of the bond offering. Failure to meet the payment requirements calls for drastic penalties, including liquidation of the issuer’s assets .

Indenture

Bond indenture (also trust indenture or deed of trust) is a legal contract issued to lenders.

Because it would be impractical for the corporation to enter into a direct agreement with each of the many bondholders, the bond indenture is held by a trustee – usually a commercial bank or other financial institution – appointed by the issuing firm to represent the rights of the bondholders. The issuer of a bond will use the indenture to describe detail about the issuer and the bond trustee for interested investors to research the background of the bond issue. This is to ensure that the bondholder has a clear idea of when to expect interest payments, as well as whom to contact if he or she has questions or concerns. If the company fails to live up to the terms of the bond indenture, the trustee may bring legal action against the company on behalf of the bondholders.

When the offering memorandum is prepared in advance of marketing a bond, the indenture will typically be summarized in the “description of notes” section. This offering memorandum, also known as a prospectus, is a document that describes a financial security for potential buyers. A prospectus commonly provides investors with material information about mutual funds, stocks, bonds, and other investments, such as a description of the company’s business, financial statements, biographies of officers and directors, detailed information about their compensation, any litigation that is taking place, a list of material properties, and any other material information.

In the United States, public debt offerings in excess of $10 million require the use of an indenture of trust under the Trust Indenture Act of 1939. The rationale for this is that it is necessary to establish a collective action mechanism under which creditors can collect in a fair, orderly manner if default takes place (like that which occurs during bankruptcy).

6.4.4: Ratings

Bond credit rating agencies assess and report the credit worthiness of a corporation’s or government’s debt issues.

Learning Objective

Use the ratings system to assess the risk associated with different bonds

Key Points

• Ratings play a critical role in determining how much companies and other entities that issue debt, including sovereign governments, have to pay to access credit markets; for example, the amount of interest they pay on their issued debt.
• The ratings are assigned by credit rating agencies such as Moody’s, Standard & Poor’s, and Fitch. Ratings to have letter designations (such as AAA, B, CC), which represent the quality of a bond.
• A bond is considered investment-grade (IG) if its credit rating is BBB- or higher by Standard & Poor’s, or Baa3 or higher by Moody’s, or BBB(low) or higher by DBRS. Bond ratings below BBB/Baa are not considered to be investment grade; such bonds are called junk bonds.

Key Term

credit rating agencies

A credit rating agency (CRA) is a company that assigns credit ratings to issuers of certain types of debt obligations, as well as to the debt instruments themselves.

Ratings Overview

In investment, the bond credit rating assesses the credit worthiness of a corporation’s or government’s debt issue. The credit rating is analogous to a credit rating for individuals. The “quality” of the issue refers to the probability that the bondholders will receive the amounts promised on the due dates.

The credit rating is a financial indicator to potential investors of debt securities, such as bonds. Ratings play a critical role in determining the amount that companies (and other entities that issue debt, including sovereign governments) have to pay to access credit markets; for example, the amount of interest that must be paid on issued debt. The ratings are assigned by credit rating agencies, such as Moody’s, Standard & Poor’s, and Fitch Ratings, and are given in letter designations (AAA, B, CC), which represent the quality of a bond. Generally they are bonds that are judged by the rating agency as likely enough to meet payment obligations; banks are thus allowed to invest in them. “”

Credit Rating Equivalents

Credit ratings are used to report on the credit worthiness of a bond issuing company or government

Investment-grade Bonds

A bond is considered investment-grade, or IG, if its credit rating is BBB- or higher by Standard & Poor’s, or Baa3 or higher by Moody’s, or BBB(low) or higher by DBRS.

Bond ratings below BBB/Baa are not considered to be investment-grade; these bonds are called junk bonds. Junk bonds are also called high-yield bonds. These are bonds that are rated below investment grade by the credit rating agencies. As these bonds are more risky than investment grade bonds, investors expect them to earn a higher yield. The threshold between investment-grade and speculative-grade ratings has important market implications for issuers’ borrowing costs.

The risks associated with investment-grade bonds (or investment-grade corporate debt) are considered significantly higher than those associated with first-class government bonds. The difference between rates for first-class government bonds and investment-grade bonds is called “investment-grade spread. ” The range of this spread is an indicator of the market’s belief in the stability of the economy. The higher these investment-grade spreads (or risk premiums) are, the weaker the economy is considered.

Rating Agency Criticism

Until the early 1970s, bond credit ratings agencies were paid for their work by investors who wanted impartial information on the credit worthiness of securities issuers and their particular offerings. Starting in the early 1970s, the “Big Three” ratings agencies (S&P, Moody’s, and Fitch) began to receive payment for their work by the securities issuers for whom they issued ratings, which led to current charges that these ratings agencies can no longer always be impartial when issuing ratings for securities issuers. Securities issuers have been accused of “shopping” for the best ratings from S&P, Moody’s, and Fitch, in order to attract investors, until at least one of the agencies delivers favorable ratings.

6.5: Advantages and Disadvantages of Bonds

6.5.1: Advantages of Bonds

Bonds have some advantages over stocks, including relatively low volatility, high liquidity, legal protection, and a variety of term structures.

Learning Objective

Discuss the advantages of owning a bond

Key Points

• Bonds are a debt security under which the issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest (the coupon) and or repay the principal at a later date, which is termed the maturity.
• The volatility of bonds (especially short and medium dated bonds) is lower than that of equities (stocks). Thus bonds are generally viewed as safer investments than stocks.
• Bonds are often liquid – it is often fairly easy for an institution to sell a large quantity of bonds without affecting the price much.
• Bondholders also enjoy a measure of legal protection: under the law of most countries, if a company goes bankrupt, its bondholders will often receive some money back (the recovery amount).
• There are also a variety of bonds to fit different needs of investors.

Key Terms

inflation-linked bonds

Inflation-indexed bonds (also known as inflation-linked bonds or colloquially as linkers) are bonds where the principal is indexed to inflation. They are thus designed to cut out the inflation risk of an investment.

Zero coupon bonds

A zero-coupon bond (also called a discount bond or deep discount bond) is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity.

Convertible bonds

A convertible bond is a type of bond that the holder can convert into shares of common stock in the issuing company or cash of equal value, at an agreed-upon price.

Definition and Purpose of a Bond

In finance, a bond is an instrument of indebtedness of the bond issuer to the holders. It is a debt security under which the issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest (the coupon). In addition, the issuer might have to repay the principal at a later date, which is termed the maturity. Interest is usually payable at fixed intervals (semiannual, annual, and sometimes monthly). Very often the bond is negotiable; in other words, the ownership of the instrument can be transferred in the secondary market.

San Francisco Pacific Railroad Bond

A bond is an instrument of indebtedness of the bond issuer to the holders. It is a debt security under which the issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest (the coupon). In addition, the issuer might have to repay the principal at a later date, which is termed the maturity.

Bonds are bought and traded mostly by institutions like central banks, sovereign wealth funds, pension funds, insurance companies, hedge funds, and banks. Insurance companies and pension funds have liabilities, which essentially include fixed amounts payable on predetermined dates. They buy the bonds to match their liabilities and may be compelled by law to do this. Most individuals who want to own bonds do so through bond funds. Still, in the U.S., nearly 10% of all outstanding bonds are held directly by households.

Advantages of Bonds

Bonds have a clear advantage over other securities. The volatility of bonds (especially short and medium dated bonds) is lower than that of equities (stocks). Thus bonds are generally viewed as safer investments than stocks. In addition, bonds do suffer from less day-to-day volatility than stocks, and the interest payments of bonds are sometimes higher than the general level of dividend payments.

Bonds are often liquid. It is often fairly easy for an institution to sell a large quantity of bonds without affecting the price much, which may be more difficult for equities. In effect, bonds are attractive because of the comparative certainty of a fixed interest payment twice a year and a fixed lump sum at maturity.

Bondholders also enjoy a measure of legal protection: under the law of most countries, if a company goes bankrupt, its bondholders will often receive some money back (the recovery amount), whereas the company’s equity stock often ends up valueless. Furthermore, bonds come with indentures (an indenture is a formal debt agreement that establishes the terms of a bond issue) and covenants (the clauses of such an agreement). Covenants specify the rights of bondholders and the duties of issuers, such as actions that the issuer is obligated to perform or is prohibited from performing.

There are also a variety of bonds to fit different needs of investors, including fixed rated bonds, floating rate bonds, zero coupon bonds, convertible bonds, and inflation linked bonds.

6.5.2: Disadvantages of Bonds

Bonds are subject to risks such as the interest rate risk, prepayment risk, credit risk, reinvestment risk, and liquidity risk.

Learning Objective

Discuss the disadvantages of owning a bond

Key Points

• A bond is an instrument of indebtedness of the bond issuer to the holders. It is a debt security under which the issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest and possibly repay the principal at a later date, which is termed the maturity.
• Fixed rate bonds are subject to interest rate risk, meaning that their market prices will decrease in value when the generally prevailing interest rates rise.
• Bonds are also subject to various other risks such as call and prepayment risk, credit risk, reinvestment risk, liquidity risk, event risk, exchange rate risk, volatility risk, inflation risk, sovereign risk, and yield curve risk.
• A company’s bondholders may lose much or all their money if the company goes bankrupt. There is no guarantee of how much money will remain to repay bondholders.
• Some bonds are callable. This creates reinvestment risk, meaning the investor is forced to find a new place for his money. As a consequence, the investor might not be able to find as good a deal, especially because this usually happens when interest rates are falling.

Key Terms

Reinvestment risk

The reinvestment risk is the possibility that the investor might be forced to find a new place for his money. As a consequence, the investor might not be able to find as good a deal, especially because this usually happens when interest rates are falling.

Exchange rate risk

The exchange rate risk is a financial risk posed by an exposure to unanticipated changes in the exchange rate between two currencies.

Definition and Purpose of a Bond

A bond is a debt owed by the enterprise to the bondholder. Commercial bonds are normally issued in units of 1,000 dollars. Bondholders receive regular interest on their investment, depending on the terms of the bond. As a safe security, bonds are widely bought and traded by financial institutions. However, bonds have certain disadvantages.

Bond

A bond is a debt owned by the enterprise to the bondholder.

Fixed rate bonds are subject to interest rate risk, meaning that their market prices will decrease in value when the generally prevailing interest rates rise. Since the payments are fixed, a decrease in the market price of the bond means an increase in its yield. When the market interest rate rises, the market price of bonds will fall, reflecting the ability of investors to get a higher interest rate on their money elsewhere — perhaps by purchasing a newly issued bond that already features the newly higher interest rate.

Disadvantages of Bonds

Bonds are also subject to various other risks such as call and prepayment risk, credit risk, reinvestment risk, liquidity risk, event risk, exchange rate risk, volatility risk, inflation risk, sovereign risk, and yield curve risk.

Price changes in a bond will immediately affect mutual funds that hold these bonds. If the value of the bonds in a trading portfolio falls, the value of the portfolio also falls. This can be damaging for professional investors such as banks, insurance companies, pension funds, and asset managers (irrespective of whether the value is immediately “marked to market” or not). If there is any chance a holder of individual bonds may need to sell his bonds and “cash out”, the interest rate risk could become a real problem.

Bond prices can become volatile depending on the credit rating of the issuer – for instance if credit rating agencies like Standard and Poor’s and Moody’s upgrade or downgrade the credit rating of the issuer. An unanticipated downgrade will cause the market price of the bond to fall. As with interest rate risk, this risk does not affect the bond’s interest payments (provided the issuer does not actually default), but puts at risk the market price, which affects mutual funds holding these bonds, and holders of individual bonds who may have to sell them.

A company’s bondholders may lose much or all their money if the company goes bankrupt. Under the laws of many countries (including the United States and Canada), bondholders are in line to receive the proceeds of the sale of the assets of a liquidated company ahead of some other creditors. Bank lenders, deposit holders (in the case of a deposit taking institution such as a bank) and trade creditors may take precedence. There is no guarantee of how much money will remain to repay bondholders. In a bankruptcy involving reorganization or recapitalization, as opposed to liquidation, bondholders may end up having the value of their bonds reduced, often through an exchange for a smaller number of newly issued bonds.

Some bonds are callable, meaning that even though the company has agreed to make payments plus interest toward the debt for a certain period of time, the company can choose to pay off the bond early. This creates reinvestment risk, meaning the investor is forced to find a new place for his money. As a consequence, the investor might not be able to find as good a deal, especially because this usually happens when interest rates are falling.

6.6: Types of Bonds

6.6.1: Government Bonds

A government bond is a bond issued by a national government denominated in the country’s domestic currency.

Learning Objective

Analyze the risks and characteristics of government bonds

Key Points

• A government bond is a bond issued by a national government, generally promising to pay a certain amount (the face value) on a certain date, as well as periodic interest payments. Such bonds are often denominated in the country’s domestic currency.
• In the primary market, Government Bonds are often issued via auctions at Stock Exchanges. In the secondary market, government bonds are traded at Stock Exchanges.
• Although, government bonds are usually referred to as risk-free, there are currency, inflation, and default risks for government bondholders.

Key Terms

purchasing power

Purchasing power (sometimes retroactively called adjusted for inflation) is the amount of goods or services that can be purchased with a unit of currency.

purchasing power parity

a theory of long-term equilibrium exchange rates based on relative price levels of two countries

A government bond is a bond issued by a national government, generally promising to pay a certain amount (the face value) on a certain date as well as periodic interest payments. Such bonds are often denominated in the country’s domestic currency. Government bonds are sometimes regarded as risk-free bonds because national governments can raise taxes or reduce spending up to a certain point. In many cases, they “print more money” to redeem the bond at maturity. Most developed country governments are prohibited by law from printing money directly, that function having been relegated to their central banks. However, central banks may buy government bonds in order to finance government spending, thereby monetizing the debt .

Government Bond

The short-term bond of Kolchak government in 1919 with a face value of 500 rubles.

Bonds issued by national governments in foreign currencies are normally referred to as sovereign bonds. Investors in sovereign bonds denominated in foreign currency have the additional risk that the issuer may be unable to obtain foreign currency to redeem the bonds. For example, in the 2010 Greek debt crisis the debt was held by Greece in Euros. One proposed solution was for Greece to go back to issuing its own Drachma.

In the primary market, Government Bonds are often issued via auctions at Stock Exchanges. There are several different methods of issuing such as auctions, including guarantee, combined auction and guarantee, and others. There are two types of interest rates: fixed and floating. In the secondary market, government bonds are traded at Stock Exchanges. Unlikely equity system, the bond secondary market uses a completely different system with different method of trading. At the secondary market, each bond will be assigned with very own bond code (ISIN code).

Government bonds are usually referred to as risk-free bonds because the government can raise taxes or create additional currency in order to redeem the bond at maturity. Some counter examples do exist where a government has defaulted on its domestic currency debt, such as Russia in 1998 (the “ruble crisis”), although this is very rare (see national bankruptcy). Another example is Greece in 2011. Its bonds were considered very risky, in part because Greece did not have its own currency.

There is currency risk for government bondholders. As an example, in the U.S., Treasury securities are denominated in U.S. dollars. In this instance, the term “risk-free” means free of credit risk. However, other risks still exist, such as currency risk for foreign investors (for example non-U.S. investors of U.S. Treasury securities would have received lower returns in 2004 because the value of the U.S. dollar declined against most other currencies). Secondly, there is inflation risk, in that the principal repaid at maturity will have less purchasing power than anticipated if the inflation rate is higher than expected. Many governments issue inflation-indexed bonds, which protect investors against inflation risk by increasing the interest rate given to the investor as the inflation rate of the economy increases.

6.6.2: Zero-Coupon Bonds

A zero-coupon bond is a bond with no coupon payments, bought at a price lower than its face value, with the face value repaid at the time of maturity.

Learning Objective

Distinguish zero coupon bonds from other types

Key Points

• Zero-coupon bonds may be created from fixed rate bonds by a financial institution separating (“stripping off”) the coupons from the principal. In other words, the separated coupons and the final principal payment of the bond may be traded separately.
• Zero coupon bonds have a duration equal to the bond’s time to maturity, which makes them sensitive to any changes in the interest rates.
• Pension funds and insurance companies like to own long maturity zero-coupon bonds since these bonds’ prices are particularly sensitive to changes in the interest rate and, therefore, offset or immunize the interest rate risk of these firms’ long-term liabilities.

Key Terms

immunize

In finance, interest rate immunization is a strategy that ensures that a change in interest rates will not affect the value of a portfolio. Similarly, immunization can be used to ensure that the value of a pension fund’s or a firm’s assets will increase or decrease in exactly the opposite amount of their liabilities, thus leaving the value of the pension fund’s surplus or firm’s equity unchanged, regardless of changes in the interest rate.

Pension funds

A pension fund is any plan, fund, or scheme which provides retirement income.

Zero coupon bonds were first introduced in 1960s, but they did not become popular until the 1980s. A zero-coupon bond (also called a “discount bond” or “deep discount bond”) is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity. It does not make periodic interest payments, or have so-called “coupons,” hence the term zero-coupon bond. When the bond reaches maturity, its investor receives its par (or face) value. Examples of zero-coupon bonds include U.S. Treasury bills, U.S. savings bonds, and long-term zero-coupon bonds.

SMAC bond

Bond on VMOK with the signature on Boris Saraf.

Zero-coupon bonds may be created from fixed rate bonds by a financial institution separating (“stripping off”) the coupons from the principal. In other words, the separated coupons and the final principal payment of the bond may be traded separately. Investment banks or dealers separate coupons from the principal of coupon bonds, which is known as the “residue,” so that different investors may receive the principal and each of the coupon payments. This creates a supply of new zero coupon bonds. The coupons and residue are sold separately to investors. Each of these investments then pays a single lump sum. This method of creating zero coupon bonds is known as stripping, and the contracts are known as strip bonds. “STRIPS” stands for Separate Trading of Registered Interest and Principal Securities.

Zero coupon bonds may be long- or short-term investments. Long-term zero coupon maturity dates typically start at 10 to 15 years. The bonds can be held until maturity or sold on secondary bond markets. Short-term zero coupon bonds generally have maturities of less than one year and are called bills. The U.S. Treasury bill market is the most active and liquid debt market in the world.

Zero coupon bonds have a duration equal to the bond’s time to maturity, which makes them sensitive to any changes in the interest rates. The impact of interest rate fluctuations on strip bonds is higher than for a coupon bond.

Pension funds and insurance companies like to own long maturity zero-coupon bonds because of the bonds’ high duration. This high duration means that these bonds’ prices are particularly sensitive to changes in the interest rate and, therefore, offset or immunize the interest rate risk of these firms’ long-term liabilities.

6.6.3: Floating-Rate Bonds

Floating rate bonds are bonds that have a variable coupon equal to a money market reference rate (e.g., LIBOR), plus a quoted spread.

Learning Objective

Describe a floating-rate bond

Key Points

• FRBs are typically quoted as a spread over the reference rate. At the beginning of each coupon period, the coupon is calculated by taking the fixing of the reference rate for that day and adding the spread. A typical coupon would look like three months USD LIBOR +0.20%.
• FRBs carry little interest rate risk. A FRB has a duration close to zero, and its price shows very low sensitivity to changes in market rates. As FRBs are almost immune to interest rate risk. The risk that remains is a credit risk.
• Securities dealers make markets in FRBs. They are traded over the counter, instead of on a stock exchange. In Europe, most FRBs are liquid, as the biggest investors are banks. In the United States, FRBs are mostly held to maturity, so the markets aren’t as liquid.

Key Terms

duration

A measure of the sensitivity of the price of a financial asset to changes in interest rates, computed for a simple bond as a weighted average of the maturities of the interest and principal payments associated with it

LIBOR

The London Interbank Offered Rate is the average interest rate estimated by leading banks in London that they would be charged if borrowing from other banks.

floating-rate bond

a debt instruments with a variable coupon

Floating rate bonds (FRBs) are bonds that have a variable coupon, equal to a money market reference rate, like LIBOR or federal funds rate, plus a quoted spread (i.e., quoted margin). The spread is a rate that remains constant. Almost all FRBs have quarterly coupons (i.e., they pay out interest every three months), though counter examples do exist. At the beginning of each coupon period, the coupon is calculated by taking the fixing of the reference rate for that day and adding the spread. A typical coupon would look like three months USD LIBOR +0.20%.

In the United States, government sponsored enterprises (GSEs), such as the Federal Home Loan Banks, the Federal National Mortgage Association (Fannie Mae), and the Federal Home Loan Mortgage Corporation (Freddie Mac), are important issuers. In Europe, the main issuers are banks.

Municipal bond

Municipal bond issued in 1929 by city of Kraków (Poland).

There are many variations of floating-rate bonds. For instance, some FRBs have special features, such as maximum or minimum coupons, called “capped FRBs” and “floored FRBs. ” Those with both minimum and maximum coupons are called collared FRBs. Perpetual FRBs are another form of FRBs that are also called irredeemable or unrated FRBs and are akin to a form of capital. FRBs can also be obtained synthetically by the combination of a fixed rate bond and an interest rate swap. This combination is known as an “asset swap. “

FRBs carry little interest rate risk. A FRB has a duration close to zero, and its price shows very low sensitivity to changes in market rates. When market rates rise, the expected coupons of the FRB increase in line with the increase in forward rates, which means its price remains constant. Thus, FRBs differ from fixed rate bonds, whose prices decline when market rates rise. As FRBs are almost immune to interest rate risk, they are considered conservative investments for investors who believe market rates will increase. The risk that remains is credit risk.

Securities dealers make markets in FRBs. They are traded over the counter, instead of on a stock exchange. In Europe, most FRBs are liquid, as the biggest investors are banks. In the United States, FRBs are mostly held to maturity, so the markets aren’t as liquid. In the wholesale markets, FRBs are typically quoted as a spread over the reference rate.

6.6.4: Other Types of Bonds

Other bonds include register vs. bearer bonds, convertible bonds, exchangeable bonds, asset-backed securities, and foreign currency bonds.

Learning Objective

Classify the different types of bonds

Key Points

• Bonds directly linked to interest rates include fixed rate bonds, floating rate bonds, and zero coupon bonds.
• Convertible bonds are bonds that let a bondholder exchange a bond to a number of shares of the issuer’s common stock. Exchangeable bonds allows for exchange to shares of a corporation other than the issuer.
• Asset-backed securities are bonds whose interest and principal payments are backed by underlying cash flows from other assets.
• Subordinated bonds are those that have a lower priority than other bonds of the issuer in case of liquidation.
• Foreign currency bonds are issued by companies, banks, governments, and other sovereign entities in foreign currencies, as it may appear to be more stable and predictable than their domestic currency.

Key Terms

gross domestic product

A measure of the economic production of a particular territory in financial capital terms over a specific time period.

tranches

One of a number of related securities offered as part of the same transaction.

LIBOR

The London Interbank Offered Rate is the average interest rate estimated by leading banks in London that they would be charged if borrowing from other banks.

General Categorization

Based on coupon interest rates, bonds can be classified into

• Fixed rate bonds
• Floating rate bonds
• Zero-coupon bonds

Fixed rate bonds have a coupon that remains constant throughout the life of the bond. A variation is a stepped-coupon bonds, whose coupon increases during the life of the bond.

Floating rate notes (FRNs, floaters) have a variable coupon that is linked to a reference rate of interest, such as LIBOR or Euribor. For example the coupon may be defined as three month USD LIBOR + 0.20%. The coupon rate is recalculated periodically, typically every one or three months.

Zero-coupon bonds pay no regular interest. They are issued at a substantial discount to par value, so that the interest is effectively rolled up to maturity (and usually taxed as such). The bondholder receives the full principal amount on the redemption date. Zero-coupon bonds may be created from fixed rate bonds by a financial institution separating (“stripping off”) the coupons from the principal. In other words, the separated coupons and the final principal payment of the bond may be traded separately .

Government Bond

Bond of National Loan issued by Polish National Government in 1863.

Additional Types

There are additional special classes of bonds, including:

Inflation linked bonds (linkers) are those in which the principal amount and the interest payments are indexed to inflation. It is one type of floating rate bond. The interest rate is normally lower than for fixed rate bonds, with a comparable maturity. However, as the principal amount grows, the payments increase with inflation. Treasury Inflation-Protected Securities (TIPS) and I-bonds are examples of inflation linked bonds issued by the U.S. government. There are also other indexed bonds. For example equity-linked notes and bonds indexed on a business indicator (income, added value) or on a country’s gross domestic product (GDP).

Convertible bonds are bonds that let a bondholder exchange a bond for a number of shares of the issuer’s common stock. Exchangeable bonds allows for exchange to shares of a corporation other than the issuer.

Asset-backed securities are bonds whose interest and principal payments are backed by underlying cash flows from other assets. Examples of asset-backed securities are mortgage-backed securities (MBS’s), collateralized mortgage obligations (CMOs), and collateralized debt obligations (CDOs).

Subordinated bonds are those that have a lower priority than other bonds of the issuer in case of liquidation. In case of bankruptcy, there is a hierarchy of creditors. First the liquidator is paid, then government taxes, etc. The first bond holders in line to be paid are those holding what is called senior bonds. After they have been paid, the subordinated bond holders are paid. As a result, the risk is higher. Therefore, subordinated bonds usually have a lower credit rating than senior bonds. The main examples of subordinated bonds can be found in bonds issued by banks and asset-backed securities. The latter are often issued in tranches. The senior tranches get paid back first, the subordinated tranches later.

Perpetual bonds are also often called perpetuities or “perps. ” They have no maturity date. The most famous of these are the UK Consols, which are also known as Treasury Annuities or Undated Treasuries.

A registered bond is a bond whose ownership (and any subsequent purchaser) is recorded by the issuer or by a transfer agent. It is the alternative to a bearer bond. Interest payments, and the principal upon maturity, are sent to the registered owner. On the contrary, a bearer bond is an official certificate issued without a named holder. In other words, the person who has the paper certificate can claim the value of the bond. Often they are registered by a number to prevent counterfeiting, but may be traded like cash. Bearer bonds are very risky because they can be lost or stolen. Especially after federal income tax began in the United States, bearer bonds were seen as an opportunity to conceal income or assets.

A serial bond is a bond that matures in installments over a period of time. In effect, a $100,000, 5-year serial bond would mature in a $20,000 annuity over a 5-year interval.

Some companies, banks, governments, and other sovereign entities may decide to issue bonds in foreign currencies because it may appear to be more stable and predictable than their domestic currency. Issuing bonds denominated in foreign currencies also gives issuers the ability to access investment capital available in foreign markets. Some examples include:

• Eurodollar bond – U.S. dollar-denominated bond issued by a non-U.S. (European) entity.
• U.S. Yankee bond – a US dollar-denominated bond issued by a non-U.S. entity in the U.S. market.
• Samurai bond – a Japanese yen-denominated bond issued by a non-Japanese entity in the Japanese market.
• Bulldog bond – a pound-sterling-denominated bond issued in England by a foreign institution or government.
• Kimchi bond – a Korean won-denominated bond issued by a non-Korean entity in the Korean market.

6.7: Bond Markets

6.7.1: Purchase Process

Most individuals purchase bonds via a broker or through bond funds.

Learning Objective

Describe the process for purchasing a bond

Key Points

• Buying a bond involves setting up an account with a broker and requesting that the broker buy bonds on the buyer’s behalf.
• An individual can also purchase bonds by investing in bond funds, which hold baskets of bonds rather than competing for individual bond sales.
• Most bond funds pay out dividends more frequently than individual bonds.

Key Terms

hedge funds

An investment fund that can undertake a wider range of investment and trading activities than other funds, but which is generally only open to certain types of investors specified by regulators.

bond funds

A bond fund or debt fund is a fund that invests in bonds or other debt securities. Bond funds can be contrasted with stock funds and money funds.

Pension funds

Any plan, fund, or scheme which provides retirement income.

Bonds are bought and traded mostly by institutions like central banks, sovereign wealth funds, pension funds, insurance companies, hedge funds, and banks. Insurance companies and pension funds have liabilities which essentially include fixed amounts payable on predetermined dates. They buy the bonds to match their liabilities, and may be compelled by law to do this. Most individuals who want to own bonds purchase bonds via a broker or do so through bond funds. Still, in the U.S., nearly 10% of all bonds outstanding are held directly by households.

Buying a bond involves setting up an account with a broker and requesting that the broker buy bonds on the buyer’s behalf. Brokers also can furnish considerable market information regarding prices, products, and market conditions. Like with stocks, accounts can be set up with an online discount broker to buy bonds while paying lower transaction fees. It is a good idea to look at several different brokers and their commission rates and services before choosing one. Additionally, bonds can be purchased directly from the U.S. federal government without the use of a broker and without paying broker commission fees.

Bond Brokers

Bonds can be purchased through brokerages, such Fidelity Investments.

An individual can also purchase bonds by investing in bond funds, which hold baskets of bonds rather than competing for individual bond sales. Bond funds typically pay periodic dividends that include interest payments on the fund’s underlying securities plus periodic realized capital appreciation. Bond funds typically pay higher dividends than certificates of deposits (CDs) and money market accounts. Most bond funds pay out dividends more frequently than individual bonds. Fund managers provide dedicated management and save the individual investor from researching issuer creditworthiness, maturity, price, face value, coupon rate, yield, and countless other factors that affect bond investing. Bond funds invest in many individual bonds, so that even a relatively small investment is diversified.

6.7.2: Price Transparency

Since bonds are traded in a decentralized, over-the-counter market dominated by dealers, there can be a lack of price transparency.

Learning Objective

Explain why bond markets may not have price transparency

Key Points

• A market is transparent if much is known–by many–about what products, services, or capital assets are available at what price and where.
• In most developed bond markets, such as the United States, Japan, and western Europe, bonds trade in decentralized, dealer-based, over-the-counter markets.
• Poor transparency contributes to investor differences in bond valuations, as well as other inefficiencies that may lead to economic losses for market participants and, ultimately, inhibit business development.

Key Terms

market liquidity

In business, economics or investment, market liquidity is an asset’s ability to be sold without causing a significant movement in the price and with minimum loss of value.

transparency

(figuratively) openness, degree of accessibility to view

In economics, a market is transparent if much is known–by many– about what products, services, or capital assets are available at what price and where.

There are two types of price transparency:

1. Knowing what price will be charged to me
2. Knowing what price will be charged to you

The two types of price transparency have different implications for differential pricing. Bond markets, unlike stock or share markets, sometimes do not have a centralized exchange or trading system. Rather, in most developed bond markets such as the United States, Japan, and western Europe, bonds trade in decentralized, dealer-based, over-the-counter markets. This convention, combined with the large number of debt issues outstanding, is largely responsible for the lack of price transparency that exists in the fixed income markets.

New York Stock Exchange

Most bonds are not sold in centralized marketplaces, such as the New York Stock Exchange, leading to a lack of price transparency.

Poor transparency contributes to investor differences in bond valuations, as well as other inefficiencies that may lead to economic losses for market participants, and, ultimately, inhibit business development. In such a market, market liquidity is provided by dealers and other market participants committing risk capital to trading activity. In the bond market, when an investor buys or sells a bond, the counterpart to the trade is almost always a bank or securities firm acting as a dealer. In some cases, when a dealer buys a bond from an investor, the dealer carries the bond “in inventory. ” In other words, the dealer holds it for his own account. The dealer is then subject to risks of price fluctuation. In other cases, the dealer immediately resells the bond to another investor.

Bond markets can also differ from stock markets in that, in some markets, investors sometimes do not pay brokerage commissions to dealers with whom they buy or sell bonds. Rather, the dealers earn revenue by means of the spread, or difference, between the price at which the dealer buys a bond from one investor–the “bid” price–and the price at which he or she sells the same bond to another investor—the “ask” or “offer” price. The bid/offer spread represents the total transaction cost associated with transferring a bond from one investor to another. In summary, since bonds are traded in a decentralized, over-the-counter market dominated by dealers, there is a lack of price transparency for bond markets.

6.8: Valuing Bonds

6.8.1: Present Value of Payments

The value of a bond is obtained by discounting the bond’s expected cash flows to the present using an appropriate discount rate.

Learning Objective

Calculate the present value of an annuity

Key Points

• The bond price can be summarized as the sum of the present value of the par value repaid at maturity and the present value of coupon payments.
• The present value of coupon payments is the present value of an annuity of coupon payments.
• The present value of an annuity is the value of a stream of payments, discounted by the interest rate to account for the payments being made at various moments in the future.

Key Term

discount rate

The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.

The bond price can be calculated using the present value approach. Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Therefore, the value of a bond is obtained by discounting the bond’s expected cash flows to the present using an appropriate discount rate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist. The formula for calculating a bond’s price uses the basic present value (PV) formula for a given discount rate .

Bond Price

Bond price is the present value of coupon payments and face value paid at maturity.

F = face value, i_F = contractual interest rate, C = F * i_F = coupon payment (periodic interest payment), N = number of payments, i = market interest rate, or required yield, or observed / appropriate yield to maturity, M = value at maturity, usually equals face value, and P = market price of bond.

The bond price can be summarized as the sum of the present value of the par value repaid at maturity and the present value of coupon payments. The present value of coupon payments is the present value of an annuity of coupon payments.

An annuity is a series of payments made at fixed intervals of time. The present value of an annuity is the value of a stream of payments, discounted by the interest rate to account for the payments being made at various moments in the future. The present value is calculated by:

i is the number of periods and n is the per period interest rate.

6.8.2: Par Value at Maturity

Par value is stated value or face value, with a typical bond making a repayment of par value at maturity.

Learning Objective

Calculate a bond’s par value

Key Points

• A bond selling at par has a coupon rate such that the bond is worth an amount equivalent to its original issue value or its value upon redemption at maturity.
• A typical bond makes coupon payments at fixed intervals during the life of it and a final repayment of par value at maturity. Together with coupon payments, the par value at maturity is discounted back to the time of purchase to calculate the bond price.
• Par value of a bond usually does not change, except for inflation-linked bonds whose par value is adjusted by inflation rates every predetermined period of time.

Key Term

inflation-linked bonds

Inflation-indexed bonds (also known as inflation-linked bonds or colloquially as linkers) are bonds where the principal is indexed to inflation. They are thus designed to cut out the inflation risk of an investment.

Par value, in finance and accounting, means the stated value or face value. From this comes the expressions at par (at the par value), over par (over par value) and under par (under par value). A bond selling at par has a coupon rate such that the bond is worth an amount equivalent to its original issue value or its value upon redemption at maturity. Corporate bonds usually have par values of $1,000 while municipal bonds generally have face values of $500. Federal government bonds tend to have much higher face values at $10,000.

A typical bond makes coupon payments at fixed intervals during the life of it and a final repayment of par value at maturity. Together with coupon payments, the par value at maturity is discounted back to the time of purchase to calculate the bond price.

Below is the formula for calculating a bond’s price, which uses the basic present value (PV) formula for a given discount rate .

Bond Price Formula

Bond price is the present value of coupon payments and the par value at maturity.

F = face value, iF = contractual interest rate, C = F * iF = coupon payment (periodic interest payment), N = number of payments, i = market interest rate, or required yield, or observed/ appropriate yield to maturity, M = value at maturity, usually equals face value, P = market price of bond.

Par value of a bond usually does not change, except for inflation-linked bonds whose par value is adjusted by inflation rates every predetermined period of time. The coupon payments of such bonds are also accordingly adjusted even though the coupon interest rate is unchanged.

6.8.3: Yield to Maturity

Yield to maturity is the discount rate at which the sum of all future cash flows from the bond are equal to the price of the bond.

Learning Objective

Classify a bond based on its market value and Yield to Maturity

Key Points

• The Yield to maturity is the internal rate of return earned by an investor who bought the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.
• Yield to maturity(YTM) = [(Face value/Present value)1/Time period]-1.
• If the YTM is less than the bond’s coupon rate, then the market value of the bond is greater than par value (premium bond). If a bond’s coupon rate is less than its YTM, then the bond is selling at a discount. If a bond’s coupon rate is equal to its YTM, then the bond is selling at par.
• There are some variants of YTM: yield to call, yield to put, yield to worst…

Key Terms

quote

To name the current price, notably of a financial security.

internal rate of return

IRR. The rate of return on an investment which causes the net present value of all future cash flows to be zero.

call premium

the additional cost paid by the issuer for the right to buy back the bond at a predtermined price at a certain time in the future

The Yield to maturity (YTM) or redemption yield of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule .

Yield to Maturity

Development of yield to maturity of bonds of 2019 maturity of a number of Eurozone governments.

Contrary to popular belief, including concepts often cited in advanced financial literature, Yield to maturity does not depend upon a reinvestment of dividends. Yield to maturity, rather, is simply the discount rate at which the sum of all future cash flows from the bond (coupons and principal) is equal to the price of the bond. The formula for yield to maturity:

Yield to maturity (YTM) = [(Face value / Present value)^{1/Time period}]-1

The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but usually market convention is followed: in a number of major markets the convention is to quote yields semi-annually (for example, an annual effective yield of 10.25% would be quoted as 5.00%, because 1.05 x 1.05 = 1.1025).

If the yield to maturity for a bond is less than the bond’s coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa).

• If a bond’s coupon rate is less than its YTM, then the bond is selling at a discount.
• If a bond’s coupon rate is more than its YTM, then the bond is selling at a premium.
• If a bond’s coupon rate is equal to its YTM, then the bond is selling at par.

As some bonds have different characteristics, there are some variants of YTM:

• Yield to call: when a bond is callable (can be repurchased by the issuer before the maturity), the market looks also to the Yield to call, which is the same calculation of the YTM, but assumes that the bond will be called, so the cash flow is shortened.
• Yield to put: same as yield to call, but when the bond holder has the option to sell the bond back to the issuer at a fixed price on specified date.
• Yield to worst: when a bond is callable, puttable, exchangeable, or has other features, the yield to worst is the lowest yield of yield to maturity, yield to call, yield to put, and others.

For instance, you buy ABC Company bond which matures in 1 year and has a 5% interest rate (coupon) and has a par value of $100. You pay $90 for the bond. The current yield is 5.56% ((5/90)*100). If you hold the bond until maturity, ABC Company will pay you $5 as interest and $100 par value for the matured bond. Now for your $90 investment, you get $105, so your yield to maturity is 16.67% [= (105/90)-1] or [=(105-90)/90].

6.8.4: Inflation Premium

An inflation premium is the part of prevailing interest rates that results from lenders compensating for expected inflation.

Learning Objective

Explain how to determine and use an inflation premium

Key Points

• Investors seek this premium to compensate for the erosion in the value of their capital due to inflation.
• Actual interest rates (without factoring in inflation) are viewed by economists and investors as being the nominal (stated) interest rate minus the inflation premium.
• Letting r denote the real interest rate, i denote the nominal interest rate, and let π denote the inflation rate, the Fisher equation is: i = r + π. In the Fisher equation, π is the inflation premium.

Key Term

systematic risks

In finance and economics, systematic risk (sometimes called aggregate risk, market risk, or undiversifiable risk) is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggregate income.

An inflation premium is the part of prevailing interest rates that results from lenders compensating for expected inflation by pushing nominal interest rates to higher levels.

Inflation rate graph

Inflation rate in the Confederacy during the American Civil War.

In economics and finance, an individual who lends money for repayment at a later point in time expects to be compensated for the time value of money, or not having the use of that money while it is lent. In addition, they will want to be compensated for the risks of the money having less purchasing power when the loan is repaid. These risks are systematic risks, regulatory risks and inflationary risks. The first includes the possibility that the borrower will default or be unable to pay on the originally agreed upon terms, or that collateral backing the loan will prove to be less valuable than estimated. The second includes taxation and changes in the law which would prevent the lender from collecting on a loan or having to pay more in taxes on the amount repaid than originally estimated. The third takes into account that the money repaid may not have as much buying power from the perspective of the lender as the money originally lent, that is inflation, and may include fluctuations in the value of the currencies involved. The inflation premium will compensate for the third risk, so investors seek this premium to compensate for the erosion in the value of their capital, due to inflation.

Actual interest rates (without factoring in inflation) are viewed by economists and investors as being the nominal (stated) interest rate minus the inflation premium.

The Fisher equation in financial mathematics and economics estimates the relationship between nominal and real interest rates under inflation. In economics, this equation is used to predict nominal and real interest rate behavior. Letting r denote the real interest rate, i denote the nominal interest rate, and let π denote the inflation rate, the Fisher equation is: i = r + π. In the Fisher equation, π is the inflation premium.

For example, if an investor were able to lock in a 5% interest rate for the coming year and anticipates a 2% rise in prices, he would expect to earn a real interest rate of 3%. 2% is the inflation premium. This is not a single number, as different investors have different expectations of future inflation.

Since the inflation rate over the course of a loan is not known initially, volatility in inflation represents a risk to both the lender and the borrower.

6.8.5: Differences Between Real and Nominal Rates

Nominal rate refers to the rate before adjustment for inflation; the real rate is the nominal rate minus inflation: r = R – i or, 1+r = (1+r)(1+E(r)).

Learning Objective

Differentiate between real and nominal interest rates

Key Points

• Nominal rate refers to the rate before adjustment for inflation; the real rate is the nominal rate minus inflation.
• Fisher equation states that the real interest rate is approximately the nominal interest rate minus the inflation rate: 1 + i = (1+r) (1+E(r)).
• Simple equation between nominal rates and real rates: i = R – r.

Key Term

purchasing power

Purchasing power (sometimes retroactively called adjusted for inflation) is the amount of goods or services that can be purchased with a unit of currency.

In finance and economics, nominal rate refers to the rate before adjustment for inflation (in contrast with the real rate). The real rate is the nominal rate minus inflation. In the case of a loan, it is this real interest that the lender receives as income. If the lender is receiving 8% from a loan and inflation is 8%, then the real rate of interest is zero, because nominal interest and inflation are equal. A lender would have no net benefit from such a loan because inflation fully diminishes the value of the loan’s profit.

The relationship between real and nominal rates can be described in the equation:

Real and nominal

The relationship between real and nominal interest rates is captured by the formula.

Where r is the real rate, i is the inflation rate, and R is the nominal rate.

The real rate can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate: 1 + i = (1+r) (1+E(r)), where i = nominal interest rate; r = real interest rate; E(r) = expected inflation rate.

For example, if somebody lends $1,000 for a year at 10%, and receives $1,100 back at the end of the year, this represents a 10% increase in his purchasing power if prices for the average goods and services that he buys are unchanged from what they were at the beginning of the year. However, if the prices of the food, clothing, housing, and other things that he wishes to purchase have increased 20% over this period, he has in fact suffered a real loss of about 12% in his purchasing power.

In this analysis, the nominal rate is the stated rate, and the real rate is the rate after the expected losses due to inflation. Since the future inflation rate can only be estimated, the ex ante and ex post (before and after the fact) real rates may be different; the premium paid to actual inflation may be higher or lower.

6.8.6: Time to Maturity

“Time to maturity” refers to the length of time before the par value of a bond must be returned to the bondholder.

Learning Objective

Discuss the importance of a bond’s maturity when determining its value

Key Points

• The maturity can be any length of time, but debt securities with a term of less than one year are generally not designated as bonds. Instead, they are considered money market instruments.
• In the market for United States Treasury securities, there are three categories of bond maturities: short-term, medium-term and long-term bonds.
• A bond that takes longer to mature necessarily has a greater duration. The bond price in this type of a situation, therefore, is more sensitive to changes in interest rates.

Key Terms

duration

A measure of the sensitivity of the price of a financial asset to changes in interest rates, computed for a simple bond as a weighted average of the maturities of the interest and principal payments associated with it

money market

A market for trading short-term debt instruments, such as treasury bills, commercial paper, bankers’ acceptances, and certificates of deposit

Time to Maturity

“Time to maturity” refers to the length of time that can elapse before the par value (face value) for a bond must be returned to a bondholder. This time may be as short as a few months, or longer than 50 years. Once this time has been reached, the bondholder should receive the par value for their particular bond.

The issuer of a bond has to repay the nominal amount for that bond on the maturity date. After this date, as long as all due payments have been made, the issuer will have no further obligations to the bondholders. The length of time until a bond’s matures is referred to as its term, tenor, or maturity. These dates can technically be any length of time, but debt securities with a term of less than one year are generally not designated as bonds. Instead, they are designated as money market instruments .

Money market interest rates

Interest rates of one-month maturity of German banks from 1967 to 2003

Most bonds have a term of up to 30 years. That being said, bonds have been issued with terms of 50 years or more, and historically, issues have arisen where bonds completely lack maturity dates (irredeemables). In the market for United States Treasury securities, there are three categories of bond maturities:

• Short term (bills): maturities between one to five years (Instruments that mature in less than one year are considered Money Market Instruments. )
• Medium term (notes): maturities between six to twelve years
• Long term (bonds): maturities greater than twelve years

Because bonds with long maturities necessarily have long durations, the bond prices in these situations are more sensitive to interest rate changes. In other words, the price risk of such bonds is higher. The fair price of a “straight bond,” a bond with no embedded options, is usually determined by discounting its expected cash flows at the appropriate discount rate. Although this present value relationship reflects the theoretical approach to determining the value of a bond, in practice, the price is (usually) determined with reference to other, more liquid instruments.

In general, coupon and par value being equal, a bond with a short time to maturity will trade at a higher value than one with a longer time to maturity. This is because the par value is discounted at a higher rate further into the future.

Finally, it is important to recognize that future interest rates are uncertain, and that the discount rate is not adequately represented by a single fixed number (this would be the case if an option was written on the bond in question) stochastic calculus may be employed. Where the market price of a bond is less than its face value (par value), the bond is selling at a discount. Conversely, if the market price of bond is greater than its face value, the bond is selling at a premium.

6.8.7: Calculating Yield to Maturity Using the Bond Price

The yield to maturity is the discount rate that returns the bond’s market price: YTM = [(Face value/Bond price)1/Time period]-1.

Learning Objective

Calculate a bond’s yield to maturity

Key Points

• To achieve a return equal to YTM (i.e., where it is the required return on the bond), the bond owner must buy the bond at price P0, hold the bond until maturity, and redeem the bond at par.
• If a bond’s coupon rate is less than its YTM, then the bond is selling at a discount. If a bond’s coupon rate is more than its YTM, then the bond is selling at a premium. If a bond’s coupon rate is equal to its YTM, then the bond is selling at par.
• Formula for yield to maturity: Yield to maturity(YTM) = [(Face value/Bond price)1/Time period]-1.

Key Term

discount rate

The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.

YTM

The yield to maturity is the discount rate which returns the market price of the bond. YTM is the internal rate of return of an investment in the bond made at the observed price.

USD Yield Curve

2005 USD yield curve

To achieve a return equal to YTM (i.e., where it is the required return on the bond), the bond owner must buy the bond at price P₀, hold the bond until maturity, and redeem the bond at par.

If the yield to maturity for a bond is less than the bond’s coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa). If a bond’s coupon rate is less than its YTM, then the bond is selling at a discount. If a bond’s coupon rate is more than its YTM, then the bond is selling at a premium. If a bond’s coupon rate is equal to its YTM, then the bond is selling at par.

Calculating YTM

Formula for yield to maturity: Yield to maturity(YTM) = [(Face value/Bond price)^{1/Time period}]-1

As can be seen from the formula, the yield to maturity and bond price are inversely correlated.

Consider a 30-year, zero-coupon bond with a face value of $100. If the bond is priced at an annual YTM of 10%, it will cost $5.73 today (the present value of this cash flow, 100/(1.1)30 = 5.73). Over the coming 30 years, the price will advance to $100, and the annualized return will be 10%.

What happens in the meantime? Suppose that over the first 10 years of the holding period, interest rates decline, and the yield-to-maturity on the bond falls to 7%. With 20 years remaining to maturity, the price of the bond will be 100/1.0720, or $25.84. Even though the yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to-maturity bargained for when the bond was purchased was only 10%, the return earned over the first 10 years is 16.25%. This can be found by evaluating (1+i) from the equation (1+i)10 = (25.842/5.731), giving 1.1625.

Over the remaining 20 years of the bond, the annual rate earned is not 16.25%, but rather 7%. This can be found by evaluating (1+i) from the equation (1+i)20 = 100/25.84, giving 1.07. Over the entire 30 year holding period, the original $5.73 invested increased to $100, so 10% per annum was earned, irrespective of any interest rate changes in between.

6.8.8: Impact of Payment Frequency on Bond Prices

Payment frequency can be annual, semi annual, quarterly, or monthly; the more frequently a bond makes coupon payments, the higher the bond price.

Learning Objective

Calculate the price of a bond

Key Points

• Payment frequency can be annual, semi annual, quarterly, monthly, weekly, daily, or continuous.
• Bond price is the sum of the present value of face value paid back at maturity and the present value of an annuity of coupon payments. The present value of face value received at maturity is the same. However, the present values of annuities of coupon payments vary among payment frequencies.
• The more frequent a bond makes coupon payments, the higher the bond price, given equal coupon, par, and face.

Key Term

annuity

A specified income payable at stated intervals for a fixed or a contingent period, often for the recipient’s life, in consideration of a stipulated premium paid either in prior installment payments or in a single payment. For example, a retirement annuity paid to a public officer following his or her retirement.

The payment schedule of financial instruments defines the dates at which payments are made by one party to another on, for example, a bond or a derivative. It can be either customised or parameterized. Payment frequency can be annual, semi annual, quarterly, monthly, weekly, daily, or continuous.

Bond prices is the present value of all coupon payments and the face value paid at maturity. The formula to calculate bond prices:

Bond price formula

Bond price is the present value of all coupon payments and the face value paid at maturity.

F = face value, i_F = contractual interest rate, C = F * i_F = coupon payment (periodic interest payment), N = number of payments, i = market interest rate, or required yield, or observed / appropriate yield to maturity, M = value at maturity, usually equals face value, P = market price of bond.

In other words, bond price is the sum of the present value of face value paid back at maturity and the present value of an annuity of coupon payments. For bonds of different payment frequencies, the present value of face value received at maturity is the same. However, the present values of annuities of coupon payments vary among payment frequencies.

The present value of an annuity is the value of a stream of payments, discounted by the interest rate to account for the payments are being made at various moments in the future. The formula is:

Annuity formula

The formula to calculate PV of annuities.

Where n is the number of terms or number of payments n =1 (annually), n = 2 (semi-annually), n = 4 (quarterly)… and i is the per period interest rate.

According to the formula, the greater n, the greater the present value of the annuity (coupon payments). To put it differently, the more frequent a bond makes coupon payments, the higher the bond price.

6.8.9: Deciding to Refund Bonds

Refunding occurs when an entity that has issued callable bonds calls those debt securities to issue new debt at a lower coupon rate.

Learning Objective

Explain when to refund a debt issue

Key Points

• The issue of new, lower-interest debt allows the company to prematurely refund the older, higher-interest debt.
• Bond refunding occurs when a) interest rates in the market are sufficiently less than the coupon rate on the old bond, b) the price of the old bond is less than par. and c) the sinking fund has accumulated enough money to retire the bond issue.
• The decision of whether to refund a particular debt issue is usually based on a capital budgeting (present value) analysis.

Key Term

sinking fund

A sinking fund is a fund established by a government agency or business for the purpose of reducing debt by repaying or purchasing outstanding loans and securities held against the entity. It helps keep the borrower liquid so it can repay the bondholder.

Refunding occurs when an entity that has issued callable bonds calls those debt securities from the debt holders with the express purpose of reissuing new debt at a lower coupon rate. In essence, the issue of new, lower-interest debt allows the company to prematurely refund the older, higher-interest debt. On the contrary, nonrefundable bonds may be callable, but they cannot be re-issued with a lower coupon rate (i.e., they cannot be refunded).

French Bond

French Bond for the Akhtala mines issued in 1887.

The decision of whether to refund a particular debt issue is usually based on a capital budgeting (present value) analysis. The principal benefit, or cash inflow, is the present value of the after-tax interest savings over the life of the issue.

Bond refunding occurs when all three of the following are true

1. Interest rates in the market are sufficiently less than the coupon rate on the old bond
2. The price of the old bond is less than par
3. The sinking fund has accumulated enough money to retire the bond issue.

The three steps of whether to make a refunding decision are as follows:

Step 1: Calculate the present value of interest savings (cash inflows):

Interest savings = annual interest of old issue – annual interest of new issue

Step 2: Calculate the net investment (net cash outflow at time 0). This involves computing the after-tax call premium, the issuance cost of the new issue, the issuance cost of the old issue, and the overlapping interest. The call premium is a cash outflow.

Step 3: Finally, calculate the net present value of refunding.

Net present value of refunding = Present value of interest savings – Present value of net investment

6.9: Bond Risk

6.9.1: Price Risk

Price risk is the risk that the market price of a bond will fall, usually due to a rise in the market interest rate.

Learning Objective

Identify a bond’s price risk

Key Points

• The market price of bonds will decrease in value when the generally prevailing interest rates rise and vice versa.
• Unless you plan to buy or sell them in the open market, changing interest rates do not affect the interest payments to the bondholder.
• Price changes in a bond will immediately affect mutual funds that hold these bonds. If the value of the bonds in their trading portfolio falls, the value of the portfolio also falls.

Key Term

mutual funds

A type of professionally-managed collective investment vehicle that pools money from many investors to purchase securities. While there is no legal definition, the term is most commonly applied only to those collective investment vehicles that are regulated, available to the general public and open-ended in nature.

Interest rates and bond prices carry an inverse relationship. Bond price risk is closely related to fluctuations in interest rates. Fixed-rate bonds are subject to interest rate risk, meaning that their market prices will decrease in value when the generally prevailing interest rates rise. Since the payments are fixed, a decrease in the market price of the bond means an increase in its yield. When the market interest rate rises, the market price of bonds will fall, reflecting investors’ ability to get a higher interest rate on their money elsewhere — perhaps by purchasing a newly-issued bond that already features the new higher interest rate. On the flip side, if the prevailing interest rate were on the decline, investors would naturally buy bonds that pay lower rates of interest. This would force bond prices up.

Bond price and yield

Several curves depicting the inverse relationship between bond price and yield (interest rates).

Unless you plan to buy or sell them in the open market, changing interest rates do not affect the interest payments to the bondholder, so long-term investors who want a specific amount at the maturity date do not need to worry about price swings in their bonds and do not suffer from interest rate risk. However, because of the interest rate risk, bonds with longer terms are more risky than bonds with shorter terms.

Price changes in a bond will immediately affect mutual funds that hold these bonds. If the value of the bonds in their trading portfolio falls, the value of the portfolio also falls. This can be damaging for professional investors such as banks, insurance companies, pension funds and asset managers (irrespective of whether the value is immediately “marked to market” or not). If there is any chance a holder of individual bonds may need to sell his bonds and “cash out”, interest rate risk could become a real problem.

Bond prices can become volatile depending on the credit rating of the issuer – for instance if the credit rating agencies like Standard & Poor’s and Moody’s upgrade or downgrade the credit rating of the issuer. An unanticipated downgrade will cause the market price of the bond to fall. As with interest rate risk, this risk does not affect the bond’s interest payments (provided the issuer does not actually default), but puts at risk the market price, which affects mutual funds holding these bonds, and holders of individual bonds who may have to sell them.

6.9.2: Reinvestment Risk

Reinvestment risk is the risk that a bond is repaid early, and an investor has to find a new place to invest with the risk of lower returns.

Learning Objective

Define reinvestment risk

Key Points

• Reinvestment risk is more likely when interest rates are declining.
• Reinvestment risk affects the yield-to-maturity of a bond, which is calculated on the premise that all future coupon payments will be reinvested at the interest rate in effect when the bond was first purchased.
• Two factors that have a bearing on the degree of reinvestment risk are maturity of the bond and the coupon interest rate.

Key Term

Yield to maturity

The Yield to maturity (YTM) or redemption yield of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.

Reinvestment risk is one of the main genres of financial risk. The term describes the risk that a particular investment might be canceled or stopped somehow, and that one may have to find a new place to invest their money with the risk being there might not be a similarly attractive investment available. This primarily occurs if bonds (which are portions of loans to entities) are paid back earlier than expected.

The risk resulting from the fact that interest or dividends earned from an investment may not be able to be reinvested in such a way that they earn the same rate of return as the invested funds that generated them. Reinvestment risk is more likely when interest rates are declining. For example, falling interest rates may prevent bond coupon payments from earning the same rate of return as the original bond. Pension funds are also subject to reinvestment risk. Especially with the short-term nature of cash investments, there is always the risk that future proceeds will have to be reinvested at a lower interest rate.

Interest rates

Reinvestment risk is more likely when interest rates are declining.

Reinvestment risk affects the yield-to-maturity of a bond, which is calculated on the premise that all future coupon payments will be reinvested at the interest rate in effect when the bond was first purchased.

Two factors that have a bearing on the degree of reinvestment risk are:

Maturity of the bond – The longer the maturity of the bond, the higher the likelihood that interest rates will be lower than they were at the time of the bond purchase.

Interest rate on the bond – The higher the interest rate, the bigger the coupon payments that have to be reinvested, and, consequently, the reinvestment risk. Zero coupon bonds are the only fixed-income instruments to have no reinvestment risk, since they have no interim coupon payments.

6.9.3: Comparing Price Risk and Reinvestment Risk

Price risk is positively correlated to changes in interest rates, while reinvestment risk is inversely correlated.

Learning Objective

Differentiate between price risk and reinvestment risk

Key Points

• Price risk and reinvestment risk are both the uncertainty associated with the effects of changes in market interest rates.
• Price risk and changes in interest rates are positively correlated.
• Reinvestment risk and changes in interest rates are inversely correlated.

Key Term

duration

A measure of the sensitivity of the price of a financial asset to changes in interest rates, computed for a simple bond as a weighted average of the maturities of the interest and principal payments associated with it

Overview

Price risk and reinvestment risk both represent the uncertainty associated with the effects of changes in market interest rates. Both types of interest rate risks are important considerations in investments, corporate financial planning, and banking.

Pacific Railroad Bond

$1,000 (30 year, 7%) “Pacific Railroad Bond” (#93 of 200) issued by the City and County of San Francisco.

Price Risk

Price risk is the uncertainty associated with potential changes in the price of an asset caused by changes in interest rate levels in the economy. The price risk is sometimes referred to as maturity risk since the greater the maturity of an investment (the greater the duration), the greater the change in price for a given change in interest rates. Bond market prices will decrease in value when the generally prevailing interest rates rise (price risk is on the rise). Since the payments are fixed, a decrease in the market price of the bond means an increase in its yield. When the market interest rate rises, the market price of bonds will fall, reflecting investors’ ability to get a higher interest rate on their money elsewhere — perhaps by purchasing a newly issued bond that already features the newly higher interest rate. When interest rates fall, bond prices increase, and there is less price risk. To sum up, price risk and interest rates are positively correlated.

Reinvestment Risk

Reinvestment risk is the risk that a particular investment might be canceled or stopped somehow, and that one may have to find a new place to invest their money with the risk that there might not be a similarly attractive investment available. This primarily occurs if bonds (which are portions of loans to entities) are paid back earlier than expected. When interest rates increase, there is less likelihood that a bond is called and paid back before maturity. So there is little reinvestment risk. When interest rates decrease, there is more likelihood that the bond is called and paid back earlier than expected. There is, accordingly, more reinvestment risk. Reinvestment risk and interest rates are inversely correlated.

Discussion

In summary, price risk and reinvestment risk are two main financial risks resulting from changes in interest rates. The former is positively correlated to interest rates, while reinvestment risk is inversely correlated to fluctuations in interest rates.

6.9.4: Default Risk

Default risk is the risk that a bond issuer will default on any type of debt by failing to make payments which it is obligated to make.

Learning Objective

Define default risk

Key Points

• With default risk, the risk is primarily that of the bondholder and includes lost principal and interest, disruption to cash flows, and increased collection costs.
• To reduce the bondholders’ credit risk, the lender may perform a credit check on the prospective borrower and may require the issuer to take out appropriate insurance.
• A company’s bondholders may lose much or all their money if the company goes bankrupt. There is no guarantee of how much money will remain to repay bondholders.

Key Terms

liquidated

In law, liquidation is the process by which a company (or part of a company) is brought to an end and the assets and property of the company redistributed.

insolvent

Unable to pay one’s bills as they fall due.

Default risk (or credit risk) of a bond refers to the risk that a bond issuer will default on any type of debt by failing to make payments which it is obligated to do. The risk is primarily that of the bondholder and includes lost principal and interest, disruption to cash flows, and increased collection costs. The loss may be complete or partial and can arise in a number of circumstances. For example, a company is unable to repay amounts secured by a fixed or floating charge over the assets of the company, a business or consumer does not pay a trade invoice when due, a business does not pay an employee’s earned wages when due, a business or government bond issuer does not make a payment on a coupon or principal payment when due, an insolvent insurance company does not pay a policy obligation, and an insolvent bank won’t return funds to a depositor .

Prices of sovereign credit default swaps

Credit default swaps are an instrument to protect against default risk. This image shows the monthly prices of sovereign credit default swaps from January 2010 till September 2011 of Greece, Portugal, Ireland, Hungary, Italy, Spain, Belgium, France, Germany, and the UK (Greece is illustrated by blue line). Higher credit default swap prices mean that investors perceive a higher risk of default.

To reduce the bondholders’ credit risk, the lender may perform a credit check on the prospective borrower, may require the issuer to take out appropriate insurance, such as mortgage insurance or seek security or guarantees of third parties, besides other possible strategies. In general, the higher the risk, the higher will be the interest rate that the issuer will have to pay.

A company’s bondholders may lose much or all their money if the company goes bankrupt. Under the laws of many countries (including the United States and Canada), bondholders are in line to receive the proceeds of the sale of the assets of a liquidated company ahead of some other creditors. Bank lenders, deposit holders (in the case of a deposit taking institution such as a bank), and trade creditors may take precedence.

There is no guarantee of how much money will remain to repay bondholders. As an example, after an accounting scandal and a Chapter 11 bankruptcy at the giant telecommunications company Worldcom, in 2004 its bondholders ended up being paid 35.7 cents on the dollar. In a bankruptcy involving reorganization or recapitalization, as opposed to liquidation, bondholders may end up having the value of their bonds reduced, often through an exchange for a smaller number of newly issued bonds.

6.9.5: Bond Rating System

The credit rating is a financial indicator assigned by credit rating agencies; bond ratings below BBB-/Baa are considered junk bonds.

Learning Objective

Discuss the role of NRSROs in the bond market

Key Points

• In investment, the bond credit rating assesses the credit worthiness of a corporation’s or government debt issues.
• The credit rating is a financial indicator to potential investors of debt securities, such as bonds. These are assigned by credit rating agencies such as Moody’s, Standard & Poor’s, and Fitch Ratings to have letter designations (such as AAA, B, CC) which represent the quality of a bond.
• Bond ratings below BBB-/Baa are considered not to be investment grade and are colloquially called junk bonds.

Key Term

asset-backed securities

An asset-backed security is a security that has value and income payments derived from and collateralized (or “backed”) by a specified pool of underlying assets. The pool of assets is typically a group of small and illiquid assets that are unable to be sold individually.

In investment, the bond credit rating assesses the credit worthiness of a corporation’s or government’s debt issues. It is analogous to credit ratings for individuals.The credit rating is a financial indicator to potential investors of debt securities, such as bonds. These are assigned by credit rating agencies such as Moody’s, Standard & Poor’s, and Fitch Ratings to have letter designations (such as AAA, B, CC), which represent the quality of a bond. Bond ratings below BBB-/Baa are considered to be not investment grade and are colloquially called “junk bonds. “

Bond rating

Bond ratings below BBB-/Baa are considered to be not investment grade and are colloquially called “junk bonds. “

Credit rating agencies registered as such with the SEC are “Nationally recognized statistical rating organizations. ” The following firms are currently registered as NRSROs: A.M. Best Company, Inc.; DBRS Ltd.; Egan-Jones Rating Company; Fitch, Inc.; Japan Credit Rating Agency, Ltd.; LACE Financial Corp.; Moody’s Investors Service, Inc.; Rating and Investment Information, Inc.; and Standard & Poor’s Ratings Services.

Under the Credit Rating Agency Reform Act, an NRSRO may be registered with respect to up to five classes of credit ratings: (1) financial institutions, brokers, or dealers; (2) insurance companies; (3) corporate issuers; (4) issuers of asset-backed securities; and (5) issuers of government securities, municipal securities, or securities issued by a foreign government. S&P, Moody’s, and Fitch dominate the market with approximately 90-95% of world market share.

Moody’s assigns bond credit ratings of Aaa, Aa, A, Baa, Ba, B, Caa, Ca, C, with WR and NR as withdrawn and not rated. Standard & Poor’s and Fitch assign bond credit ratings of AAA, AA, A, BBB, BB, B, CCC, CC, C, and D.

A bond is considered investment grade or IG if its credit rating is BBB- or higher by Standard & Poor’s or Baa3 or higher by Moody’s or BBB (low) or higher by DBRS. Generally, they are bonds that are judged by the rating agency as likely enough to meet payment obligations that banks are allowed to invest in them. Ratings play a critical role in determining how much companies and other entities that issue debt, including sovereign governments, have to pay to access credit markets (i.e., the amount of interest they pay on their issued debt). The threshold between investment-grade and speculative-grade ratings has important market implications for issuers’ borrowing costs. Bonds that are not rated as investment-grade bonds are known as high-yield bonds or more derisively as junk bonds. The risks associated with investment-grade bonds (or investment-grade corporate debt) are considered significantly higher than those associated with first-class government bonds.

6.9.6: Bankruptcy and Bond Value

There is no guarantee of how much money will remain to repay bondholders in a bankruptcy, therefore, the value of the bond is uncertain.

Learning Objective

Identify which stakeholders take precedence in receiving cash from a bankrupt business

Key Points

• When a business is unable to service its debt or pay its creditors, it or its creditors can file with a federal bankruptcy court for protection under either Chapter 7 or Chapter 11 of the Bankruptcy code.
• If a company goes bankrupt, its bondholders will often receive some money back (the recovery amount).
• In a bankruptcy involving reorganization or recapitalization, as opposed to liquidation, bondholders may end up having the value of their bonds reduced, often through an exchange for a smaller number of newly-issued bonds.

Key Terms

recapitalization

A restructuring of a company’s mixture of equity and debt.

liquidation

The selling of the assets of a business as part of the process of dissolving the business.

A company’s bondholders may lose much or all their money if the company goes bankrupt. Under the laws of many countries (including the United States and Canada), bondholders are in line to receive the proceeds of the sale of the assets of a liquidated company ahead of some other creditors.

Bank lenders, deposit holders (in the case of a deposit-taking institution such as a bank) and trade creditors may take precedence. However, compared to equity holders, bondholders also enjoy a measure of legal protection: under the law of most countries, if a company goes bankrupt, its bondholders will often receive some money back (the recovery amount), whereas the company’s equity stock often ends up valueless.

When a business is unable to service its debt or pay its creditors, the business or its creditors can file with a federal bankruptcy court for protection under either Chapter 7 or Chapter 11 of the Bankruptcy code. In Chapter 7, the business ceases operations, a trustee sells all of its assets, and then distributes the proceeds to its creditors. Any residual amount is returned to the owners of the company. In Chapter 11, in most instances, the debtor remains in control of its business operations as a debtor in possession, and is subject to the oversight and jurisdiction of the court.

Bankruptcy Courthouse

Old U.S. Post Office and Court House, now used by the U.S. Bankruptcy Court for the Northern District of Florida.

There is no guarantee of how much money will remain to repay bondholders, therefore, the value of the bond is uncertain. As an example, after an accounting scandal and a chapter 11 bankruptcy at the giant telecommunications company Worldcom in 2004, its bondholders ended up being paid 35.7 cents on the dollar. In a bankruptcy involving reorganization or recapitalization, as opposed to liquidation, bondholders may end up having the value of their bonds reduced, often through an exchange for a smaller number of newly-issued bonds.

5.3: Present Value, Single Amount

5.3.1: Single-Period Investment

Learning Objective

Calculate the present value of a future, single-period payment

Key Points

• A single period investment has the number of periods (n or t) equal to one.
• For both simple and compound interest, the PV is FV divided by 1+i.
• The time value of money framework says that money in the future is not worth as much as money in the present.

Key Terms

interest rate

The percentage of an amount of money charged for its use per some period of time. It can also be thought of as the cost of not having money for one period, or the amount paid on an investment per year.

period

The length of time during which interest accrues.

The time value of money framework says that money in the future is not worth as much as money in the present. Investors would prefer to have the money today because then they are able to spend it, save it, or invest it right now instead of having to wait to be able to use it.

The difference between what the money is worth today and what it will be worth at a point in the future can be quantified. The value of the money today is called the present value (PV), and the value of the money in the future is called the future value (FV). There is also a name for the cost of not having the money today: the interest rate or discount rate (i or r). For example, if the interest rate is 3% per year, it means that you would be willing to pay 3% of the money to have it one year sooner. The amount of time is also represented by a variable: the number of periods (n). One period could be any length of time, such as one day, one month, or one year, but it must be clearly defined, consistent with the time units in the interest rate, and constant throughout your calculations.

FV of a single payment

The FV is related to the PV by being i% more each period.

All of these variables are related through an equation that helps you find the PV of a single amount of money. That is, it tells you what a single payment is worth today, but not what a series of payments is worth today (that will come later). relates all of the variables together. In order to find the PV, you must know the FV, i, and n.

When considering a single-period investment, n is, by definition, one. That means that the PV is simply FV divided by 1+i. There is a cost to not having the money for one year, which is what the interest rate represents. Therefore, the PV is i% less than the FV.

5.3.2: Multi-Period Investment

Learning Objective

Calculate the return on a multi-period investment over time

Key Points

• A dollar today is worth more than a dollar tomorrow, and the time value of money must take into account foregone opportunities.
• Single period investments are relatively simple to calculate in terms of future value, applying the interest rate to a present value a single time.
• Multi-period investments require a slightly more complex equation, where interest gets compounded based on the number of periods the investment spans.
• As a result of multiple periods, it is usually a good idea to calculate the average rate of return (cumulatively) over the lifetime of the investment.

Key Term

Compound interest

An interest rate applied to multiple applications of interest during the lifetime of the investment.

When investing, the time value of money is a core concept investors simply cannot ignore. A dollar today is valued higher than a dollar tomorrow, and when utilizing the capital it is important to recognize the opportunity cost involved in what could have been invested in instead. 

Single Period Investments

With single period investments, the concept of time value of money is relatively straightforward. The future value is simply the present value applied to the interest rate compounded one time. When comparing this to the opportunity costs involved, the rate of return of an alternative investment during the same time is similarly straightforward.

The variables involved in understanding the time value of money in these investments are:

• Present Value (PV)
• Future Value (FV)
• Interest Rate (i or r) [Note: for all formulas, express interest in its decimal form, not as a whole number. 7% is .07, 12% is .12, and so on. ]
• Number of Periods (t or n)

With these variables, a single period investment could be calculated as follows:

‘t’ in this equation would simply be 1, simplifying this equation to FV = PV(1+r).

Multi-period Investments

With multi-periods in mind, interest begins to compound. Compound interest simple means that the interest from the first period is added to the future present value, and the interest rate the next time around is now being applied to a larger amount. This turns into an exponential calculation of interest, calculated as follows:

This means that the interest rate of a given period may not be the same percentage as the interest rate over multiple periods (in most situations). A useful tool at this point is a way to create an average rate of return over the life of the investment, which can be derived with the following:

Conclusion

All and all, the difference from a time value of money perspective between single and multiple period investments is relatively straightforward. Normalizing expected returns in present value terms (or projecting future returns over multiple time periods of compounding interest) paints a clearer and more accurate picture of the actual worth of a given investment opportunity.

Time Value of Money

Time value of money requires an understanding of how return rates impact fixed values over time.

Time value of money requires an understanding of how return rates impact fixed values over time.

5.3.3: The Discount Rate

Learning Objective

Describe what real world costs to the investor comprise an investment’s interest rate

Key Points

• The discount rate represents some cost (or group of costs) to the investor or creditor.
• Some costs to the investor or creditor are opportunity cost, liquidity cost, risk, and inflation.
• The discount rate is used by both the creditor and debtor to find the present value of an amount of money.

Key Terms

discount rate

The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.

discounting

The process of finding the present value using the discount rate.

discount

to account for the time value of money

Another common name for finding present value (PV) is discounting. Discounting is the procedure of finding what a future sum of money is worth today. As you know from the previous sections, to find the PV of a payment you need to know the future value (FV), the number of time periods in question, and the interest rate. The interest rate, in this context, is more commonly called the discount rate.

The discount rate represents some cost (or group of costs) to the investor or creditor. The sum of these costs amounts to a percentage which becomes the interest rate (plus a small profit, sometimes). Here are some of the most significant costs from the investor/creditor’s point of view:

Borrowing and lending

Banks like HSBC take such costs into account when determining the terms of a loan for borrowers.

1. Opportunity Cost: The cost of not having the cash on hand at a certain point of time. If the investor/creditor had the cash s/he could spend it, but since it has been invested/loaned out, s/he incurs the cost of not being able to spend it.
2. Inflation: The real value of a single dollar decreases over time with inflation. That means that even if everything else is constant, a $100 item will retail for more than $100 in the future. Inflation is generally positive in most countries at most times (if it’s not, it’s called deflation, but it’s rare).
3. Risk: There is a chance that you will not get your money back because it is a bad investment, the debtor defaults. You require compensation for taking on that risk.
4. Liquidity: Investing or loaning out cash necessarily reduces your liquidity.

All of these costs combine to determine the interest rate on an account, and that interest rate in turn is the rate at which the sum is discounted.

The PV and the discount rate are related through the same formula we have been using,
.

If FV and n are held as constants, then as the discount rate (i) increases, PV decreases. PV and the discount rate, therefore, vary inversely, a fundamental relationship in finance. Suppose you expect $1,000 dollars in one year’s time (FV = $1,000) . To determine the present value, you would need to discount it by some interest rate (i). If this discount rate were 5%, the $1,000 in a year’s time would be the equivalent of $952.38 to you today (1000/[1.00 + 0.05]).

5.3.4: Number of Periods

Learning Objective

Define what a period is in terms of present value calculations

Key Points

• A period is just a general term for a length of time. It can be anything- one month, one year, one decade- but it must be clearly defined and fixed.
• For both simple and compound interest, the number of periods varies jointly with FV and inversely with PV.
• The number of periods is also part of the units of the discount rate: if one period is one year, the discount rate must be defined as X% per year. If one period is one month, the discount rate must be X% per month.

Key Term

period

The length of time during which interest accrues.

In , nrepresents the number of periods. A period is just a general term for a length of time. It can be anything- one month, one year, one decade- but it must be clearly defined and fixed. The length of one period must be the same at the beginning of an investment and at the end. It is also part of the units of the discount rate: if one period is one year, the discount rate must be defined as X% per year. If one period is one month, the discount rate must be X% per month.

FV of a single payment

The PV and FV are directly related.

The number of periods corresponds to the number of times the interest is accrued. In the case of simple interest the number of periods, t, is multiplied by their interest rate. This makes sense because if you earn $30 of interest in the first period, you also earn $30 of interest in the last period, so the total amount of interest earned is simple t x $30.

Simple interest is rarely used in comparison to compound interest . In compound interest, the interest in one period is also paid on all interest accrued in previous periods. Therefore, there is an exponential relationship between PV and FV, which is reflected in (1+i)ⁿ .

Car

Car loans, mortgages, and student loans all generally have compound interest.

For both forms of interest, the number of periods varies jointly with FV and inversely with PV. Logically, if more time passes between the present and the future, the FV must be higher or the PV lower (assuming the discount rate remains constant).

5.3.5: Calculating Present Value

Learning Objective

Distinguish between the formula used for calculating present value with simple interest and the formula used for present value with compound interest

Key Points

• The first step is to identify if the interest is simple or compound. Most of the time, it is compound.
• The interest rate and number of periods must have consistent units.
• The PV is what a future sum is worth today given a specific interest rate (often called a “discount rate”).

Key Terms

compound interest

Interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest.

simple interest

interest paid only on the principal.

Finding the present value (PV) of an amount of money is finding the amount of money today that is worth the same as an amount of money in the future, given a certain interest rate.

Calculating the present value (PV) of a single amount is a matter of combining all of the different parts we have already discussed. But first, you must determine whether the type of interest is simple or compound interest. If the interest is simple interest, you plug the numbers into the simple interest formula.

Simple Interest Formula

Simple interest is when interest is only paid on the amount you originally invested (the principal). You don’t earn interest on interest you previously earned.

If it is compound interest, you can rearrange the compound interest formula to calculate the present value.

Present Value Single Payment

Finding the PV is a matter of plugging in for the three other variables.

Inputs

• Future Value: The known value of the money at a declared point in the future.
• Interest Rate (Discount Rate): Represented as either i or r. This is the percentage of interest paid each period.
• Number of periods: Represented as n or t.

Once you know these three variables, you can plug them into the appropriate equation. If the problem doesn’t say otherwise, it’s safe to assume the interest compounds. If you happen to be using a program like Excel, the interest is compounded in the PV formula. Simple interest is pretty rare.

One area where there is often a mistake is in defining the number of periods and the interest rate. They have to have consistent units, which may require some work. For example, interest is often listed as X% per year. The problem may talk about finding the PV 24 months before the FV, but the number of periods must be in years since the interest rate is listed per year. Therefore, n = 2. As long as the units are consistent, however, finding the PV is done by plug-and-chug.

5.4: Annuities

5.4.1: Annuities

An annuity is a type of investment in which regular payments are made over the course of multiple periods.

Learning Objective

Classify the different types of annuity

Key Points

• Annuities have payments of a fixed size paid at regular intervals.
• There are three types of annuities: annuities-due, ordinary annuities, and perpetuities.
• Annuities help both the creditor and debtor have predictable cash flows, and it spreads payments of the investment out over time.

Key Term

period

The length of time during which interest accrues.

An annuity is a type of multi-period investment where there is a certain principal deposited and then regular payments made over the course of the investment. The payments are all a fixed size. For example, a car loan may be an annuity: In order to get the car, you are given a loan to buy the car. In return you make an initial payment (down payment), and then payments each month of a fixed amount. There is still an interest rate implicitly charged in the loan. The sum of all the payments will be greater than the loan amount, just as with a regular loan, but the payment schedule is spread out over time.

Suppose you are the bank that makes the car loan. There are three advantages to making the loan an annuity. The first is that there is a regular, known cash flow. You know how much money you’ll be getting from the loan and when you’ll be getting them. The second is that it should be easier for the person you are loaning to to repay, because they are not expected to pay one large amount at once. The third reason why banks like to make annuity loans is that it helps them monitor the financial health of the debtor. If the debtor starts missing payments, the bank knows right away that there is a problem, and they could potentially amend the loan to make it better for both parties.

Similar advantages apply to the debtor. There are predictable payments, and paying smaller amounts over multiple periods may be advantageous over paying the whole loan plus interest and fees back at once.

Since annuities, by definition, extend over multiple periods, there are different types of annuities based on when in the period the payments are made. The three types are:

1. Annuity-due: Payments are made at the beginning of the period . For example, if a period is one month, payments are made on the first of each month.
2. Ordinary Annuity: Payments are made at the end of the period . If a period is one month, this means that payments are made on the 28th/30th/31st of each month. Mortgage payments are usually ordinary annuities.
3. Perpetuities: Payments continue forever. This is much rarer than the first two types.

5.4.2: Future Value of Annuity

The future value of an annuity is the sum of the future values of all of the payments in the annuity.

Learning Objective

Calculate the future value of different types of annuities

Key Points

• To find the FV, you need to know the payment amount, the interest rate of the account the payments are deposited in, the number of periods per year, and the time frame in years.
• The first and last payments of an annuity due both occur one period before they would in an ordinary annuity, so they have different values in the future.
• There are different formulas for annuities due and ordinary annuities because of when the first and last payments occur.

Key Terms

annuity-due

An investment with fixed-payments that occur at regular intervals, paid at the beginning of each period.

ordinary repair

expense accrued in normal maintenance of an asset

annuity-due

a stream of fixed payments where payments are made at the beginning of each period

ordinary annuity

An investment with fixed-payments that occur at regular intervals, paid at the end of each period.

The future value of an annuity is the sum of the future values of all of the payments in the annuity. It is possible to take the FV of all cash flows and add them together, but this isn’t really pragmatic if there are more than a couple of payments.

If you were to manually find the FV of all the payments, it would be important to be explicit about when the inception and termination of the annuity is. For an annuity-due, the payments occur at the beginning of each period, so the first payment is at the inception of the annuity, and the last one occurs one period before the termination.

For an ordinary annuity, however, the payments occur at the end of the period. This means the first payment is one period after the start of the annuity, and the last one occurs right at the end. There are different FV calculations for annuities due and ordinary annuities because of when the first and last payments occur.

There are some formulas to make calculating the FV of an annuity easier. For both of the formulas we will discuss, you need to know the payment amount (m, though often written as pmt or p), the interest rate of the account the payments are deposited in (r, though sometimes i), the number of periods per year (n), and the time frame in years (t).

The formula for an ordinary annuity is as follows:

where m is the payment amount, r is the interest rate, n is the number of periods per year, and t is the length of time in years.

In contrast, the formula for an annuity-due is as follows:

Provided you know m, r, n, and t, therefore, you can find the future value (FV) of an annuity.

5.4.3: Present Value of Annuity

The PV of an annuity can be found by calculating the PV of each individual payment and then summing them up.

Learning Objective

Calculate the present value of annuities

Key Points

• The PV for both annuities-due and ordinary annuities can be calculated using the size of the payments, the interest rate, and number of periods.
• The PV of a perpetuity can be found by dividing the size of the payments by the interest rate.
• Payment size is represented as p, pmt, or A; interest rate by i or r; and number of periods by n or t.

Key Term

perpetuity

An annuity in which the periodic payments begin on a fixed date and continue indefinitely.

The Present Value (PV) of an annuity can be found by calculating the PV of each individual payment and then summing them up . As in the case of finding the Future Value (FV) of an annuity, it is important to note when each payment occurs. Annuities-due have payments at the beginning of each period, and ordinary annuities have them at the end.

Recall that the first payment of an annuity-due occurs at the start of the annuity, and the final payment occurs one period before the end. The PV of an annuity-due can be calculated as follows:

where
is the size of the payment (sometimes
or
),
is the interest rate, and
is the number of periods.

An ordinary annuity has annuity payments at the end of each period, so the formula is slightly different than for an annuity-due. An ordinary annuity has one full period before the first payment (so it must be discounted) and the last payment occurs at the termination of the annuity (so it must be discounted for one period more than the last period in an annuity-due). The formula is:

where, again,
,
, and
are the size of the payment, the interest rate, and the number of periods, respectively.

Both annuities-due and ordinary annuities have a finite number of payments, so it is possible, though cumbersome, to find the PV for each period. For perpetuities, however, there are an infinite number of periods, so we need a formula to find the PV. The formula for calculating the PV is the size of each payment divided by the interest rate.

Example 1

Suppose you have won a lottery that pays $1,000 per month for the next 20 years. But, you prefer to have the entire amount now. If the interest rate is 8%, how much will you accept?

Consider for argument purposes that two people, Mr. Cash, and Mr. Credit, have won the same lottery of $1,000 per month for the next 20 years. Now, Mr. Credit is happy with his $1,000 monthly payment, but Mr. Cash wants to have the entire amount now. Our job is to determine how much Mr. Cash should get. We reason as follows: If Mr. Cash accepts x dollars, then the x dollars deposited at 8% for 20 years should yield the same amount as the $1,000 monthly payments for 20 years. In other words, we are comparing the future values for both Mr. Cash and Mr. Credit, and we would like the future values to be equal.

Since Mr. Cash is receiving a lump sum of x dollars, its future value is given by the lump sum formula:

Since Mr. Credit is receiving a sequence of payments, or an annuity, of $1,000 per month, its future value is given by the annuity formula:

The only way Mr. Cash will agree to the amount he receives is if these two future values are equal. So we set them equal and solve for the unknown:

The reader should also note that if Mr. Cash takes his lump sum of $119,554.36 and invests it at 8% compounded monthly, he will have $589,020.41 in 20 years.

Example 2

Find the monthly payment for a car costing $15,000 if the loan is amortized over five years at an interest rate of 9%.

Again, consider the following scenario: Two people, Mr. Cash and Mr. Credit, go to buy the same car that costs $15,000. Mr. Cash pays cash and drives away, but Mr. Credit wants to make monthly payments for five years. Our job is to determine the amount of the monthly payment.

We reason as follows: If Mr. Credit pays x dollars per month, then the x dollar payment deposited each month at 9% for 5 years should yield the same amount as the $15,000 lump sum deposited for 5 years. Again, we are comparing the future values for both Mr. Cash and Mr. Credit, and we would like them to be the same.

Since Mr. Cash is paying a lump sum of $15,000, its future value is given by the lump sum formula:

Mr. Credit wishes to make a sequence of payments, or an annuity, of x dollars per month, and its future value is given by the annuity formula:

We set the two future amounts equal and solve for the unknown:

5.4.4: Calculating Annuities

Understanding the relationship between each variable and the broader concept of the time value of money enables simple valuation calculations of annuities.

Learning Objective

Calculate the present or future value of various annuities based on the information given

Key Points

• Annuities are basically loans that are paid back over a set period of time at a set interest rate with consistent payments each period.
• A mortgage or car loan are simple examples of an annuity. Borrowers agree to pay a given amount each month when borrowing capital to compensate for the risk and the time value of money.
• The six potential variables included in an annuity calculation are the present value, the future value, interest, time (number of periods), payment amount, and payment growth (if applicable).
• Through integrating each of these (excluding payment growth, if payments are consistent over time), it is simple to solve for the present of future value of a given annuity.

Key Term

annuity

A right to receive amounts of money regularly over a certain fixed period in repayment of a loan or investment (or perpetually, in the case of a perpetuity).

Annuities Defined

To understand how to calculate an annuity, it’s useful to understand the variables that impact the calculation. An annuity is essentially a loan, a multi-period investment that is paid back over a fixed (or perpetual, in the case of a perpetuity)  period of time. The amount paid back over time is relative to the amount of time it takes to pay it back, the interest rate being applied, and the principal (when creating the annuity, this is the present value). 

Generally speaking, annuities and perpetuities will have consistent payments over time. However, it is also an option to scale payments up or down, for various reasons. 

Variables

This gives us six simple variables to use in our calculations:

1. Present Value (PV) – This is the value of the annuity at time 0 (when the annuity is first created)
2. Future Value (FV) – This is the value of the annuity at time n (i.e. at the conclusion of the life of the annuity).
3. Payments (A) – Each period will require individual payments that will be represented by this amount. 
4. Number of Payments (n) – The number of payments (A) will equate to the number of expected periods of payment over the life of the annuity.
5. Interest (i) – Annuities occur over time, and thus a given rate of return (interest) is applied to capture the time value of money.
6. Growth (g) – For annuities that have changes in payments, there is a growth rate applied to these payments over time.

Calculating Annuities

With all of the inputs above at hand, it’s fairly simply to value various types of annuities. Generally investors, lenders, and borrowers are interested in the present and future value of annuities.

Present Value

The present value of an annuity can be calculated as follows:

For a growth annuity (where the payment amount changes at a predetermined rate over the life of the annuity), the present value can be calculated as follows:

Future Value

The future value of an annuity can be determined using this equation:

In a situation where payments grow over time, the future value can be determined using this equation:

Various Formula Arrangements

It is also possible to use existing information to solve for missing information. Which is to say, if you know interest and time, you can solve for the following (given the following):

Annuities Equations

This table is a useful way to view the calculation of annuities variables from a number of directions. Understanding how to manipulate the formula will underline the relationship between the variables, and provide some conceptual clarity as to what annuities are.

This table is a useful way to view the calculation of annuities variables from a number of directions. Understanding how to manipulate the formula will underline the relationship between the variables, and provide some conceptual clarity as to what annuities are.

5.5: Valuing Multiple Cash Flows

5.5.1: Future Value, Multiple Flows

To find the FV of multiple cash flows, sum the FV of each cash flow.

Learning Objective

Calculate the Future Value of Multiple Annuities

Key Points

• The FV of multiple cash flows is the sum of the FV of each cash flow.
• To sum the FV of each cash flow, each must be calculated to the same point in the future.
• If the multiple cash flows are a fixed size, occur at regular intervals, and earn a constant interest rate, it is an annuity. There are formulas for calculating the FV of an annuity.

Key Terms

incremental cash flows

the additional money flowing in or out of a business due to a project

annuity

A specified income payable at stated intervals for a fixed or a contingent period, often for the recipient’s life, in consideration of a stipulated premium paid either in prior installment payments or in a single payment. For example, a retirement annuity paid to a public officer following his or her retirement.

cash flow

The sum of cash revenues and expenditures over a period of time.

Future Value, Multiple Cash Flows

Finding the future value (FV) of multiple cash flows means that there are more than one payment/investment, and a business wants to find the total FV at a certain point in time. These payments can have varying sizes, occur at varying times, and earn varying interest rates, but they all have a certain value at a specific time in the future.

The first step in finding the FV of multiple cash flows is to define when the future is. Once that is done, you can determine the FV of each cash flow using the formula in . Then, simply add all of the future values together.

FV of a single payment

The FV of multiple cash flows is the sum of the future values of each cash flow.

Manually calculating the FV of each cash flow and then summing them together can be a tedious process. If the cash flows are irregular, don’t happen at regular intervals, or earn different interest rates, there isn’t a special way to find the total FV.

However, if the cash flows do happen at regular intervals, are a fixed size, and earn a uniform interest rate, there is an easier way to find the total FV. Investments that have these three traits are called “annuities. “

There are formulas to find the FV of an annuity depending on some characteristics, such as whether the payments occur at the beginning or end of each period. There is a module that goes through exactly how to calculate the FV of annuities.

If the multiple cash flows are a part of an annuity, you’re in luck; there is a simple way to find the FV. If the cash flows aren’t uniform, don’t occur at fixed intervals, or earn different interest rates, the only way to find the FV is do find the FV of each cash flow and then add them together.

5.5.2: Present Value, Multiple Flows

The PV of multiple cash flows is simply the sum of the present values of each individual cash flow.

Learning Objective

Calculate the present value of an investment portfolio that has multiple cash flows

Key Points

• To find the PV of multiple cash flows, each cash flow much be discounted to a specific point in time and then added to the others.
• To discount annuities to a time prior to their start date, they must be discounted to the start date, and then discounted to the present as a single cash flow.
• Multiple cash flow investments that are not annuities unfortunately cannot be discounted by any other method but by discounting each cash flow and summing them together.

Key Terms

discount

To find the value of a sum of money at some earlier point in time. To find the present value.

net present value

the present value of a project or an investment decision determined by summing the discounted incoming and outgoing future cash flows resulting from the decision

The PV of multiple cash flows follows the same logic as the FV of multiple cash flows. The PV of multiple cash flows is simply the sum of the present values of each individual cash flow .

Sum FV

The PV of an investment is the sum of the present values of all its payments.

Each cash flow must be discounted to the same point in time. For example, you cannot sum the PV of two loans at the beginning of the loans if one starts in 2012 and one starts in 2014. If you want to find the PV in 2012, you need to discount the second loan an additional two years, even though it doesn’t start until 2014.

The calculations get markedly simpler if the cash flows make up an annuity. In order to be an annuity (and use the formulas explained in the annuity module), the cash flows need to have three traits:

1. Constant payment size
2. Payments occur at fixed intervals
3. A constant interest rate

Things may get slightly messy if there are multiple annuities, and you need to discount them to a date before the beginning of the payments.

Suppose there are two sets of cash flows which you determine are both annuities. The first extends from 1/1/14 to 1/1/16, and the second extends from 1/1/15 to 1/1/17. You want to find the total PV of all the cash flows on 1/1/13.

The annuity formulas are good for determining the PV at the date of the inception of the annuity. That means that it’s not enough to simply plug in the payment size, interest rate, and number of periods between 1/1/13 and the end of the annuities. If you do, that supposes that both annuities begin on 1/1/13, but neither do. Instead, you have to first find the PV of the first annuity on 1/1/14 and the second on 1/1/15 because that’s when the annuities begin.

You now have two present values, but both are still in the future. You then can discount those present values as if they were single sums to 1/1/13.

Unfortunately, if the cash flows do not fit the characteristics of an annuity, there isn’t a simple way to find the PV of multiple cash flows: each cash flow much be discounted and then all of the PVs must be summed together.

Example

A corporation must decide whether to introduce a new product line. The new product will have start-up expenditures, operational expenditures, and then it will have associated incoming cash receipts (sales) and disbursements (Cash paid for materials, supplies, direct labor, maintenance, repairs, and direct overhead) over 12 years. This project will have an immediate (t=0) cash outflow of 100,000 (which might include all cash paid for the machinery, transportation-in and set-up expenditures, and initial employee training disbursements. ) The annual net cash flow (receipts less disbursements) from this new line for years 1-12 is forecast as follows: -54672, -39161, 3054, 7128, 25927, 28838, 46088, 77076, 46726, 76852, 132332, 166047, reflecting two years of running deficits as experience and sales are built up, with net cash receipts forecast positive after that. At the end of the 12 years it’s estimated that the entire line becomes obsolete and its scrap value just covers all the removal and disposal expenditures. All values are after-tax, and the required rate of return is given to be 10%. (This also makes the simplifying assumption that the net cash received or paid is lumped into a single transaction occurring on the last day of each year. )

The present value (PV) can be calculated for each year:

T=0: 

T=1: 

T=2: 

T=3: 

T=4: 

T=5: 

T=6: 

T=7: 

T=8: 

T=9: 

T=10: 

T=11: 

T=12: 

The sum of all these present values is the net present value, which equals 65,816.04. Since the NPV is greater than zero, it would be better to invest in the project than to do nothing, and the corporation should invest in this project if there is no alternative with a higher NPV.

5.6: Additional Detail on Present and Future Values

5.6.1: The Relationship Between Present and Future Value

Present value (PV) and future value (FV) measure how much the value of money has changed over time.

Learning Objective

Discuss the relationship between present value and future value

Key Points

• The future value (FV) measures the nominal future sum of money that a given sum of money is “worth” at a specified time in the future assuming a certain interest rate, or more generally, rate of return. The FV is calculated by multiplying the present value by the accumulation function.
• PV and FV vary jointly: when one increases, the other increases, assuming that the interest rate and number of periods remain constant.
• As the interest rate (discount rate) and number of periods increase, FV increases or PV decreases.

Key Terms

discounting

The process of finding the present value using the discount rate.

present value

a future amount of money that has been discounted to reflect its current value, as if it existed today

capitalization

The process of finding the future value of a sum by evaluating the present value.

The future value (FV) measures the nominal future sum of money that a given sum of money is “worth” at a specified time in the future assuming a certain interest rate, or more generally, rate of return. The FV is calculated by multiplying the present value by the accumulation function. The value does not include corrections for inflation or other factors that affect the true value of money in the future. The process of finding the FV is often called capitalization.

On the other hand, the present value (PV) is the value on a given date of a payment or series of payments made at other times. The process of finding the PV from the FV is called discounting.

PV and FV are related , which reflects compounding interest (simple interest has n multiplied by i, instead of as the exponent). Since it’s really rare to use simple interest, this formula is the important one.

FV of a single payment

The PV and FV are directly related.

PV and FV vary directly: when one increases, the other increases, assuming that the interest rate and number of periods remain constant.

The interest rate (or discount rate) and the number of periods are the two other variables that affect the FV and PV. The higher the interest rate, the lower the PV and the higher the FV. The same relationships apply for the number of periods. The more time that passes, or the more interest accrued per period, the higher the FV will be if the PV is constant, and vice versa.

The formula implicitly assumes that there is only a single payment. If there are multiple payments, the PV is the sum of the present values of each payment and the FV is the sum of the future values of each payment.

5.6.2: Calculating Perpetuities

The present value of a perpetuity is simply the payment size divided by the interest rate and there is no future value.

Learning Objective

Calculate the present value of a perpetuity

Key Points

• Perpetuities are a special type of annuity; a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever.
• To find the future value of a perpetuity requires having a future date, which effectively converts the perpetuity to an ordinary annuity until that point.
• Perpetuities with growing payments are called Growing Perpetuities; the growth rate is subtracted from the interest rate in the present value equation.

Key Term

growth rate

The percentage by which the payments grow each period.

Perpetuities are a special type of annuity; a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. Essentially, they are ordinary annuities, but have no end date. There aren’t many actual perpetuities, but the United Kingdom has issued them in the past.

Since there is no end date, the annuity formulas we have explored don’t apply here. There is no end date, so there is no future value formula. To find the FV of a perpetuity would require setting a number of periods which would mean that the perpetuity up to that point can be treated as an ordinary annuity.

There is, however, a PV formula for perpetuities . The PV is simply the payment size (A) divided by the interest rate (r). Notice that there is no n, or number of periods. More accurately, is what results when you take the limit of the ordinary annuity PV formula as n → ∞.

It is also possible that an annuity has payments that grow at a certain rate per period. The rate at which the payments change is fittingly called the growth rate (g). The PV of a growing perpetuity is represented as
. It is essentially the same as in except that the growth rate is subtracted from the interest rate. Another way to think about it is that for a normal perpetuity, the growth rate is just 0, so the formula boils down to the payment size divided by r.

5.6.3: Calculating Values for Different Durations of Compounding Periods

Finding the Effective Annual Rate (EAR) accounts for compounding during the year, and is easily adjusted to different period durations.

Learning Objective

Calculate the present and future value of something that has different compounding periods

Key Points

• The units of the period (e.g. one year) must be the same as the units in the interest rate (e.g. 7% per year).
• When interest compounds more than once a year, the effective interest rate (EAR) is different from the nominal interest rate.
• The equation in skips the step of solving for EAR, and is directly usable to find the present or future value of a sum.

Key Terms

Future Value

The value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is “worth” at a specified time in the future, assuming a certain interest rate, or more generally, rate of return, it is the present value multiplied by the accumulation function.

present value

Also known as present discounted value, is the value on a given date of a payment or series of payments made at other times. If the payments are in the future, they are discounted to reflect the time value of money and other factors such as investment risk. If they are in the past, their value is correspondingly enhanced to reflect that those payments have been (or could have been) earning interest in the intervening time. Present value calculations are widely used in business and economics to provide a means to compare cash flows at different times on a meaningful “like to like” basis.

Sometimes, the units of the number of periods does not match the units in the interest rate. For example, the interest rate could be 12% compounded monthly, but one period is one year. Since the units have to be consistent to find the PV or FV, you could change one period to one month. But suppose you want to convert the interest rate into an annual rate. Since interest generally compounds, it is not as simple as multiplying 1% by 12 (1% compounded each month). This atom will discuss how to handle different compounding periods.

Effective Annual Rate

The effective annual rate (EAR) is a measurement of how much interest actually accrues per year if it compounds more than once per year. The EAR can be found through the formula in where i is the nominal interest rate and n is the number of times the interest compounds per year (for continuous compounding, see ). Once the EAR is solved, that becomes the interest rate that is used in any of the capitalization or discounting formulas.

EAR with Continuous Compounding

The effective rate when interest compounds continuously.

Calculating the effective annual rate

The effective annual rate for interest that compounds more than once per year.

For example, if there is 8% interest that compounds quarterly, you plug .08 in for i and 4 in for n. That calculates an EAR of .0824 or 8.24%. You can think of it as 2% interest accruing every quarter, but since the interest compounds, the amount of interest that actually accrues is slightly more than 8%. If you wanted to find the FV of a sum of money, you would have to use 8.24% not 8%.

Solving for Present and Future Values with Different Compounding Periods

Solving for the EAR and then using that number as the effective interest rate in present and future value (PV/FV) calculations is demonstrated here. Luckily, it’s possible to incorporate compounding periods into the standard time-value of money formula. The equation in is the same as the formulas we have used before, except with different notation. In this equation, A(t) corresponds to FV, A₀ corresponds to Present Value, r is the nominal interest rate, n is the number of compounding periods per year, and t is the number of years.

FV Periodic Compounding

Finding the FV (A(t)) given the PV (Ao), nominal interest rate (r), number of compounding periods per year (n), and number of years (t).

The equation follows the same logic as the standard formula. r/n is simply the nominal interest per compounding period, and nt represents the total number of compounding periods.

Solving for n

The last tricky part of using these formulas is figuring out how many periods there are. If PV, FV, and the interest rate are known, solving for the number of periods can be tricky because n is in the exponent. It makes solving for n manually messy. shows an easy way to solve for n. Remember that the units are important: the units on n must be consistent with the units of the interest rate (i).

Solving for n

This formula allows you to figure out how many periods are needed to achieve a certain future value, given a present value and an interest rate.

5.6.4: Comparing Interest Rates

Variables, such as compounding, inflation, and the cost of capital must be considered before comparing interest rates.

Learning Objective

Discuss the differences between effective interest rates, real interest rates, and cost of capital

Key Points

• A nominal interest rate that compounds has a different effective rate (EAR), because interest is accrued on interest.
• The Fisher Equation approximates the amount of interest accrued after accounting for inflation.
• A company will theoretically only invest if the expected return is higher than their cost of capital, even if the return has a high nominal value.

Key Term

inflation

An increase in the general level of prices or in the cost of living.

The amount of interest you would have to pay on a loan or would earn on an investment is clearly an important consideration when making any financial decisions. However, it is not enough to simply compare the nominal values of two interest rates to see which is higher.

Effective Interest Rates

The reason why the nominal interest rate is only part of the story is due to compounding. Since interest compounds, the amount of interest actually accrued may be different than the nominal amount. The last section went through one method for finding the amount of interest that actually accrues: the Effective Annual Rate (EAR).

The EAR is a calculation that account for interest that compounds more than one time per year. It provides an annual interest rate that accounts for compounded interest during the year. If two investments are otherwise identical, you would naturally pick the one with the higher EAR, even if the nominal rate is lower.

Real Interest Rates

Interest rates are charged for a number of reasons, but one is to ensure that the creditor lowers his or her exposure to inflation. Inflation causes a nominal amount of money in the present to have less purchasing power in the future. Expected inflation rates are an integral part of determining whether or not an interest rate is high enough for the creditor.

The Fisher Equation is a simple way of determining the real interest rate, or the interest rate accrued after accounting for inflation. To find the real interest rate, simply subtract the expected inflation rate from the nominal interest rate.

Fisher Equation

The nominal interest rate is approximately the sum of the real interest rate and inflation.

For example, suppose you have the option of choosing to invest in two companies. Company 1 will pay you 5% per year, but is in a country with an expected inflation rate of 4% per year. Company 2 will only pay 3% per year, but is in a country with an expected inflation of 1% per year. By the Fisher Equation, the real interest rates are 1% and 2% for Company 1 and Company 2, respectively. Thus, Company 2 is the better investment, even though Company 1 pays a higher nominal interest rate.

Cost of Capital

Another major consideration is whether or not the interest rate is higher than your cost of capital. The cost of capital is the rate of return that capital could be expected to earn in an alternative investment of equivalent risk. Many companies have a standard cost of capital that they use to determine whether or not an investment is worthwhile.

In theory, a company will never make an investment if the expected return on the investment is less than their cost of capital. Even if a 10% annual return sounds really nice, a company with a 13% cost of capital will not make that investment.

5.6.5: Calculating Values for Fractional Time Periods

The value of money and the balance of the account may be different when considering fractional time periods.

Learning Objective

Calculate the future and present value of an account when a fraction of a compounding period has passed

Key Points

• The balance of an account only changes when interest is paid. To find the balance, round the fractional time period down to the period when interest was last accrued.
• To find the PV or FV, ignore when interest was last paid an use the fractional time period as the time period in the equation.
• The discount rate is really the cost of not having the money over time, so for PV/FV calculations, it doesn’t matter if the interest hasn’t been added to the account yet.

Key Terms

time period assumption

business profit or loses are measured on timely basis

compounding period

The length of time between the points at which interest is paid.

time value of money

the value of an asset accounting for a given amount of interest earned or inflation accrued over a given period

Up to this point, we have implicitly assumed that the number of periods in question matches to a multiple of the compounding period. That means that the point in the future is also a point where interest accrues. But what happens if we are dealing with fractional time periods?

Compounding periods can be any length of time, and the length of the period affects the rate at which interest accrues.

Compounding Interest

The effect of earning 20% annual interest on an initial $1,000 investment at various compounding frequencies.

Suppose the compounding period is one year, starting January1, 2012. If the problem asks you to find the value at June 1, 2014, there is a bit of a conundrum. The last time interest was actually paid was at January 1, 2014, but the time-value of money theory clearly suggests that it should be worth more in June than in January.

In the case of fractional time periods, the devil is in the details. The question could ask for the future value, present value, etc., or it could ask for the future balance, which have different answers.

Future/Present Value

If the problem asks for the future value (FV) or present value (PV), it doesn’t really matter that you are dealing with a fractional time period. You can plug in a fractional time period to the appropriate equation to find the FV or PV. The reasoning behind this is that the interest rate in the equation isn’t exactly the interest rate that is earned on the money. It is the same as that number, but more broadly, is the cost of not having the money for a time period. Since there is still a cost to not having the money for that fraction of a compounding period, the FV still rises.

Account Balance

The question could alternatively ask for the balance of the account. In this case, you need to find the amount of money that is actually in the account, so you round the number of periods down to the nearest whole number (assuming one period is the same as a compounding period; if not, round down to the nearest compounding period). Even if interest compounds every period, and you are asked to find the balance at the 6.9999^th period, you need to round down to 6. The last time the account actually accrued interest was at period 6; the interest for period 7 has not yet been paid.

If the account accrues interest continuously, there is no problem: there can’t be a fractional time period, so the balance of the account is always exactly the value of the money.

5.6.6: Loans and Loan Amortization

When borrowing money to be paid back via a number of installments over time, it is important to understand the time value of money and how to build an amortization schedule.

Learning Objective

Understand amortization schedules

Key Points

• Amortization of a loan is the process of identifying a payment amount for each period of repayment on a given outstanding debt.
• Repaying capital over time at an interest rate requires an amortization schedule, which both parties agree to prior to the exchange of capital. This schedule determines the repayment period, as well as the amount of repayment per period.
• Time value of money is a central concept to amortization. A dollar today, for example, is worth more than a dollar tomorrow due to the opportunity cost of other investments.
• When purchasing a home for $100,000 over 30 years at 8% interest (consistent payments each month), for example, the total amount of repayment is more than 2.5 times the original principal of $100,000.

Key Term

amortization

This is the process of scheduling intervals of payment over time to pay back an existing debt, taking into account the time value of money.

 When lending money (or borrowing, depending on your perspective), it is common to have multiple payback periods over time (i.e. multiple, smaller cash flow installments to pay back the larger borrowed sum). In these situations, an amortization schedule will be created. This will determine how much will be paid back each period, and how many periods of repayment will be required to cover the principal balance. This must be agreed upon prior to the initial borrowing occurs, and signed by both parties.

Time Value of Money

Now if you add up all of the separate payments in an amortization schedule, you’ll find the total exceeds the amount borrowed. This is because amortization schedules must take into account the time value of money. Time value of money is a fairly simple concept at it’s core: a dollar today is worth more than a dollar tomorrow. 

Why? Because capital can be invested, and those investments can yield returns. Lending your money to someone means incurring the opportunity cost of the other things you could do with that money. This gets even more drastic as the scale of capital increases, as the returns on capital over time are expressed in a percentage of the capital invested. Say you spend $100 on some stock, and turn 10% on that investment. You now have $110, a profit of $10. Say instead of only a $100, you put in $10,000. Now you have $11,000, a profit of $1,000. 

Principle and Interest

As a result of this calculation, amortization schedules charge interest over time as a percentage of the principal borrowed. The calculation will incorporate the number of payment periods (n), the principal (P), the amortization payment (A) and the interest rate (r).

To make this a bit more realistic, let’s insert some numbers. Let’s say you find a dream house, at the reasonable rate of $100,000. Unfortunately, a bit of irresponsible borrowing in your past means you must pay 8% interest over a 30 year loan, which will be paid via a monthly amortization schedule (12 months x 30 years = 360 payments total). If you do the math, you should find yourself paying $734 per month 360 times. 360 x 734 will leave you in the ballpark of $264,000 in total repayment. that means you are paying more than 2.5 times as much for this house due to time value of money! This bit of knowledge is absolutely critical for personal financial decisions, as well as for high level business decisions. 

Amortization Schedule Example

This shows the first few installments in the example discussed above (i.e. borrowing $100,000 at 8% interest paid monthly over 30 years).

This shows the first few installments in the example discussed above (i.e. borrowing $100,000 at 8% interest paid monthly over 30 years).

5.7: Yield

5.7.1: Calculating the Yield of a Single-Period Investment

The yield of a single period investment is simply
.

Learning Objective

Differentiate between the different methods of calculating yield of a single period investment

Key Points

• There are a number of ways to calculate yield, but the most common ones are to calculate the percent change from the initial investment, APR, and APY (or EAR).
• APR (annual percentage rate) is a commonly used calculation that figures out the nominal amount of interest accrued per year. It does not account for compounding interest.
• APY (annual percentage yield) is a way of using the nominal interest rate to calculate the effective interest rate per year. It accounts for compounding interest.
• EAR (effective annual rate) is a special type of APY that uses APR as the nominal interest rate.

Key Terms

effective-interest method

amortizing a debt according to the effective interest rate paid

Nominal Interest

The amount of interest accrued per year without accounting for compounding.

Effective Interest

The amount of interest accrued per year after accounting for compounding.

Determining Yield

The yield on an investment is the amount of money that is returned to the owner at the end of the term. In short, it’s how much you get back on your investment.

Naturally, this is a number that people care a lot about. The whole point of making an investment is to get a yield. There are a number of different ways to calculate an investment’s yield, though. You may get slightly different numbers using different methods, so it’s important to make sure that you use the same method when you are comparing yields. This section will address the yield calculation methods you are most likely to encounter, though there are many more.

Change-In-Value

The most basic type of yield calculation is the change-in-value calculation. This is simply the change in value (FV minus PV) divided by the PV times 100%. This calculation measures how different the FV is from the PV as a percentage of PV.

Percent Change

The percent change in value is the change in value from PV to FV (V2 to V1) divided by PV (V1) times 100%.

Annual Percentage Rate

Another common way of calculating yield is to determine the Annual Percentage Rate, or APR. You may have heard of APR from ads for car loans or credit cards. These generally have monthly loans or fees, but if you want to get an idea of how much you will accrue in interest per year, you need to calculate an APR. Nominal APR is simply the interest rate multiplied by the number of payment periods per year. However, since interest compounds, nominal APR is not a very accurate measure of the amount of interest you actually accrue.

Effective Annual Rate

To find the effective APR, the actual amount of interest you would accrue per year, we use the Effective Annual Rate, or EAR.

EAR

The Effective Annual Rate is the amount of interest actually accrued per year based on the APR. n is the number of compounding periods of APR per year.

For example, you may see an ad that says you can get a car loan at an APR of 10% compounded monthly. That means that APR=.10 and n=12 (the APR compounds 12 times per year). That means the EAR is 10.47%.

The EAR is a form of the Annual Percentage Yield (APY). APY may also be calculated using interest rates other than APR, so a more general formula is in . The logic behind calculating APY is the same as that used when calculating EAR: we want to know how much you actually accrue in interest per year. Interest usually compounds, so there is a difference between the nominal interest rate (e.g. monthly interest times 12) and the effective interest rate.

Annual Percentage Yield

The Annual Percentage Yield is a way or normalizing the nominal interest rate. Basically, it is a way to account for the time factor in order to get a more accurate number for the actual interest rate.inom is the nominal interest rate.N is the number of compounding periods per year.

5.7.2: Calculating the Yield of an Annuity

The yield of an annuity is commonly found using either the percent change in the value from PV to FV, or the internal rate of return.

Learning Objective

Calculate the yield of an annuity using the internal rate of return method

Key Points

• The yield of an annuity may be found by discounting to find the PV, and then finding the percentage change from the PV to the FV.
• The Internal Rate of Return (IRR) is the discount rate at which the NPV of an investment equals 0.
• The IRR calculates an annualized yield of an annuity.

Key Terms

Net Present Value (NPV)

The present value of a project or an investment decision determined by summing the discounted incoming and outgoing future cash flows resulting from the decision.

Internal Rate of Return (IRR)

The discount rate that will cause the NPV of an investment to equal 0.

yield

In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return. Yield applies to various stated rates of return on stocks (common and preferred, and convertible), fixed income instruments (bonds, notes, bills, strips, zero coupon), and some other investment type insurance products

The yield of annuity can be calculated in similar ways to the yield for a single payment, but two methods are most common.

The first is the standard percentage-change method. Just as for a single payment, this method calculated the percentage difference between the FV and the PV. Since annuities include multiple payments over the lifetime of the investment, the PV (or V₁ in is the present value of the entire investment, not just the first payment.

The second popular method is called the internal rate of return (IRR). The IRR is the interest rate (or discount rate) that causes the Net Present Value (NPV) of the annuity to equal 0. That means that the PV of the cash outflows equals the PV of the cash inflows. The higher the IRR, the more desirable is the investment. In theory, you should make investment with an IRR greater than the cost of capital.

Let’s take an example investment: It is not technically an annuity because the payments vary, but still is a good example for how to find IRR:

Suppose you have a potential investment that would require you to make a $4,000 investment today, but would return cash flows of $1,200, $1,410, $1,875, and $1,050 in the four successive years. This investment has an implicit rate of return, but you don’t know what it is. You plug the numbers into the NPV formula and set NPV equal to 0. You then solve for r, which is your IRR (it’s not easy to solve this problem by hand. You will likely need to use a business calculator or Excel). When r = 14.3%, NPV = 0, so therefore the IRR of the investment is 14.3%.

IRR Example

The setup to find the IRR of the investment with cash flows of -4000, 1200, 1410, 1875, and 1050. By setting NPV = 0 and solving for r, you can find the IRR of this investment.

4.3: Forecasting the Income Statement

4.3.1: Sales Forecast Input

Learning Objective

Apply forecasting techniques to determine a company’s target volume

Key Points

• Net sales are operating revenues earned by a company for selling its products or rendering its services.
• Gross sales are the sum of all sales during a time period. Net sales are gross sales minus sales returns, sales allowances, and sales discounts.
• The purpose of profit-based sales target metrics is to ensure that marketing and sales objectives mesh with profit targets.

Key Terms

fixed costs

In economics, fixed costs are business expenses that are not dependent on the level of goods or services produced by the business.

contribution margin

In cost-volume-profit analysis, a form of management accounting, contribution margin is the marginal profit per unit sale.

Sales

Net sales are operating revenues earned by a company for selling its products or rendering its services. Also referred to as revenue, they are reported directly on the income statement as Sales or Net sales.

For financial ratios that use income statement sales values, “sales” refers to net sales, not gross sales. Sales are the unique transactions that occur in professional selling or during marketing initiatives.

The term sales in a marketing, advertising or a general business context often refers to a contract in which a buyer has agreed to purchase some products at a set time in the future. “Outstanding orders” refers to sales orders that have not been filled.

A sale is a transfer of property for money or credit. In double-entry bookkeeping, a sale of merchandise is recorded in the general journal as a debit to cash or accounts receivable and a credit to the sales account. A discount from list price might be noted if it applies to the sale (discount expense debit).

Fees for services are recorded separately from sales of merchandise, but the bookkeeping transactions for recording sales of services are similar to those for recording sales of tangible goods.

Sales Forecasting

An example of sales forecasting for a company over a decade.

Forecasting: Gross Sales and Net Sales

Net sales = Gross sales – (Customer discounts, returns, allowances)

Gross sales are the sum of all sales during a time period. Net sales are gross sales minus sales returns, sales allowances, and sales discounts. Gross sales do not normally appear on an income statement. The sales figures reported on an income statement are net sales.

• sales returns are refunds to customers for returned merchandise/credit notes
• debit notes
• sales journal entries non-current, current batch-processed transactions, predictive analytics in strategic management/administration/governance research metaframeworks
• sales allowances are reductions in sales price for merchandise with minor defects, the allowance agreed upon after the customer has purchased the merchandise
• sales discounts allowed are reduced payments from the customer based on invoice payment terms such as 2/10, n/30 (2% discount if paid within 10 days, net invoice total due in 30 days)
• interest received for amounts in arrears
• includes/excludes amounts capital goods & services, non-capital goods & services, input valued-added tax, with cost of non-capital goods sold
• input vat – output vat
• sales of portfolio items and capital gains taxes
• Sales Returns and Allowances and Sales Discounts are contra-revenue accounts

Sales Forecasting

In launching a program, managers often start with an idea of the dollar profit they desire and ask what sales levels will be required to reach it. Target volume is the unit sales quantity required to meet an earnings goal. Target revenue is the corresponding figure for dollar sales. Both of these metrics can be viewed as extensions of break-even analysis. Increasingly, marketers are expected to generate volumes that meet the target profits of their firm. This will often require them to revise sales targets as prices and costs change.

• Target volume: the volume of sales necessary to generate the profits specified in a company’s plans.
• Target Volume = [Fixed costs + Target Profits] / Contribution per Unit
• The formula for target volume will be familiar to those who have performed break-even analysis. The only change is to add the required profit target to the fixed costs. From another perspective, the break-even volume equation can be viewed as a special case of the general target volume calculation — one in which the profit target is zero, and a company seeks only to cover its fixed costs.
• In target volume calculations, the company broadens this objective to solve for a desired profit.
• Target Revenue = Target Volume * Selling Price per Unit; or
• Target Revenue = 100 * [ { Fixed Costs + Target Profits } / Contribution Margin ]

The purpose of profit-based sales target metrics is to ensure that marketing and sales objectives mesh with profit targets. In target volume and target revenue calculations, managers go beyond break-even analysis (the point at which a company sells enough to cover its fixed costs) to determine the level of unit sales or revenues needed not only to cover a firm’s costs but also to attain its profit targets.

4.3.2: Inputs to the Production Schedule

Learning Objective

Differentiate the different production schedule inputs

Key Points

• A good purchased as a “raw material” goes into the manufacture of a product.
• A good only partially completed during the manufacturing process is called “work in process”.
• When the good is completed as to manufacturing but not yet sold or distributed to the end-user, it is called a “finished good”.
• Inventory management is primarily about specifying the shape and percentage of stocked goods.
• Basic reasons for keeping an inventory involve time, uncertainty and economics of scales.

Key Term

ABC analysis

The ABC analysis is a business term used to define an inventory categorization technique often used in materials management. It is also known as Selective Inventory Control. Policies based on ABC analysis: A ITEMS, very tight control and accurate records; B ITEMS, less tightly controlled, and good records; and C ITEMS, simplest controls possible and minimal records.

Example

• By taking the Costs-To-Date divided by the Cost Estimate, the “percentage complete” for the project is calculated. For example: Assume a project is estimated to cost $70,000 by the time the work is complete, Assume at the end of December, $35,000 has been spent to date for the project, $35,000 divided by $70,000 is 50%, therefore, the project can be considered 50% complete at December 31.

Production schedule inputs:

• A good purchased as a “raw material” goes into the manufacture of a product.
• A good only partially completed during the manufacturing process is called “work in process. “
• When the good is completed as to manufacturing but not yet sold or distributed to the end user, it is called a “finished good. “

Raw materials – materials and components scheduled for use in making a product.

A raw material is the basic material from which a product is manufactured or made, frequently used with an extended meaning. For example, the term is used to denote material that came from nature and is in an unprocessed or minimally processed state. Latex, iron ore, logs, and crude oil, and salt water are examples. The use of raw material by non-human species includes twigs and found objects as used by birds to make nests.

Work in process, WIP – materials and components that have begun their transformation to finished goods.

Work in process (WIP) or in-process inventory includes the set at large of unfinished items for products in a production process. These items are not yet completed but either just being fabricated or waiting in a queue for further processing or in a buffer storage. The term is used in production and supply chain management.

Optimal production management aims to minimize work in process. Work in process requires storage space, represents bound capital not available for investment, and carries an inherent risk of earlier expiration of shelf life of the products. A queue leading to a production step shows that the step is well buffered for shortage in supplies from preceding steps, but may also indicate insufficient capacity to process the output from these preceding steps.

Finished goods – goods ready for sale to customers.

Finished goods are goods that have completed the manufacturing process but have not yet been sold or distributed to the end user. Finished goods is a relative term. In a Supply chain management flow, the finished goods of a supplier can constitute the raw material of a buyer.

Goods for resale – returned goods that are salable.

Inventory management

Inventory management is primarily about specifying the shape and percentage of stocked goods. It is required at different locations within a facility or within many locations of a supply network to precede the regular and planned course of production and stock of materials.

The scope of inventory management concerns the fine lines between replenishment lead time, carrying costs of inventory, asset management, inventory forecasting, inventory valuation, inventory visibility, future inventory price forecasting, physical inventory, available physical space for inventory, quality management, replenishment, returns and defective goods, and demand forecasting. Balancing these competing requirements leads to optimal inventory levels, which is an on-going process as the business needs shift and react to the wider environment.

Inventory management involves a retailer seeking to acquire and maintain a proper merchandise assortment while ordering, shipping, handling, and related costs are kept in check. It also involves systems and processes that identify inventory requirements, set targets, provide replenishment techniques, report actual and projected inventory status, and handle all functions related to the tracking and management of material. This would include the monitoring of material moved into and out of stockroom locations and the reconciling of the inventory balances. It also may include ABC analysis, lot tracking, cycle counting support, etc. Management of the inventories, with the primary objective of determining/controlling stock levels within the physical distribution system, functions to balance the need for product availability against the need for minimizing stock holding and handling costs.

Production budget

Production budget is important for inventory and sales revenue

There are three basic reasons for keeping an inventory:

• Time: The time lags present in the supply chain, from supplier to user at every stage, requires that you maintain certain amounts of inventory to use in this lead time. However, in practice, inventory is to be maintained for consumption during variations in lead time. Lead time itself can be addressed by ordering that many days in advance.
• Uncertainty: Inventories are maintained as buffers to meet uncertainties in demand, supply and movements of goods.
• Economies of scale: Ideal condition of “one unit at a time at a place where a user needs it, when he needs it” principle tends to incur lots of costs in terms of logistics. So bulk buying, movement, and storing brings in economies of scale, thus inventory.

A Sample Production Plan

An example of a production plan covering one week.

4.3.3: Inputs to COGS

Learning Objective

Classify the different components of Cost of Goods Sold (COGS)

Key Points

• Costs include all costs of purchase, costs of conversion, and other costs incurred in bringing the inventories to their present location and condition.
• The key components of cost generally include: parts – raw materials and supplies used, labor – including associated costs such as payroll taxes and benefits, and overhead of the business allocable to production.
• A miscalculation or faulty estimation can be amplified drastically, causing a vastly different forecasted amount of income than what will actually come to pass.

Key Terms

overhead

Any cost or expenditure (monetary, time, effort or otherwise) incurred in a project or activity, which does not directly contribute to the progress or outcome of the project or activity.

allocate

To distribute according to a plan.

Cost of goods sold (COGS) refer to the inventory costs of the goods a business has sold during a particular period. Costs include all costs of purchase, costs of conversion, and other costs incurred in bringing the inventories to their present location and condition. Costs of goods made by the business include material, labor, and allocated overhead. The costs of those goods not yet sold are deferred as costs of inventory until the inventory is sold or written down in value.

A Sample Income Statement

Expenses are listed on a company’s income statement.

Because costs of goods sold is a major expense for most companies, it is an extremely important input to a forecast of the income statement. A miscalculation or faulty estimation can be amplified drastically, causing a vastly different forecasted amount of income than what will actually come to pass. Specifically, underestimating the costs associated with goods to be sold can cause the forecasted income to be much higher than what it actually will be, and vice versa. Also, because cost of goods sold is such a broad input, encompassing many separate expenses with different methods of estimating each, it becomes difficult to accurately forecast all phases.

Components of COGS

Parts, Raw Materials, and Supplies Used

Most businesses make more than one of a particular item. Therefore, costs are incurred for multiple items rather than a particular item sold. Determining how much of each of these components to allocate to particular goods requires either tracking the particular costs or making some allocations of costs. Parts and raw materials are often tracked to particular sets (e.g., batches or production runs) of goods, then allocated to each item.

Labor and Associated Costs

Labor costs include direct labor and indirect labor. Direct labor costs are the wages paid to those employees who spend all their time working directly on the product being manufactured. Indirect labor costs are the wages paid to other factory employees involved in production. Costs of payroll taxes and employee benefits are generally included in labor costs, but may be treated as overhead costs. Labor costs may be allocated to an item or set of items based on timekeeping records.

Overhead of the Business Allocable to Production

Determining overhead costs often involves making assumptions about what costs should be associated with production activities and what costs should be associated with other activities. Traditional methods attempt to make these assumptions based on past experience and management judgment as to factual relationships. Activity based costing attempts to allocate costs based on those factors that drive the business to incur the costs.

Variable production overheads are allocated to units produced based on actual use of production facilities. Fixed production overheads are often allocated based on normal capacities or expected production. More or fewer goods may be produced than expected when developing cost assumptions (like burden rates). These differences in production levels often result in too much or too little cost being assigned to the goods produced. This also gives rise to variances.

4.3.4: Other Expenses

Learning Objective

Differentiate the different inputs that are classified as “other expenses”

Key Points

• Other expenses include operation expenses section and non-operation expenses section.
• Operation section expenses include SG&A, depreciation, amortization, and R&D expenses.
• Non-operation section expenses include finance costs, income tax expense, and discontinued operations expenses.
• SG&A is usually understood as a major portion of non-production related costs, in contrast to production costs such as direct labour.

Key Terms

intangible assets

Intangible assets are defined as identifiable non-monetary assets that cannot be seen, touched or physically measured, and are created through time and effort, and are identifiable as a separate asset.

deferred tax liabilities

Deferred tax liabilities generally arise where tax relief is provided in advance of an accounting expense, or income is accrued but not taxed until received.

Example

• Extraordinary items: natural disaster might not qualify depending on location.

Operation Section:

Expenses

Operational expenses and non-operational expenses are the main cash outflow of a business.

Selling, General, and Administrative expenses (SG&A or SGA)

Selling, General, and Administrative expenses (SG&A or SGA) consist of the combined payroll costs. SGA is usually understood as a major portion of non-production related costs, in contrast to production costs such as direct labor.

• Selling expenses – represent expenses needed to sell products (e.g. salaries of sales people, commissions and travel expenses, advertising, freight, shipping, depreciation of sales store buildings and equipment, rent, and all expenses and taxes directly related to producing and selling product, etc. )
• General expenses- general operating expenses and taxes that are directly related to the general operation of the company, but don’t relate to the other two categories.
• Administrative expenses – executive salaries, general support, and all associated taxes related to the overall administration of the company.

Depreciation

1. The decrease in value of assets (fair value depreciation).

2. The allocation of the cost of assets to periods in which the assets are used (depreciation with the matching principle).

The former affects values of businesses and entities. The latter affects net income. Generally, the cost is allocated, as depreciation expense, among the periods in which the asset is expected to be used. Such expense is recognized by businesses for financial reporting and tax purposes. Methods of computing depreciation may vary by asset for the same business. Methods and lives may be specified in accounting and/or tax rules in a country. Several standard methods of computing depreciation expense may be used, including fixed percentage, straight line, and declining balance methods. Depreciation expense generally begins when the asset is placed in service.

Amortization

Amortization (or amortisation) is the process of decreasing or accounting for an amount over a period. When used in the context of a home purchase, amortization is the process by which loan principal decreases over the life of a loan. With each mortgage payment that is made, a portion of the payment is applied towards reducing the principal, and another portion of the payment is applied towards paying the interest on the loan. An amortization table shows this ratio of principal and interest and demonstrates how a loan’s principal amount decreases over time. Amortization is generally known as depreciation of intangible assets of a firm.

Research & Development (R&D) Expenses

The term R&D or research and development refers to a specific group of activities within a business. The activities that are classified as R&D differ from company to company, but there are two primary models. In one model, the primary function of an R&D group is to develop new products. In the other model, the primary function of an R&D group is to discover and create new knowledge about scientific and technological topics for the purpose of uncovering and enabling development of valuable new products, processes, and services.

Non-operating section

• Other expenses or losses – expenses or losses not related to primary business operations, (e.g. foreign exchange loss).
• Finance costs – costs of borrowing from various creditors (e.g. interest expenses, bank charges).
• Income tax expense – sum of the amount of tax payable to tax authorities in the current reporting period (current tax liabilities/ tax payable) and the amount of deferred tax liabilities (or assets).
• Discontinued operations are the most common type of irregular items. Shifting business location(s), stopping production temporarily, or changes due to technological improvement do not qualify as discontinued operations. Discontinued operations must be shown separately.
• Extraordinary items are both unusual (abnormal) and infrequent, for example, unexpected natural disaster, expropriation, prohibitions under new regulations.

4.3.5: Pro Forma Income Statement

Learning Objective

Prepare a pro forma income statement

Key Points

• The pro forma accounting is a statement of the company’s financial activities while excluding “unusual and nonrecurring transactions” when stating how much money the company actually made.
• Income statement is a company’s financial statement that indicates how the revenue is transformed into the net income during a certain period of time.
• Pro forma Income statement includes revenue, COGS, operational expenses and non-operational expenses.

Key Terms

depreciation

The measurement of the decline in value of assets. Not to be confused with impairment, which is the measurement of the unplanned, extraordinary decline in value of assets.

pro forma

For the sake of form only.

write-off

The term written-off describes a reduction in recognized value. In accounting terminology, it refers to recognition of the reduced or zero value of an asset.

Pro forma

The term pro forma, Latin for “as a matter of form” or “for the sake of form”, is a term applied to practices or documents that are done as a pure formality, perfunctorily, or seek to satisfy the minimum requirements or to conform to a convention or doctrine. It has different meanings in different fields.

Pro forma financial statements are prepared in advance of a planned transaction, such as a merger, an acquisition, a new capital investment, or a change in capital structure like an incurrence of new debt or issuance of equity.

The pro forma models the anticipated results of the transaction, with particular emphasis on the projected cash flows, net revenues and (for taxable entities) taxes. Consequently, pro forma statements summarize the projected future status of a company, based on the current financial statements. For example, when a transaction with a material effect on a company’s financial condition is contemplated, the Finance Department will prepare, for management and Board review, a business plan containing pro forma financial statements demonstrating the expected effect of the proposed transaction on the company’s financial viability. Lenders and investors will require such statements to structure or confirm compliance with debt covenants, such as debt service reserve coverage and debt to equity ratios. Similarly, when a new corporation is envisioned, its founders will prepare pro forma financial statements for the information of prospective investors.

Pro forma accounting is a statement of the company’s financial activities while excluding “unusual and nonrecurring transactions” when stating how much money the company actually made. Expenses often excluded from pro forma results include company restructuring costs, a decline in the value of the company’s investments, or other accounting charges, such as adjusting the current balance sheet to fix faulty accounting practices in previous years.

Income Statement

The income statement is a company’s financial statement that indicates how the revenue is transformed into the net income (the result after all revenues and expenses have been accounted for, also known as Net Profit or the “bottom line”). It displays the revenues recognized for a specific period, and the cost and expenses charged against these revenues, including write-offs (e.g., depreciation and amortization of various assets) and taxes.

Pro Forma Income Statement

Pro forma figures should be clearly labeled as such and the reason for any deviation from reported past figures clearly explained. A pro forma Income statement could be planned and prepared in advance, which includes the items below:

Operating Section:

• Revenue – Cash inflows or other enhancements of assets of an entity during a period from delivering or producing goods, rendering services, or other activities that constitute the entity’s ongoing major operations. It is usually presented as sales minus sales discounts, returns, and allowances.
• Expenses – Cash outflows or other using-up of assets or incurrence of liabilities during a period from delivering or producing goods, rendering services, or carrying out other activities that constitute the entity’s ongoing major operations.
• Cost of Goods Sold (COGS) / Cost of Sales – represents the direct costs attributable to goods produced and sold by a business (manufacturing or merchandizing). It includes material costs, direct labour, and overhead costs (as in absorption costing).
• Selling, General and Administrative expenses (SG&A or SGA) – consist of the combined payroll costs. SGA is usually understood as a major portion of non-production related costs, in contrast to production costs such as direct labour.
• Depreciation / Amortization – the charge with respect to fixed assets / intangible assets that have been capitalised on the balance sheet for a specific (accounting) period. It is a systematic and rational allocation of cost rather than the recognition of market value decrement.
• Research & Development (R&D) expenses – expenses included in research and development.

Non-Operating Section:

• Other revenues or gains – income from other than primary business activities (e.g. rent, income from patents). It also includes gains that are either unusual or infrequent, but not both (e.g. gain from sale of securities or gain from disposal of fixed assets)
• Other expenses or losses – not related to primary business operations, (e.g. foreign exchange loss).
• Finance costs – costs of borrowing from various creditors (e.g. interest expenses, bank charges).
• Income tax expense – sum of the amount of tax payable to tax authorities in the current reporting period (current tax liabilities / tax payable) and the amount of deferred tax liabilities (or assets).
• Irregular items – these are reported separately because this way users can better predict future cash flows – irregular items most likely will not recur. These are reported net of taxes.
• Discontinued operations is the most common type of irregular items. Shifting business location(s), stopping production temporarily, or changes due to technological improvement do not qualify as discontinued operations. Discontinued operations must be shown separately.

4.4: Forecasting the Balance Sheet

4.4.1: Pro Forma Balance Sheet

A pro forma balance sheet summarizes the projected future status of a company after a planned transaction, based on the current financial statements.

Learning Objective

Prepare pro forma balance sheets when the situation requires

Key Points

• The pro forma accounting is a statement of the company’s financial activities while excluding “unusual and nonrecurring transactions” when stating how much money the company actually made.
• In business, pro forma financial statements are prepared in advance of a planned transaction, such as a merger, an acquisition, a new capital investment, or a change in capital structure such as incurrence of new debt or issuance of equity.
• Pro forma figures should be clearly labeled as such and the reason for any deviation from reported past figures clearly explained.

Key Terms

a merger, an acquisition

Mergers and acquisitions (abbreviated M&A) is an aspect of corporate strategy, corporate finance, and management dealing with the buying, selling, dividing, and combining of different companies and similar entities that can help an enterprise grow rapidly in its sector or location of origin, or a new field or new location, without creating a subsidiary, other child entity or using a joint venture.

intangible assets

Intangible assets are defined as identifiable non-monetary assets that cannot be seen, touched, or physically measured. They are created through time and effort, and are identifiable as a separate asset.

warranties

In business and legal transactions, a warranty is an assurance by one party to the other party that specific facts or conditions are true or will happen. The other party is permitted to rely on that assurance and seek some type of remedy if it is not true or followed.

Example

• For example, when a transaction with a material effect on a company’s financial condition is contemplated, the Finance Department will prepare, for management and board review, a business plan containing pro forma financial statements demonstrating the expected effect of the proposed transaction on the company’s financial viability.

Pro Forma Financial Statements

In business, pro forma financial statements are prepared in advance of a planned transaction, such as a merger, an acquisition, a new capital investment, or a change in capital structure such as incurrence of new debt or issuance of equity. The pro forma models the anticipated results of the transaction, with particular emphasis on the projected cash flows, net revenues and (for taxable entities) taxes. Consequently, pro forma statements summarize the projected future status of a company, based on the current financial statements. For example, when a transaction with a material effect on a company’s financial condition is contemplated, the Finance Department will prepare, for management and Board review, a business plan containing pro forma financial statements demonstrating the expected effect of the proposed transaction on the company’s financial viability.

Pro Forma Balance Sheet

If applicable to the business, summary values for the following items should be included in the pro forma balance sheet :

Balance Sheet

Simple balance sheet including basic items

• Assets

• Current assets
• Cash and cash equivalents
• Accounts receivable
• Inventories
• Prepaid expenses for future services that will be used within a year
• Non-current assets (Fixed assets)
• Property, plant and equipment
• Investment property, such as real estate held for investment purposes
• Intangible assets
• Financial assets (excluding investments accounted for using the equity method, accounts receivables, and cash and cash equivalents)
• Investments accounted for using the equity method
• Biological assets, which are living plants or animals. Bearer biological assets are plants or animals which bear agricultural produce for harvest, such as apple trees grown to produce apples and sheep raised to produce wool.

• Liabilities

• Accounts payable
• Provisions for warranties or court decisions
• Financial liabilities (excluding provisions and accounts payable), such as promissory notes and corporate bonds
• Liabilities and assets for current tax
• Deferred tax liabilities and deferred tax assets
• Unearned revenue for services paid for by customers, but not yet provided
• Equity
• The net assets shown by the balance sheet equals the third part of the balance sheet, which is known as the shareholders’ equity. It comprises:
• Issued capital and reserves attributable to equity holders of the parent company (controlling interest)
• Non-controlling interest in equity
• Formally, shareholders’ equity is part of the company’s liabilities: they are funds “owing” to shareholders (after payment of all other liabilities). Usually, however, “liabilities” is used in the more restrictive sense of liabilities excluding shareholders’ equity. The balance of assets and liabilities (including shareholders’ equity) is not a coincidence. Records of the values of each account in the balance sheet are maintained using a system of accounting known as double-entry bookkeeping. In this sense, shareholders’ equity by construction must equal assets minus liabilities, and are a residual.
• Regarding the items in equity section, the following disclosures are required:
• Numbers of shares authorized, issued and fully paid, and issued but not fully paid
• Par value of shares
• Reconciliation of shares outstanding at the beginning and the end of the period
• Description of rights, preferences, and restrictions of shares
• Treasury shares, including shares held by subsidiaries and associates
• Shares reserved for issuance under options and contracts
• A description of the nature and purpose of each reserve within owners’ equity

Lenders and investors will require such statements to structure or confirm compliance with debt covenants such as debt service reserve coverage and debt to equity ratios. Similarly, when a new corporation is envisioned, its founders will prepare pro forma financial statements for the information of prospective investors. Pro forma figures should be clearly labeled as such and the reason for any deviation from reported past figures clearly explained.

4.4.2: Balance Sheet Analysis

Balance sheet analysis is process of understanding the risk and profitability of a firm through analysis of reported financial information.

Learning Objective

Analyze a company’s balance sheet

Key Points

• Balance sheet is a summary of the financial balances of a sole proprietorship, a business partnership, a corporation or other business organization. Assets, liabilities and ownership equity are listed as of a specific date, such as the end of its financial year.
• Balance sheet analysis (or financial analysis) the process of understanding the risk and profitability of a firm (business, sub-business or project) through analysis of reported financial information, particularly annual and quarterly reports.
• Financial ratio analysis should be based on regrouped and adjusted financial statements. Two types of ratio analysis are performed: 3.1) Analysis of risk and 3.2) analysis of profitability.
• Balance sheet analysis consists of 1) reformulating reported Balance sheet, 2) analysis and adjustments of measurement errors, and 3) financial ratio analysis on the basis of reformulated and adjusted Balance sheet.

Key Terms

RNOA

return on net operating assets

NFD

net financial debt

NFIR

the net financial interest rate

Balance sheet

In financial accounting, a balance sheet or statement of financial position is a summary of the financial balances of a sole proprietorship, a business partnership, a corporation or other business organization. Assets, liabilities and ownership equity are listed as of a specific date, such as the end of its financial year. A balance sheet is often described as a “snapshot of a company’s financial condition”. Of the four basic financial statements, the balance sheet is the only statement which applies to a single point in time of a business’ calendar year.

A business operating entirely in cash can measure its profits by withdrawing the entire bank balance at the end of the period, plus any cash in hand. However, many businesses are not paid immediately; they build up inventories of goods and they acquire buildings and equipment. In other words: businesses have assets and so they cannot, even if they want to, immediately turn these into cash at the end of each period. Often, these businesses owe money to suppliers and to tax authorities, and the proprietors do not withdraw all their original capital and profits at the end of each period. In other words businesses also have liabilities.

Balance Sheet

An example of a classified balance sheet.

Balance sheet analysis

Balance sheet analysis (or financial analysis) the process of understanding the risk and profitability of a firm (business, sub-business or project) through analysis of reported financial information, particularly annual and quarterly reports.

Balance sheet analysis consists of 1) reformulating reported Balance sheet, 2) analysis and adjustments of measurement errors, and 3) financial ratio analysis on the basis of reformulated and adjusted Balance sheet. The two first steps are often dropped in practice, meaning that financial ratios are just calculated on the basis of the reported numbers, perhaps with some adjustments. Financial statement analysis is the foundation for evaluating and pricing credit risk and for doing fundamental company valuation.

Financial ratio analysis should be based on regrouped and adjusted financial statements. Two types of ratio analysis are performed: 3.1) Analysis of risk and 3.2) analysis of profitability:

3.1) Analysis of risk typically aims at detecting the underlying credit risk of the firm. Risk analysis consists of liquidity and solvency analysis. Liquidity analysis aims at analyzing whether the firm has enough liquidity to meet its obligations when they should be paid. A usual technique to analyze illiquidity risk is to focus on ratios such as the current ratio and interest coverage. Cash flow analysis is also useful. Solvency analysis aims at analyzing whether the firm is financed so that it is able to recover from a losses or a period of losses.

3.2) Analysis of profitability refers to the analysis of return on capital, for example return on equity, ROE, defined as earnings divided by average equity. Return on equity, ROE, could be decomposed: ROE = RNOA + (RNOA – NFIR) * NFD/E

Purposes of balance sheet analysis

“The objective of financial statements is to provide information about the financial position, performance and changes in financial position of an enterprise that is useful to a wide range of users in making economic decisions. ” Financial statements should be understandable, relevant, reliable and comparable. Reported assets, liabilities, equity, income and expenses are directly related to an organization’s financial position.

Financial statements are intended to be understandable by readers who have “a reasonable knowledge of business and economic activities and accounting and who are willing to study the information diligently. ” Financial statements may be used by users for different purposes:

• Owners and managers require financial statements to make important business decisions that affect its continued operations. Financial analysis is then performed on these statements to provide management with a more detailed understanding of the figures. These statements are also used as part of management’s annual report to the stockholders.
• Employees also need these reports in making collective bargaining agreements (CBA) with the management, in the case of labor unions or for individuals in discussing their compensation, promotion and rankings.
• Prospective investors make use of financial statements to assess the viability of investing in a business. Financial analyses are often used by investors and are prepared by professionals (financial analysts), thus providing them with the basis for making investment decisions.
• Financial institutions (banks and other lending companies) use them to decide whether to grant a company with fresh working capital or extend debt securities (such as a long-term bank loan or debentures) to finance expansion and other significant expenditures.
• Government entities (tax authorities) need financial statements to ascertain the propriety and accuracy of taxes and other duties declared and paid by a company.
• Vendors who extend credit to a business require financial statements to assess the creditworthiness of the business.
• Media and the general public are also interested in financial statements for a variety of reasons.

4.5: Building a Cash Budget

4.5.1: Receipts

Forecasting incoming cash flows via receipts is a useful tool for organizations to determine the amount of cash that will be available on hand.

Learning Objective

Learn what organizational assets can be considered cash receivables, and understand how to forecast these receivables

Key Points

• Forecasting receipts is an important responsibility in corporate finance, as predicting cash on hand is critical in ensuring that organizations can invest their capital in a meaningful way.
• Receipts and disbursements are the two inputs of cash flow forecasting, particularly in the short term. Receipts include accounts receivable, interest on short-term investments, and the sale of assets.
• In the shorter term, predicting receipts is largely a process of compiling existing established contractual agreements. In the longer term, receipts can be predicted through understanding trends and growth over time.

Key Terms

disbursements

Money paid out or spent.

Receipts

Potential sources of incoming cash over a given time frame.

Why Forecast Receipts?

The broader field of cash flow forecasting is integral to ensuring organizational liquidity. Maintaining cash receipts over a given time frame enables organizations to have cash at hand in a predictable fashion, thus allowing them to reinvest in business operations to avoid the opportunity cost of having unused cash and cash receivables. Forecasting cash inflows and outflows in advance is a primary role of corporate financiers and accountants, and enables efficient use of existing assets to capture maximum competitive value in the marketplace.

Cash Receipts and Disbursements (R&D)

The direct method of projecting incoming cash flow is through understanding cash receipts and disbursements of the time period being projected. 

Receipts

Receipts generally refer to the collection of accounts receivable, which are the payments of paying customers over time. Receipts also refer to the returns off of short-term investments as well as the sale of various assets. There are other potential incoming cash flows that also fall under receipts, which are worth noting on a case by case basis.

Disbursements

On the inverse side of receipts, disbursements are outgoing cash flows during a short-term business operation. These can quite accurately project accounts payable, payroll costs, dividend payments, interest payments, and other short-term alterations to existing cash flow. By comparing receipts with disbursements, the overall available cash flow can be derived.

How to Forecast Receipts

As with all forecasting, shorter term forecasts are more certain than longer term forecasts (in general). Short term forecasts can be quite accurate, as the various accounts receivable, accounts payable, short-term investments and short-term costs are often relatively established (contractually and operationally). In shorter term situations, most forecasting is done through implementing what is known with the probability that these obligations will be met.

With longer term forecasting, it can be useful to consider past averages over time. Larger organizations can look at their average cash receipts over the past few years, and couple that with growth trajectories to project what level of cash inflow is likely over a given time frame. It’s important to keep in mind that forecasts are only estimations, and organizations should be aware of the error margins involved.

Normal Distributions

When creating a forecast utilizing past data, it is important to recognize the degree of certainty that can be reasonably applied to this forecast. By creating a normalized distribution, and identifying the percentage likelihood of a certain outcome, organizations can better prepare for all likely outcomes.

When creating a forecast utilizing past data, it is important to recognize the degree of certainty that can be reasonably applied to this forecast. By creating a normalized distribution, and identifying the percentage likelihood of a certain outcome, organizations can better prepare for all likely outcomes.

4.5.2: Payments

Cash payments describe cash flowing out of a business resulting from operating activities, investment activities and financing activities.

Learning Objective

Analyze a company’s disbursement cycle

Key Points

• Cash payments must be made for relevant expenses, which include those to suppliers for inventory or other supplies, employees for wages, government for taxes, and lenders for interest on borrowed money.
• A company’s objective in regards to the cash dispersement cycle should be to increase the cycle time, or delay making payments until they are due.
• Typical cash outflows from investing activities include purchase of capital assets, purchase of bonds/notes or shares of other entities, and loans to other entities.
• Typical cash outflows from financing activities include payments of dividends to the company’s own shareholders, redemption (repurchase) of company’s own shares, and repayment of principal and interest on company’s own bonds or notes.

Key Term

disbursement

Money paid out or spent.

Why is cash flow forecasting important? If a business runs out of cash and is not able to obtain new financing, it will become insolvent. It is no excuse for management to claim that they didn’t see a cash flow crisis coming. So in business, “cash is king”.

Cash Payments

Cash payments describe cash flowing out of a business. These cash payments can result from operating activities, investment activities and financing activities.

Generally speaking, normal operating activities refer to the cash effects of transactions involving revenues and expenses that impact net income. Cash payments must be made for relevant expenses. Typical payments include those to:

• Suppliers for inventory or other supplies
• Employees for wages
• Government for taxes
• Lenders for interest on borrowed money

Typical cash outflows from investing activities include:

• Purchase of capital assets
• Purchase of bonds/notes or shares of other entities
• Loans to other entities

Typical cash outflows from financing activities include:

• Payments of dividends to the company’s own shareholders
• Redemption (repurchase) of company’s own shares
• Repayment of principal and interest on company’s own bonds or notes

Sample Paystub

This is an example of a paystub to an employee, one of the most significant cash disbursements necessary for a company.

Disbursement Cycle

The cash disbursement cycle is important to consider when analyzing cash payments. This is the total time between when an obligation occurs and when the payment clears the bank. A company’s objective regarding the cash disbursement cycle should be to increase the cycle time, or delay making payments until they are due. A firm may delay payments by:

1. Mailing checks from locations not close to customers. This will increase the mail time, or mail float, within the disbursement cycle.
2. Disbursing checks from a remote bank. This will increase the time required for the payment to clear the bank.
3. Purchasing with credit cards so that the time required for making payment is much longer. By using a credit card, you will receive a bill at the end of the month payable in 30 days. This creates more processing time or processing float.

Therefore, when a company manages cash flow cycles, it tries to control three types of float times:

1. Mail float, or the time spent for a payment in the mail.
2. Clearance float, or the time spent for a payment to clear the bank.
3. Processing float, or the time required to process cash flow transactions.

4.5.3: The Forecast Budget

Understanding cash and liquidity needs is critical for organizations to capture opportunities and ensure all profitable processes are funded.

Learning Objective

Understand the various methods of forecasting budgets, and the importance of doing so regularly

Key Points

• Liquidity, or the ability to have cash on hand when it is required, is critical to capturing opportunities and ensuring smooth operations.
• Forecasting budgets in advance enables organizations to project what cash will be required during a given operating time frame and to keep these resources available when necessary.
• For larger organizations, this is usually done at the departmental or operational level, projecting different budgets for different operational teams.
• There are a number of methods involved in forecast budgets, including the direct method, the adjusted net income method, and the accrual reversal method.

Key Terms

forecast

A projection of cash inflows and/or outflows.

liquidity

The ease of turning assets into cash.

The Purpose of Forecasting

Financial planning is a critical financial tool for funding profitable operations and dividing existing organizational assets optimally to pursue revenue maximization. The forecast budget will project what cash flows will be needed for each organizational process, and how those cash flows will be utilized over a fixed period of time. If there is a problem with liquidity during an operational period, it can result in huge opportunity costs (i.e. an organization being unable to capture an existing opportunity in the market).

How to Forecast

There are a number of ways to approach financial forecasting for a cash budget. A cash budget is all about liquidity, and therefore forecasting what available liquidity will be required over a given period is the primary input for forecasting budgets. There are a number of different approaches, though most of them rely on understanding the inputs required for various business operations.

The inputs include the following cash obligations during regular operations:

• Payroll
• Payment of accounts payable
• Dividends 
• Interest on debt
• Sourcing raw materials

It’s also worth noting that various cash inflows will occur during a given time period. For example, accounts receivable, short-term financing options, and various other sources of income may directly convert into usable capital. However, budgeting should either build these into the current budget forecast or utilize them during the next calculation of budgetary requirements.

The Direct Method

At its simplest, cash flow forecasting and budgeting can be computed directly based off of fixed information over a short time frame. This works particularly well for consistent businesses that run routine operations with limited risk-taking and diversification in process.

The Adjusted Net Income Method (ANI)

The adjusted net income method starts by calculating operating income (EBIT or EBITDA) and adding/subtracting short-term changes in the balance sheet, such as those that occur to inventories, payable, receivables and other short-term. This gives the organization some idea of what short-term cash flows are typically required during an operational period.

Pro-forma Balance Sheet

Pro-formas are financial statements created in advance as a projection or estimation of what that document will look like after the financial period is finished. By using a pro-forma balance sheet for the upcoming period being budgeted for, the short-term assets and liabilities (if accurately projected) will underline the amount of cash that should be set aside for budgeting purposes.

Accrual Reversal Method

A third option for projecting cash budgets is accrual reversal. This process relies on statistical distributions, reversing large accruals, and projecting cash effects via algorithms. This method requires a good deal of data and statistical skill, and is best utilized for mid-term forecasting (unlike the direct method, which is much better for a shorter time frame). The advantage of this method is that it is often accurate to the day or week, enabling high accuracy.

Budget Forecast Example

This chart demonstrates a forecast budget to the reality of what actually occurred. Budgeting is an estimation, often adjustments over time.

This chart demonstrates a forecast budget to the reality of what actually occurred. Budgeting is an estimation, often adjustments over time.

4.6: Analyzing Forecasts

4.6.1: Ratio Analysis and EPS

Ratio analysis and EPS are used to compare the strengths and weaknesses of various companies with industry or company benchmarks.

Learning Objective

Classify the different type of financial ratios

Key Points

• Financial analysts use financial ratios to compare the strengths and weaknesses in various companies.
• Financial ratios quantify many aspects of a business and are an integral part of the financial statement analysis. Financial ratios are categorized according to the financial aspect of the business which the ratio measures.
• Earnings per share (EPS) is the amount of earnings per each outstanding share of a company’s stock.

Key Terms

Diluted EPS

Diluted Earnings Per Share (diluted EPS) is a company’s earnings per share (EPS) calculated using fully diluted shares outstanding (i.e. including the impact of stock option grants and convertible bonds).

Preferred dividends

Preferred stock usually carries no voting rights, but may carry a dividend and may have priority over common stock in the payment of dividends and upon liquidation.

Financial Accounting Standards Board (FASB)

The Financial Accounting Standards Board (FASB) is a private, not-for-profit organization whose primary purpose is to develop generally accepted accounting principles (GAAP) within the United States in the public’s interest.

Example

• If preferred dividends total $100,000, then that is money not available to distribute to each share of common stock.

Ratio Analysis

A financial ratio (or accounting ratio) is a relative magnitude of two selected numerical values taken from an enterprise’s financial statements. Often used in accounting, there are many standard ratios used to try to evaluate the overall financial condition of a corporation or other organization. Financial ratios may be used by managers within a firm, by current and potential shareholders (owners) of a firm, and by a firm’s creditors. Financial analysts use financial ratios to compare the strengths and weaknesses in various companies. If shares in a company are traded in a financial market, the market price of the shares is used in certain financial ratios.

Values used in calculating financial ratios are taken from the balance sheet, income statement, statement of cash flows or (sometimes) the statement of retained earnings. These comprise the firm’s “accounting statements” or financial statements. The statements’ data is based on the accounting method and accounting standards used by the organization.

Financial ratios quantify many aspects of a business and are an integral part of the financial statement analysis. Financial ratios are categorized according to the financial aspect of the business which the ratio measures .

Ratio analysis

Ratio analysis includes profitability ratios, activity (efficiency) ratios, debt ratios, liquidity ratios and market (value) ratios

Liquidity ratios:

Liquidity ratios measure the availability of cash to pay

debt

.

Current ratio (Working Capital Ratio): Current assets / Current liabilities

Acid-test ratio (Quick ratio): (Current assets – Inventory – Prepayments) / Current liabilities

Activity ratios:

Activity ratios measure how quickly a firm converts non-cash assets to cash assets.

Average collection period: Accounts receivable / (Annual credit sales / 365 days)

Average payment period: Accounts payable / (Annual credit purchases / 365 days)

Inventory conversion ratio: 365 days / Inventory turnover

Cash Conversion Cycle: Inventory conversion period + Receivables conversion period – Payables conversion period

Debt ratios

Debt ratios measure the firm’s ability to repay long-term debt.

Debt ratio: Total liabilities / Total assets

Times interest earned ratio (Interest Coverage Ratio): EBIT / Annual interest expense

Profitability
ratios

Profitability ratios measure the firm’s use of its assets and control of its expenses to generate an acceptable rate of

return

.

Gross margin, Gross profit margin or Gross Profit Rate: Gross profit / Net sales

Profit margin, net margin or net profit margin: Net profit / Net sales

Return on equity (ROE): Net income / Average shareholders equity

Return on assets (ROA ratio or Du Pont Ratio): Net income / Average total assets

Market ratios

Market ratios measure

investor

response to owning a company’s stock and also the cost of issuing stock. These are concerned with the

return on

investment

for shareholders, and with the relationship between return and the value of an investment in company’s shares.

Earnings per share (EPS): Net earnings / Number of shares

Payout ratio: Dividends / Earnings

P/E ratio: Market price per share / Diluted EPS

Ratios generally are not useful unless they are benchmarked against something else, like past performance or another company. Thus, the ratios of firms in different industries, which face different risks, capital requirements, and competition are usually hard to compare.

Earnings per share (EPS)

Earnings per share (EPS) is the amount of earnings per each outstanding share of a company’s stock. In the United States, the Financial Accounting Standards Board (FASB) requires companies’ income statements to report EPS for each of the major categories of the income statement: continuing operations, discontinued operations, extraordinary items, and net income.

The EPS formula does not include preferred dividends for categories outside of continued operations and net income. Earnings per share for continuing operations and net income are more complicated in that any preferred dividends are removed from net income before calculating EPS. This is because preferred stock rights have precedence over common stock.

Earnings Per Share (Basic Formula):

Earnings per Share = Profit / Weighted average common shares

Ratios generally are not useful unless they are benchmarked against something else, like past performance or another company. Thus, the ratios of firms in different industries, which face different risks, capital requirements, and competition are usually hard to compare.

4.6.2: Impacts of Forecasting on a Business

Since actual business activities are planned in relation to forecasting, it is very important that realistic expectations and estimations be undertaken.

Learning Objective

Describe how forecasting can help a business improve its operations

Key Points

• Business planning and forecasting refers to the set of activities where business operations are planned against the business strategy.
• Forecasting financial statements comprises the estimation of several values – including sales, costs, and expected interest rates.
• It is always easier to forecast future performance of a business if your business is already up and running because there are past trading results to look at.
• Forecasting can be used in Supply Chain Management to make sure that the right product is at the right place at the right time.
• On a broader level, economic forecasting is the process of making predictions about the economy as a whole.

Key Terms

supply chain management

Supply chain management (SCM) is the management of a network of interconnected businesses involved in the provision of product and service packages required by the end customers in a supply chain.

inflation

In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.

Egain Forecasting

a method of controlling building heating by calculating demand for heating energy that should be supplied to the building in each time unit.

Example

• The financial and economic crisis that erupted in 2007 – arguably the worst since the Great Depression of the 1930’s – was not foreseen by most of the forecasters, even if a few lone analysts had been crying wolf for some time (for example, Nouriel Roubini and Robert Shiller).

Business planning and forecasting refers to the set of activities where business operations are planned against the business strategy, and what forecast activities or results may occur from operational execution during a particular time period. In preparing financial forecasts, firms should always assume they will be reviewed by a bank manager, regulatory agency, or investor. With this goal in mind, the firm should be guided to keep forecasts tidy and easy to understand by grouping cash inflows and outflows in simple ways that are easy to understand quickly.

Forecasting financial statements comprises the estimation of several values – including sales, costs, and expected interest rates. Since actual business activities are planned in relation to these estimations, it is very important that realistic expectations and estimations be undertaken. With this in mind, there are specific points of interest to lenders and investors that need to be addressed. The profitability of a business reflects a sound relationship between market-driven sales projections and accurate cost estimates.

• Have you planned to have sufficient cash to meet your regular bills and also non-regular costs (like annual insurance premiums)?
• Does the financial position of the business remain sound when growth is forecast (this is what the balance sheet is for)?
• Is there a sensible balance between borrowings and the amount contributed by the owner (when the business is raising capital in its own right)?
• Are short and long-term obligations matched with relevant finance options?
• Do key business ratios remain within sensible bounds?

It is always easier to forecast future performance of a business when the business is already up and running because there are past trading results to look at. When a completely new venture is being planned a certain amount of imagination and estimation is required. However, this is in no way a license to be overly optimistic.

Forecasting has applications in many situations and impacts multiple aspects of a business. One such aspect is Supply Chain Management. Forecasting can be used in Supply Chain Management to make sure that the right product is at the right place at the right time. Accurate forecasting will help retailers reduce excess inventory and therefore increase the profit margin. Accurate forecasting will also help them meet consumer demand. On a broader level, economic forecasting is the process of making predictions about the economy as a whole. Forecasts can be carried out at a high level of aggregation — for GDP, inflation, unemployment or the fiscal deficit — or at a more disaggregated level — for specific sectors of the economy or even specific firms .

Economic Impact

Studies on the economic impact of business operations should be taken into account when forecasting financial statements and business activities. For example, a mining company may take into account a study such as the one pictured here.

Other important areas of forecasting include:

• Egain Forecasting
• Land use forecasting
• Player and team performance in sports
• Political Forecasting
• Product forecasting
• Sales Forecasting
• Technology forecasting
• Telecommunications forecasting
• Transport planning and Transportation forecasting
• Weather forecasting

4.6.3: Regression Analysis for Forecast Improvement

Regression Analysis is a causal / econometric forecasting method that is widely used for prediction and forecasting improvement.

Learning Objective

Explain how regression analysis works

Key Points

• Regression Analysis is a causal / econometric forecasting method. Some forecasting methods use the assumption that it is possible to identify the underlying factors that might influence the variable that is being forecast.
• Regression analysis includes several classical assumptions.
• Regression analysis includes many techniques for modeling and analyzing several variables when the focus is on the relationship between a dependent variable and one or more independent variables.
• A large body of techniques for carrying out regression analysis has been developed. Familiar methods, such as linear regression and ordinary least squares regression, are parametric.

Key Terms

Ordinary least squares regression

In statistics, ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model. This method minimizes the sum of squared vertical distances between the observed responses in the dataset and the responses predicted by the linear approximation.

linear regression

In statistics, linear regression is an approach to modeling the relationship between a scalar dependent variable y and one or more explanatory variables denoted X.

independent

not contingent or depending on something else

Example

• One can forecast based on linear relationships. If one variable is linearly related to the other for a long enough period of time, it may be beneficial to predict such a relationship in the future.

Regression Analysis

Regression Analysis is a causal / econometric forecasting method. Some forecasting methods are based on the assumption that it is possible to identify underlying factors that might influence a variable that is being forecast. For example, including information about weather conditions might improve the ability of a model to predict umbrella sales. This is a model of seasonality that shows a regular pattern of up and down fluctuations. In addition to weather, seasonality can also result from holidays and customs such as predicting that sales in college football apparel will be higher during football season as opposed to the off season.

Regression analysis includes a large group of methods that can be used to predict future values of a variable using information about other variables. These methods include both parametric (linear or non-linear) and non-parametric techniques.

Classical assumptions for regression analysis include:

• The sample is representative of the population for the inference prediction.
• The error is a random variable with a mean of zero conditional on the explanatory variables.
• The independent variables are measured with no error. (Note: If this is not so, modeling may be performed instead, using errors-in-variables model techniques).
• The predictors are linearly independent, i.e. it is not possible to express any predictor as a linear combination of the others.
• The errors are uncorrelated, that is, the variance– co-variance matrix of the errors is diagonal, and each non-zero element is the variance of the error.
• The variance of the error is constant across observations (homoscedasticity). (Note: If not, weighted least squares or other methods might instead be used).

In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.

Regression analysis

Regression analysis shows the relationship between a dependent variable and one or more independent variables.

Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables — that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by a probability distribution.

Forecast Improvement

Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables is related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However, this can lead to illusions or false relationships, so caution is advisable.

A large body of techniques for carrying out regression analysis has been developed. Familiar methods, such as linear regression and ordinary least squares regression, are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional.

The performance of regression analysis methods in practice depends on the form of the data generating process and how it relates to the regression approach being used. Since the true form of the data-generating process is generally not known, regression analysis often depends to some extent on making assumptions about this process. These assumptions are sometimes testable if a large amount of data is available. Regression models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally. However, in many applications, especially with small effects or questions of causality based on observational data, regression methods give misleading results.

4.6.4: Impact of Modifying Inputs on Business Operations

Modifying inputs such as accounts receivable, inventory, and accounts payable will significantly influence forecasting and business operations.

Learning Objective

Explain how modifying different inputs will influence financial forecasts

Key Points

• Accounts receivable has a great effect on a firm’s expected cash inflows, and thus modifying this input on a forecast will affect how much cash a company decides to have on hand.
• Because of its prevalence as an expense, modifying the amount of inventory will have far reaching consequences on all forecasted financial statements.
• Accounts payable will influence the current liabilities of a business; therefore, its modification will change a company’s perspective on the amount of cash-on-hand needed.

Key Terms

forecast

An estimation of a future condition.

solvency

The state of having enough funds or liquid assets to pay all of one’s debts; the state of being solvent.

liquidity

Availability of cash over short term: ability to service short-term debt.

Example

• For example, 2%,30 Net 31 terms mean that the payor will deduct 2% from the invoice if payment is made within 30 days. If the payment is made on Day 31 then the full amount is paid.

Inputs

The inputs of accounts receivable, inventory, accounts payable, and other line items on financial statements provide important data for financial forecasting. Modifying any one of these inputs can lead to major changes in forecasts. Similarly, drastic differences in expected values and actual values in regard to these inputs can cause problems for a company, possibly even leading to insolvency.

Accounts Receivable

Accounts receivable is money owed to a business by its customers and shown on its balance sheet as an asset. It is one of a series of accounting transactions dealing with the billing of a customer for goods and services that the customer has ordered. A business must not only anticipate the level of sales that will be made on credit, but it must also anticipate when payment on these accounts will occur and account for the fact that some of these credit accounts will default. Accounts receivable has a great effect on a firm’s expected cash inflows, and thus modifying this input on a forecast will affect how much cash a company decides to have on hand.

Inventory

Inventory management is primarily about specifying the scope and percentage of stocked goods. It is required at different locations within a facility or within many locations of a supply network to precede the regular and planned course of production and stock of materials. The scope of inventory management concerns the fine lines between replenishment lead time, carrying costs of inventory, asset management, inventory forecasting, inventory valuation, inventory visibility, future inventory price forecasting, physical inventory, available physical space for inventory, quality management, replenishment, returns and defective goods, and demand forecasting. Balancing these competing requirements leads to optimal inventory levels, which is an on-going process as the business needs shift and react to the wider environment.

Companies that rely on the sale of physical goods — i.e., those that must carry inventory — must manage inventory in such as way as to decrease expenses as much as possible. Since inventory is such a prevalent expense, accurate forecasting is of the utmost importance. Moreover, the modification of this particular input will have expansive effects on all of the financial statements a firm must forecast.

Inventory

Inventory management is a modifying input that can impact financial forecasts

Accounts Payable

Accounts payable is money owed by a business to its suppliers and is shown on its balance sheet as a liability. Commonly, a supplier will ship a product, issue an invoice, and collect payment later, which describes a cash conversion cycle. This is the period of time during which the supplier has already paid for raw materials but hasn’t been paid in return by the final customer.

Accounts payable will influence the current liabilities of a business, which will accordingly influence the liquidity of the business. A major requirement for a business to continue its operations is for that business to maintain solvency. Modifying accounts payable will drastically change the amount of cash-on-hand required for a business.

3.3: Profitability Ratios

3.3.1: Operating Margin

Learning Objective

Calculate a company’s operating margin

Key Points

• The operating margin equals operating income divided by revenue.
• The operating margin shows how much profit a company makes for each dollar in revenue. Since revenues and expenses are considered ‘operating’ in most companies, this is a good way to measure a company’s profitability.
• Although It is a good starting point for analyzing many companies, there are items like interest and taxes that are not included in operating income. Therefore, the operating margin is an imperfect measurement a company’s profitability.

Key Term

operating income

Revenue – operating expenses. (Does not include other expenses such as taxes and depreciation).

Operating Margin

The financial job of a company is to earn a profit, which is different than earning revenue. If a company doesn’t earn a profit, their revenues aren’t helping the company grow. It is not only important to see how much a company has sold, it is important to see how much a company is making.

The operating margin (also called the operating profit margin or return on sales) is a ratio that shines a light on how much money a company is actually making in profit. It is found by dividing operating income by revenue, where operating income is revenue minus operating expenses .

Operating margin formula

The operating margin is found by dividing net operating income by total revenue.

The higher the ratio is, the more profitable the company is from its operations. For example, an operating margin of 0.5 means that for every dollar the company takes in revenue, it earns $0.50 in profit. A company that is not making any money will have an operating margin of 0: it is selling its products or services, but isn’t earning any profit from those sales.

However, the operating margin is not a perfect measurement. It does not include things like capital investment, which is necessary for the future profitability of the company. Furthermore, the operating margin is simply revenue. That means that it does not include things like interest and income tax expenses. Since non-operating incomes and expenses can significantly affect the financial well-being of a company, the operating margin is not the only measurement that investors scrutinize. The operating margin is a useful tool for determining how profitable the operations of a company are, but not necessarily how profitable the company is as a whole.

3.3.2: Profit Margin

Learning Objective

Calculate a company’s net and gross profit margin

Key Points

• Profit margin is the profit divided by revenue.
• There are two types of profit margin: gross profit margin and net profit margin.
• A higher profit margin is better for the company, but there may be strategic decisions made to lower the profit margin or to even have it be negative.

Key Terms

gross profit

The difference between net sales and the cost of goods sold.

net profit

The gross revenue minus all expenses.

Profit Margin

Profit margin is one of the most used profitability ratios. Profit margin refers to the amount of profit that a company earns through sales.

The profit margin ratio is broadly the ratio of profit to total sales times 100%. The higher the profit margin, the more profit a company earns on each sale.

Since there are two types of profit (gross and net), there are two types of profit margin calculations. Recall that gross profit is simply the revenue minus the cost of goods sold (COGS). Net profit is the gross profit minus all other expenses. The gross profit margin calculation uses gross profit and the net profit margin calculation uses net profit . The difference between the two is that the gross profit margin shows the relationship between revenue and COGS, while the net profit margin shows the percentage of the money spent by customers that is turned into profit.

Net Profit Margin

The percentage of net profit (gross profit minus all other expenses) earned on a company’s sales.

Gross Profit Margin

The percentage of gross profit earned on the company’s sales.

Companies need to have a positive profit margin in order to earn income, although having a negative profit margin may be advantageous in some instances (e.g. intentionally selling a new product below cost in order to gain market share).

The profit margin is mostly used for internal comparison. It is difficult to accurately compare the net profit ratio for different entities. Individual businesses’ operating and financing arrangements vary so much that different entities are bound to have different levels of expenditure. Comparing one business’ arrangements with another has little meaning. A low profit margin indicates a low margin of safety. There is a higher risk that a decline in sales will erase profits and result in a net loss or a negative margin.

3.3.3: Return on Total Assets

Learning Objective

Calculate a company’s return on assets

Key Points

• ROA is net income divided by total assets.
• The ROA is the product of two common ratios: profit margin and asset turnover.
• A higher ROA is better, but there is no metric for a good or bad ROA. An ROA depends on the company, the industry and the economic environment.
• ROA is based on the book value of assets, which can be starkly different from the market value of assets.

Key Terms

net income

Gross profit minus operating expenses and taxes.

asset

Something or someone of any value; any portion of one’s property or effects so considered.

Return
on Assets

The return on assets ratio (ROA) is found by dividing net income by total assets. The higher the ratio, the better the company is at using their assets to generate income. ROA was developed by DuPont to show how effectively assets are being used. It is also a measure of how much the company relies on assets to generate profit.

Return on Assets

The return on assets ratio is net income divided by total assets. That can then be broken down into the product of profit margins and asset turnover.

Components of ROA

ROA can be broken down into multiple parts. The ROA is the product of two other common ratios – profit margin and asset turnover. When profit margin and asset turnover are multiplied together, the denominator of profit margin and the numerator of asset turnover cancel each other out, returning us to the original ratio of net income to total assets.

Profit margin is net income divided by sales, measuring the percent of each dollar in sales that is profit for the company. Asset turnover is sales divided by total assets. This ratio measures how much each dollar in asset generates in sales. A higher ratio means that each dollar in assets produces more for the company.

Limits of ROA

ROA does have some drawbacks. First, it gives no indication of how the assets were financed. A company could have a high ROA, but still be in financial straits because all the assets were paid for through leveraging. Second, the total assets are based on the carrying value of the assets, not the market value. If there is a large discrepancy between the carrying and market value of the assets, the ratio could provide misleading numbers. Finally, there is no metric to find a good or bad ROA. Companies that operate in capital intensive industries will tend to have lower ROAs than those who do not. The ROA is entirely contextual to the company, the industry and the economic environment.

3.3.4: Basic Earning Power (BEP) Ratio

Learning Objective

Calculate a company’s Basic Earning Power ratio

Key Points

• The higher the BEP ratio, the more effective a company is at generating income from its assets.
• Using EBIT instead of operating income means that the ratio considers all income earned by the company, not just income from operating activity. This gives a more complete picture of how the company makes money.
• BEP is useful for comparing firms with different tax situations and different degrees of financial leverage.

Key Terms

EBIT

Earnings before interest and taxes. A measure of a business’s profitability.

Return on Assets

A measure of a company’s profitability. Calculated by dividing the net income for an accounting period by the average of the total assets the business held during that same period.

BEP Ratio

Another profitability ratio is the Basic Earning Power ratio (BEP). The purpose of BEP is to determine how effectively a firm uses its assets to generate income.

The BEP ratio is simply EBIT divided by total assets . The higher the BEP ratio, the more effective a company is at generating income from its assets.

Basic Earnings Power Ratio

BEP is calculated as the ratio of Earnings Before Interest and Taxes to Total Assets.

This may seem remarkably similar to the return on assets ratio (ROA), which is operating income divided by total assets. EBIT, or earnings before interest and taxes, is a measure of how much money a company makes, but is not necessarily the same as operating income:

EBIT = Revenue – Operating expenses+

Non-operating

income

Operating income = Revenue – Operating expenses

The distinction between EBIT and Operating Income is non-operating income. Since EBIT includes non-operating income (such as dividends paid on the stock a company holds of another), it is a more inclusive way to measure the actual income of a company. However, in most cases, EBIT is relatively close to Operating Income.

The advantage of using EBIT, and thus BEP, is that it allows for more accurate comparisons of companies. BEP disregards different tax situations and degrees of financial leverage while still providing an idea of how good a company is at using its assets to generate income.

BEP, like all profitability ratios, does not provide a complete picture of which company is better or more attractive to investors. Investors should favor a company with a higher BEP over a company with a lower BEP because that means it extracts more value from its assets, but they still need to consider how things like leverage and tax rates affect the company.

3.3.5: Return on Common Equity

Learning Objective

Calculate the Return on Equity (ROE) for a business

Key Points

• ROE is net income divided by total shareholders’ equity.
• ROE is also the product of return on assets (ROA) and financial leverage.
• ROE shows how well a company uses investment funds to generate earnings growth. There is no standard for a good or bad ROE, but a higher ROE is better.

Key Term

equity

Ownership, especially in terms of net monetary value, of a business.