12.4: Scenario and Simulation Assessments

12.4.1: Sensitivity Analysis

Learning Objective

Describe how sensitivity analysis is used to make investment decisions

Key Points

• Since variations from the base assumptions are expected, businessmen and women want to know how much their output (eg., revenue) will be affected by the variations.
• Sensitivity analysis helps find the optimal levels for inputs (eg., raw material prices, number of employees, sales price) .
• Sensitivity analysis is a statistical tool based on seeing how inputs and parameters affect outputs. Generally, each input is changed one at a time to see how it affects output. However, this does not account for interconnectedness between inputs; they may not be independent variables.

Key Terms

sensitivity analysis

the study of how the uncertainty in the output of a mathematical model or system can be apportioned to different sources of uncertainty in its inputs

parameter

A variable kept constant during an experiment, calculation, or similar.

Capital budgeting is, by definition, forward looking. When dealing with expected resources and demands, uncertainty is a major factor. Sensitivity analysis is a statistical tool that determines how consequential deviations from the expected value occur. Sensitivity Analysis deals with finding out the amount by which we can change the input data for the output of our linear programming model to remain comparatively unchanged. This helps us in determining the sensitivity of the data we supply for the problem. It also helps to determine the optimal levels of each input.

Sensitivity analysis can be useful for a number of reasons, including:

• Support decision making or the development of recommendations for decision makers (e.g., testing the robustness of a result).
• Enhance communication from modelers to decision makers (e.g., by making recommendations more credible, understandable, compelling or persuasive).
• Increase understanding or quantification of the system (e.g., understanding relationships between input and output variables).
• Model development (e.g., searching for errors in the model).

In order to conduct a sensitivity analysis, all of the inputs and parameters are connected via an algorithm to produce the output. For example, a model of the inputs and parameters for a company interest in creating a new product may include information about expected availability of raw material, inflation rates, and number of employees working in R&D. The output would be the profit generated by the new product. The sensitivity analysis entails changing each variable and seeing how that changes the output . Generally, only one variable is changed at once, with all of the others fixed at their base value. This makes it easy to see how much a variable affects the output. However, not all of the inputs may be independent so changing inputs one at a time does not account for interaction between the inputs.

Sensitivity of a Variable

Sensitivity analysis determines how much an output is expected to change due to changes in a variable or parameter. In this case, the output (y-axis) decreases exponentially with an increase in the input (x-axis). This is mapped out for each input.

12.4.2: Scenario Analysis

Learning Objective

Explain scenario analysis is used by investors

Key Points

• Scenario analysis is designed to see the consequences of an action under different sets of factors. For example, it shows how an investment’s NPV would differ under high and low inflation.
• Scenarios should be feasible enough to provide an accurate picture of the outcomes. A “good” scenario for an investor should not include winning the lottery because, though good, it is neither probable nor realistic for analyzing possible results.
• Many scenario analyses use 3 scenarios: base case, worst case and best case. However, the number and conditions of the scenarios in each analysis can vary.

Key Terms

scenario analysis

a process of analyzing possible future events by considering alternative possible outcomes

analysis

A process of dismantling or separating into constituent elements in order to study the nature, function, or meaning.

scenario

A set of factors that can affect the consequences of an action. The environment.

Scenario Analysis

Scenario analysis is a strategic process of analyzing decisions by considering alternative possible outcomes (sometimes called “alternative worlds”). It is not a predictive mechanism, but rather an analytic tool to manage uncertainty today. .

Scenario Analysis

This scenario analysis shows how changes in factors like yield and transport cost can affect profits.

For example, a firm might use scenario analysis to determine the net present value (NPV) of a potential investment under high and low inflation scenarios.

In another example, a bank might attempt to forecast several possible scenarios for the economy (e.g. rapid vs. moderate vs. slow growth) or it might try to forecast financial market returns (for bonds, stocks and cash) in each of those scenarios. Perhaps, it might also consider sub-sets of each of the possibilities. It might further seek to determine correlations and assign probabilities to the scenarios (and sub-sets if any). By analyzing these various scenarios, the bank will be in a better position to consider how best to allocate its assets.

Many scenario analyses use three different scenarios: base case, worst case and best case. The base case is the expected scenario: if all things proceed normally, this is what the expected outcome will be. The worst and best cases are obviously scenarios with less and more favorable conditions, but they are still confined by a sense of feasibility. For example, an investor creating the worst case scenario would not be well served to have it include a meteor strike that destroys the company. While clearly a bad scenario, it is not realistic enough to be helpful.

The purpose of scenario analysis is not to identify the exact conditions of each scenario; it just needs to approximate them to provide a plausible idea of what might happen.

12.4.3: Monte Carlo Simulation

Learning Objective

Describe how Monte Carlo simulations are used

Key Points

• The statistical distribution is estimated for each input (eg. inflation rate, market risk). Then, simulations are run to see how constantly changing inputs (based on their distribution) affect the output. The outputs are averaged to find the estimated output.
• Monte Carlo simulations are great for when there are multiple inputs that can all change and may be unrelated.
• Monte Carlo simulations can be applied in many areas of business, such as bond pricing, but are especially useful when estimating the “base case” is difficult to do by hand.

Key Term

distribution

A probability distribution; the set of relative likelihoods that a variable will have a value in a given interval.

In order to account of complex, interconnected factors, all of which may affect financial outcomes, companies turn to statistical methods. The Monte Carlo method solves a problem by directly simulating the underlying process and then calculating the average result of the process. It simulates the various sources of uncertainty (eg. inflation, default risk, market changes, etc.) that affect the value of the instrument, portfolio, or investment in question, and calculates a representative value given these possible values of the underlying inputs. In essence, the Monte Carlo method is designed to find out what happens to the outcome on average when there are changes in the inputs.

Each potential factor is assigned a probability or statistical distribution. For example, the investor may estimate the probability of default on a bond as 20%. That means that 20% of the time, he will not earn back his principal. The investor may also estimate that the inflation rate is normally distributed around a mean of 3% and standard deviation of 0.5%.

The investor estimates the probability or distribution of every factor that could change the result of the investment. Then, he essentially uses the distributions to run many many simulations of all the inputs to see how they affect the output and then finds the average output .

Monte Carlo Simulation

By running many simulations based on the probability or distribution of an input (x), the analyst can see the average output (y). This is done for multiple inputs at once to find out how they affect the output.

For example, for bonds and bond options, under each possible evolution of interest rates the investor observes a different yield curve and a different resultant bond price. To determine the bond value, these bond prices are then averaged. To value the bond option, as for equity options, the corresponding exercise values are averaged and present valued. By determining the average, the investor can figure out what the expected value is.

The advantage of the Monte Carlo method is that it is able to handle multiple moving, and possible related, inputs. As the number of factors increases, it becomes harder to figure out the “base case. ” Statistical analysis through Monte Carlo simulations is great at handling problems with multiple, inter-related, and uncertain factors.

12.4.4: Decision Trees

Learning Objective

Describe how to set up a decision tree

Key Points

• Decision trees look similar to flow charts, except they are designed to pick the most optimal strategy.
• There are three types of nodes on a decision tree: decision nodes, chance nodes, and end nodes.
• Decision trees are solved from top to bottom in order to determine the most optimal strategy. Sometimes, there may not be an obvious optimal strategy, but the tree is still useful for mapping out the options faced and their costs/benefits.

Key Term

node

A vertex point on a decision tree. Other branches may extend from it; if none do, it is an end node.

A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. They help to identify the strategy that is most likely to reach the declared goal. For an investor, this may be used to help determine which bond to buy in order to get the highest expected return with only a certain amount of risk. Decision trees are set up much like an organizational flow chart.

Decision Tree

This decision tree highlights the outcomes of different investing strategies. Next to the terminal nodes is blue text with the yield and gain.

Unlike a flow chart, a decision tree consists of three types of nodes:

1. Decision nodes – commonly represented by squares – the user gets to decide which branch to take.
2. Chance nodes – represented by circles – the branch taken is determined by probabilities.
3. End nodes – represented by triangles – there are no more branches extending from the node, and the final value of the strategy is listed.

In order to set up and use a decision tree, the user must first list each decision point. For example, in , the investor first listed the number of investments that could be made (1, 2, or 3) and then the options for the likely payoffs (optimistic, most likely, etc.). Each end node was given a value. Working from left to right (or top to bottom), the investor determined that making one investment has the highest expected value ($641,500 vs. $0). Therefore, the investor will definitely choose to make one investment. Then, to determine the payoff, the probabilities and yields are listed. This is a chance node, so the investor doesn’t know how much he will earn from the investment, but does know his options.

Decision trees can become very complex, so determining the correct strategy becomes more difficult. Decision trees are always solved from the top to the bottom (or left to right) and is just a process of picking the most optimal path or seeing the likely payoffs.

There may not be an idea strategy shown on the decision tree. In that case, the decision tree is still useful as a way to map out all of the possible strategies with their costs and benefits.

12.5: Factors Impacting Capital Budgeting

12.5.1: Risk Adjusting the Discount Rate

Discount rates are adjusted on an investment to investment basis, as different investments encounter different degrees of risk that must be considered when determining equitable returns.

Learning Objective

Realize the reasoning behind adjusting discount rates for risk, and the way this impacts the cost of capital

Key Points

• In central banking, the established discount rate will act as the benchmark for future interest rates issued. This cost will be adjusted on an investment to investment basis depending upon the degree of risk.
• Discount rates are utilized in net present value calculations (NPV) in order to determine the rate of risk and return a new venture or new project should provide.
• Calculating NPV is an extremely useful tool. An NPV analysis will take future expectations of cost and revenue and ground them in present day dollars (to take into account the time value of money). This shows if/when a project will be profitable.
• When adjusting the NPV calculation for additional risks, and thus risk-adjusting the discount rate, a variety of factors can be taken into consideration. A rNPV (risk-adjusting NPV) will assign a probability to each incoming cash flow to adjust expectations of risk in the calculation.

Key Term

discounted cash flow

An estimated future cash flow discounted by the probability of receiving that cash flow.

What is the Discount Rate?

The discount rate has a few definitions, depending on the context. For the sake of this discussion, the discount rate is the percentage used in an net present value calculation to understand the overall cost of capital (or, from the perspective of some investors, the required return) on a given project. What this means is that there is a rate, calculated by the assumption of risk, which is used to normalize the interest rate on borrowed capital (for the borrower) and/or invested capital (for the lender.

In U.S. central banking, the interest rate that banks pay the federal reserve when using securities as collateral is also referred to as the discount rate, and in this case it will act as the benchmark for future interest rates issued. 

Why Adjust for Risk?

The primary purpose of a discount rate, or an interest rate in general, is fairly simple. Capital today is worth more than capital tomorrow, due to the time value of money (i.e. the opportunity cost of foregone investments). As a result of this concept, the idea of interest rates is justified. All this means is that a borrower of capital will have to take into account the cost of that capital over a given time period, which will be calculated as an additional percentage of the overall principal borrowed being added to the principal itself on a period to period basis.

In this context, the interest rate is subjected to risk. A riskier investment will require a higher return (due to the basic premise of risk and return). After all, why invest in a riskier investment when safer investments exist unless that riskier investment offers a higher percentage of return? It is at this point that the logic behind adjusting discount rates becomes practical. All discount rates must take into account the overall risk being assumed in the investment, and adjust the rate of expected return to meet the implications of the overall risk over time. For banks, for example, the overall interest rate they would offer a risky entrepreneurial project isn’t the same as the rate they would offer an established big business.

Risk-adjusted Net Present Value

A net present value calculation is a common and useful tool that takes the overall future projected costs and returns of a new venture or business project and grounds it in today’s dollars. What this means is it calculates out the time value of money during the projected time period of the financing of the project in order to see if the returns over a given time period will exceed the costs in beginning the project. As an entrepreneur, this will tell you if/when you will reach profitability (using a variety of assumptions). It is calculated as follows:

Adjusting this for the risk-adjusted discount rate is a simple modification, where each future cash flow is multiplied by the estimated likelihood of its occurrence. In this situation, a higher degree of uncertainty (and thus risk) is built into each expected cash flow (called a discounted cash flow, or DCF). Through discounting each cash flow by the estimated probability of receiving that return, the overall riskiness of the NPV calculation is increased. With this increase in risk, the discount rate can now be risk-adjusted accordingly.

Common Risk-adjusted Discount Rates

It is important to note at this point that every calculation is different, and some start-ups will see low discount rates because investors believe strongly in what the start up is trying to accomplish. However, the discount rates typically applied to different types of companies show significant differences:

• Early start-ups: 40–60%
• More established start-ups: 30–50%
• Mature companies: 10–25%

All and all, investors must carefully consider the risk in a given investment, and adjust the discount rates accordingly. This ensures a proper assessment of the risk and return ratio for various differentiated investment projects.

Discounting Curves

This chart illustrates the devaluation of capital over time as a result of various discount rates.

This chart illustrates the devaluation of capital over time as a result of various discount rates.

12.5.2: Risk Adjusting for the Time Horizon

A longer time horizon usually requires a higher return, due to increased price volatility and uncertainty relating to possible outcomes.

Learning Objective

Explain how an investement’s duration can influence its inherent risk

Key Points

• In terms of debt investments, default risk increases as the time horizon lengthens.
• Since stock investments have more time to overcome potential downturns in value, having a longer time horizon can justify more aggressive investing.
• When there are multiple possible outcomes, management of a firm may choose to undertake real options analysis in order to factor in the various possibilities.

Key Terms

salvage value

The estimated value of an asset at the end of its useful life.

time horizon

The period of time the asset is expected to be held or a project is expected to last.

Risk Adjusting for the Time Horizon

When evaluating the riskiness of an investment, not only will investors or companies need to evaluate their preferences and risk tolerance, but it is also necessary to take into account the time horizon of the investment. A longer time horizon will generally require a higher return, due to an increased risk in price volatility and increased uncertainty relating to possible outcomes. In terms of long term debt investments, such as long term corporate or government bonds, a longer time horizon gives rise to uncertainties in the potential operations of the debtor entity as well as unforeseen movements in the market as a whole. In other words, default risk increases as the time horizon lengthens. However, when considering stock investments, having a longer time horizon can be considered safer in some respects. Since stock investments have more time to overcome potential downturns in value, having a longer time horizon can justify more aggressive investing. For example, an individual investor with a time horizon of less than five years should not be invested in stocks. However, those with time horizons over five years should consider stocks because of their growth potential. Put simply, as time horizon lengthens a higher percentages of stocks should be added to a portfolio.

Performance of Stocks, Bonds and Bills

This graph gives an illustration of investing a dollar in different asset classes in the market from 1926 to the end of 2007.

For an individual, diversifying investments in different time horizons is also important. By staying in the market through different market cycles, individuals can reduce the risk of receiving a lower return than expected–especially with investments that fluctuate significantly over the short term.

Real Options Consideration

When there are multiple possible outcomes, management of a firm may choose to undertake real options analysis in order to factor in the various possibilities. A real option itself is the right, but not the obligation, to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. When uncertainty exists as to when and how business or other conditions will eventuate, flexibility as to the timing of the relevant project is valuable and constitutes optionality. Some examples include Inflation or deferment options, where management has flexibility as to when to start a project. For example, in natural resource exploration a firm can delay mining a deposit until market conditions are favorable. Also, an option to abandon, where management may have the option to cease a project during its life, and, possibly, to realize its salvage value. Here, when the present value of the remaining cash flows falls below this salvage value, the asset may be sold. Finally, sequencing options, where management can observe outcomes from a part of a project and resolve some of the uncertainty relating to the venture overall. Once resolved, management has the option to proceed or not with the development of the other projects.

12.6: Other Considerations in Capital Budgeting

12.6.1: Other Considerations in Capital Budgeting

The real option creates economic value by generating future decision rights for management.

Learning Objective

Describe how options influence capital budgeting and investment decisions

Key Points

• Traditional NPV analysis fails to consider that management can adapt and revise its strategies in response to unexpected market and technological developments that cause cash flows to deviate from their original expectations.
• The notion of real options was developed from the idea that one can view firms’ discretionary investment opportunities as a call option on real assets, in much the same way as a financial call option provides decision rights on financial assets.
• The option to defer an investment creates value because exogenous uncertainty can be reduced with the passage of time.
• Growth options are investments made not only for immediate cash flows from the project, but also for the economic value derived from subsequent investment opportunities.

Key Terms

propensity

A tendency, preference, or attraction.

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

Real Options and Capital Budgeting

Traditional capital budgeting theory holds that investments should be made when the simple net present value (NPV) of an investment opportunity equals or exceeds zero. It also assumes that the investment must be made either now or never. However, such an investment approach fails to consider that management can adapt and revise its strategies in response to unexpected market and technological developments that cause cash flows to deviate from their original expectations. In other words, it fails to capture managers’ flexibility in adapting their decisions to evolving market and technological uncertainty. The notion of real options was developed from the idea that one can view firms’ discretionary investment opportunities as a call option on real assets, in much the same way as a financial call option provides decision rights on financial assets.

A simple financial option gives its holder the right, but not the obligation, to buy or sell a specified quantity of an underlying asset at a specified price at or before a specified date. By analogy, a real option confers on the firm the right, but not the obligation, to take some action in the future. The option is “real” because the underlying assets are usually physical and human assets rather than financial securities. The commonality in applying option-pricing models for real assets and for financial securities is that the future is uncertain. In an uncertain environment, having the flexibility to decide what to do after some of that uncertainty is resolved has value. A key feature is that the real option creates economic value by generating future decision rights – specifically, by offering management the flexibility to act upon new information such that the upside economic potential is retained while the downside losses are contained .

Project Cash Flow With Uncertainty

Projects with real options can be evaluated using a range of possible profits.

Real Options and Investment Decisions

A strategic implication of real options theory is that investment will be discouraged by exogenous uncertainty. For this reason, the timing of an investment can be crucial in determining its profitability. In other words, the option to defer an investment creates value because exogenous uncertainty can be reduced with the passage of time.

Another value-creating aspect of real options can be found in abandonment. The abandonment options comes into play when a firm purchases an asset that it may later resell or put to an alternative use, should future conditions be sufficiently adverse. Availability and recognition of this option will increase a firm’s propensity to invest relative to what would be suggested by a simple NPV rule, which assumes that the investment project continues for its physical lifetime and omits the possibility of future divestment.

Growth Options

Real investments are often made not only for immediate cash flows from the project, but also for the economic value derived from subsequent investment opportunities. Such future discretionary investment opportunities are known as growth options. For example, firms usually undertake research and development investments to strategically position themselves for the economic value from commercialization when market conditions turn favorable. Similarly, firms usually make foothold investments in a new foreign market for the possibility of expansion in the future. Such growth-oriented investment may appear uneconomical when viewed in isolation but may enable firms to capture future growth opportunities.

11.4: Net Present Value

11.4.1: Defining NPV

Learning Objective

Define Net Present Value

Key Points

• Because of the time value of money, cash inflows and outflows only can be compared at the same point in time.
• NPV discounts each inflow and outflow to the present, and then sums them to see how the value of the inflows compares to the other.
• A positive NPV means the investment is worthwhile, an NPV of 0 means the inflows equal the outflows, and a negative NPV means the investment is not good for the investor.

Key Terms

cash outflow

Any cash that is spent or invested by the investor.

cash inflow

Cash that is received by the investor. For example, dividends paid on a stock owned by the investor is a cash inflow.

Every investment includes cash outflows and cash inflows. There is the cash that is required to make the investment and (hopefully) the return.

In order to see whether the cash outflows are less than the cash inflows (i.e., the investment earns a positive return), the investor aggregates the cash flows. Since cash flows occur over a period of time, the investor knows that due to the time value of money, each cash flow has a certain value today . Thus, in order to sum the cash inflows and outflows, each cash flow must be discounted to a common point in time.

Airplane

Before purchasing a new airplane, airlines evaluate the NPV of the plan by calculating the PV of the revenue it can earn from it and the PV of its cost (e.g., purchase cost, maintenance, fuel, etc. ).

The net present value (NPV) is simply the sum of the present values (PVs) and all the outflows and inflows:

NPV = PV_Inflows+ PV_Outflows

Don’t forget that inflows and outflows have opposite signs; outflows are negative.

Also recall that PV is found by the formula
where FV is the future value (size of each cash flow), i is the discount rate, and t is the number of periods between the present and future. The PV of multiple cash flows is simply the sum of the PVs for each cash flow.

The sign of NPV can explain a lot about whether the investment is good or not:

• NPV > 0: The PV of the inflows is greater than the PV of the outflows. The money earned on the investment is worth more today than the costs, therefore, it is a good investment.
• NPV = 0: The PV of the inflows is equal to the PV of the outflows. There is no difference in value between the value of the money earned and the money invested.
• NPV < 0: The PV of the inflows is less than the PV of the outflows. The money earned on the investment is worth less today than the costs, therefore, it is a bad investment.

11.4.2: Calculating the NPV

Learning Objective

Calculate a project’s Net Present Value.

Key Points

• Cash inflows have a positive sign, while cash outflows are negative.
• To find the NPV accurately, the investor must know the exact size and time of occurrence of each cash flow. This is easy to find for some investments (like bonds), but more difficult for others (like industrial machinery).
• Investors use different rates for their discount rate such as using the weighted average cost of capital, variable rates, and reinvestment rate.

Key Terms

cash flow

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

variable

something whose value may be dictated or discovered.

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.

Calculating the NPV

The NPV of an investment is calculated by adding the PVs (present values) of all of the cash inflows and outflows . Cash inflows (such as coupon payments or the repayment of principal on a bond) have a positive sign while cash outflows (such as the money used to purchase the investment) have a negative sign.

Net Present Value (NPV) Formula

NPV is the sum of of the present values of all cash flows associated with a project. The business will receive regular payments, represented by variable R, for a period of time. This period of time is expressed in variable t. The payments are discounted using a selected interest rate, signified by the i variable.

The accurate calculation of NPV relies on knowing the amount of each cash flow and when each will occur. For securities like bonds, this is an easy requirement to meet. The bond clearly states when each coupon payment will occur, the size of each payment, when the principal will be repaid, and the cost of the bond. For other investments, this is not so simple to determine. When a new piece of machinery is purchased, for example, the investor (the purchasing company) has to estimate the size and occurrence of maintenance costs as well as the size and occurrence of the revenues generated by the machine.

The other integral input variable for calculating NPV is the discount rate. There are many methods for calculating the appropriate discount rate. A firm’s weighted average cost of capital after tax (WACC) is often used. Since many people believe that it is appropriate to use higher discount rates to adjust for risk or other factors, they may choose to use a variable discount rate.

Another approach to selecting the discount rate factor is to decide the rate that the capital needed for the project could return if invested in an alternative venture. If, for example, the capital required for Project A can earn 5% elsewhere, use this discount rate in the NPV calculation to allow a direct comparison to be made between Project A and the alternative. Related to this concept is to use the firm’s reinvestment rate. Reinvestment rate can be defined as the rate of return for the firm’s investments on average, which can also be used as the discount rate.

11.4.3: Interpreting the NPV

Learning Objective

Interpret a series of net present value calculations

Key Points

• When inflows exceed outflows and they are discounted to the present, the NPV is positive. The investment adds value for the investor. The opposite is true when NPV is negative.
• A NPV of 0 means there is no change in value from the investment.
• In theory, investors should invest when the NPV is positive and it has the highest NPV of all available investment options.
• In practice, determining NPV depends on being able to accurately determine the inputs, which is difficult.

Key Term

cash flow

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

The NPV is a metric that is able to determine whether or not an investment opportunity is a smart financial decision. NPV is the present value (PV) of all the cash flows (with inflows being positive cash flows and outflows being negative), which means that the NPV can be considered a formula for revenues minus costs. If NPV is positive, that means that the value of the revenues (cash inflows) is greater than the costs (cash outflows). When revenues are greater than costs, the investor makes a profit. The opposite is true when the NPV is negative. When the NPV is 0, there is no gain or loss.

In theory, an investor should make any investment with a positive NPV, which means the investment is making money. Similarly, an investor should refuse any option that has a negative NPV because it only subtracts from the value. When faced with multiple investment choices, the investor should always choose the option with the highest NPV. This is only true if the option with the highest NPV is not negative. If all the investment options have negative NPVs, none should be undertaken.

The decision is rarely that cut and dry, however. The NPV is only as good as the inputs. The NPV depends on knowing the discount rate, when each cash flow will occur, and the size of each flow. Cash flows may not be guaranteed in size or when they occur, and the discount rate may be hard to determine. Any inaccuracies and the NPV will be affected, too .

Machinery

Being able to accurately find the NPV of a piece of machinery means having a good idea when all costs are going to occur (when it will need fixing) and when it will generate revenue (when it will be used on a job).

11.4.4: Advantages of the NPV method

Learning Objective

Describe the advantages of using net present value to evaluate potential investments

Key Points

• When NPV is positive, it adds value to the firm. When it is negative, it subtracts value. An investor should never undertake a negative NPV project.
• As long as all options are discounted to the same point in time, NPV allows for easy comparison between investment options. The investor should undertake the investment with the highest NPV, provided it is possible.
• An advantage of NPV is that the discount rate can be customized to reflect a number of factors, such as risk in the market.

Key Term

gain (or loss)

If an investment earns more value than it costs, the difference is the gain. If it costs more than it earns, the difference is a loss.

Calculating the NPV is a way investors determine how attractive a potential investment is. Since it essentially determines the present value of the gain or loss of an investment, it is easy to understand and is a great decision making tool.

When NPV is positive, the investment is worthwhile; On the other hand, when it is negative, it should not be undertaken; and when it is 0, there is no difference in the present values of the cash outflows and inflows. In theory, an investor should undertake positive NPV investments, and never undertake negative NPV investments . Thus, NPV makes the decision making process relatively straight forward.

NPV Decision Table

NPV simply and clearly shows whether a project adds value to the firm or not. It’s easy of use in decision making is one of its advantages.

Another advantage of the NPV method is that it allows for easy comparisons of potential investments. As long as the NPV of all options are taken at the same point in time, the investor can compare the magnitude of each option. When presented with the NPVs of multiple options, the investor will simply choose the option with the highest NPV because it will provide the most additional value for the firm. However, if none of the options has a positive NPV, the investor will not choose any of them; none of the investments will add value to the firm, so the firm is better off not investing.

Furthermore, NPV is customizable so that it accurately reflects the financial concerns and demands of the firm. For example, the discount rate can be adjusted to reflect things such as risk, opportunity cost, and changing yield curve premiums on long-term debt.

11.4.5: Disadvantages of the NPV method

Learning Objective

Discuss the disadvantages of using the NPV method

Key Points

• NPV is based on future cash flows and the discount rate, both of which are hard to estimate with 100% accuracy.
• There is an opportunity cost to making an investment which is not built into the NPV calculation.
• Other metrics, such as internal rate of return, are needed to fully determine the gain or loss of an investment.

Key Term

Opportunity cost

The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity); the most valuable forgone alternative.

There are a number of disadvantages to NPV. NPV is still commonly used, but firms will also use other metrics before making investment decisions.

The first disadvantage is that NPV is only as accurate as the inputted information. It requires that the investor know the exact discount rate, the size of each cash flow, and when each cash flow will occur. Often, this is impossible to determine. For example, when developing a new product, such as a new medicine, the NPV is based on estimates of costs and revenues . The cost of developing the drug is unknown and the revenues from the sale of the drug can be hard to estimate, especially many years in the future.

Medicine

Drug developers must try to calculate the future revenues of a drug in order to find the NPV to determine if it is worth the cost of development.

Furthermore, the NPV is only useful for comparing projects at the same time; it does not fully build in opportunity cost. For example, the day after the company makes a decision about which investment to undertake based on NPV, it may discover there is a new option that offers a superior NPV. Thus, investors don’t simply pick the option with the highest NPV; they may pass on all options because they think another, better, option may come along in the future. NPV does not build in the opportunity cost of not having the capital to spend on future investment options.

Another issue with relying on NPV is that it does not provide an overall picture of the gain or loss of executing a certain project. To see a percentage gain relative to the investments for the project, internal rate of return (IRR) or other efficiency measures are used as a complement to NPV.

11.4.6: NPV Profiles

Learning Objective

Describe the relationship between a project’s discount rate and its Net Present Value

Key Points

• The NPV Profile is a graph with the discount rate on the x-axis and the NPV of the investment on the y-axis.
• Higher discount rates mean cash flows that occur sooner are more influential to NPV. Since the earlier payments tend to be the outflows, the NPV profile generally shows an inverse relationship between the discount rate and NPV.
• The discount rate at which the NPV equals 0 is called the internal rate of return (IRR).

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.

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.

NPV Profiles

The NPV calculation involves discounting all cash flows to the present based on an assumed discount rate. When the discount rate is large, there are larger differences between PV and FV (present and future value) for each cash flow than when the discount rate is small. Thus, when discount rates are large, cash flows further in the future affect NPV less than when the rates are small. Conversely, a low discount rate means that NPV is affected more by the cash flows that occur further in the future.

The relationship between NPV and the discount rate used is calculated in a chart called an NPV Profile . The independent variable is the discount rate and the dependent is the NPV. The NPV Profile assumes that all cash flows are discounted at the same rate.

NPV Profile

The NPV Profile graphs how NPV changes as the discount rate used changes.

The NPV profile usually shows an inverse relationship between the discount rate and the NPV. While this is not necessarily true for all investments, it can happen because outflows generally occur before the inflows. A higher discount rate places more emphasis on earlier cash flows, which are generally the outflows. When the value of the outflows is greater than the inflows, the NPV is negative.

A special discount rate is highlighted in the IRR, which stands for Internal Rate of Return. It is the discount rate at which the NPV is equal to zero. And it is the discount rate at which the value of the cash inflows equals the value of the cash outflows.

11.5: Cash Flow Analysis and Other Factors

11.5.1: Cash Flow Factors

Cash flow factors are the operational, financial, or investment activities which cause cash to enter or leave the organization.

Learning Objective

Describe how cash flow factors can be used to improve or evaluate a business

Key Points

• Cash flow factors can be used to calculate parameters to measure organizational performance.
• Operational cash flows are those originating from the organization’s internal business.
• Financing cash flows are those originating from the issuance of debt or equity.
• Investment cash flows are those originating from assets and capital expenditures.

Key Terms

liquidity

Availability of cash over short term: ability to service short-term debt.

parameter

A variable kept constant during an experiment, calculation, or similar.

Definition

Cash flow is the movement of money into or out of a business, project, or financial product . It is usually measured during a specified, finite period of time. Measurement of cash flow can be used for calculating other parameters that give information on a company’s value and situation.

Cash

Cash flows reflect cash entering or leaving the organization.

Statement of Cash Flow in a Business’s Financial Statements

A business’s Statement of Cash Flows illustrates its calculated net cash flow. The net cash flow of a company over a period (typically a quarter or a full year) is equal to the change in cash balance over this period: It’s positive if the cash balance increases (more cash becomes available); it’s negative if the cash balance decreases. The total net cash flow is composed of several factors:

• Operational cash flows: Cash received or expended as a result of the company’s internal business activities. This includes cash earnings plus changes to working capital. Over the medium term, this must be net positive if the company is to remain solvent.
• Investment cash flows: Cash received from the sale of long-life assets or spent on capital expenditure, such as, investments, acquisitions, and long-life assets.
• Financing cash flows: Cash received from the issue of debt and equity, or paid out as dividends, share repurchases or debt repayments.

Uses

Cash flow factors can be used for calculating parameters, such as:

• to determine a project’s rate of return or value. The cash flows into and out of projects are used as inputs in financial models, such as internal rate of return and net present value.
• to determine problems with a business’s liquidity. Being profitable does not necessarily mean being liquid. A company can fail because of a shortage of cash even while profitable.
• as an alternative measure of a business’s profits when it is believed that accrual accounting concepts do not represent economic realities. For example, a company may be notionally profitable but generating little operational cash (as may be the case for a company that barters its products rather than selling for cash). In such a case, the company may be deriving additional operating cash by issuing shares or raising additional debt finance.
• can be used to evaluate the “quality” of income generated by accrual accounting. When net income is composed of large non-cash items, it is considered low quality.
• to evaluate the risks within a financial product (e.g., matching cash requirements, evaluating default risk, re-investment requirements, etc)

Cash flow is a generic term used differently depending on the context. It may be defined by users for their own purposes. It can refer to actual past flows or projected future flows. It can refer to the total of all flows involved or a subset of those flows.

11.5.2: Replacement Projects

A replacement project is an undertaking in which the company eliminates a project at the end of its life and substitutes another investment.

Learning Objective

Analyze a possible replacement projects to determine if it should be implemented

Key Points

• The cash flow analysis must take all cash flow components into account, such as opportunity costs and depreciation and maintenance expense.
• The replacement project’s cash flows are the additional inflows and outflows to be provided by the prospective replacement project.
• The comparison between the replacement and the current project informs the decision whether to undertake the replacement and, if applicable, at what point replacement should occur.

Key Terms

capital budgeting

The budgeting process in which a company plans its capital expenditure (the spending on assets of long-term value).

sunk cost

A cost that has already been incurred and which cannot be recovered to any significant degree.

Opportunity cost

The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity); the most valuable forgone alternative.

Definition

The possibility of replacement projects must be taken into account during the process of capital budgeting and subsequent project management. A replacement project is an undertaking in which the company eliminates a project at the end of its life and substitutes another investment. This replacement project can serve the purpose of replacing an expiring investment with a new, identical one, or replacing an existing investment that is producing unfavorable results with one that management believes will perform better.

When analyzing a project, and ultimately deciding whether it is a good investment decision or not, one focuses on the expected cash flows associated with the project. These cash flows form the basis for the project’s value, usually after implementing a method of discounted cash flow analysis. Most projects have a finite useful life. Analysis can be undertaken in order to determine when the optimum point of replacement will be, as well as if replacement is a viable option in the first place. To accomplish this, one analyzes the cash flows of the current project in relation to the expected cash flows from the replacement project .

Replacing a window sill vs. keeping the old one

Replacement project analysis tells a company whether the costs of a replacement project provide a suitable return on investment.

Analysis

The net cash flows for a project take into account revenues and costs generated by the project, along with more indirect implications, such as sunk costs, opportunity costs and depreciation costs related to the project. All of these considerations taken together allow management to consider the project’s incremental cash flows, which are inflows and outflows the project produces over predictable periods of time. Discounted cash flow analysis should be undertaken for both the existing project and the potential replacement project. These analyses can then be used to compare the expected profitability of both projects; which will, in theory, lead management to make the right decision regarding the investments.

In general, there will be some sort of cash inflow from ending the old project — for example, from the terminal value realized upon the sale of existing equipment — and a subsequent cash outflow to begin the new project. The loss of expected future cash flows from the previous project, or opportunity cost, must also be taken into account. A general form that can be used to analyze these cash flows is:

Increase in Net Income + (Depreciation on New Investment – Depreciation on Old Investment)

11.5.3: Sunk Costs

Sunk costs are retrospective costs that cannot be recovered, and are therefore irrelevant to future investment decisions in the project which incurs them.

Learning Objective

Identify sunk costs when making an investment decision

Key Points

• Only prospective costs should impact an investment decision. Therefore, sunk costs are not to be considered when deciding whether to undertake a project.
• A sunk cost is distinct from an economic loss. A loss may be caused by a sunk cost, however.
• Sunk costs are irrecoverable.

Key Term

retrospective

Affecting or influencing past things; retroactive.

Definition

Sunk costs are retrospective costs that have already been incurred and cannot be recovered. Sunk costs are sometimes contrasted with prospective costs, which are future costs that may be incurred or changed if an action is taken .

Sunk

Sunk costs are irrecoverable.

Impact on Investment Decision

The idea of sunk costs is often employed when analyzing business decisions. In traditional microeconomic theory, only prospective (future) costs are relevant to an investment decision. For example the research and development of a pharmaceutical are retrospective once it is time to market the product. Once spent, such costs are sunk and should have no effect on future pricing decisions. The company will charge market prices whether R&D had cost one dollar or one million dollars. Therefore, the costs of R&D are considered sunk once they are retrospective and irrecoverable. At that point, they have no rational bearing on further investment decisions.

Difference from Economic Loss

The sunk cost is distinct from economic loss. For example, when a car is purchased, it can subsequently be resold; however, it will probably not be resold for the original purchase price. The economic loss is the difference between these values (including transaction costs). The sum originally paid should not affect any rational future decision-making about the car, regardless of the resale value. If the owner can derive more value from selling the car than not selling it, then it should be sold, regardless of the price paid. In this sense, the sunk cost is not a precise quantity, but an economic term for a sum paid in the past, which is no longer relevant to decisions about the future. The sunk cost may be used to refer to the original cost or the expected economic loss. It may also be used as shorthand for an error in analysis due to the sunk cost fallacy, irrational decision-making or, most simply, as irrelevant data.

11.5.4: Opportunity Costs

Opportunity cost refers to the value lost when a choice is made between two mutually exclusive options.

Learning Objective

Identify opportunity costs when making an economic choice

Key Points

• Opportunity cost can be seen as the second-best choice available to an economic actor.
• Opportunity cost can be measured monetarily, or more subjectively in terms of pleasure or utility.
• Opportunity cost shows not only that resources are scarce, but also that economic choices are limited.

Key Terms

implicit costs

The opportunity cost equal to what a firm must give up in order to use factors which it neither purchases nor hires.

explicit costs

a direct payment made to others in the course of running a business, such as wage, rent and materials

Definition

Opportunity cost is the cost of any activity measured in terms of the value of the next best alternative forgone (that is not chosen). In other words, it is the sacrifice of the second best choice available to someone, or group, who has picked among several mutually exclusive choices. .

Alternative choices

Choosing one alternative means another is foregone.

Economic Concept

Opportunity cost is a key concept in economics; it relates the scarcity of resources to the mutually exclusive nature of choice. The notion of opportunity cost plays a crucial role in ensuring that scarce resources are allocated efficiently. Thus, opportunity costs are not restricted to monetary or financial costs: the real cost of output forgone, lost time, pleasure or any other benefit that provides utility are also considered implicit. or opportunity, costs. In the context of cash flow analysis, opportunity cost can be thought of as a cash flow that could be generated from assets the organization already owns, if they are not used for the project in question. There is always a trade-off between making decisions on the allocation of assets.

Assessing Opportunity Cost

Opportunity cost is assessed not only in monetary or material terms, but also in terms of anything which is of value to the decision maker. For example, a person who desires to watch each of two television programs being broadcast simultaneously, and cannot record one, can only watch one of the desired programs. Therefore, the opportunity cost of watching an NFL football game could be not enjoying the college football game, or vice versa.

Examples

In a restaurant situation, the opportunity cost of eating steak could be trying the salmon. The opportunity cost of ordering both meals could be twofold: the extra $20 to buy the second meal, and reputation with peers, as the diner may be thought of as greedy or extravagant for ordering two meals. A family might decide to use a short period of vacation time to visit Disneyland rather than doing household improvement work. The opportunity cost of having happier children could therefore be a remodeled bathroom.

In a job situation, a person could either choose to run their own bakery, or work as an employee for a restaurant. There are explicit costs on the line, such as the capital necessary to start a business, purchase of all the inputs, and so forth. However, there are possible implicit benefits, such as autonomy and freedom to be “your own boss”, and implicit costs, such as the stress of running your own business. If the individual chooses to run their own bakery, their opportunity costs are the salary that the restaurant would have paid, and the smaller burden of responsibility as an employee instead of an owner.

11.5.5: Externalities

An externality is an effect of an economic action, the cost or benefit of which is shouldered by someone outside the transaction.

Learning Objective

Explain how externalities can affect different parties to a transaction

Key Points

• An externality that is a cost is a negative externality, while one that is a benefit is a positive externality.
• Prices do not reflect externalities because they affect people outside the economic transaction.
• Negative externalities can lead to over-production, while positive externalities can lead to under-production. The former case occurs because the producer does not pay the external cost, while the latter occurs because the benefit is generated without profit.

Key Term

benefit

An advantage, help, or aid from something.

Definition

In economics, an externality is a cost or benefit that is not transmitted through prices and is incurred by a party who was not involved as either a buyer or seller of the goods or services. The cost of an externality is a negative externality , or external cost, while the benefit of an externality is a positive externality, or external benefit.

Pollution

Pollution is an example of a negative externality.

Relation to Prices

In the case of both negative and positive externalities, prices in a competitive market do not reflect the full costs or benefits of producing or consuming a product or service. Producers and consumers may neither bear all of the costs nor reap all of the benefits of the economic activity.

Over- and Under-Production

Standard economic theory states that any voluntary exchange is mutually beneficial to both parties involved in the trade. This is because buyers or sellers would not trade if either thought it was not beneficial.

However, an exchange can cause additional effects on third parties. Those who suffer from external costs do so involuntarily, while those who enjoy external benefits do so at no cost. A voluntary exchange may reduce total economic benefit if external costs exist. The person who is affected by the negative externalities in the case of air pollution will see it as lowered utility: either subjective displeasure or potentially explicit costs, such as higher medical expenses.

On the other hand, a positive externality would increase the utility of third parties at no cost to them. Since collective societal welfare is improved, but the providers have no way of monetizing the benefit, less of the good will be produced than would be optimal for society as a whole.

For example, manufacturing that causes air pollution imposes costs on the whole society, while public education is a benefit to the whole society. If there exist external costs such as pollution, the good will be overproduced by a competitive market, as the producer does not take into account the external costs when producing the good.

If there are external benefits, such as in areas of education, too little of the good would be produced by private markets as producers and buyers do not take into account the external benefits to others. Here, overall cost and benefit to society is defined as the sum of the economic benefits and costs for all parties involved.

“Free Rider” Problem

Positive externalities are often associated with the free rider problem. For example, individuals who are vaccinated reduce the risk of contracting the relevant disease for all others around them, and at high levels of vaccination, society may receive large health and welfare benefits. Conversely, any one individual can refuse vaccination, still avoiding the disease by “free riding” on the costs borne by others.

Market Correction

The market-driven approach to correcting externalities is to “internalize” third-party costs and benefits, for example, by requiring a polluter to repair any damage that they cause. But in many cases internalizing costs or benefits is not feasible, especially if the true monetary values cannot be determined.

11.5.6: Tax Rate

The tax rate is the amount of tax expressed as a percentage.

Learning Objective

Differentiate the different types of tax rates

Key Points

• The methods used to present a tax rate include: statutory, average, marginal, and effective rates.
• Statutory tax rates are those imposed by law.
• Average tax rate is the total tax liability divided by taxable income.
• Marginal tax rate is the rate at a specific level of spending or income. It is also known as tax “on the last dollar,” earned or spent.
• Effective tax rate describes when varying measures of tax are divided by varying measures of the tax base. It is inconsistently defined in practice.

Key Term

margin

Collateral that the holder of a financial instrument has to deposit to cover some or all of the credit risk of their counterparty.

Definition

In a tax system, the tax rate describes the ratio at which a business or person is taxed .

Tax Rate

The tax rate is a percentage of the taxable base.

Methods

There are several methods used to present a tax rate:

• statutory
• average
• marginal
• effective

Statutory

A statutory tax rate is the legally imposed rate. An income tax could have multiple statutory rates for different income levels, whereas a sales tax may have a flat statutory rate.

Average

An average tax rate is the ratio of the amount of taxes paid to the tax base (taxable income or spending). To calculate the average tax rate on an income tax, divide the total tax liability by the taxable income.

Marginal

A marginal tax rate is the tax rate that applies to the last dollar of the tax base (taxable income or spending) and is often applied to the change in one’s tax obligation as income rises.

For an individual, this rate can be determined by increasing or decreasing the income earned or spent and calculating the change in taxes payable. An individual’s tax bracket is the range of income for which a given marginal tax rate applies.

The marginal tax rate may increase or decrease as income or consumption increases, although in most countries the tax rate is progressive in principle. In such cases, the average tax rate will be lower than the marginal tax rate. For instance, an individual may have a marginal tax rate of 45%, but pay an average tax of half this amount.

In a jurisdiction with a flat tax on earnings, every taxpayer pays the same percentage of income, regardless of income or consumption. Some proponents of this system propose to exempt a fixed amount of earnings (such as the first $10,000) from the flat tax.

Marginal tax rates may be published explicitly, together with the corresponding tax brackets, but they can also be derived from published tax tables showing the tax for each income. It may be calculated by noting how tax changes with changes in pre-tax income, rather than with taxable income.

Effective

The term effective tax rate has significantly different meanings when used in different contexts or by different sources. Generally it means that some amount of tax is divided by some amount of income or other tax base. In U.S. income tax law, the term is used in relation to determining whether a foreign income tax on specific types of income exceeds a certain percentage of U.S. tax that might apply on such income.

The popular press, Congressional Budget Office, and various think tanks have used the term to refer to varying measures of tax divided by varying measures of income, with little consistency in definition. An effective tax rate may incorporate econometric, estimated, or assumed adjustments to actual data, or may be based entirely on assumptions or simulations. It also incorporates tax breaks or exemptions.

11.5.7: Depreciation

Depreciation is the process by which an asset is used up, and its cost is allocated over a period of time.

Learning Objective

Describe the relationship between allocation of cost and the matching principle when calculating depreciation

Key Points

• Fair value depreciation is an estimate of the market value of an asset.
• The cost of an asset that is to be allocated by depreciation is the amount paid for it minus any salvage value it will have at the end of its useful life.
• Methods used for apportioning the cost over a period of time include fixed percentage, straight-line, and declining balance.

Key Term

allocate

To distribute according to a plan.

Definition

Depreciation refers to two very different but related concepts: the decrease in value of assets (fair value depreciation), and the allocation of the cost of assets to periods in which the assets are used (depreciation with the matching principle).

Fair Value Depreciation

Fair value depreciation affects the values of businesses and entities. It is a concept used in accounting and economics, defined as a rational and unbiased estimate of the potential market price of a good, service, or asset, taking into account the amount at which the asset could be bought or sold in a current transaction between willing parties.

Allocation of Cost with Matching Principle

Depreciated value

Depreciation measures how much of an asset is used up in a certain amount of time.

The allocation of the cost of an asset to periods in which it is used up affects net income. Any business or income producing activity using tangible assets incurs costs related to those assets. In determining the net income from an activity, the receipts from the activity must be reduced by appropriate costs.

One such cost is the cost of assets used but not currently consumed in the activity. Such costs must be allocated to the period of use. Where the assets produce benefit in future periods, the matching principle of accrual accounting dictates that those costs must be deferred rather than treated as a current expense.

The business records depreciation expense as an allocation of such costs for financial reporting. The costs are allocated in a rational and systematic manner as a depreciation expense to each period in which the asset is used, beginning when the asset is placed in service.

Generally this involves four criteria:

• the cost of the asset
• the expected salvage value, also known as residual value of the asset
• the estimated useful life of the asset
• a method of apportioning the cost over such life.

The cost of an asset so allocated is the difference between the amount paid for the asset and the salvage value.

Methods

Depreciation is any method of allocating net cost to those periods expected to benefit from use of the asset. Generally the cost is allocated as a 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 may be specified in the accounting or tax rules of a country. Several standard methods of computing depreciation expense may be used, including:

• fixed percentage
• straight line
• declining balance method

Depreciation expense generally begins when the asset is placed in service. For instance, a depreciation expense of 100 dollars per year for 5 years may be recognized for an asset costing 500 dollars.

11.5.8: Elective Expensing

Section 179 of the IRS code allows some pieces of property to be expensed entirely when they are purchased, rather than depreciated.

Learning Objective

Summarize section 179 of the tax code and how it applies to businesses

Key Points

• Usually this provision applies to small businesses because there are limitations on what and how much property can be expensed.
• Though buildings were not originally eligible, a 2010 law included them.
• The total deduction for a year cannot exceed the person’s income for that year.

Key Term

deduction

A sum that can be removed from tax calculations; something that is written off.

Definition

Section 179 of the United States Internal Revenue Code (26 U.S.C. § 179) allows a taxpayer to elect to deduct the cost of certain types of property on their income taxes as an expense, rather than requiring the cost of the property to be capitalized and depreciated. This property is generally limited to tangible, depreciable, personal property which is acquired by purchase for use in the active conduct of a trade or business . This can afford considerable tax savings in some circumstances.

Property

Buildings were not eligible for section 179 deductions prior to the passage of the Small Business Jobs Act of 2010; however, qualified real property may now be deducted. Depreciable property that is not eligible for a section 179 deduction is still deductible over a number of years through MACRS depreciation according to sections 167 and 168. The 179 election is optional, and the eligible property may be depreciated according to sections 167 and 168 if preferable for tax reasons. Furthermore, the 179 election may be made only for the year the equipment is placed in use and is waived if not taken for that year. However, if the election is made, it is irrevocable unless special permission is given.

Limitations

The § 179 election is subject to three important limitations:

1. There is a dollar limitation. Under section 179(b)(1), the maximum deduction a taxpayer may elect to take in a year is 500,000 dollars in 2010 and 2011, 125,000 dollars in 2012, and 25,000 dollars for years beginning after 2012.
2. If a taxpayer places more than 2 million dollars worth of section 179 property into service during a single taxable year, the 179 deduction is reduced, dollar for dollar, by the amount exceeding the 2 million threshold. This threshold is further reduced to 500,000 dollars beginning in 2012, and then 200,000 dollars afterward.
3. Lastly, the section provides that a taxpayer’s 179 deduction for any taxable year may not exceed the taxpayer’s aggregate income from the active conduct of trade or business by the taxpayer for that year. If, for example, the taxpayer’s net trade or business income from active conduct of trade or business was 72,500 dollars in 2006, then the deduction cannot exceed 72,500 dollars that year. However, any deduction not allowed in a given year under this limitation can be carried over to the next year.

Truck

Expensing is applied to property used in a business, such as trucks.

10.4: The WACC

10.4.1: Weighted Average Cost of Capital

Learning Objective

Derive the weighted average cost of capital 

Key Points

• The weighted average cost of capital (WACC) is a calculation that allows firms to understand the overall costs of acquiring financing.
• Capital inputs generally come in the form of debt and equity. Debt is usually quite simple to calculate as it is set in the terms of bonds and loans explicitly.
• Equity is a bit more complex, as it is subjected to market (systematic) risk. The capital asset pricing model is a useful tool in estimating the cost of equity.
• Applying the WACC to the estimated rate of return for new projects and ventures is a simple way to determine if a project is sufficiently profitable to offset the cost (risk) of financing.

Key Term

weighted average cost of capital

A calculation of the overall cost of capital used by an enterprise, made by totaling the cost of each source of capital used multiplied by its proportional share of the total capital used.

Weighted Average Cost of Capital Defined

Organizations have a few options available when it comes to finding funding for their operations. From debt options such as taking out loans or offering long-term corporate bonds to equity such as preferred and common stock, larger organizations tend to find a balance between these options that is optimized for the best possible weighted average cost of capital (WACC) to operate at the scale that creates the best revenue opportunity.

In short, the WACC is a measure of what all of these capital inputs will cost the organization in terms of an average interest rate. 

Why Calculate WACC?

WACC is a useful calculation, as it shows management what the cost of borrowing capital is overall. This overall cost of capital can then be a minimum required return on any new operation. For example, if it will cost 8% in capital costs to fund a project that creates 10% in profit, the organization can confidently borrow capital to fund this project. If the project would only turn 8% profit, the firm would have a difficult decision. If the project would turn 6% profit, it is quite easy to strategically argue against the new project.

How to Calculate WACC

Calculating the cost of capital is actually quite a simple equation. Most firms are only receiving from either debt or equity (though there can be quite few inputs to each of these subheadings). What this means is that the overall percentage of the business that is funded by debt (MV_d/MV_d + MV_e) must be multiplied by the cost of debt (R_d),  while similarly the percent funding of equity (MV_e/MV_d + MV_e) must be multiplied by the cost of equity (R_e) and added together. This can also be applied to the corporate tax rate in a given country of operation. This is written out as follows:

The cost of debt is usually fixed, based on the terms of a given bond or loan contract. As a result, the cost of debt is usually both certain and predictable. The cost of equity is a little bit more complex, as it is speculative and often determined (to some degree) by investor behavior. The capital asset pricing model (CAPM) is a traditional approach to determining the cost of equity:

Each of the variables here are defined as:

• E_s – expected return
• R_f – expected risk-free return
• β_s – sensitivity to market risk
• R_m -historical return
• (R_m – R_f) – risk premium of market assets over risk free assets.

By calculating the estimated cost of equity, and applying that to the WACC equation with the cost of debt and capital structure, organizations can determine the cost of capital (and thus the required return on projects/assets).

Weighted Average Cost of Capital Tree

This diagram is an excellent illustration of how various forms of debt and equity consolidate into broader calculation of debt and equity overall, and how those can combine as a total weighted average cost of capital.

This diagram is an excellent illustration of how various forms of debt and equity consolidate into broader calculation of debt and equity overall, and how those can combine as a total weighted average cost of capital.

10.4.2: The Weightings

Learning Objective

Define how a company’s weighted average cost of capital is weighted

Key Points

• The WACC must take into account the weight of each component of a company’s capital structure.
• The calculation of the WACC usually uses the market values of the various components rather than their book values.
• Market value is the price at which an asset would trade in a competitive auction setting.
• Book value refers to the value of an asset according to the account balance present on the balance sheet of a company.
• If the value of a company’s debt exceeds the value of its equity, the cost of its debt will have more “weight” in calculating its total cost of capital than the cost of equity. If the value of the company’s equity exceeds its debt, the cost of its equity will have more weight.

Key Term

Synergy

Benefits resulting from combining two different groups, people, objects, or processes.

The Weightings

To calculate the weighted average cost of capital (WACC) we must take into account the weight of each component of a company’s capital structure. To review, the equation for WACC is:

MVe stands for the market value of equity; MVd stands for the Market Value of Debt; Re stands for cost of equity; Rd stands for cost of debt; and t is the company’s tax rate. If the person analyzing a company chooses or if the market value of a company’s debt and equity is not available, the book value can be used.

The “weighting” varies based on how the company finances its activities. If the value of a company’s debt exceeds the value of its equity, the cost of its debt will have more “weight” in calculating its total cost of capital than the cost of equity. If the value of the company’s equity exceeds its debt, the cost of its equity will have more weight.

Market Value vs. Book Value

Since we are measuring expected cost of new capital, the calculation of weighted average cost of capital usually uses the market values of the various components rather than their book values. These may differ significantly.

Market value is the price at which an asset would trade in a competitive auction setting. It is the true underlying value of an asset according to theoretical standards. It is a distinct concept from market price, which is the price at which one can transact. For market price to equal market value, the market must be efficient and rational. Market value also requires the element of “special value” to be disregarded. Special value refers to a synergy that may exist between two parties that makes the fair price of a transaction higher.

Book value refers to the value of an asset according to the account balance present on the balance sheet of a company. The balance sheet is a summary of the financial balances of a company and is often described as a “snapshot of a company’s financial condition. “

An asset’s initial book value is its actual cash value or its acquisition cost. Cash assets are recorded or “booked” at actual cash value. Assets such as buildings, land, and equipment are valued based on their acquisition cost, which includes the actual cash cost of the asset, plus certain costs tied to the purchase of the asset, such as broker fees.

Domestic Balance Sheet

If the person analyzing a company chooses or if the market value of a company’s debt and equity is not available, the book value can be used. The book value of debt and equity can be found on the company’s balance sheet.

10.4.3: Factors Controlled by the Firm

Learning Objective

Recognize the strategic considerations of capital structure by understanding weighted average cost of capital and the internal rate of return

Key Points

• By understanding the weighted average cost of capital (WACC) and potential internal rates of return (IRR) of various projects, firms can have some strategic control of capital costs and investment returns.
• Each funding source will come with a different cost of capital. Averaging these funding sources into the WACC is a central tool for financial management.
• Once the costs of capital are optimized, a business can apply this cost of capital to various asset and project assessments. The IRR must exceed the WACC.

Key Term

capital structure

The way that a corporation finances its assets through some combination of equity, debt, and hybrid securities.

When pursuing financing, organizations encounter a variety of factors that impact the weighted average cost of capital. Some of these factors are within the firm’s strategic control, while others are external forces outside the firm’s control. As a financial professional or upper level strategist, understanding what capital structure options are available to a firm plays a critical role in financial management.

Capital Structure

Capital structure refers to the way in which an organization finances operations. This is generally illustrated via a balance sheet, where the overall assets are offset by the capital structure of liabilities and equity. It is through the decisions to acquire various forms of debt and equity that an organization can derive a weighted average cost of capital (WACC) that is sustainable within the context of organizational profitability. If the cost of capital is higher than the returns from those investments, the organization lacks the profitability required to justify itself. WACC is calculated as follows:

In the above equation, the first segment is measuring the cost of equity coupled with the percentage of the capital structure that is funded by equity. The second segment is making the same calculation, but this time with the cost of debt and the relative percentage of capital structure which is funded via this source. The final segment (1 – t) is the application of a corporate tax rate (depending on the country of operation. 

Understanding the cost of each input of the capital structure, firms can control (to some degree) how they fund their operations and acquisitions of assets.

Internal Rate of Return

Another important decision made by financial professionals in relation to the cost of capital revolves around the required rates of return of various projects. Investing capital into an operation always incurs the opportunity cost of investing in something else. As a result, organizations can control their operations by measuring and projecting the rate of return on each project, and investing strategically in the most profitable projects.

An internal rate of return (IRR) calculation can be useful when doing this. The IRR is going to look at the net present value (NPV) of a given project, and calculate it for a break even point (i.e. set the equation to zero, when taking cost into account). By doing so, the organization can identify the anticipated rate of return on the project. take a look at the equation below:

In this equation, n is the number of periods in a project (i.e. number of anticipated cash flows over the life of the project), C is the cash flow amount (which can vary for each period, hence the summation), r is the rate of return being solved for, and N is total number of periods (n). When solving for zero, the organization will identify what the rate of return is for each project. Deciding upon projects that provide returns greater than the WACC derived from the capital structure will set the organization down a profitable path (assuming forecasts are reliable!).

Exclusive_investments.png

When weighed different projects over time, the IRR calculation can be useful in determining which investment of capital is best over the lifetime of each project. When taking the WACC into account (derived from capital structure decisions), the organization can measure operational options against the required rate of return.

When weighed different projects over time, the IRR calculation can be useful in determining which investment of capital is best over the lifetime of each project. When taking the WACC into account (derived from capital structure decisions), the organization can measure operational options against the required rate of return.

10.4.4: Factors External to the Firm

Learning Objective

Recognize the various external factors that may impact the weighted average cost of capital

Key Points

• While organizations have some control over capital structure decisions, there are many factors at play in the external environment that are outside the control of the firm.
• Interest rates, inflation, and other economic forces can play a substantial role in the overall cost of capital.
• Fluctuations in the marketplace (i.e. market risk, or systematic risk) can be both unpredictable and influential on overall risk and return for investors, impacting capital costs.
• Corporate and investor tax legislation impacts the cost of capital, as both organizations and investors must factor tax into their investment decisions.

Key Term

systematic risk

Risk that is intrinsic to the marketplace.

When organizations begin weighing the weighted average cost of capital (WACC) and determining overall capital structure, there are some factors that are within the control of the organization, and some external factors that are not. When it comes to projecting the cost of capital, it’s useful to assess some of the external factors that may influence the overall cost.

Interest Rates

Interest rates fluctuate for a wide variety of reasons, and are a primary tool of monetary policy. Governments and central banks often make alterations to interest rates as a result of investment, unemployment, inflation, and other broader economic factors. Altering interest rates can impact the spending, borrowing, and investing habits within an economy, and therefore tend to fluctuate for economic purposes.

German Bank Interest Rates

This chart illustrates changes in interest rates in Germany over time.

This chart illustrates changes in interest rates in Germany over time.

Inflation

Related to interest rates (and a direct impact upon interest rate change) is the natural inflation or deflation of the currency being borrowed or lent. Organizations must take into account the time value of money as it pertains to that capital’s actual alterations in value, which is firmly outside the control of the organization.

Market Fluctuations

2008 is a prime example of how market forces can drastically impact equity. As markets rise and fall, the cost of capital as well as the perceived market risk (systematic risk) will naturally and relatively unpredictably fluctuate. When utilizing markets as a source of funding, the intrinsic risk of the market itself is outside of the control of the organization. 

Corporate Tax

Depending upon the region of operation, tax implications may have a significant impact on the cost of capital. In many jurisdictions, debt and interest on equity may receive certain tax breaks. Investors may also encounter taxes on returns on their investments and tax on dividends, impacting the perceived risk and return ratio of a prospective investor. Profit beyond the cost of expenses and capital will be taxed as well, which impacts the overall weighted average cost of capital.

Other Factors

The cost of capital is largely a simple trade off between the time value of money, risk, return, and opportunity cost. Any external factors in the form of opportunity costs or unexpected risks can impact the overall cost of capital.

10.4.5: Making Risk Adjustments

Learning Objective

Describe how individual projects can alter a company’s WACC of capital

Key Points

• It is possible to adjust risk by figuring the differing risk into the company’s beta.
• The beta coefficient is the risk of a new project in relation to the risk of the market as a whole.
• Therefore, if a new project of differing risk is undertaken, the beta for that project will be weighted into the company’s overall cost of capital.

Key Term

covariance

A measure of how much two random variables change together.

Making Risk Adjustments

The weighted average cost of capital is the minimum return that a company must earn on an existing asset base. This means that, when calculated, WACC will produce a rate equivalent with the current level of risk present in a company’s activities. However, some new ventures will require taking on risks outside of the company’s current scope.

In this case, adjustments will need to be made to the WACC in order to account for the differing level of risk. If the risk is very different, the company’s current WACC may be sidestepped altogether in favor of a WACC typical for companies with similar investments. It is possible to make such adjustments by figuring the differing risk into the company’s beta .

Beta Equation

The beta of an investment is equal to the covariance between the rate of return of the investment, r(a), and that of the portfolio, r(p).

The beta coefficient, expressed as a covariance, is the risk of a new project in relation to the risk of the market as a whole. A company itself will be considered, for investment purposes, as a “portfolio of assets,” and its beta coefficient will represent the weighted average of each “asset’s” beta. Therefore, if a new project of differing risk is undertaken, the beta for that project will be weighted into the company’s overall cost of capital. For example, if the project is twice as sensitive to fluctuations in the market as the company as a whole, then the project’s beta should be twice that of the company during the valuation process. This will increase the risk premium on the project and its cost of equity and subsequently the weighted average cost of capital. This increase in cost of capital will devalue the company’s stock, unless this increase was offset by a higher expected rate of return.

10.4.6: Problems with WACC

Learning Objective

Recognize the risk of using a WACC analysis to predict the overall cost of capital

Key Points

• A weighted average cost of capital (WACC) calculation is a great tool for businesses (particularly financial professionals) in understanding how much it will cost to finance a project.
• However, despite this usefulness, a WACC calculation relies on assumptions that may or may not prove true. This uncertainty should be taken into account when making projections.
• Some of these assumptions include the profitability of the project (which should exceed the cost of capital), the opportunity cost of foregone investments, and the total amount of capital required for the project.
• Whenever a firm uses forecasts such as a WACC, the most important thing to keep in mind is that future planning is based on assumptions. Identify each assumption, and mitigate the risk through understanding worst-case scenarios.

Key Term

capital requirements

The amount of money a project needs in order to be successfully funded.

WACC

The weighted average cost of capital (WACC) is a common and highly useful approach to determining how much it will cost (as a percentage) to borrow money in order to fund a given operation or project. This overall cost of borrowing capital is a great tool for financial professionals, who would like to understand how much a project will cost, and how much it will provide in return. The overall goal is to maintain a certain level of profitability when it comes to making investments in organizational projects.

As a reminder, the formula for WACC is:

Advantages

As a model, the WACC has quite a few advantages. Generally speaking, this process will take into account the differences between the cost of debt and the cost of equity in a given calculation. This allows the firm to understand how much a project funded fully by debt would differ in terms of capital costs than a project that requires a great deal of equity as well (hint: debt is almost always cheaper). It also takes into account the time value of money, normalizing cash flows for present value. Another advantage of this calculation is the simplicity of it. Upper management can quickly look at the WACC for a given project, and compare that to the forecast of the profitability. 

Problems

No forecast is perfect, however. All financial professionals and upper management executives must understand the drawbacks of WACC (along with those of virtually every attempt to project future costs and profits with present and past data). 

The simplest problem with the calculation are the assumptions it relies on. These can include:

• Profitability – When determining the cost of capital, this number isn’t particularly useful without an understanding of the return on that capital. After all, the profitability must exceed the cost of borrowing the money. Profitability in a future market is never certain, as the demands, needs, competition, and price of inputs could change any day.
• Opportunity Costs – Another important consideration are the opportunity costs, both for investors in the business and the business itself. The cost of capital, particularly on the equity side, are made through identifying the risk of this particular project compared to other projects that could be invested in. These opportunity costs will change over time, which may also change the cost of funding (depending on the contract which secures that funding).
• Amount Required – Projects often encounter unforeseen hurdles, and jumping over these hurdles may required capital that hasn’t been considered in the forecast. As the amount of capital required increases, the financial risk from investors also increases. Higher risk means higher returns, and more capital requirements during the project may increase the overall average cost of capital.

Conclusion

While the WACC calculation does rely on quite a few assumptions, this is something of a necessary risk when it comes to financial projections. Forecasts are not sure things, they are intrinsically uncertain. It is exactly due to this uncertainty that capital investments are risk, and require returns in the first place. When using this model to predict how much capital can be borrowed and at what rate, keep in mind that the situation can change any day.

9.4: Market Regulation

9.4.1: Securities Act of 1933

Learning Objective

Describe how the Securities Act of 1933 regulates stock markets

Key Points

• The Act’s objectives are to provide investors with material financial and other corporate information about issuers of public securities.
• The primary purpose of the 1933 Act is to ensure that buyers of securities receive complete and accurate information before they invest.
• Among other things, registration forms call for: a description of the securities to be offered for sale; information about the management of the issuer; information about the securities (if other than common stock); and financial statements certified by independent accountants.
• Rule 144, promulgated by the SEC under the 1933 Act, permits, under limited circumstances, the sale of restricted and controlled securities without registration.
• Regulation S is a “safe harbor” that defines when an offering of securities is deemed to be executed in another country and therefore not be subject to the registration requirement under section 5 of the 1933 Act.

Key Terms

private placements

Private placement (or non-public offering) is a funding round of securities which are sold not through a public offering, but rather through a private offering, mostly to a small number of chosen investors.

SEC

The U.S. Securities and Exchange Commission (frequently abbreviated SEC) is a federal agency[2] which holds primary responsibility for enforcing the federal securities laws and regulating the securities industry, the nation’s stock and options exchanges, and other electronic securities markets in the United States.

The Securities Act of 1933 (also known as the ’33 Act) is essentially a consumer protection law for “retail” investors (i.e. not money managers, foundations, pensions, etc.)

Purpose

The Act’s objectives are to provide investors with material, financial, and other corporate information about issuers of public securities (i.e. stocks and bonds), and to prevent fraud in the offering of such securities. The primary purpose of the ’33 Act is to ensure that buyers of securities receive complete and accurate information before they invest.

Registration Process

Unless they qualify for an exemption, securities offered or sold to the public in the U.S. must be registered by filing a registration statement with the SEC. Although the law is written to require registration of securities, it is more useful as a practical matter to consider the requirement to be that of registering offers and sales. If person A registers a sale of securities to person B, and then person B seeks to resell those securities, person B must still either file a registration statement or find an available exemption.

US SEC

The U.S. Securities and Exchange Commission (frequently abbreviated SEC) is a federal agency, which holds primary responsibility for enforcing the federal securities laws and regulating the securities industry

Many transactions are exempt from regulation under the Securities Act. Section 4 of the Act limits its application to public offerings (according to SEC guidelines, more than 25 offerees) by issuers and their underwriters (i.e. investment banks). This means that the Act primarily applies to companies offering securities to the public, and not to transactions between investors or to sales of stock to small groups of investors (i.e. private placements. )

The prospectus, which is the document through which an issuer’s securities are marketed to a potential investor, is included as part of the registration statement. The SEC prescribes the relevant forms on which an issuer’s securities must be registered. Among other things, registration forms call for:

• a description of the securities to be offered for sale;
• information about the management of the issuer;
• information about the securities (if other than common stock); and
• financial statements certified by independent accountants.

For public offerings, the main requirement of the Securities Act is registration. An issuer must prepare an extensive statement describing the securities to be offered and detailing the nature of the issuer’s business. Once this statement is registered with and approved by the SEC, its data and forecasts are placed in a prospectus for potential investors. Any offering of the securities by the issuer or underwriter must thereafter be accompanied by the prospectus.

Rule 144

Rule 144, promulgated by the SEC under the 1933 Act, permits, under limited circumstances, the sale of restricted and controlled securities without registration. In addition to restrictions on the minimum length of time for which such securities must be held and the maximum volume permitted to be sold, the issuer must agree to the sale. If certain requirements are met, Form 144 must be filed with the SEC. Often, the issuer requires that a legal opinion be given indicating that the resale complies with the rule. The amount of securities sold during any subsequent three-month period generally does not exceed any of the following limitations:

• 1% of the stock outstanding
• the average weekly reported volume of trading in the securities on all national securities exchanges for the preceding four weeks
• the average weekly volume of trading of the securities reported through the consolidated transactions reporting system (NASDAQ)
• Notice of resale is provided to the SEC if the amount of securities sold in reliance on Rule 144 in any three-month period exceeds 5,000 shares or if they have an aggregate sales price in excess of $50,000. After one year, Rule 144(k) allows for the permanent removal of the restriction except as to ‘insiders’.
• In cases of mergers, buyouts or takeovers, owners of securities who had previously filed Form 144 and still wish to sell restricted and controlled securities must refile Form 144 once the merger, buyout, or takeover has been completed.

Regulation S

Regulation S is a “safe harbor” that defines when an offering of securities is deemed to be executed in another country and therefore not be subject to the registration requirement under section 5 of the 1933 Act. The regulation includes two safe harbor provisions: an issuer safe harbor and a resale safe harbor. In each case, the regulation demands that offers and sales of the securities be made outside the United States and that no offering participant (which includes the issuer, the banks assisting with the offer, and their respective affiliates) engage in “directed selling efforts. ” In the case of issuers for whose securities there is substantial U.S. market interest, the regulation also requires that no offers and sales be made to U.S. persons (including U.S. persons physically located outside the United States).

9.4.2: Securities Exchange Act of 1934

Learning Objective

Define how the Securities Exchange Act of 1934 regulates the US securities markets

Key Points

• The Securities Exchange Act of 1934 is a law governing the secondary trading of securities in the United States of America. The Act and related statutes form the basis for the regulation of the financial markets and their participants in the United States.
• One area subject to 34 Act regulation is the actual securities exchange: New York Stock Exchange, the American Stock Exchange, and regional exchanges like the Cincinnati Stock Exchange, Philadelphia Stock Exchange and Pacific Stock Exchange.
• The ’34 Act also regulates broker-dealers without a status for trading securities. A telecommunications infrastructure was developed to provide for trading without a physical location.
• In 1938 the Exchange Act was amended by the Maloney Act, which authorized the formation and registration of national securities associations to supervise the conduct of their members subject to the oversight of the SEC.
• In the last 30 years, brokers have created two additional systems for trading securities. The alternative trading system, or ATS, is a quasi exchange where stocks are commonly purchased and sold through a smaller, private network of brokers, dealers, and other market participants.

Key Term

NASDAQ

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

The Securities Exchange Act of 1934 (also called the Exchange Act, ’34 Act, or Act of ’34) is a law governing the secondary trading of securities, including stocks, bonds, and debentures, in the United States of America. It was a sweeping piece of legislation. The Act and related statutes form the basis for the regulation of the financial markets and their participants in the United States. The 1934 Act also established the Securities and Exchange Commission (SEC), the agency primarily responsible for enforcement of United States federal securities law.

Securities Exchange Act of 1934

Act of 1934 governs the secondary trading of securities.

While the Securities Act is very limited in scope, the Securities Exchange Act (also known as the Exchange Act or 1934 Act) is much broader. It regulates stock exchanges, brokers, dealers, and even private traders.

Companies raise billions of dollars by issuing securities in what is known as the primary market. In contrast with the Securities Act of 1933, which regulates these original issues, the Securities Exchange Act of 1934 regulates the secondary trading of those securities between persons often unrelated to the issuer, in most cases through brokers or dealers. Trillions of dollars are made and lost each year through trading in the secondary market.

Securities exchanges

One area subject to 34 Act regulation is the actual securities exchange — the physical place where people purchase and sell securities (stocks, bonds, notes of debenture). Some of the well known exchanges include the New York Stock Exchange, the American Stock Exchange, and regional exchanges like the Cincinnati Stock Exchange, Philadelphia Stock Exchange and Pacific Stock Exchange. At those places, agents of the exchange or specialists, act as middlemen for the competing interests to buy and sell securities. An important function of the specialist is to inject liquidity and price continuity into the market. Given that people come to the exchange to easily acquire securities or to easily dispose of a portfolio of securities, the specialist’s role is important to the exchange.

Securities associations

The ’34 Act also regulates broker-dealers without a status for trading securities. A telecommunications infrastructure was developed and allows for for trading without a physical location. Previously these brokers would find stock prices through newspaper printings and conduct trades verbally by telephone. Today, a digital information network connects these brokers. This system is called NASDAQ, standing for the National Association of Securities Dealers Automated Quotation System.

Self-regulatory organizations (SRO)

In 1938, the Exchange Act was amended by the Maloney Act, which authorized the formation and registration of national securities associations to supervise the conduct of their members subject to the oversight of the SEC. That amendment led to the creation of the National Association of Securities Dealers, Inc. – the NASD, which is a Self-Regulatory Organization (or SRO). The NASD had primary responsibility for the oversight of brokers and brokerage firms, and later, the NASDAQ stock market.

Other trading platforms

In the last 30 years, brokers have created two additional systems for trading securities. The alternative trading system, or ATS, is a quasi exchange where stocks are commonly purchased and sold through a smaller, private network of brokers, dealers, and other market participants. The ATS is different from exchanges and associations in that the volumes for ATS trades are comparatively low, and the trades tend to be controlled by a small number of brokers or dealers. ATS acts as a niche market, a private pool of liquidity. Reg ATS, an SEC regulation issued in the late 1990s, requires these small markets to 1) register as a broker with the NASD, 2) register as an exchange, or 3) operate as an unregulated ATS, staying under low trading caps.

Issuers

While the ’33 Act recognizes that timely information about the issuer is vital to effective pricing of securities, the Act’s disclosure requirement (the registration statement and prospectus) is a one-time affair. The ’34 Act extends this requirement to securities traded in the secondary market. Provided that the company has more than a certain number of shareholders and has a certain amount of assets (500 shareholders, above $10 million in assets, per sections 12, 13, and 15 of the Act), the ’34 Act requires that issuers regularly file company information with the SEC on certain forms (the annual 10-K filing and the quarterly 10-Q filing).

Antifraud provisions

While the ’33 Act contains an antifraud provision (Section 17), when the ’34 Act was enacted, questions remained about the reach of that antifraud provision and whether a private right of action—that is, the right of an individual citizen to sue an issuer of stock or related market actor, as opposed to government suits—existed for purchasers.

9.4.3: Securities Acts Amendments of 1975

Learning Objective

Define how the Securities Act Amendments of 1975 regulate U.S. stock markets

Key Points

• The 1975 amendments, also called the National Exchange Market System Act, directed the securities and exchange commission to work with the industry toward establishing a national market system together with a system for the nationwide clearance and settlement of securities transactions.
• The National Market System (NMS) is the national system for trading equities in the United States.
• A national market system plan (or NMS plan) is a structured method of transmitting securities transactions in real-time.
• In 2005, the rules promoting the national market system were consolidated into REG NMS.
• The order protection rule has generated controversies since it requires traders to transact on a trading venue at the lowest price rather than on a venue that offers the quickest execution or the most reliability.

Key Terms

settlement

Settlement of securities is a business process whereby securities or interests in securities are delivered, usually against (in simultaneous exchange for) payment of money, to fulfill contractual obligations, such as those arising under securities trades.

clearance

In banking and finance, clearing denotes all activities from the time a commitment is made for a transaction until it is settled. Clearing is necessary because the speed of trades is much faster than the cycle time for completing the underlying transaction.

Example

• For example, if the best two quotes in one market are superior to the best quote in another market, a portion of an incoming market order may still trade at the inferior market at the inferior price even though the second best quote on the superior market is still available. If more than just the top of the book (the best quote) were protected by the order rule, the market order would have transacted at a superior price and the limit order offering the superior price would have transacted more quickly.

The 1975 amendments, also called the National Exchange Market System Act, directed the securities and exchange commission to work with the industry toward establishing a national market system together with a system for the nationwide clearance and settlement of securities transactions.

SEC

The amendments are direct SEC to enable the establishment of a National Market System.

National market system plan

A national market system plan (or NMS plan) is a structured method of transmitting securities transactions in real-time. In the United States, national market systems are governed by section 11A of the Securities Exchange Act of 1934.

In addition to processing the transactions themselves, these plans also show the price and volume data for these transactions. Information on each securities trade is sent to a central network at the Securities Industry Automation Corporation (SIAC) where it is then distributed and consolidated with other trades on the same “tape”.

Securities Industry Automation Corporation (SIAC)

The Securities Industry Automation Corporation (SIAC) is a subsidiary of the NYSE Euronext. Its purpose is to provide technical services for the exchanges themselves, members and other financial institutions. In this role, SIAC provides the computers and other systems required to run the exchanges. It also owns communication lines and hardware that provide real-time quotes and transaction information to all market participants from the Consolidated Tape/Ticker System (CTS), Consolidated Quotation System (CQS), and Options Price Reporting Authority (OPRA).

National Market System (NMS)

The National Market System (NMS) is the national system for trading equities in the United States.

Regulation NMS (or Reg NMS — Regulation National Market System) is a regulation promulgated and defined by the United States Securities and Exchange Commission (SEC) as “a series of initiatives designed to modernize and strengthen the national market system for equity securities. ” It was established in 2007 and seeks to foster both “competition among individual markets and competition among individual orders” in order to promote efficient and fair price formation across securities markets. In 1972, before the SEC began its pursuit of a national market system, the market for securities was quite fragmented. The same stock sometimes traded at different prices at different trading venues, and the NYSE ticker tape did not report transactions of NYSE-listed stocks that took place on regional exchanges or on other over-the-counter securities markets. This fragmentation made it difficult for traders to compare prices of stocks. In 1975, Congress authorized the SEC to facilitate a national market system.

Formation of Reg NMS

In 2005, the rules promoting the national market system were consolidated into REG NMS. Some of the more notable rules include:

• Order Protection (or Trade Through) Rule – provides intermarket price priority for quotations that are immediately and automatically accessible (Rule 611)
• Access Rule – addresses access to market data such as quotations (Rule 610)
• Sub-Penny Rule – establishes minimum pricing increments (Rule 612)
• Market Data Rules: a) Allocation amendment – institutes a new Market Data Revenue Allocation Formula, b) Governance amendment – creates advisory committees, c) Distribution and Display Rules – governing market data (Rule 600, 601 & 603).

The order protection rule has generated controversies since it requires traders to transact on a trading venue at the lowest price rather than on a venue that offers the quickest execution or the most reliability. Thus, some have described it as an improper government intervention into private business affairs. Defenders of the rule argue that it really just requires what brokers should be doing if they are acting in their customer’s best interests. Still, others have argued that the rule is too lax because it only protects the quotes at the top of the book.

9.4.4: Sarbanes–Oxley Act of 2002

Learning Objective

Identify the responsibilities imposed on companies by the Sarbanes-Oxley Act of 2002

Key Points

• As a result of SOX, top management must now individually certify the accuracy of financial information. In addition, penalties for fraudulent financial activity are much more severe.
• SOX increased the independence of the outside auditors who review the accuracy of corporate financial statements, and increased the oversight role of boards of directors.
• The bill was enacted as a reaction to a number of major corporate and accounting scandals including those affecting Enron, Tyco International, Adelphia, Peregrine Systems, and WorldCom.
• Opponents claim it has reduced America’s international competitive edge against foreign financial service providers; Proponents say that SOX has been a “godsend” for improving the confidence of fund managers and other investors with regard to the veracity of corporate financial statements.

Key Terms

conflicts of interest

A conflict of interest (COI) occurs when an individual or organization is involved in multiple interests, one of which could possibly corrupt the motivation for an act in the other.

off-balance-sheet

Off-balance sheet (OBS), or Incognito Leverage, usually means an asset or debt or financing activity not on the company’s balance sheet.

boards of directors

A board of directors is a body of elected or appointed members who jointly oversee the activities of a company or organization.

Example

• For example, Section 302 requires that the company’s “principal officers” (typically the Chief Executive Officer and Chief Financial Officer) certify and approve the integrity of their company financial reports quarterly.

The Sarbanes–Oxley Act of 2002

The Sarbanes–Oxley Act of 2002 is a federal law that set new or enhanced standards for all public company boards, management, and public accounting firms in the United States. It is also known as the Public Company Accounting Reform and Investor Protection Act (in the Senate) and Corporate and Auditing Accountability and Responsibility Act (in the House) and more commonly called Sarbanes–Oxley, Sarbox or SOX. It It is named after sponsors U.S. Senator Paul Sarbanes (D-MD) and U.S. Representative Michael G. Oxley (R-OH). As a result of SOX, top management must now individually certify the accuracy of financial information. In addition, penalties for fraudulent financial activity are much more severe. SOX also increased the independence of the outside auditors who review the accuracy of corporate financial statements, and increased the oversight role of boards of directors.

Senator Sarbanes and Representative Oxley

Senator Sarbanes and Representative Oxley sponsored the 2002 Act.

The bill was enacted as a reaction to a number of major corporate and accounting scandals including those affecting Enron, Tyco International, Adelphia, Peregrine Systems, and WorldCom. These scandals, which cost investors billions of dollars when the share prices of affected companies collapsed, shook public confidence in the nation’s securities markets.

In response to the perception that stricter financial governance laws are needed, SOX-type laws have been subsequently enacted in Japan, Germany, France, Italy, Australia, India, South Africa, and Turkey.

Public Company Accounting Oversight Board (PCAOB)

Title I provides independent oversight of public accounting firms providing audit services (auditors). It also creates a central oversight board tasked with registering auditors, defining the specific processes and procedures for compliance audits, inspecting and policing conduct and quality control, and enforcing compliance with the specific mandates of SOX.

Auditor Independence

Title II consists of nine sections and establishes standards for external auditor independence, to limit conflicts of interest. It also addresses new auditor approval requirements, audit partner rotation, and auditor reporting requirements. It restricts auditing companies from providing non-audit services (e.g., consulting) for the same clients.

Corporate Responsibility

Title III consists of eight sections and mandates that senior executives take individual responsibility for the accuracy and completeness of corporate financial reports. It enumerates specific limits on the behaviors of corporate officers and describes specific forfeitures of benefits and civil penalties for non-compliance.

Enhanced Financial Disclosures

Title IV describes enhanced reporting requirements for financial transactions, including off-balance-sheet transactions, pro-forma figures and stock transactions of corporate officers. It requires internal controls for assuring the accuracy of financial reports and disclosures, and mandates both audits and reports on those controls.

Analyst Conflicts of Interest

Title V consists of only one section, which includes measures designed to help restore investor confidence in the reporting of securities analysts. It defines the codes of conduct for securities analysts and requires disclosure of knowable conflicts of interest.

Commission Resources and Authority

Title VI defines practices to restore investor confidence in securities analysts. It also defines the SEC’s authority to censure or bar securities professionals from practice and defines conditions under which a person can be barred from practicing as a broker, advisor, or dealer.

Studies and Reports

Title VII consists of five sections and requires the Comptroller General and the SEC to perform various studies and report their findings.

Corporate and Criminal Fraud Accountability

Title VIII describes specific criminal penalties for manipulation, destruction or alteration of financial records or other interference with investigations, while providing certain protections for whistle-blowers.

White Collar Crime Penalty Enhancement

Title IX increases the criminal penalties associated with white-collar crimes and conspiracies. It recommends stronger sentencing guidelines and specifically adds failure to certify corporate financial reports as a criminal offense.

Corporate Tax Returns

Title X consists of one section. Section 1001 states that the Chief Executive Officer should sign the company tax return.

Corporate Fraud Accountability

Title XI consists of seven sections. Section 1101 recommends a name for this title as “Corporate Fraud Accountability Act of 2002”. It identifies corporate fraud and records tampering as criminal offenses and joins those offenses to specific penalties. It also revises sentencing guidelines and strengthens their penalties. This enables the SEC to resort to temporarily freezing transactions or payments that have been deemed “large” or “unusual”.

Debate continues over the perceived benefits and costs of SOX. Opponents of the bill claim it has reduced America’s international competitive edge against foreign financial service providers, saying SOX has introduced an overly complex regulatory environment into U.S. financial markets. Proponents of the measure say that SOX has been a “godsend” for improving the confidence of fund managers and other investors with regard to the veracity of corporate financial statements.

9.4.5: Global Research Settlement

Learning Objective

Describe how the Global Research Settlement addressed conflicts of interest in the market

Key Points

• The Global Settlement was an enforcement agreement reached on April 28, 2003 between the SEC, NASD, NYSE, and ten of the United States’s largest investment firms to address issues of conflict of interest within their businesses.
• The central issue at hand that had been previously decided in court was the conflict of interest between the investment banking and analysis departments of ten of the largest investment firms in the United States.
• As part of the settlement decision published on December 20, 2002, several regulations designed to prevent abuse stemming from pressure by investment bankers on analysts to provide “favorable” appraisals were instantiated.
• Other than these regulatory actions, the firms involved in the settlement were also to pay fines to their investors, to fund investor education, and to pay for independent third-party market research.

Key Terms

IPOs

An initial public offering (IPO) or stock market launch is a type of public offering where shares of stock in a company are sold to the general public, on a securities exchange, for the first time.

conflict of interest

A conflict of interest (COI) occurs when an individual or organization is involved in multiple interests, one of which could possibly corrupt the motivation for an act in the other.

The Global Settlement was an enforcement agreement reached on April 28, 2003 between the Securities and Exchange Commission (SEC), National Association of Securities Dealers (NASD), New York Stock Exchange (NYSE), and ten of the United States’s largest investment firms. The agreement was meant to address issues of conflict of interest within their businesses.

The central issue at hand that had previously been decided in court was the conflict of interest between the investment banking and analysis departments of ten of the largest investment firms in the United States. The investment firms involved in the settlement had all engaged in actions and practices that had aided and abetted the inappropriate influence of their research analysts by their investment bankers seeking lucrative fees. A typical violation addressed by the settlement was the case of CSFB and Salomon Smith Barney, which were alleged to have engaged in inappropriate spinning of “hot” IPOs and issued fraudulent research reports in violation of various sections within the Securities Exchange Act of 1934. Similarly, UBS Warburg and Piper Jaffray were alleged to have received payments for investment research without disclosing such payments in violation of the Securities Act of 1933.

Payments

The table shows the payments of each company

Enforcement actions

As part of the settlement decision published on December 20, 2002, several regulations designed to prevent abuse stemming from pressure by investment bankers on analysts to provide “favorable” appraisals were put in place. Most importantly, these firms would have to literally insulate their banking and analysis departments from each other physically and with Chinese walls. In addition, budget allocation to management in research departments will be independent of investment departments. Research analysts will also be prohibited from going on pitches and roadshows with bankers during advertising and promotion of IPOs. Similarly, the Global Settlement also increased the IPO “quiet period” from 25 days to 40 days. Finally, research analysts’ historical ratings must be disclosed and made available.

Other than these regulatory actions, the firms involved in the settlement were required to pay fines to their investors, to fund investor education, and to pay for independent third-party market research. A total fine of $1.435 billion was assessed and is described in the table below.

8.4: Risk

8.4.1: Types of 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

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.

7.4: Stock Markets

7.4.1: Market Actors

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

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

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

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.

6.4: Understanding Bonds

6.4.1: The Nature of Bonds

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

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

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

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.