## Factors Affecting the Price of a Bond

A bond’s book value is affected by its term, face value, coupon rate, and discount rate.

### Learning Objectives

Explain how a bond’s value is affected by its term, face value, coupon and discount rate

### Key Takeaways

#### Key Points

- A bond ‘s term, or maturity, is how long the issuing company has until it must repay the entirety of what it owes.
- Otherwise known as the principal or nominal amount, this is the amount of money that the organization issuing the bond has to pay interest on and generally has to repay when the bond is redeemed at the end of the term.
- A bond’s coupon is the interest rate that the business must pay on the bond’s face value.
- The discount rate is a a measure of what the bondholder’s return would be if he invested his money in something other than the bond. In practical terms, the discount rate generally equals the coupon rate or interest rate associated with similar investment securities.

#### Key Terms

**discount rate**: The interest rate used to discount future cashflows of a financial instrument; the annual interest rate used to decrease the amounts of future cashflows to yield their present value.**bond**: Evidence of a long-term debt, by which the bond issuer (the borrower) is obliged to pay interest when due, and repay the principal at maturity, as specified on the face of the bond certificate. The rights of the holder are specified in the bond indenture, which contains the legal terms and conditions under which the bond was issued. Bonds are available in two forms: registered bonds and bearer bonds.

A bond is a financial security that is created when a person transfers funds to a company or government, with the understanding that at some point in the future the entity issuing the bond will have to repay the amount, plus interest. Generally, the person who holds the actual bond document is the one with the right to receive payment. This allows people who originally acquire a bond to sell it on the open market for an immediate payout, as opposed to waiting for the issuing entity to pay the debt back. Note that the trading value of a bond (its market price) can vary from its face value depending on differences between the coupon and market interest rates.

### A bond’s book value is determined by several factors.

### Term

A bond’s term, or maturity, is how long the issuing company has until it must repay the entirety of what it owes. Sometimes a business will make interest payments during the term of the bond, but a term ends when all of the payments associated with the bond are completed.

### Face Value of Bond

Otherwise known as the principal or nominal amount, this is the amount of money that the organization issuing the bond has to pay interest on and generally has to repay when the bond is redeemed at the end of the term. The redemption amount generally equals how much the original investor paid to acquire the bond. However, the redemption amount can be different than the acquisition cost.

### Coupon

A bond’s coupon is the interest rate that the business must pay on the bond’s face value. These interest payments are generally paid periodically during the bond’s term, although some bonds pay all the interest it owes at the end of the period. While the coupon rate is generally a fixed amount, it can also be “indexed. ” This means that the interest rate is calculated by taking an established rate that fluctuates over time, such as a bank’s lending rate, and adding a “premium” percentage amount to determine the bond’s coupon rate. As a result, the interest that is paid to the bond holder fluctuates over time with an indexed coupon rate.

### Discount Rate

A bond’s value is measured based on the present value of the future interest payments the bond holder will receive. To calculate the present value, each payment is adjusted using the discount rate. The discount rate is a measure of what the bondholder’s return would be if he invested his money in another security. In practical terms, the discount rate generally equals the coupon rate or interest rate associated with similar investment securities.

## Bond Valuation Method

A bond’s value is measured by its sale price, but a business can estimate a bond’s price before issuance by calculating its present value.

### Learning Objectives

Summarize how a company would calculate the value of their bonds

### Key Takeaways

#### Key Points

- When calculating the present value of a bond, use the market rate as the discount rate.
- Regardless of whether the bond is sold at a premium or discount, a company must list a “bond payable” liability equal to the face value of the bond.
- If the market rate is greater than the bond’s contract rate, the bond will be sold at a discount. If the market rate is less than the bond’s contract rate, the bond will be sold at a premium.

#### Key Terms

**contract rate**: Another term for coupon rate, this is the amount of interest the business will pay on the principal of the bond.**market rate**: The interest rate associated with other bonds that have a similar risk factor.**market interest rate**: the interest rate determined through various investment systems, such as the stock market or the bond market

### Bond Valuation

A business must record a liability in its records when it issues a series of bonds. The value of the liability the business will record must equal the amount of money or goods it receives when it issues the bond. Whether the amount the business will receive equals its face value depends on the difference between the bond’s contract rate and the market rate of interest at the time the bond is issued.

The bond’s contract rate is another term for the bond’s coupon rate. It is what the issuing company uses to calculate what it must pay in interest on the bond. The market rate is what other bonds that have a similar risk pay in interest.

Regardless of what the contract and market rates are, the business must always report a bond payable liability equal to the face value of the bonds issued. If the market rate is greater than the coupon rate, the bonds will probably be sold for an amount less than the bonds’ face value and the business will have to report a “bond discount. ” The value of the bond discount will be the difference between what the bonds’ face value and what the business received when it sold the bonds. If the market rate is less than the coupon rate, the bonds will probably be sold for an amount greater than the bonds’ value. The business will then need to record a “bond premium” for the difference between the amount of cash the business received and the bonds’ face value.

### Calculating the Premium and Discount

If the market and coupon rates differ, the issuing company must calculate the present value of the bond to determine what price to charge when it sells the security on the open market. The present value of a bond is composed of two components; the principal and the interest payments. The discount rate for both the principal and interest payment components is the market rate when the bond was issued.

## Bonds Issued at Par Value

To record a bond issued at par value, credit the “bond payable” liability account for the total face value of the bonds and debit cash for the same amount.

### Learning Objectives

Explain how a company would record a bond issued a par value

### Key Takeaways

#### Key Points

- Recording a bond issued at par value is a simple process, since there is generally no premium or discount associated with the bond’s sale.
- To record interest paid on a bond issued at par value, debit the amount paid to the bond interest expense account and credit the same amount to the cash account.
- When the bond is paid off, record any final interest payment. Then debit the bond payable account and credit the cash account for the full face value of the bonds.

#### Key Terms

**par value**: The amount or value listed on a bill, note, stamp, etc.; the stated value or amount.**par value stock**: shares with a value stated in the corporate charter below which shares of that class cannot be sold upon initial offering**no-par value stock**: shares issued by a company without a minimum price for which they must be sold

Bonds issued at par value are relatively simple to calculate and record. When a bond is issued at par value it is sold for the face value amount. This generally means that the bond’s market and contract rates are equal to each other, meaning that there is no bond premium or discount.

When a business issues a bond, it participates in three types of transactions. First, the business issues the bond in exchange for cash. Next, it generally pays interest during the term of the bond. Finally, it pays off the obligation by repaying the face amount and the last interest payment. Each of these transactions must be recorded in the company’s financial records with a series of journal entries.

### Issuing the Bond

When the bond is issued, the company must record a liability called “bond payable. ” This is generally a long-term liability. It is created by recording a credit equal to the face value of all the bonds that are issued. To balance this entry, the company must also debit cash equal to the face value of all the bonds issued. Since the bonds are sold at par value, the amount of cash the company receives should equal the total face value of the issued bonds.

Cash – debit face value (increase cash balance)

Bond payable – credit face value (increase bonds payable)

### Interest Payments

When the company makes an interest payment, it must credit, or decrease, its cash balance by the amount it paid in interest. To balance the entry, the company must record a debit equal to the amount it paid in its bond interest expense account.

Bond Interest Expense – debit interest payment (increase interest expense line)

Cash – credit interest payment (decrease cash balance)

### Paying Off the Bond

When the bond is paid off, the company must record two transactions. First, it must record any final interest payments that are made. Then, it must record the bond principal being paid off. This is done by debiting the bond payable account and crediting the cash account for the full book value of the bond.

Bond Interest Expense – debit interest payment

Cash – credit final interest payment

Bond Payable – debit face value

Cash – credit face value

## Bonds Issued at a Discount

When a business sells a bond at a discount, it must record a discount balance in its records and amortize that amount over the bond’s term.

### Learning Objectives

Explain how to record a bond issued at a discount

### Key Takeaways

#### Key Points

- When the bond is sold, the company credits the “bonds payable” liability account by the bonds’ face value. The company debits the cash account by the amount of money it receives from the sale. The difference between the face value and sales price is debited as the discount value.
- The amortization rate for the bond’s discount balance is calculated by dividing the discount amount by the number of periods the company has to pay interest.
- To record interest expense, a business credits the bond discount account by the amortization rate and credits cash by the amount of money it pays in interest expense. Interest expense is debited by the sum of the amortization rate and how much it pays in interest to the bond holder.
- When the bond matures, the business must record the repayment of the principal to the bondholder, as well as all final interest payments. At this time, the discount on bond payable and bond payable accounts must be zeroed out, and all cash payments must be recorded.

#### Key Terms

**amortize**: To wipe out (a debt, liability etc. ) gradually or in installments.

### Issuing Bonds at a Discount

For the issuer, recording a bond issued at a discount can be a little more difficult than recording a bond issued at par value. Because the issuer receives less cash for the bond than the face value, this difference must be recorded in the company records as a discount expense. When a bond is sold at a discount, the market rate of the bond exceeds the contract rate. As a result, the bond must be sold at an amount less than its face value. In addition, that discounted amount must be amortized over the term of the bond. When the company amortizes the discount associated with the bond, it increases its interest expense beyond what it actually pays to the bondholder.

### Recording the Bond Sale

When a bond is sold, the company records a liability by crediting the “bonds payable” account for the bond’s total face value. Next, the company debits the cash account by the amount of money it receives from the bond sale. The business then debits the difference between the bond’s face value and what it receives in cash from the sale. That is the discount amount.

Assume a business sells a 10 year, $100,000 bond for $90,000. The journal entry for that transaction would be as follows:

Cash $90,000 Dr.

Discount on Bond Payable $10,000 Dr.

Bond Payable $100,000 Cr.

### Recording Interest Payments

As the company pays interest, the discount on the bond payable is amortized. Generally, the amortization rate is calculated by dividing the discount by the number of periods the company has to pay interest.

Using the example from above, assume the company pays 6% interest on the $100,000 bond annually. That means that the amortization rate on the bond payable equal $1,000 ($100,000/10 years). While the business would only have to pay the bondholder $6,000 in cash, its total interest expense equals $7,000, or the amount of interest it pays plus the amortization rate. The journal entry would be:

Bond Interest Expense $7,000 Dr.

Discount on Bond Payable $1,000 Cr.

Cash $6,000 Cr.

### Recording Bond Maturity

When the bond matures, the business must record the repayment of the principal to the bondholder, as well as all final interest payments. At this time, the discount on bond payable and bond payable accounts must be zeroed out, and all cash payments must be recorded.

Using our example from above, the final set of bond journal entries should look like this:

Bond Interest Expense $7,000 Dr.

Discount on Cash Payable $1,000 Cr.

Cash $6,000 Cr.

Bond Payable $100,000 Dr.

Cash $100,000 Cr.

## Bonds Issued at a Premium

When a bond is sold at a premium, the difference between the sales price and face value of the bond must be amortized over the bond’s term.

### Learning Objectives

Explain how to record bonds issued at a premium

### Key Takeaways

#### Key Points

- When the bond is issued, the company must debit the cash by the amount that the business receives, credit a bond payable liability account by an amount equal to the face value of the bonds, and credit a bond premium account by the difference between the sale price and the bond’s face value.
- To calculate the amortization rate of the bond premium, a company generally divides the bond premium amount by the number of interest payments that will be made during the term of the bond.
- When recording interest payments, the company credits cash by the amount paid to the bond holder, debits the bond premium account by the amortization rate, and debit interest expense for the difference between the amount paid in interest and the premium’s amortization for the period.
- When the bond reaches maturity, the company must pay the bondholder the face value of the bond, finish amortizing the premium, and pay any remaining interest obligations. When all the final journal entries are made, the bond premium and bond payable account must equal zero.

#### Key Terms

**amortize**: To wipe out (a debt, liability etc. ) gradually or in installments.

When a bond is issued at a premium, that means that the bond is sold for an amount greater than the bond’s face value. This generally means that the bond’s contract rate is greater than the market rate. Like with a bond that is sold at a discount, the difference between the bond’s face value and sales price must be amortized over the term of the bond. However, unlike with a bond sold at a discount, the process of amortizing the premium will decrease the bond’s interest expense recorded on the issuing company’s financial records. The issuing company will still be required to pay the bondholder the interest payments guaranteed by the bond.

### Bond Issue

When the bond is issued, the company must debit the cash account by the amount that the business receives for the bond sale. A liability, titled “bond payable,” must be created and credited by an amount equal to the face value of the issued bonds. The difference between the cash from the bond sale and the face value of the bond must be credited to a bond premium account.

For example, assume a business issues a 10-year bond that pays 6% interest annually, with a face value of $100,000. This bond sells for $110,000. The resulting journal entry would be:

Cash – $110,000

Bond Payable – $100,000

Bond Premium – $100,000

### Interest Payments on the Bond

When the business pays interest, it must also amortize the bond premium at that time. To calculate the amortization rate of the bond premium, a company generally divides the bond premium amount by the number of interest payments that will be made during the term of the bond. Every time interest is paid, the company must credit cash for the interest amount paid to the bond holder. The company must debit the bond premium account by the amortization rate. The difference between the amount paid in interest and the premium’s amortization for the period is the interest expense for that period.

Using the example from above, the $10,000 premium would be divided by 10 annual interest payments. This would make the amortization rate of the bond’s premium equal to $1,000 per year. The company must pay $6,000 in interest annually, so the company’s annual interest expense equals $5,000. The resulting journal entry is:

Bond Interest Expense – $5,000

Bond Premium – $1,000

Cash – $6,000

### Bond Reaches Maturity

When the bond reaches maturity, the company must pay the bondholder the face value of the bond, finish amortizing the premium, and pay any remaining interest obligations. When all the final journal entries are made, the bond premium and bond payable account must equal zero.

Using the example, this is what the final journal entries must look like:

Bond Interest Expense – $5,000

Bond Premium – $1,000

Cash – $6,000

Bond Payable – $100,000

Cash – $100,000

## Valuing Zero-Coupon Bonds

The value of a zero-coupon bond equals the present value of its face value discounted by the bond’s contract rate.

### Learning Objectives

Explain how to value a zero coupon bond

### Key Takeaways

#### Key Points

- A zero-coupon bond is one that does not make ongoing interest payment to the bondholder over the term of the bond.
- [latex]quad frac { Facequad Valuequad ofquad Bond }{ { (1+quad interestquad ratequad ofquad bond) }^{ Termquad ofquad Bond } } = Present Value of Zero-Coupon Bond.[/latex]
- The issuing entity will sell the zero-coupon bond at lower than face value. When the bond’s term is over, the issuing business will repay the bond at its face value.

#### Key Terms

**zero-coupon bond**: 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.

A zero-coupon bond is one that does not pay interest over the term of the bond. Instead, the entity will sell the bond at lower than face value. When the bond’s term is over, the issuing business will repay the bond at its face value. The bondholder generates a return paying less than what he receives in payment at the end of the bond’s term.

While the business may not make periodic interest payments, interest income is still generated. The interest income is merely accumulated and paid at the end of the bond’s term.

### Formula for Calculating Value of Zero-Coupon Bond

*Zero-Coupon Bond Value = Face Value of Bond / (1+ interest Rate)*

Generally, the price of a zero-coupon bond is based on the present value of the amount the issuing business will pay the bondholder when the bond matures. The amount the company pays at the end of the term equals the bond’s face value. The present value is determined using the interest rate stated on the bond. The bond’s term is used as the time period in the present value calculation.

It is important when completing the zero-coupon bond calculation to ensure the time period and term of the bond are expressed in similar terms. If the interest rate of the bond is expressed as a monthly rate and the term of the bond is 10 years, the bond term should be expressed as 120 months when making the calculation.

### Example Calculation

Assume a business issues a 2 year note, paying 5% interest with a face value of $100,000. To calculate its present value, you would raise 1.05 to the tenth power. This equals 1.1025. You then divide $100,000 by 1.1025. The result is that the bond would have a present value of $90,702.95.

Source: Accounting