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Chapter 9: Problem 11

Assume that a firm has several long-term bonds outstanding at different interest rates. Explain the relationship between bond coupon rates and current market interest rates that would cause the bonds to sell at par, below par, and above par value

Short Answer

Expert verified
The bond's coupon rate determines if it is sold at premium, discount, or at par value. If the bond's coupon rate equals the prevailing market rate, the bond sells at par value. If the coupon rate is less than the market rate, the bond sells below par (discount), and if the coupon rate is more than the market rate, the bond sells above par (premium).

Step by step solution

01

Basics of Bonds

First, it's important to understand how bonds work. A bond is a type of loan made by an investor to a borrower (typically a corporation or government). A bond's coupon value is the annual interest paid to the bondholder, while the par value is the bond's face value or the principal amount that will be repaid at maturity.
02

Bond Value and coupon rate

The value of a bond in the market is mostly determined by its coupon rate in relation to the current market interest rate. A bond's coupon rate is the interest rate that the issuer will pay to the bondholder annually, expressed as a percentage of the bond's par value.
03

Value of a Bond at Par

A bond is sold at par value when the bond's coupon rate equals the prevailing market rate. This means that investors are simply getting the market interest rate and the bond will sell for a price equivalent to its face or par value.
04

Value of a Bond Below Par (Discount)

A bond sells below par, or at a discount, when the bond's coupon rate is less than the prevailing market rate. This is because investors could buy new bonds in the market that pay the higher interest rate, so if they are going to buy the older, low-coupon bond, they will only do so at a discounted price.
05

Value of a Bond Above Par (Premium)

A bond sells above par, or at a premium, when the bond's coupon rate is more than the prevailing market rate. High-coupon bonds are attractive to investors because they pay more interest than new bonds being issued at the current lower market rate, so investors are willing to pay a premium for them.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coupon Rate
A bond's coupon rate is a key determinant of its attractiveness to investors. It is defined as the annual interest payment made to the bondholder by the issuer, expressed as a percentage of the bond's par value. This fixed rate is decided at the time of issuance and does not change over the life of the bond.

If a bond has a par value of $1,000 and a coupon rate of 5%, the bondholder will receive $50 in interest each year until maturity.

Understanding the coupon rate helps investors compare different bonds and assess the income they can expect to receive from their investments.
Market Interest Rate
Market interest rate is a pivotal factor that greatly influences bond prices and investor decisions. This rate represents the return investors demand for loaning their money, fluctuating based on economic conditions, including inflation and central bank policies.

When market interest rates rise, new bonds are issued with higher yields, impacting the attractiveness of existing bonds. Conversely, if market rates fall, existing bonds with higher coupon rates become more attractive.

The interplay between the coupon rate and market interest rate determines whether a bond will sell at par, a discount, or a premium.
Par Value
Par value, also known as face value, is the amount a bondholder receives when the bond matures, assuming no default. It is the initial capital invested and is typically set at $1,000.

This concept is fundamental as it is the benchmark against which coupons and market interest rates are measured to assess bond value.

When a bond is "at par," it sells for its original face value. A bondholder can therefore expect to receive the par value after the bond reaches maturity, along with the coupon payments during its term.
Bond Discount
A bond discounts below par value when its coupon rate is less than the market interest rate. This situation often arises when market interest rates have increased since the bond was issued.

When investors can buy newer bonds offering higher interest rates, older bonds with lower coupon rates must sell at a lower price to offer a comparable return.

This discount compensates for the lower interest income received from the bond compared to current market offerings. As a result, investors buy these discounted bonds to potentially capitalize on capital gain as they approach maturity.
Bond Premium
A bond can sell at a premium when its coupon rate is higher than the market interest rate, making it attractive in the current market. This implies that, when rates fall, bonds offering higher returns are sought after.

For example, if market rates decrease from 5% to 3%, a bond with a 5% coupon rate becomes more valuable, prompting investors to pay an amount above its par value for the extra interest income.

Holding such bonds may yield higher-than-market interest earnings and thus buyers are ready to pay this premium for the added benefit.

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Most popular questions from this chapter

If a long-term bond is issued at a premium, both the carrying value of the bond and the recognized interest expense will decrease in each successive period during which the bond is outstanding. Explain why this occurs.

Retrieve the most recent 10-K filings for Kmart, Wal-Mart, Gillette, and Mem Co. from the EDGAR archives (www.sec.gov/edaux/searches.htm). Examine the long-term debt section of the Notes to the Financial Statements: a. Calculate the ratio of long-term debt to total assets for each company for the last two years. Comment on any changes that you observe. b. Analyze the long-term debt for each company, using the following format: c. Compare Kmart to Wal-Mart. Which company obtained better terms from its lenders? Why? d. Compare Gillette to Mem. Which company obtained better terms from its Ienders? Why?

Use the balance sheet equation to analyze the effects of issuing the following Iong-term bonds. Assume a market interest rate of \(12 \%\) and semiannual compounding. Set up separate columns as necessary. a. \(10,000,000\) bonds for one year at a coupon interest rate of \(10 \%\) b. \(20,000,000\) bonds for three years at a coupon interest rate of \(12 \%\) c. \(5,000,000\) bonds for 10 years at a coupon interest rate of \(10 \%\) d. Discuss why some of these bonds were issued at a premium or a discount.

Use the balance sheet equation to analyze the financial statement effects of the following transactions involving long-term bonds. Assume semiannual compounding. Set up separate columns as necessary and use a separate cash col- umn a. Issue \(20,000,000\) of five-year bonds carrying a coupon interest rate of \(8 \%\) payable semiannually. The market rate of interest at the time of issuance for similar bonds was \(12 \%\) b. Record interest paid after the first six months. c. Record interest due and paid at the end of the first year. d. Record interest due and paid during each six-month period during the second year. e. How much cash will be paid at the end of the fifth year? f. Show the effects of the bond repayment on the financial statements at the end of the fifth year. g. Discuss why these bonds were issued and recorded at a premium or discount.

Whether a firm uses straight-line or accelerated depreciation in accounting for a Iong-lived depreciable asset, the total amount of depreciation expense over the entire service life of the asset will be the same. If so, why is the choice among these depreciation methods for financial statement purposes important? Why is the timing of depreciation expense on a firm's tax return important?
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