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Chapter 7: Problem 17

BOND RETURNS Last year Joan purchased a \$1,000 face value corporate bond with an 11\% annual coupon rate and a 10 -year maturity. At the time of the purchase, it had an expected yield to maturity of \(9.79 \%\). If Joan sold the bond today for \(\$ 1,060.49\), what rate of return would she have earned for the past year?

Short Answer

Expert verified
Joan's rate of return for the past year was 17.05%.

Step by step solution

01

Calculate Annual Coupon Payment

The annual coupon payment is calculated by multiplying the bond's face value by the coupon rate. Here, the face value is \(1,000 and the coupon rate is 11%.\[\text{Annual Coupon Payment} = \\)1,000 \times 0.11 = \$110\]
02

Calculate Total Amount Received From Bond

The total amount received after one year from the bond includes the coupon payment plus the selling price of the bond.\[\text{Total Received} = \\(110 + \\)1,060.49 = \$1,170.49\]
03

Calculate Initial Purchase Price of the Bond

Initially, Joan purchased the bond for its face value, which is $1,000.
04

Calculate Total Return

The total return on the bond can be calculated as the difference between the total amount received and the initial purchase price.\[\text{Total Return} = \\(1,170.49 - \\)1,000 = \$170.49\]
05

Calculate Rate of Return

The rate of return can be determined by dividing the total return by the initial purchase price and then multiplying by 100 to convert it to a percentage.\[\text{Rate of Return} = \left(\frac{\\(170.49}{\\)1,000}\right) \times 100 = 17.049\%\]

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Key Concepts

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

Coupon Rate
The coupon rate of a bond is a crucial factor to understand. It represents the annual interest payment that a bondholder will receive, based on the bond's face value. For Joan's bond, the coupon rate is 11%, meaning each year she receives 11% of the bond's \(1,000 face value as interest.
This calculation is straightforward:
  • Face Value: \)1,000
  • Coupon Rate: 11%
  • Annual Coupon Payment: \(1,000 \times 0.11 = \)110
It's important to note that the coupon rate is fixed at the time of issuance. Therefore, regardless of changes in market interest rates or the bond's selling price, the coupon rate remains the same throughout the bond's life.
Yield to Maturity
Yield to maturity (YTM) is often used as a measure of the bond's long-term return, assuming that the bondholder holds the bond until it matures. It considers all future coupon payments and the face value repayment at maturity. For Joan鈥檚 bond, the expected YTM at the time of purchase was 9.79%.
  • YTM involves complex calculations that consider the present value of future payments.
  • It helps investors compare the profitability of different bonds.
  • Unlike the coupon rate, YTM changes with the bond鈥檚 price and market interest rates.
Investors rely on YTM to assess whether a bond is a good investment, considering their desired returns and the risks involved.
Rate of Return
The rate of return indicates the percentage of profit or loss on an investment over a specific period. For Joan, calculating the rate of return involves identifying how much she earned from the bond compared to her initial investment. Here's how she calculated it:
  • Total Received from Sale: \(1,170.49
  • Initial Purchase Price: \)1,000
  • Total Return: \(1,170.49 - \)1,000 = $170.49
  • Rate of Return: \(\left(\frac{170.49}{1,000}\right)\times 100 = 17.049\%\)
This calculation shows Joan earned a 17.049% return over the past year, a significant gain considering the initially expected yield was only 9.79%.
Corporate Bond
Corporate bonds are debt securities issued by companies to raise capital. Companies offer these bonds to investors, promising to pay regular interest (coupons) and to return the principal amount at maturity. These investments offer higher returns compared to government bonds but come with higher risk due to company performance uncertainties.
  • They provide steady income through fixed interest payments.
  • Risk varies depending on the issuing company's creditworthiness.
  • They are usually traded in the bond market, influencing their prices and YTMs.
For Joan, owning a corporate bond in a stable company helped her achieve a sizable return, as the company's performance likely influenced the appreciation of her bond.
Investment Calculation
Calculating returns on investments is essential for assessing financial performance. Joan's bond investment provides a practical example of the necessary steps:
  • Calculate the annual interest from the coupon rate.
  • Determine the total amount received upon selling the bond.
  • Subtract the initial purchase price from the total received to find the total return.
  • Compute the rate of return by expressing the total return as a percentage of the initial investment.
These calculations help investors like Joan understand the profitability of their investments and make informed decisions based on the results. Being precise in such calculations ensures better financial planning and investment strategies.

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Most popular questions from this chapter

BOND VALUATION \(\quad\) Bond \(X\) is noncallable and has 20 years to maturity, a \(9 \%\) annual coupon, and a \(\$ 1,000\) par value. Your required return on Bond \(X\) is \(10 \% ;\) and if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15 -year bond with similar risk will be \(8.5 \%\). How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.)

YIELD TO MATURITY A firm's bonds have a maturity of 10 years with a \(\$ 1,000\) face value, have an \(8 \%\) semiannual coupon, are callable in 5 years at \(\$ 1,050,\) and currently sell at a price of \(\$ 1,100 .\) What are their nominal yield to maturity and their nominal yield to call? What return should investors expect to earn on these bonds?

EXPECTED INTEREST RATE Lloyd Corporation's \(14 \%\) coupon rate, semiannual payment, \(\$ 1,000\) par value bonds, which mature in 30 years, are callable 5 years from today at \(\$ 1,050\) They sell at a price of \(\$ 1,353.54\), and the yield curve is flat. Assume that interest rates are expected to remain at their current level. a. What is the best estimate of these bonds' remaining life? b. If Lloyd plans to raise additional capital and wants to use debt financing, what coupon rate would it have to set in order to issue new bonds at par?

YIELD TO MATURITY AND FUTURE PRICE A bond has a \(\$ 1,000\) par value, 10 years to maturity, and a \(7 \%\) annual coupon and sells for \(\$ 985\) a. What is its yield to maturity (YTM)? b. Assume that the yield to maturity remains constant for the next 3 years. What will the price be 3 years from today?

YIELD TO MATURITY Heymann Company bonds have 4 years left to maturity. Interest is paid annually, and the bonds have a \(\$ 1,000\) par value and a coupon rate of \(9 \%.\) a. What is the yield to maturity at a current market price of (1) \(\$ 829\) and (2) \(\$ 1,104 ?\) b. Would you pay \(\$ 829\) for each bond if you thought that a "fair" market interest rate for such bonds was \(12 \%-\) that is, if \(\mathrm{r}_{\mathrm{d}}=12 \% ?\) Explain your answer.
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