A firm issues a 10-year, $1,000 par value bond. The required rate of return is 10%....

A firm issues a 10-year, $1,000 par value bond. The required rate of return is 10%.

1. What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $878.00? Another bond that sells for $1,134.20? What does a bond selling at a discount or at a premium tell you about the relationship between r_d and the bond’s coupon rate?

2.What are the total return, the current yield, and the capital gains yield for the discount bond in Question 3 at $878.00? At $1,134.20? (Assume the bond is held to maturity and the company does not default on the bond.)

Solutions

Expert Solution

Q - 1

YTM for the discount bond = RATE (Period, PMT, PV, FV) = RATE (10, 9% x 1000, -878, 1000) = 11.08%

YTM for the premium bond = RATE (Period, PMT, PV, FV) = RATE (10, 9% x 1000, -1134.20, 1000) = 7.08%

A bond selling at a discount will have YTM (r_d) > Coupon rate while a bond trading at a premium will have YTM (r_d) > the bond’s coupon rate

Q - 2

Total Return = YTM

Current Yield = Annual coupon / Current Price

Capital Gains yield = YTM - Current Yield

For the discount bond in Question 3 at $878.00

Total Return = YTM = 11.08%

Current Yield = Annual coupon / Current Price = 9% x 1000 / 878 = 10.25%

Capital Gains yield = YTM - Current Yield = 11.08% - 10.25% = 0.83%

For the premium bond in Question 3 at At $1,134.20

Total Return = YTM = 7.08%

Current Yield = Annual coupon / Current Price = 9% x 1000 / 1,134.20 = 7.94%

Capital Gains yield = YTM - Current Yield = 7.08% - 7.94% = - 0.85%

jeff jeffy answered 5 months ago

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