World, Inc. has bonds outstanding with 7 years left to maturity. The bonds have
ID: 2383187 • Letter: W
Question
World, Inc. has bonds outstanding with 7 years left to maturity. The bonds have a 6% annual coupon rate and were issued a year ago at their par value of $1,000. The interest rates have shifted and the bond's market price has fallen to 922.80. The capital gains yield last year was -9.65%.
What is the yield to maturity? (5pts)
For the coming year, what are the expected current yield ( annual coupon price divided by the current price) and capital gains yield (difference between YTM and current yield)? (5pts)
Will the actual realized yields be equal to the expected yields if interest rates change? If not, how will they differ? (5pts)
Explanation / Answer
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Current yield, capital gains yield, and yield to maturity Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 8 percent annual coupon rate and were issued 1 year ago at their par value of $1,000, but due to changes in interest rates, the bond's market price has fallen to $901.40. The capital gains yield last year was _9.86 percent.
a. What is the yield to maturity?
b. For the coming year, what is the expected current yield and the expected capital
gains yield?
c. Will the actual realized yields be equal to the expected yields if interest rates change? If not, how will they differ?
a. The current yield is defined as the annual coupon payment divided by the current price.
CY = $80/$901.40 = 8.875%.
b. Solving for YTM:
N = 9, PV = -901.40, PMT = 80, FV = 1000
I = YTM = 9.6911%.
c. Expected capital gains yield can be found as the difference between YTM and the current yield.
CGY = YTM - CY = 9.691% - 8.875% = 0.816%.
Alternatively, you can solve for the capital gains yield by first finding the expected price next year.
N = 8, I = 9.6911, PMT = 80, FV = 1000
PV = -$908.76. VB = $908.76.
Hence, the capital gains yield is the percent price appreciation over the next year.
CGY = (P1 - P0)/P0 = ($908.76 - $901.40)/$901.40 = 0.816%.
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