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.
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?
- The current yield is defined as the annual coupon payment divided by the current price.
CY = $80/$901.40 = 8.875%.
- Solving for YTM:
N = 9, PV = -901.40, PMT = 80, FV = 1000
I = YTM = 9.6911%.
- 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%.
