Question

Bond P is a premium bond with a coupon rate of 9.3 percent. Bond D is a discount bond with a coupon rate of 5.3 percent. Both bonds make annual payments, have a YTM of 7.3 percent, have a par value of $1,000, and have eight years to maturity. 

a. What is the current yield for Bond P? For Bond D? 

b. If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? For Bond D?

		Bond P		Bond D
a.	Current yield	8.32	%	5.67	%
b.	Capital gains yield	-1.02	%	1.63	%

Answer 1

Bond P:

Par Value = $1,000

Annual Coupon Rate = 9.30%
Annual Coupon = 9.30% * $1,000
Annual Coupon = $93

Time to Maturity = 8 years
Annual YTM = 7.30%

Current Price = $93 * PVIFA(7.30%, 8) + $1,000 * PVIF(7.30%, 8)
Current Price = $93 * (1 - (1/1.073)^8) / 0.073 + $1,000 / 1.073^8
Current Price = $1,118.05

Current Yield = Annual Coupon / Current Price
Current Yield = $93 / $1,118.05
Current Yield = 0.0832 or 8.32%

Capital Gain Yield = Annual YTM - Current Yield
Capital Gain Yield = 7.30% - 8.32%
Capital Gain Yield = -1.02%

Bond D:

Par Value = $1,000

Annual Coupon Rate = 5.30%
Annual Coupon = 5.30% * $1,000
Annual Coupon = $53

Time to Maturity = 8 years
Annual YTM = 7.30%

Current Price = $53 * PVIFA(7.30%, 8) + $1,000 * PVIF(7.30%, 8)
Current Price = $53 * (1 - (1/1.073)^8) / 0.073 + $1,000 / 1.073^8
Current Price = $881.95

Current Yield = Annual Coupon / Current Price
Current Yield = $53 / $881.95
Current Yield = 0.0601 or 6.01%

Capital Gain Yield = Annual YTM - Current Yield
Capital Gain Yield = 7.30% - 6.01%
Capital Gain Yield = 1.29%