Question

Bond P is a premium bond with a 12 percent coupon. Bond D is a 7 percent coupon bond currently selling at a discount. Both bonds make annual payments, have a YTM of 9 percent, and have seven years to maturity.

  

What is the current yield for Bond P and Bond D? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

	Current yield
Bond P	%
Bond D	%

If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P and Bond D? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)))

	Capital gains yield
Bond P	%
Bond D	%

Answer 1

Bond P:

Face Value = $1,000

Annual Coupon Rate = 12.00%
Annual Coupon = 12.00% * $1,000
Annual Coupon = $120

Time to Maturity = 7 years
Annual YTM = 9.00%

Current Price = $120 * PVIFA(9.00%, 7) + $1,000 * PVIF(9.00%, 7)
Current Price = $120 * (1 - (1/1.09)^7) / 0.09 + $1,000 * (1/1.09)^7
Current Price = $120 * 5.032953 + $1,000 * 0.547034
Current Price = $1,150.99

Current Yield = Annual Coupon / Current Price
Current Yield = $120 / $1,150.99
Current Yield = 0.1043 or 10.43%

Capital Gain Yield = Yield to Maturity - Current Yield
Capital Gain Yield = 9.00% - 10.43%
Capital Gain Yield = -1.43%

Bond D:

Face Value = $1,000

Annual Coupon Rate = 7.00%
Annual Coupon = 7.00% * $1,000
Annual Coupon = $70

Time to Maturity = 7 years
Annual YTM = 9.00%

Current Price = $70 * PVIFA(9.00%, 7) + $1,000 * PVIF(9.00%, 7)
Current Price = $70 * (1 - (1/1.09)^7) / 0.09 + $1,000 * (1/1.09)^7
Current Price = $70 * 5.032953 + $1,000 * 0.547034
Current Price = $899.34

Current Yield = Annual Coupon / Current Price
Current Yield = $70 / $899.34
Current Yield = 0.0778 or 7.78%

Capital Gain Yield = Yield to Maturity - Current Yield
Capital Gain Yield = 9.00% - 7.78%
Capital Gain Yield = 1.22%