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Bond P is a premium bond with a coupon rate of 10 percent. Bond D has a coupon r

ID: 2779721 • Letter: B

Question

Bond P is a premium bond with a coupon rate of 10 percent. Bond D has a coupon rate of 5 percent and is currently selling at a discount. Both bonds make annual payments, have a YTM of 7 percent, and have nine years to maturity.

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

Current yield:

Bond P =

Bond D =

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

Capital gains yield:

Bond P =

Bond D =

Explanation / Answer

Answer a.

BOND P:

Face Value = $1,000
Annual Coupon = 10%*$1,000 = $100
Annual YTM = 7%
Time to Maturity = 9 years

Current Price = $100 * PVIFA(7%, 9) + $1,000 * PVIF(7%, 9)
Current Price = $100 * (1 - (1/1.07)^9) / 0.07 + $1,000 / 1.07^9
Current Price = $1,195.46

Current Yield = Annual Coupon / Current Price
Current Yield = $100 / $1,195.46
Current Yield = 8.36%

BOND D:

Face Value = $1,000
Annual Coupon = 5%*$1,000 = $50
Annual YTM = 7%
Time to Maturity = 9 years

Current Price = $50 * PVIFA(7%, 9) + $1,000 * PVIF(7%, 9)
Current Price = $50 * (1 - (1/1.07)^9) / 0.07 + $1,000 / 1.07^9
Current Price = $869.70

Current Yield = Annual Coupon / Current Price
Current Yield = $50 / $869.70
Current Yield = 5.75%

Answer b.

BOND P:

Face Value = $1,000
Current Price = $1,195.46
Annual Coupon = 10%*$1,000 = $100
Annual YTM = 7%
Time to Maturity = 8 years

Next Year Price = $100 * PVIFA(7%, 8) + $1,000 * PVIF(7%, 8)
Next Year Price = $100 * (1 - (1/1.07)^8) / 0.07 + $1,000 / 1.07^8
Next Year Price = $1,179.14

Capital Gain Yield = (Next Year Price - Current Price) / Current Price
Capital Gain Yield = ($1,179.14 - $1,195.46) / $1,195.46
Capital Gain Yield = -1.37%

BOND D:

Face Value = $1,000
Current Price = $869.70
Annual Coupon = 5%*$1,000 = $50
Annual YTM = 7%
Time to Maturity = 8 years

Current Price = $50 * PVIFA(7%, 8) + $1,000 * PVIF(7%, 8)
Current Price = $50 * (1 - (1/1.07)^8) / 0.07 + $1,000 / 1.07^8
Current Price = $880.57

Capital Gain Yield = (Next Year Price - Current Price) / Current Price
Capital Gain Yield = ($880.57 - $869.70) / $869.70
Capital Gain Yield = 1.25%