Question

Bond P is a premium bond with a coupon rate of 8 percent. Bond D has a coupon rate of 3 percent and is currently selling at a discount. Both bonds make annual payments, have a YTM of 5 percent, and have ten years to maturity.

  

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.)

Answer 1

Given information for bond P:
Coupon rate=8%
YTM or discount rate=5%
Time to maturity=10 years
Let's take the face value of the bond as $1000
Then present value or PV=$1,231.65 (Calculations done in excel)

1 period closer to maturity

Coupon rate=8%
YTM or discount rate=5%
Time to maturity=9 years
Let's take the face value of the bond as $1000
Then present value or PV= $1,213.23 (Calculations done in excel)

Change in Price=$1,231.65-$1,213.23=$18.42

Capital Gain/Loss yield= [PV (at maturity 10 years) - PV (at maturity 9 years)]/(PV when maturity is 9 years)
=$18.42/$1,213.23= 0.015182612 or 1.52%

Given information for bond D:
Coupon rate=3%
YTM or discount rate=5%
Time to maturity=10 years
Let's take the face value of the bond as $1000
Then present value or PV=$845.57 (Calculations done in excel)

1 period closer to maturity

Coupon rate=3%
YTM or discount rate=5%
Time to maturity=9 years
Let's take the face value of the bond as $1000
Then present value or PV=$857.84   (Calculations done in excel)

Change in Price=$845.57-$857.84=-$12.27
Capital Gain/Loss yield= [PV (at maturity 10 years) - PV (at maturity 9 years)]/(PV when maturity is 9 years)

=-$12.27/$857.84=-0.014303367 or -1.43%