Question

Bond P is a premium bond with a coupon rate of 9 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 10 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.) 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

Answer:

a) 7% as their market price will adjsut to give the same yield as the market

b) bond P = -10.17

 bonds D  = 10.07

Explanation:

we have to calcualte the price variation of the bonds from now (10 years to maturity) to next year (9 years)

Bond P

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 90.000

time 10

rate 0.07

$90 \times \frac{1-(1+0.07)^{-10} }{0.07} = PV$

PV $632.1223

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   10.00

rate  0.07

$\frac{1000}{(1 + 0.07)^{10} } = PV$  

PV   508.35

PV c $632.1223

PV m  $508.3493

Total $1,140.4716

then, at time = 9

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 90.000

time 9

rate 0.07

$90 \times \frac{1-(1+0.07)^{-9} }{0.07} = PV$

PV $586.3709

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   9.00

rate  0.07

$\frac{1000}{(1 + 0.07)^{9} } = PV$  

PV   543.93

PV c $586.3709

PV m  $543.9337

Total $1,130.3046

Capital loss: 1,130.30 - 1,140.47 = -10.17

We repeat the process for bond D

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 50.000

time 10

rate 0.07

$50 \times \frac{1-(1+0.07)^{-10} }{0.07} = PV$

PV $351.1791

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   10.00

rate  0.07

$\frac{1000}{(1 + 0.07)^{10} } = PV$  

PV   508.35

PV c $351.1791

PV m  $508.3493

Total $859.5284

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 50.000

time 9

rate 0.07

$50 \times \frac{1-(1+0.07)^{-9} }{0.07} = PV$

PV $325.7616

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   9.00

rate  0.07

$\frac{1000}{(1 + 0.07)^{9} } = PV$  

PV   543.93

PV c $325.7616

PV m  $543.9337

Total $869.6954

Capital gain: 869.70 - 859.53 = 10.07