Question

Consider three bonds with 8% coupon rates, all making annual coupon payments and all selling at a face value of $1,000. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years.
a. What will be the price of the 4-year bond if its yield increases to 9%?
b. What will be the price of the 8-year bond if its yield increases to 9%?
c. What will be the price of the 30-year bond if its yield increases to 9%?
d. What will be the price of the 4-year bond if its yield decreases to 7%?
e. What will be the price of the 8-year bond if its yield decreases to 7%?
f. What will be the price of the 30-year bond if its yield decreases to 7%?

Answer 1

Answer:

A) 967.60

B) 944.65

C) 897.26

D)1,033.87

E)1,059.71

F)1,124.09

Explanation:

We must calcualte the present vale of the coupon payment and maturity at the gven market rate and time

A)

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

C 80.000

time 4

rate 0.09

$80 \times \frac{1-(1+0.09)^{-4} }{0.09} = PV$

PV $259.1776

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

Maturity   1,000.00

time   4.00

rate  0.09

$\frac{1000}{(1 + 0.09)^{4} } = PV$  

PV   708.43

PV c $259.1776

PV m  $708.4252

Total $967.6028

B)

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

C 80.000

time 8

rate 0.09

$80 \times \frac{1-(1+0.09)^{-8} }{0.09} = PV$

PV $442.7855

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

Maturity   1,000.00

time   8.00

rate  0.09

$\frac{1000}{(1 + 0.09)^{8} } = PV$  

PV   501.87

PV c $442.7855

PV m  $501.8663

Total $944.6518

C)

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

C 80.000

time 30

rate 0.09

$80 \times \frac{1-(1+0.09)^{-30} }{0.09} = PV$

PV $821.8923

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

Maturity   1,000.00

time   30.00

rate  0.09

$\frac{1000}{(1 + 0.09)^{30} } = PV$  

PV   75.37

PV c $821.8923

PV m  $75.3711

Total $897.2635

D)

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

C 80.000

time 4

rate 0.07

$80 \times \frac{1-(1+0.07)^{-4} }{0.07} = PV$

PV $270.9769

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

Maturity   1,000.00

time   4.00

rate  0.07

$\frac{1000}{(1 + 0.07)^{4} } = PV$  

PV   762.90

PV c $270.9769

PV m  $762.8952

Total $1,033.8721

E)

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

C 80.000

time 8

rate 0.07

$80 \times \frac{1-(1+0.07)^{-8} }{0.07} = PV$

PV $477.7039

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

Maturity   1,000.00

time   8.00

rate  0.07

$\frac{1000}{(1 + 0.07)^{8} } = PV$  

PV   582.01

PV c $477.7039

PV m  $582.0091

Total $1,059.7130

F)

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

C 80.000

time 30

rate 0.07

$80 \times \frac{1-(1+0.07)^{-30} }{0.07} = PV$

PV $992.7233

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

Maturity   1,000.00

time   30.00

rate  0.07

$\frac{1000}{(1 + 0.07)^{30} } = PV$  

PV   131.37

PV c $992.7233

PV m  $131.3671

Total $1,124.0904