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

Answer 2

1. The price of the 4-year bond if its yield increases to 9% is $967.03.
2. The price of the 4-year bond if its yield decreases to 7% is $1033.87.
3. The price of the 8-year bond if its yield increases to 9% is $944.65.
4. The price of the 8-year bond if its yield decreases to 7% is $1059.71.
5. The price of the 30-year bond if its yield increases to 9% is $821.89.
6. The price of the 30-year bond if its yield decreases to 7% is $992.72

What is the price of the bonds?

The price of the bonds can be determined by calculating the present value of the bonds. Present value is the sum of discounted cash flows.

Present value can be calculated with a fiancial calculator.

Cash flow each year from year 1 to 4 = $80

Cash flow in year 4 = 1000

Price when yield is 9% = $967.03.

Price when yield is 7% =  $1033.87.

Cash flow each year from year 1 to 8 = $80

Cash flow in year 8 = 1000

Price when yield is 9% = $944.65.

Price when yield is 7% = $1059.71.

Cash flow each year from year 1 to 30 = $80

Cash flow in year 30 = 1000

Price when yield is 9% = $821.89.

Price when yield is 7% = $992.72

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