Question

 ​(Bond valuation​ relationships)  You own a bond that pays ​$120 in annual​ interest, with a ​$1,000 par value. It matures in 20 years. The​ market's required yield to maturity on a​ comparable-risk bond is 11 percent.

a.  Calculate the value of the bond.

b.  How does the value change if the yield to maturity on a​ comparable-risk bond​ (i) increases to 16 percent or​ (ii) decreases to 8 ​percent?

c.  Explain the implications of your answers in part b as they relate to​ interest-rate risk, premium​ bonds, and discount bonds.

d.  Assume that the bond matures in 4 years instead of 20

years and recalculate your answers in parts a and b.

e.  Explain the implications of your answers in part d as they relate to​ interest-rate risk, premium​ bonds, and discount bonds.

Answer 1

A) Using financial calculator to calculate the price of the bond

Inputs: N= 20

I/y= 11%

Pmt= 120

Fv= 1,000

Pv= compute

We get, price of the bond as $1,079.63

B) i) Using financial calculator to calculate the price of the bond

Inputs: N= 20

I/y= 16%

Pmt= 120

Fv= 1,000

Pv= compute

We get, price of the bond as $762.85

ii) Using financial calculator to calculate the price of the bond

Inputs: N= 20

I/y= 8%

Pmt= 120

Fv= 1,000

Pv= compute

We get, price of the bond as $1,392.73

C) In the first case, the bond is a discount bond as it has higher yield to maturity than coupon rate. Due to the increase in ytm from 11% to 16%, the value of the bond decreases . This shows that the interest rate risk has increased.

In the second case, the bond is a premium bond as it has lower yield to maturity than coupon rate. Due the decrease in interest rate from 11% to 8% , the value of the bond has increased. This implies that the interest rate risk has decreased, which has led to the increase in value of bond.

D)

i) Using financial calculator to calculate the price of the bond

Inputs: N= 4

I/y= 11%

Pmt= 120

Fv= 1,000

Pv= compute

We get, price of the bond as $1,031.02

ii) interest rate is 16%

Using financial calculator to calculate the price of the bond

Inputs: N= 4

I/y= 16%

Pmt= 120

Fv= 1,000

Pv= compute

We get, price of the bond as $888.07

iii) interest rate is 8%

Using financial calculator to calculate the price of the bond

Inputs: N= 4

I/y= 8%

Pmt= 120

Fv= 1,000

Pv= compute

We get, price of the bond as $1,132.49