Question

Refer to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) decline from 10 percent to 6 percent.
  
a. What is the bond price at 10 percent?

b. What is the bond price at 6 percent?
  
c. What would be your percentage return on investment if you bought when rates were 10 percent and sold when rates were 6 percent? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
  

Answer 1

Suppose the face value of the bond is $1,000 and are issued at par i.e.,for $1,000.

If the bonds are 10% bonds and the market rate of interest is also 10% the price of the bond is equal to the issue face value of the bond.

The price of the bond is calculated as follows.

1. Present value of the interest payments received over the bond period.

plus

2. present value of the maturity value of the bond

minus

3. Issue price of the bond.

a. When the market rate is 10%.

The annual interest payment on the above bond @10% = $100. (10% of $1,000)

Present value of $100 received for 20 years @ 10% = 100 x 8.514 = $851.40

Present value of $1,000 to be received after 20 years = 1,000 x 0.149 = $149.00

Total present value = $851.40+$149.00 = $1,000.

That means when the coupon rate and the market rate ar the same the price of the bond is the same as the face value of the bond.

b. When the market rate is 6%.

The annual interest payment on the above bond = $100. (10% of $1,000)

Present value of $100 received for 20 years @6 % = 100 x 11.470 = $1,147.00

Present value of $1,000 to be received after 20 years = 1,000 x 0.312 = $312.00

Total present value = $1,147+$312.00 = $1,459.

That means when the coupon rate is more than the market rate , the price of the bond will be higher than the face value as the bond is giving better price than the market.

c. When a bond bought @10% market rate is sold when the market rate is 6% the rate of return is

(Makret rate at 6% - market rate at 10%) / Market rate at 10% = (1,459 - 1,000) / 1,000 = 459 / 1000 = 45.9%