7-10. (Bond valuation) You own a bond that pays $70 in annual interest, with a $

Question

7-10. (Bond valuation) You own a bond that pays $70 in annual interest, with a $1,000 par value. It matures in 15 years. Your required rate of return is 7 percent.

a. Calculate the value of the bond.

b. How does the value change if your required rate of return (1) increases to 9 percent or (2) decreases to 5 percent?

c. Explain the implications of your answers in part (b) as they relate to interest rate risk, pre- mium bonds, and discount bonds.

d. Assume that the bond matures in 5 years instead of 15 years.

Recompute your answers in part (b). e. Explain the implications of your answers in part (d) as they relate to interest rate risk, pre- mium bonds, and discount bonds.

Explanation / Answer

a) Price = present value of future vash flows

Price = 70/(1+7%) + 70/(1+7%)^2 ......................70/(1+7%)^15 + 1000/(1+7%)^15

price = 70*(1-1/1.07^15)/7%+ 1000/(1+7%)^15= $1000

b) 1) (1) increases to 9 percent

price = 70*(1-1/1.09^15)/9%+ 1000/(1+9%)^15=$838.79

(2) decreases to 5 percent

price = 70*(1-1/1.05^15)/5%+ 1000/(1+5%)^15=$1,207.59

c. As the required rate of return increases, value of bond decreases and vice versa

required rate of return is 7 percent - par bond

required rate of return is 9 percent - discount bond

required rate of return is 5 percent - premium bond

d.

d) 1) (1) increases to 9 percent

price = 70*(1-1/1.09^5)/9%+ 1000/(1+9%)^5=$922.21

(2) decreases to 5 percent

price = 70*(1-1/1.05^5)/5%+ 1000/(1+5%)^5=$1086.59

As the required rate of return increases, value of bond decreases and vice versa

but the variation is less if the maturity period is less

If maturity period is high than there is more risk with the changes in interest rate.

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