# Time Value of Money

Question 1

Pacific Homecare has three bond issues outstanding. All three bonds pay $100 in annual interest plus $1,000 at maturity. Bond S has a maturity of five years, Bond M has a 15-year maturity, and Bond L matures in 30 years.

a. What is the value of these bonds when the required interest rate is 5 percent, 10 percent, and 15 perrcent?

b. Why is the price of Bond L more sensitive to interest rate changes than the price of Bond S?

Question 2

Six years ago, Bradford Community Hospital issued 20-year municipal bonds with a 7 percent annual coupon rate. The bonds were called today for a $70 call premium-that is, bondholders received $1,070 for each bond. What is the realized rate of return for those investors who bought the bonds for $1,000 when they were issued?

#### Solution Preview

a. What is the value of these bonds when the required interest rate is 5 percent, 10 percent, and 15 percent?

Case : Interest Rate=5%

For Bond S,

Number of coupon payments=n=5

Coupon amount=C=$100

Maturity amount=M=$1000

Interest Rate=r=5%

Value of Bond S= C/r*(1-1/(1+r)^n)+M/(1+r)^n=100/5%*(1-1/(1+5%)^5)+1000/(1+5%)^5=$1216.47

For Bond M,

Number of coupon payments=n=15

Coupon amount=C=$100

Maturity amount=M=$1000

Interest Rate=r=5%

Value of Bond M= C/r*(1-1/(1+r)^n)+M/(1+r)^n=100/5%*(1-1/(1+5%)^15)+1000/(1+5%)^15=$1518.98

For Bond L,

Number of coupon payments=n=30

Coupon amount=C=$100

Maturity amount=M=$1000

Interest Rate=r=5%

Value of Bond L= C/r*(1-1/(1+r)^n)+M/(1+r)^n=100/5%*(1-1/(1+5%)^30)+1000/(1+5%)^30=$1768.62

Case : Interest Rate=10%

For Bond S,

Number of coupon payments=n=5

Coupon ...

#### Solution Summary

There are two problems. Solution to first problem depicts the steps to calculate value of a coupon paying bond. Solution to second problem calculates the realized rate of return.