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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.

$2.19