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    Time Value of Money

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    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?

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    https://brainmass.com/math/basic-algebra/time-value-of-money-432042

    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