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29 January, 14:36

A 20-year maturity bond with par value of $1,000 makes semiannual coupon payments at a coupon rate of 8%. Find the bond equivalent and effective annual yield to maturity of the bond for the following bond prices.

a. $940.

b. $1,000.

c. $1,060.

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  1. 29 January, 16:05
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    a. At $940, Effective annual yield to maturity is 8.64 %

    b. At $1,000, Effective annual yield to maturity is 8 %

    c. At $1,060, Effective annual yield to maturity is 7.42%

    Explanation:

    Part a. Effective annual yield to maturity of the bond at bond price of $940.

    PV = - $940

    N = 20 * 2 = 40

    PMT = 1000 * 8% * (1/2) = $ 40

    FV = $1,000

    YTM = 4.3176

    Therefore Effective annual yield to maturity is 4.3176 * 2 = 8.64 %

    Part b. Effective annual yield to maturity of the bond at bond price of $1,000.

    PV = - $1,000

    N = 20 * 2 = 40

    PMT = 1000 * 8% * (1/2) = $ 40

    FV = $1,000

    YTM = 4.00

    Therefore Effective annual yield to maturity is 4.00 * 2 = 8 %

    Part c. Effective annual yield to maturity of the bond at bond price of $1,060.

    PV = - $1,060

    N = 20 * 2 = 40

    PMT = 1000 * 8% * (1/2) = $ 40

    FV = $1,000

    YTM = 3.7098

    Therefore Effective annual yield to maturity is 3.7098 * 2 = 7.42%
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