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30 November, 11:28

Matt purchased a 20-year par value bond with an annual coupon rate of 8% compounded semiannually for a price of 1722.25. The coupons begin paying 6-months after the bond is purchased, and the bond can be called at par value X on any coupon date starting at the end of year 15, after the coupon is paid. The price guarantees that Matt will receive a nominal annual yield rate of at least 6% compounded semiannually. Note: The price guarantees that the yield will be a minimum of 6%. Find X (a) 1460 (b) 1440 (c) 1420 (d) 1400 (e) 1380

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  1. 30 November, 15:27
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    (b) 1440

    Explanation:

    As the coupon rate of 8% is greater than the yield to maturity (YTM) of 6% annually, the bond is selling at a premium. Hence, the bond will be called at the earliest i. e. 15 years.

    Coupon = Call Price * Semi-annual coupon rate = X * [0.08 / 2] = X * 0.04

    Yield to call = 6% annually = 3% semi-annually

    Time = 15 years * 2 = 30

    We know that,

    Current Price of bond = Coupon * [1 - (1 + YTC) - call date] / YTC + Call Price / (1 + YTC) call date

    1,722.25 = [X * 0.04] * [1 - (1 + 0.03) - 30] / 0.03 + [X / (1 + 0.03) 30]

    1,722.25 = [X * 0.04] * 19.60 + [X * 0.41]

    1,722.25 = X * [ (0.04 * 19.60) + 0.41]

    1,722.25 = X * 1.194

    X = 1,722.25 / 1.194 X=$ 1,442.42 / approx $ 1,440
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