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27 March, 13:44

A company needs $8 million in new capital for expanded composites manufacturing. It is offering small-denomination corporate bonds at a deep discount price of $800 for a 4% $1000 face value bond that matures in 20 years and pays the dividend semiannually. Find the nominal and effective annual rates, compounded semiannually, that this company is paying per investor

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  1. 27 March, 16:40
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    nominal interest rate = 4% annual

    effective interest rate = 5.56% annual

    Explanation:

    the bond's nominal rate is basically the coupon rate

    to calculate the bond's effective interest rate we must calculate its yield to maturity:

    YTM = [coupon + [ (face value - present value) / n]} / [ (face value + present value) / 2]

    coupon = $1,000 x 4% x 1/2 = $20 FV = $1,000 PV = $800 n = 40

    YTM = [20 + [ (1,000 - 800) / 40]} / [ (1,000 + 800) / 2]

    YTM = 25 / 900 = 2.777 semiannual ⇒ 5.56% annual
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