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24 May, 03:23

Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 23 years to maturity, and a coupon rate of 3.8 percent paid annually. If the yield to maturity is 4.7 percent, what is the current price of the bond?

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  1. 24 May, 04:13
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    The current price of the bond is $875.09

    Explanation:

    The bonds are priced based on the present value of the coupon payments that will be made on the bond till maturity, treated as an annuity, and the face value of the bond. The formula for the current price of the bond is,

    Present Value of bond = PMT * [ 1 - (1+r) ^-n / r] + Face value / (1+r) ^n

    Where,

    r is the market interest rate or yield to maturity

    n is the number of years to maturity for an annual bond

    PMT is the coupon payment or interest payment per year for an annual bond

    PMT = 1000 * 0.038 = 38

    Present Value of bond = 38 * [ 1 - (1+0.047) ^-23 / 0.047] + 1000 / (1+0.047) ^23

    Present value of the bond = $875.094 rounded off to 875.09
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