Question

MicroDrive has issued bonds that have a 6% coupon rate, payable semiannually. The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 5%. What is the current price of the bonds?

Answer 1

Price of the bond could be calculated using below formula.

P = C/ 2 [1 - {(1 + YTM/2) ^2*n}/ (YTM/2)] + [F/ (1 + YTM/2) ^2*n]

Where,

                Face value (F) = $1000

                Coupon rate = 0.06

                YTM or Required rate = 0.05

                Time to maturity (n) = 8 years

                Annual coupon C = $60

Let's put all the values in the formula to find the bond current value

P = 60/ 2 [{1 - (1 + 0.05/2) ^-2*8}/ (0.05/ 2)] + [1000/ (1 + 0.05/2) ^2*8]

    = 30 [{1 - (1 + 0.025) ^ -16}/ (0.025)] + [1000/ (1 + 0.025) ^16]

    = 30 [{1 - (1.025) ^ -16}/ (0.025)] + [1000/ (1.025) ^16]

    = 30 [{1 - 0.67362}/ (0.025)] + [1000/ 1.48451]

    = 30 [0.32638/ 0.025] + [673.62295]

    = 30 [13.0552] + [673.62295]

    = 391.656 + 673.62295

    = 1065.27895

So price of the bond is $1065.28

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Hope this answer your query.

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