The Metchosin Corporation has two different bonds currently outstanding. Bond M has a face value of $40,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2,500 every six months over the subsequent eight years, and finally pays $2,800 every six months over the last six years. Bond N also has a face value of $40,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 8% compounded semiannually, what is the current price of bond M and bond N?

we must first calculate the effective interest rate:

the effective interest rate = 1.08 = (1 + r)²

√1.08 = √(1 + r)²

1.03923 = 1 + r

r = 3.923%

I used an excel spreadsheet to calculate the present value of bond M's coupon payments.

Bond M's price:

PV of face value = $40,000 / (1.03923)⁴⁰ = $8,582.09

PV of coupon payments = $27,449.05

market price = $36,031.14

to determine the market value of bond N (zero coupon bond) we can use the following formula:

market value = future value / (1 + r)ⁿ

market price = $40,000 / (1.03923)⁴⁰ = $8,582.09

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