J&J Manufacturing issued a bond with a $1,000 par value. The bond has a coupon rate of 7% and makes payments semiannually. If the bond has 30 years remaining and the annual market interest rate is 9.4%, what will the bond sell for today?

Question

Quizplus · Accepted Answer

The bond will sell for less than its par value because the coupon rate is less than the market interest rate. To find the present value of the bond, we calculate the present value of the annuity (coupon payments) and the present value of the par value. The formula for the present value of an annuity is PVA = PMT * [(1 - (1 + r)^-n) / r], where PMT is the payment per period, r is the market interest rate per period, and n is the total number of periods. For the par value, the formula is PV = F / (1 + r)^n, where F is the future value or par value. Given that the bond makes semiannual payments, we adjust the annual market interest rate and the number of years accordingly: r = 9.4% / 2 = 4.7% per period, n = 30 * 2 = 60 periods, and PMT = 7% of $1,000 / 2 = $35 per period. Plugging these values into the formulas gives us the bond's present value, which is closest to $760.91.

J&J Manufacturing Issued a Bond with a $1,000 Par Value