Calculate the market value of a $100,000 bond that carries a coupon rate of 8% and has 7½ years remaining to maturity. The current market rate on this bond is 6.68% compounded semiannually.

Question

Quizplus · Accepted Answer

The market value of a bond can be calculated using the present value of its future cash flows, which include the present value of its coupon payments and the present value of its face value at maturity. Given that the bond has a coupon rate of 8% on a $100,000 face value, it pays $4,000 in interest per year, or $2,000 every six months. Since the market rate is 6.68% compounded semiannually, the effective semiannual rate is 3.34% (6.68% / 2). The bond has 7.5 years left to maturity, which equals 15 six-month periods.The present value of the coupon payments (an annuity) can be calculated using the formula PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the payment per period, r is the interest rate per period, and n is the total number of periods. Plugging in the values gives us PV = $2,000 * [(1 - (1 + 0.0334)^-15) / 0.0334], which equals approximately $24,689.The present value of the face value of the bond (a lump sum) can be calculated using the formula PV = FV / (1 + r)^n, where FV is the face value. Plugging in the values gives us PV = $100,000 / (1 + 0.0334)^15, which equals approximately $83,000.Adding these two components gives us the market value of the bond: approximately $24,689 + $83,000 = $107,689.

Calculate the Market Value of a $100,000 Bond That Carries