Westover Ridge offers a 9% coupon bond with semiannual payments and a yield to maturity of 11.68%. The bonds mature in 16 years. What is the market price per bond if the face value is $1,000?

Question

Quizplus · Accepted Answer

The market price of a bond can be calculated using the formula for the present value of an annuity (for the coupon payments) plus the present value of a lump sum (for the face value of the bond at maturity). Given a 9% annual coupon rate with semiannual payments, the semiannual coupon rate is 4.5% (9% / 2) of the $1,000 face value, which equals $45 per period. With a yield to maturity of 11.68% annually, the semiannual yield is 5.84% (11.68% / 2). The bond matures in 16 years, which equals 32 semiannual periods. The present value of the annuity (coupon payments) is calculated using the formula PV = C * [1 - (1 + r)^-n] / r, where C is the coupon payment per period, r is the semiannual yield rate as a decimal, and n is the total number of periods. The present value of the lump sum (face value) is calculated using the formula PV = F / (1 + r)^n, where F is the face value. Adding these two present values gives the market price of the bond. Plugging in the given values, the calculation confirms that the correct market price is closest to option A, $807.86.

Westover Ridge Offers a 9% Coupon Bond with Semiannual Payments