Calculate the market value of a 25-year, $1,000 Alberta Government bond that has nine years remaining to maturity, a coupon rate of 9% and is trading today at a yield rate of 7.2% (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 9% on a $1,000 face value, it pays $45 in interest every six months ($1,000 * 9% / 2). Since the yield rate is 7.2% compounded semiannually, the semiannual yield rate is 3.6% (7.2% / 2). With nine years to maturity, there are 18 six-month periods remaining.The present value of the coupon payments (an annuity) can be calculated using the formula: PV = C * [1 - (1 + r)^-n] / r, where C is the semiannual coupon payment, r is the semiannual yield rate (as a decimal), and n is the total number of payments. Substituting the values, we get: PV = $45 * [1 - (1 + 0.036)^-18] / 0.036.The present value of the face value (a lump sum) can be calculated using the formula: PV = F / (1 + r)^n, where F is the face value. Substituting the values, we get: PV = $1,000 / (1 + 0.036)^18.Adding these two present values gives the market value of the bond. Calculating these values:PV of coupon payments = $45 * [1 - (1 + 0.036)^-18] / 0.036 ≈ $611.83PV of face value = $1,000 / (1 + 0.036)^18 ≈ $506.32Market value of the bond ≈ $611.83 + $506.32 ≈ $1,118.15Therefore, the closest answer is $1,118 (Choice B).

Calculate the Market Value of a 25-Year, $1,000 Alberta Government