USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
XLR Corporation just issued a $1,000 par value bond with a 7 percent yield to maturity, twenty years to maturity, with an 8 percent semi-annual coupon rate.
-Refer to Exhibit 12.2. If market interest rates are constant, what will the price of the XLR Corporate bond be in three years?
A) $904.29
B) $1,097.63
C) $1,098.50
D) $1,102.85
E) $1,105.62

Question

Quizplus · Accepted Answer

The price of the bond in three years can be calculated using the present value of its remaining payments (17 years of semi-annual coupon payments and the principal repayment at maturity), discounted at the bond's yield to maturity (7% annually, or 3.5% semi-annually). Given the bond's semi-annual coupon rate of 8% on a $1,000 par value, the semi-annual coupon payment is $40. Using the formula for the present value of an annuity for the coupon payments and the present value formula for a single sum for the par value, and discounting these at the bond's yield to maturity of 3.5% per period for the remaining 34 periods (17 years * 2), the calculated price closely matches choice C, $1,098.50. This indicates that, despite the bond having a higher coupon rate than the yield to maturity, its price will adjust over time to reflect the present value of its future cash flows at the current market rates.