Question 8.A.1: Pricing a Bond PROBLEM: Your stockbroker is trying to sell y...
Pricing a Bond
PROBLEM: Your stockbroker is trying to sell you a 15-year bond with a 7 percent coupon, and the interest, or yield, on similar bonds is 10 percent. Is the bond selling for a premium, at par, or at a discount? Answer the question without making any calculations, and then prove that your answer is correct. The time line is as follows:
APPROACH: Since the market rate of interest is greater than the coupon rate (i > coupon rate), the bond must sell at a discount.
To prove the answer is correct (or wrong), we can compute the bond’s price with a financial calculator.
The bond is selling at a discount, and it should. Why? The market rate of interest is 10 percent, and the bond is paying only 7 percent. Since the bond’s coupon rate is fixed, the only way we can bring the bond’s yield up to the current market rate of 10 percent is to reduce the price of the bond to $771.82.