Question

A 6 percent coupon bond, with 12 years left to maturity, is priced to offer a 6.5 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.25 percent. What is the change in price of the bond, in dollars? Assume semi-annual interest payments and $1,000 par value. (Round your answer to 2 decimal places. Do not include a dollar sign. If the price decreases, use a negative "-" sign. If the price increases, use a "+" sign.)

Answer 1

Assuming face value to be $1000

Number of periods = 12 * 2 = 24

Semi annual coupon = [(6 / 100) * 1000] / 2 = 30

Semi annual rate = 6.5% / 2 = 3.25%

Current price = Coupon * [1 - 1 / (1 + rate)^time] / rate + face value / (1 + rate)^time

Current price = 30 * [1 - 1 / (1 + 0.0325)^24] / 0.0325 + 1000 / (1 + 0.0325)^24

Current price = 30 * [1 - 0.46413] / 0.0325 + 464.12884

Current price = 30 * 16.48834 + 464.12884

Current price = $958.77914

Price in 1 year:

Number of periods = 11 * 2 = 22

Semi annual coupon = [(6 / 100) * 1000] / 2 = 30

Semi annual rate = 6.25% / 2 = 3.125%

Current price = Coupon * [1 - 1 / (1 + rate)^time] / rate + face value / (1 + rate)^time

Current price = 30 * [1 - 1 / (1 + 0.03125)^22] / 0.03125 + 1000 / (1 + 0.03125)^22

Current price = 30 * [1 - 0.50815] / 0.03125 + 508.15107

Current price = 30 * 15.73917 + 508.15107

Current price = $980.32604

Change in price of bond = 980.32604 - 958.77914

Change in price of bond = 21.55