Question

1. A $1,000 face value bond of Acme Inc. pays an annual coupon and carries a coupon rate of 8.25%. It was a 30 year bond when issued and it has 11 years remaining to maturity. If it currently has a yield to maturity of 5.75%.

(a) What interest payments do bondholders receive each year?

(b) What is the current bond price?

(c) What is the bond price if the yield to maturity rises to 7.625%?

Answer 1

1)

Interest payments = (8.25 / 100) * 1000

Interest payments = $82.5

2)

Price of bond = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price of bond = 82.5 * [1 - 1 / (1 + 0.0575)^11] / 0.0575 + 1000 / (1 + 0.0575)^11

Price of bond = 82.5 * [1 - 0.54065] / 0.0575 + 540.649572

Price of bond = 82.5 * 7.988703 + 540.649572

Price of bond = $1,199.72

3)

Price of bond = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price of bond = 82.5 * [1 - 1 / (1 + 0.07625)^11] / 0.07625 + 1000 / (1 + 0.07625)^11

Price of bond = 82.5 * [1 - 0.44561] / 0.07625 + 445.610269

Price of bond = 82.5 * 7.270685 + 445.610269

Price of bond = $1,045.44