Question

A $1,000 par value bond with 5 years left to maturity pays an interest payment semiannually with a 8 percent coupon rate and is priced to have a 5.5 percent yield to maturity. If interest rates surprisingly change by 0.27 percent, by how much would the bond’s price change?

Answer 1

Current price:

Semi annual coupon = (0.08 * 1000) / 2 = 40

Number of periods = 5 * 2 = 10

Semi annual rate = 5.5% / 2 = 2.75%

Current price = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Current price = 40 * [1 - 1 / (1 + 0.0275)^10] / 0.0275 + 1000 / (1 + 0.0275)^10

Current price = 40 * [1 - 0.762398] / 0.0275 + 762.397906

Current price = 40 * 8.640076 + 762.397906

Current price = $1,108.00

New price:

Assuming interest rate went UP by 0.27%

New interest rate = (5.5% + 0.27%) / 2 = 2.885%

New price = 40 * [1 - 1 / (1 + 0.02885)^10] / 0.02885 + 1000 / (1 + 0.02885)^10

New price = 40 * [1 - 0.752453] / 0.02885 + 752.453005

New price = 40 * 8.580485 + 752.453005

New price = $1,095.67

Price will change by = 1,108 - 1,095.67 = $12.33