Question

A bond has a coupon rate of 8 percent, 7 years to maturity, semiannual interest payments, and a YTM of 7 percent. If interest rates suddenly rise by 1.5 percent, what will be the percentage change in the bond price?

Answer 1

Current price:

Assuming face value to be $1000

Semi annual coupon = (8% of 1000) / 2 = 40

Number of periods = 7 * 2 = 14

Semi annual YTM = 7% / 2 = 3.5%

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

Price = 40 * [1 - 1 / (1 + 0.035)^14] / 0.035 + 1000 / (1 + 0.035)^14

Price = 40 * [1 - 0.617782] / 0.035 + 617.78179

Price = 40 * 10.92052 + 617.78179

Price = $1,054.6026

Change in yield:

New YTM = 7% + 1.5% = 8.5%

Assuming face value to be $1000

Semi annual coupon = (8% of 1000) / 2 = 40

Number of periods = 7 * 2 = 14

Semi annual YTM = 8.5% / 2 = 4.25%

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

Price = 40 * [1 - 1 / (1 + 0.0425)^14] / 0.0425 + 1000 / (1 + 0.0425)^14

Price = 40 * [1 - 0.558387] / 0.0425 + 558.386756

Price = 40 * 10.3909 + 558.386756

Price = $974.02275

Percentage change in bond price = [(Ending price - beginning price) / beginning price] * 100

Percentage change in bond price = [(974.02275 - 1,054.6026) / 1,054.6026] * 100

Percentage change in bond price = -7.64%