Question

Problem 7-16 Interest Rate Risk [LO2] Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has four years to maturity, whereas Bond Dave has 15 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16) Percentage change in price of Bond Sam Percentage change in price of Bond Dave If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Round your answers to 2 decimal places. (e.g., 32.16) Percentage change in price of Bond Sam Percentage change in price of Bond Dave

Answer 1

When the bonds are selling at par then its YTM will be equal to Coupon Rate. Thus

Bond Sam Current YTM = 7%

Bond Dave Current YTM = 7%

a. If Interest Rates Rise by 2% then YTM will be 9%

Price of Bond Sam = Coupon * PVAF ( 4.5%, 8) + Maturity * PVF ( 4.5%, 8)

Price of Bond Sam = 35 * 6.5959 + 1000 * 0.7032

Price of Bond Sam = $934.04

Percentage Change in price of Bond Sam = (New Price - Initial Price) / Initial Price

Percentage Change in price of Bond Sam = (934.04 - 1000) / 1000

Percentage Change in price of Bond Sam = - 6.60%

Price of Bond Dave = Coupon * PVAF ( 4.5%, 30) + Maturity * PVF ( 4.5%, 30)

Price of Bond Dave = 35 * 16.2889 + 1000 * 0.2670

Price of Bond Dave = $837.11

Percentage Change in price of Bond Dave = (New Price - Initial Price) / Initial Price

Percentage Change in price of Bond Dave = (837.11 - 1000) / 1000

Percentage Change in price of Bond Dave = - 16.29%

b. If Interest Rates Fall by 2% then YTM will be 5%

Price of Bond Sam = Coupon * PVAF ( 2.5%, 8) + Maturity * PVF ( 2.5%, 8)

Price of Bond Sam = 35 * 7.1701 + 1000 * 0.8207

Price of Bond Sam = $1071.70

Percentage Change in price of Bond Sam = (New Price - Initial Price) / Initial Price

Percentage Change in price of Bond Sam = (1071.70 - 1000) / 1000

Percentage Change in price of Bond Sam = + 7.17%

Price of Bond Dave = Coupon * PVAF ( 2.5%, 30) + Maturity * PVF ( 2.5%, 30)

Price of Bond Dave = 35 * 20.9303 + 1000 * 0.4767

Price of Bond Dave = $1209.30

Percentage Change in price of Bond Dave = (New Price - Initial Price) / Initial Price

Percentage Change in price of Bond Dave = (1209.30 - 1000) / 1000

Percentage Change in price of Bond Dave = + 20.93%