Laurel Inc and Hardy Corp both have 7 percent coupon bonds o

Laurel, Inc., and Hardy Corp. both have 7 percent coupon bonds outstanding, with semiannual interest payments, and both are priced at par value. The Laurel, Inc., bond has three years to maturity, whereas the Hardy Corp. bond has 16 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage change in price of Laurel Percentage change in price of Hardy If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of these bonds be then? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage change in price of Laurel Percentage change in price of Hardy

Solution

It is mentioned in the question that the bonds are priced at par value. Hence YTM = coupon rate = 7%.

Scenario 1: Interest rate increases by 2% - So the new rate = 7%+2% = 9%.

Also the coupon payment is semi-annual so quantum of each payment = (7% of $1,000)/2 = $35

Thus new price of Laurel = 35*(PVIFA 4.5%, 6)+1000*(PVIF 4.5%,6) = 948.42

Price of Hardy = 35*(PVIFA 4.5%, 32) + 1000*(PVIF 4.5%,32) = 832.11

Thus % change for Laurel = (948.42-1000)/1000 = -5.16%

% change for Hardy = (832.11-1000)/1000 = -16.79%

Scenario 2: Interest rates falls by 2% - so the new rate = 7%-2% = 5%

Price of Laurel = 35*(PVIFA 2.5%, 6)+1000*(PVIF 2.5%,6) = 1055.08

Price of Hardy = 35*(PVIFA 2.5%, 32) + 1000*(PVIF 2.5%,32) = 1218.5

Thus % change for Laurel = (1055.8-1000)/1000 = 5.51%

% change for Hardy = (1218.5-1000)/1000 = 21.85%