Question

aurel, 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 four years to maturity, whereas the Hardy Corp. bond has 15 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.) 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.)

Answer 1

Because bonds are priced at par that means original price = 1000 and YTM =coupon rate = 7% for both

Part 1

Change in YTM =2

Bond Laurel

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =4x2

Bond Price =∑ [(7*1000/200)/(1 + 9/200)^k]     +   1000/(1 + 9/200)^4x2

k=1

Bond Price = 934.04

%age change in price =(New price-Old price)*100/old price

%age change in price = (934.04-1000)*100/1000

= -6.6%

Bond Hardy

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =15x2

Bond Price =∑ [(7*1000/200)/(1 + 9/200)^k]     +   1000/(1 + 9/200)^15x2

k=1

Bond Price = 837.11

%age change in price =(New price-Old price)*100/old price

%age change in price = (837.11-1000)*100/1000

= -16.29%

Part 2

Change in YTM =-2

Bond Laurel

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =4x2

Bond Price =∑ [(7*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^4x2

k=1

Bond Price = 1071.7

%age change in price =(New price-Old price)*100/old price

%age change in price = (1071.7-1000)*100/1000

= 7.17%

Bond Hardy

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =15x2

Bond Price =∑ [(7*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^15x2

k=1

Bond Price = 1209.3

%age change in price =(New price-Old price)*100/old price

%age change in price = (1209.3-1000)*100/1000

= 20.93%