In: Finance
Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 16 years to maturity. |
a. |
If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (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.) |
b. | 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? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) |
Because bonds are priced at par that means original price = 1000 and YTM =coupon rate = 9% for both |
Part 1 |
Change in YTM =2 |
Bond Sam |
K = Nx2 |
Bond Price =∑ [( Coupon)/(1 + YTM/2)^k] + Par value/(1 + YTM/2)^Nx2 |
k=1 |
K =3x2 |
Bond Price =∑ [(9*1000/200)/(1 + 11/200)^k] + 1000/(1 + 11/200)^3x2 |
k=1 |
Bond Price = 950.04 |
%age change in price =(New price-Old price)*100/old price |
%age change in price = (950.04-1000)*100/1000 |
= -5% |
Bond Dave |
K = Nx2 |
Bond Price =∑ [( Coupon)/(1 + YTM/2)^k] + Par value/(1 + YTM/2)^Nx2 |
k=1 |
K =16x2 |
Bond Price =∑ [(9*1000/200)/(1 + 11/200)^k] + 1000/(1 + 11/200)^16x2 |
k=1 |
Bond Price = 850.96 |
%age change in price =(New price-Old price)*100/old price |
%age change in price = (850.96-1000)*100/1000 |
= -14.9% |
Part 2 |
Change in YTM =-2 |
Bond Sam |
K = Nx2 |
Bond Price =∑ [( Coupon)/(1 + YTM/2)^k] + Par value/(1 + YTM/2)^Nx2 |
k=1 |
K =3x2 |
Bond Price =∑ [(9*1000/200)/(1 + 7/200)^k] + 1000/(1 + 7/200)^3x2 |
k=1 |
Bond Price = 1053.29 |
%age change in price =(New price-Old price)*100/old price |
%age change in price = (1053.29-1000)*100/1000 |
= 5.33% |
Bond Dave |
K = Nx2 |
Bond Price =∑ [( Coupon)/(1 + YTM/2)^k] + Par value/(1 + YTM/2)^Nx2 |
k=1 |
K =16x2 |
Bond Price =∑ [(9*1000/200)/(1 + 7/200)^k] + 1000/(1 + 7/200)^16x2 |
k=1 |
Bond Price = 1190.69 |
%age change in price =(New price-Old price)*100/old price |
%age change in price = (1190.69-1000)*100/1000 |
= 19.07% |