Question

Consider the following​ bonds:

Bond	Coupon Rate ​(annual payments)	Maturity ​(years)
A	0.0​%	15
B	0.0​%	10
C	4.2​%	15
D	8.2​%	10

What is the percentage change in the price of each bond if its yield to maturity falls from

6.9 % to 5.9 %​?

The price of bond A at 6.9% YTM per $100 face value is ​$? (Round to the nearest​ cent.)

Answer 1

A

K = N

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

k=1

K =15

Bond Price =∑ [(0*100/100)/(1 + 6.9/100)^k]     +   100/(1 + 6.9/100)^15

k=1

Bond Price = 36.76

Change in YTM =-1

Bond

K = Nx2

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

k=1

K =15x2

Bond Price =∑ [(0*100/200)/(1 + 5.9/200)^k]     +   100/(1 + 5.9/200)^15x2

k=1

Bond Price = 41.8

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

%age change in price = (41.8-36.76)*100/36.76

= 13.71%

B

K = N

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

k=1

K =10

Bond Price =∑ [(0*100/100)/(1 + 6.9/100)^k]     +   100/(1 + 6.9/100)^10

k=1

Bond Price = 51.31

Change in YTM =-1

Bond

K = Nx2

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

k=1

K =10x2

Bond Price =∑ [(0*100/200)/(1 + 5.9/200)^k]     +   100/(1 + 5.9/200)^10x2

k=1

Bond Price = 55.91

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

%age change in price = (55.91-51.31)*100/51.31

= 8.97%

C

K = N

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

k=1

K =15

Bond Price =∑ [(4.2*100/100)/(1 + 6.9/100)^k]     +   100/(1 + 6.9/100)^15

k=1

Bond Price = 75.25

Change in YTM =-1

Bond

K = Nx2

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

k=1

K =15x2

Bond Price =∑ [(4.2*100/200)/(1 + 5.9/200)^k]     +   100/(1 + 5.9/200)^15x2

k=1

Bond Price = 83.23

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

%age change in price = (83.23-75.25)*100/75.25

= 10.6%

D

K = N

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

k=1

K =10

Bond Price =∑ [(8.2*100/100)/(1 + 6.9/100)^k]     +   100/(1 + 6.9/100)^10

k=1

Bond Price = 109.17

Change in YTM =-1

Bond

K = Nx2

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

k=1

K =10x2

Bond Price =∑ [(8.2*100/200)/(1 + 5.9/200)^k]     +   100/(1 + 5.9/200)^10x2

k=1

Bond Price = 117.19

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

%age change in price = (117.19-109.17)*100/109.17

= 7.35%