Question

	Face Value	Coupon Rate	Years to Maturity	Market Rate
a)	$100	r = 10.75%	4	j2 = 12.5%
b)	$1,000	r = 7%	11	j2 = 7%
c)	$10,000	r = 6.75%	21	j2 = 5%

Calculate the purchase price of the following bonds. Indicate whether the bonds are priced at a discount, at par or at a premium. Give your answers in dollars and cents to the nearest cent.

Quoted coupon rates and market rates are nominal annual rates compounded semi-annually.

a)Price = $

This bond is priced at:

a discount
par
a premium

b)Price = $

This bond is priced at:

a discount
par
a premium

c)Price = $

This bond is priced at:

a discount
par
a premium

Answer 1

a)

K = Nx2

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

k=1

K =4x2

Bond Price =∑ [(10.75*100/200)/(1 + 12.5/200)^k]     +   100/(1 + 12.5/200)^4x2

k=1

Bond Price = 94.62

Price is less than par value hence it is a discount bond

b)

K = Nx2

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

k=1

K =11x2

Bond Price =∑ [(7*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^11x2

k=1

Bond Price = 1000

Price is equal to par value hence it is priced at par

c)

K = Nx2

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

k=1

K =21x2

Bond Price =∑ [(6.75*10000/200)/(1 + 5/200)^k]     +   10000/(1 + 5/200)^21x2

k=1

Bond Price = 12259.3

Price is more than par value hence it is a premium bond