Question

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.

	Face Value	Coupon Rate	Years to Maturity	Market Rate
a)	$100	r = 9%	5	j2 = 9%
b)	$1,000	r = 9.25%	9	j2 = 7.5%
c)	$10,000	r = 8.5%	21	j2 = 10.25%

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) Price of a bond= PV of future cash flows discounted at required rate of return

= coupon* annuity factor (9%,5 yrs) + face value* disc. factor(9%,5th yr)

= 9*3.890 + 100*0.650

= 100 (approx)

The bond is trading at par (evident because coupon rate= required return, i.e, market rate)

(b)

Price of a bond= PV of future cash flows discounted at required rate of return

= coupon* annuity factor (7.5%,9 yrs) + face value* disc. factor(7.5%,9th yr)

= 92.5*6.3789 + 1000*0.521

= 590.05 + 521

= 1111.05

Bond is trading at premium (since coupon rate> market rate)

(c)  

Price of a bond= PV of future cash flows discounted at required rate of return

= coupon* annuity factor (10.25%,21 yrs) + face value* disc. factor(10.25%,21st yr)

= 7224.26 + 1288

= $ 8512.26

Bond is trading at discount (since coupon rate< market rate)