Question

# Calculate the purchase price of the following bonds. Indicate whether the bonds are priced at a...

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

b)Price = \$

This bond is priced at:

a discount
par

c)Price = \$

This bond is priced at:

a discount
par

(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)

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