Question

	Bond A	Bond B
Maturity (years)	20	30
Coupon rate (%)	12	8
Par value	$1,000	$1,000

1. If both bonds had a required rate of return of 10%, what would the bonds’ prices be?

2. Explain what it means when a bond is selling at a discount, a premium, or at its face amount (par value). Based on results in part (a), would you consider both bonds to be selling at a discount, premium, or at par?

Answer 1

We will use the =pv function of excel to find the present value of these future cash flows. The present value will be the price so that arbitrage is not possible.

Bond A : It has 12% coupon meaning 120 payment every year.

=Pv(0.10,20,120,1000) = 1170.27

Therefore, price of Bond A is 1170.27 dollars. It is sold at a premium.

Bond B : it has yearly payments of 80

=Pv(.1,30,80,1000) = 811.46 dollars. It is sold at a discount.

Bonds that are priced lower than face value are said to be selling at a discount. Bonds which are priced higher than face value are said to be selling at a premium. And next we have bonds which are selling at face value. These bonds have return equal to yearly coupon payments.

Thus we can see that price of bond A is more than its face value and that of bond B is less than its face value. We could have known this fact before calculating too. When coupon payments are more than required rate of return then the bonds are priced at a premium. When coupon payments are less than required rate of return, we need more return and that is possible when bonds sell at a discount to face value. As bond A has higher coupon rate than required return (12>10) so it is sold at a premium. Bond B has coupon rate lower than required return (10>8) thus it is sold at a discount to compensate for lower coupons.