Question

Problem 13. Suppose there are two bonds you are considering Bond A Bond B

	Bond A	Bond B
Maturity (years)	20	30
Coupon rate (%)	12	8
Par value	1000	1000

(a) If both bonds had a required rate of return of 10%, what would the bonds' prices be?

(b) 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

a. The price for bond A can be calculated as

120/1.1 + 120/(1.1^2) + ....1120/1.1^20

We can use excel to solve this. Manually it can also be done by using formula for Geometric Progression.

In excel we can use =pv function for present value of bond.

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

Similarly price of bond B is

=pv(0.10,30,80,1000) = 811.46

b. When the price of the bond is below the face value, then it is said to be selling at a discount, creating a capital appreciation upon maturity. When the price of the bond is higher than face value, then it is said to be tradinng at a premium. Bonds are sold at a discount when the market interest rate is higher than the coupon payment rate. Similarly, when market interest rate is lower than coupon payment rate then the bond sells at a premium.

Without even calculating the prices for bond A&B, we can know that the price of bond A will be at a premium and that of B will be at a discount. The coupon payment for bond A is 12% which is higher than market rate of 10%. Hence it is sold at a premium. The coupon rate of bond B is lower than market rate causing it to be sold for a discount.