Final answer:
The price of a bond is determined based on its stated interest rate versus the market interest rate, affecting whether it sells at a discount or premium. Present value calculations for both the interest payments and the principal repayment using the market rate are needed to find the exact price.
Step-by-step explanation:
When a bond's stated interest rate is lower than the effective (market) interest rate, the bond will sell at a discount, meaning you would pay less than the face value. Conversely, if the stated interest rate is higher than the market rate, the bond will sell at a premium, and you will pay more than face value. To determine the price of the bond, present value calculations must be made for both the interest payments and the principal repayment, using the market interest rate as the discount rate.
Example Calculation :
For case a, where the maturity is 10 years, the interest is paid annually, the stated rate is 7%, and the market rate is 9%, the bond's price will be the present value of the annuity of interest payments plus the present value of the single principal repayment at maturity:
- Interest payment (coupon) per year = 7% of $1.5 million = $105,000.
- Present value of annuity (10 years at 9%) of $105,000.
- Present value of $1.5 million discounted back 10 years at 9%.
The bond will therefore sell at a discount. The exact price can be calculated using present value formulas or financial calculators.