Final answer:
The annual coupon rate of a bond can be calculated by using the Present Value of an Annuity formula, setting the bond's market price equal to the present value of its future cash flows, and adjusting for semiannual payments and the given market interest rate.
Step-by-step explanation:
To calculate the annual coupon rate on the bond, given that the bond's market price is $1,322 and it has 25 years to maturity, we can first determine the annual coupon payment by setting the market price of the bond equal to the present value of its future cash flows. The market interest rate for similar bonds is 8% annually, but since the bond pays interest semiannually, we need to use 4% (which is 8% / 2) as the semiannual discount rate and double the number of years to reflect the semiannual periods.
To find the annual coupon payment (C), we use the Present Value of an Annuity formula:
P = C * [(1 - (1 + r)^(-n)) / r]
Where:
- P = Market price of the bond ($1,322)
- C = Semiannual coupon payment
- r = Market interest rate per period (0.04 or 4% semiannually)
- n = Total number of periods (25 years * 2 = 50 periods)
By rearranging the formula to solve for C and using the values above, we can calculate the semiannual coupon payment. After determining the semiannual coupon payment, we multiply by 2 to get the annual coupon rate.
This calculation involves iterating to find the precise annual coupon payment that makes the present value of the cash flows equal to the market price of the bond. Financial calculators or spreadsheet software are often used to perform this iterative calculation due to its complexity.