Final answer:
To calculate the coupon rate of a bond that was bought at a price of $1135.90 and requires an 8% return, one must determine the semi-annual interest payment using present value formulas and then annualize this payment to find the coupon rate. This process typically requires a financial calculator or spreadsheet software.
Step-by-step explanation:
To determine the coupon rate on a bond when you require an 8% return, and you have paid $1135.90 for a bond with 10 years to maturity, you must perform present value calculations based on the bond's expected cash flows, which includes semi-annual interest payments and the lump-sum principal repayment at maturity. The price you paid for the bond reflects the present value of these cash flows discounted at your required return.
To find the coupon rate for this bond, let us start by knowing that the bond pays semi-annual interest payments, and you are requiring an 8% annual return, which will be 4% semi-annually. This bond was purchased at a premium, indicating that the coupon rate is higher than the market rate (your required rate of return). Using financial formulas or a financial calculator, we can input the following: the present value (price paid for the bond), the number of periods (20 semi-annual periods for a 10-year bond), the yield per period (4%), and the face value ($1,000), to solve for the periodic interest payment. The coupon rate can then be calculated by doubling the semi-annual interest payment (since there are two payments per year) and dividing by the bond's face value.
Calculating the exact coupon rate requires a financial calculator or spreadsheet software to perform the iterative calculation involved in solving for the coupon rate. It is not something that can be done with a simple formula, but rather involves trial and error or a built-in financial function such as 'RATE' in spreadsheet programs.