What is the maximum price that should be paid for a 7-year bond with a 12 percent coupon rate and a current market rate of 8 percent?
To calculate the maximum price that should be paid for the bond, we need to determine the present value of its future cash flows, including coupon payments and face value. The correct answer is $1,211.
Calculating Maximum Price for the 7-Year Bond:
1. Coupon Payment Calculation:
The bond pays a 12 percent coupon rate with semiannual payments, making the coupon payment per period 6%.
2. Number of Periods:
Since it's a 7-year bond with semiannual payments, the total number of periods is 14.
3. Present Value of Coupon Payments:
Using the formula for present value of an ordinary annuity, we calculate the present value of the coupon payments by discounting each cash flow back to the present with the market rate of 8%.
4. Present Value of Face Value:
The bond will also pay the face value of $1,000 at maturity, which we calculate using the present value formula.
5. Maximum Price Calculation:
Summing up the present values of the coupon payments and face value gives us the maximum price that should be paid for the bond.
Therefore, the maximum price that should be paid for the 7-year bond with a 12 percent coupon rate and an 8 percent market rate is $1,211. This calculation ensures that the investment aligns with the current market conditions and potential returns.