Final answer:
The price of a bond can be determined by calculating the present value of its future coupon payments and face value, discounted at the current market yield. In this case, use the present value formula for an annuity to discount the annual coupon payments and a lump sum calculation for the face value, both at a 7% discount rate.
Step-by-step explanation:
To calculate the price of a bond offering a coupon rate of 14%, paid annually, with a face value of $1,000, and a maturity of 11 years when the current market yield is 7%, you need to discount each of the coupon payments and the face value back to present value terms at the given market yield.
The annual coupon payment is calculated as face value multiplied by the coupon rate ($1,000 * 0.14 = $140). Each of these payments should be discounted back at the market yield of 7% for each of the 11 years. In addition, the face value paid at the end of the 11th year must also be discounted back at the same market yield.Using the formula for the present value of an annuity for the coupon payments and the present value of a lump sum for the face value, the calculation becomes:
Present Value of the Annuity (PVA) = Payment * ((1 - (1 + r)^-n) / r)
Where:
- Payment = Annual coupon payment ($140)
- r = Market yield / discount rate (7% or 0.07)
- n = Number of years to maturity (11)
Present Value of the Lump Sum (PVLS) = Face Value / (1 + r)^n
The bond price is the sum of PVA and PVLS, rounded to two decimals.