Final answer:
The bond price can be calculated using the present value of the bond's future cash flows. In this case, the bond price is $1159.97.
Step-by-step explanation:
To calculate the bond price, one needs to consider the present value of the bond's future cash flows. In this case, the bond has a 20-year maturity, a face value of $1000, and an annual coupon rate of 7%. Since the bond pays annual coupons, each coupon payment will be $70 (7% of $1000). The Yield to Maturity (YTM) is 6%, which represents the market interest rate for similar bonds.
Using the formula for the present value of a bond's cash flows, the bond price can be calculated as follows:
- Calculate the present value of the bond's coupon payments. Since the coupon payments are fixed at $70 per year for 20 years, we can calculate the present value using the formula for the present value of an ordinary annuity: PV = C * (1 - (1 + r)^-n) / r, where C is the coupon payment, r is the discount rate, and n is the number of periods. Plugging in the values, we get PV = $70 * (1 - (1 + 0.06)^-20) / 0.06 = $848.17.
- Calculate the present value of the bond's face value. The face value of the bond is $1000, which will be received at the end of the 20-year period. To calculate the present value, we use the formula PV = F / (1 + r)^n, where F is the future value, r is the discount rate, and n is the number of periods. Plugging in the values, we get PV = $1000 / (1 + 0.06)^20 = $311.80.
- Add the present value of the coupon payments and the present value of the face value to get the bond price: $848.17 + $311.80 = $1159.97.
Therefore, the bond price is $1159.97.