Final answer:
To calculate the bond's price when comparable debt yields 6 percent, we can use the present value of annuity formula and the present value of a future lump sum formula. Using a coupon rate of 5 percent, a maturity period of twelve years, and a discount rate of 6 percent, we find that the bond's price would be $1,005.82.
Step-by-step explanation:
To calculate the bond's price when comparable debt yields 6 percent, we need to determine the present value of the bond's cash flows. The bond has a coupon rate of 5 percent and matures after twelve years. Since the bond pays interest annually, we can use the formula for the present value of an annuity to calculate the present value of the coupon payments. The present value of the face value at maturity can be calculated using the formula for the present value of a future lump sum. Adding these two present values together gives us the bond's price.
The formula for the present value of an annuity is PV = C * [(1 - (1 + r)-n) / r], where PV is the present value, C is the coupon payment, r is the discount rate, and n is the number of periods. Plugging in the values for the bond, we have PV = 50 * [(1 - (1 + 0.06)-12) / 0.06] = $435.70 (rounded to two decimal places).
The formula for the present value of a future lump sum is PV = F / (1 + r)n, where PV is the present value, F is the future value, r is the discount rate, and n is the number of periods. Plugging in the values for the bond, we have PV = 1000 / (1 + 0.06)12 = $570.12 (rounded to two decimal places).
Adding the present values of the coupon payments and the face value, we have the bond's price of $435.70 + $570.12 = $1,005.82 (rounded to two decimal places).