Final answer:
To find the current price of the GTF Corporation bond with a 5 percent coupon rate and market interest rate of 6 percent, calculate the present value of the ongoing coupon payments and the par value at maturity, then sum these amounts. Because the market interest rate is higher than the coupon rate, the bond will be traded at a discount.
Step-by-step explanation:
To determine the current price of a GTF Corporation bond with a 5 percent coupon rate, 10 years left to maturity, and a market interest rate of 6 percent, we need to calculate the present value of the bond's future cash flows. The bond's cash flows consist of annual interest payments of 5 percent of the $1,000 par value (which is $50 per year) for 10 years, plus a final payment of the $1,000 par value at maturity.
The present value of these cash flows can be calculated using the formula for the present value of an annuity (for the interest payments) and the present value of a single sum (for the final par value payment). The formula takes into consideration the current market interest rate, which is 6 percent in this case. Since the market rate is higher than the coupon rate, the bond will be priced at a discount.
To calculate the present value of the annual interest payments (an annuity), we use the present value annuity formula, and for the final par value payment, we use the present value of a single sum formula:
- Present Value of Annuity (PVA) = Pmt × [(1 - (1 + r)^-n) / r]
- Present Value of Single Sum (PVSS) = FV / (1 + r)^n
Where Pmt is the annual payment ($50), r is the market interest rate (6% or 0.06), n is the number of years until maturity (10), and FV is the future value or par value ($1,000).
After calculating both the PVA and the PVSS, we sum them up to get the current bond price:
PVA = $50 × [(1 - (1 + 0.06)^-10) / 0.06]
PVSS = $1,000 / (1 + 0.06)^10
The final step is to add the present value of the annuity to the present value of the single sum to find the current bond price.