Question

On January 1, 2021, Frontier World issues $40.0 million of 8% bonds, due in 15 years, with interest payable semiannually on June 30 and December 31 each year. The proceeds will be used to build a new ride that combines a roller coaster, a water ride, a dark tunnel, and the great smell of outdoor barbeque, all in one ride. 3-a. If the market rate is 9%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Do not round interest rate factors. Enter your answers in dollars not in millions. Round "Market interest rate" to 1 decimal place. Round your final answers to the nearest whole dollar.)

Answer 1

To calculate the issue price of the bonds, we need to use the present value formula and the appropriate factor(s) from the tables provided. Here are the steps:

1. Determine the number of periods. Since the bonds have a maturity of 15 years and interest is payable semiannually, there will be 30 periods (15 years * 2 periods per year).

2. Determine the periodic interest rate. The market rate is given as 9%. Since interest is payable semiannually, the periodic interest rate is half of the annual rate, which is 4.5% (9% / 2).

3. Calculate the present value of the interest payments. The bonds have a coupon rate of 8%, which is applied to the face value of $40.0 million. The interest payments are semiannual, so we need to divide the coupon rate by 2. Using the Present Value of an Ordinary Annuity (PVA) table, find the factor for 30 periods and a periodic interest rate of 4.5%. The factor is 13.218. Multiply this factor by the semiannual interest payment of $40.0 million * 8% / 2 = $1.6 million. The present value of the interest payments is $21.148 million ($1.6 million * 13.218).

4. Calculate the present value of the principal payment. To calculate the present value of the principal, we need to use the Present Value of a Single Amount (PV) table. Find the factor for 30 periods and a periodic interest rate of 4.5%. The factor is 0.335. Multiply this factor by the face value of $40.0 million to get the present value of the principal payment, which is $13.4 million ($40.0 million * 0.335).

5. Calculate the issue price. The issue price is the sum of the present value of the interest payments and the present value of the principal payment. Add $21.148 million and $13.4 million to get the issue price, which is $34.548 million.

Therefore, the issue price of the bonds is $34.548 million.