Question

Assume General Motors Corporation is planning to issue bonds with a face value of $250,000 and a coupon rate of 6 percent. The bonds mature in five years and pay interest semiannually every June 30 and December 31. All of the bonds were sold on January 1 of this year. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided. Round your final answer to a whole dollar. ) Determine the issuance price of the bonds assuming an annual market rate of interest of 8 percent

Answer 1

The issuance price of the bonds, assuming an annual market rate of interest of 8 percent, is $227,195.75.

To determine the issuance price of the bonds, we need to calculate the present value of the bond's future cash flows, which include both the periodic interest payments and the face value repayment at maturity.

Step 1: Calculate the periodic interest payments:
The coupon rate is 6%, and since interest is paid semiannually, we need to divide the coupon rate by 2. Therefore, the periodic interest rate is 6%/2 = 3% or 0.03.

Step 2: Calculate the number of periods:
The bonds mature in five years, and interest is paid semiannually. So, the total number of periods is 5 years × 2 = 10 periods.

Step 3: Calculate the present value of the interest payments:
Using the Present Value of an Annuity (PVA) table, we find the factor for 10 periods at an interest rate of 8% (annual market rate). The factor is 7.6061.

To calculate the present value of the interest payments, we multiply the periodic interest payment ($250,000 × 0.03 = $7,500) by the PVA factor:
Present value of interest payments = $7,500 × 7.6061 = $57,045.75.

Step 4: Calculate the present value of the face value repayment:
To calculate the present value of the face value repayment, we use the Present Value of a Single Amount (PV) table. The face value of the bond is $250,000, and the factor for 5 years at an interest rate of 8% is 0.6806.

Present value of face value repayment = $250,000 × 0.6806 = $170,150.

Step 5: Calculate the issuance price of the bonds:
The issuance price of the bonds is equal to the present value of the interest payments plus the present value of the face value repayment.
Issuance price = $57,045.75 + $170,150 = $227,195.75.

Answer 2

The issuance price of the bonds is the present value of the bonds, which is $232,156

How to solve

We can use the present value formula to calculate the issuance price of the bonds. The present value formula is:

Present Value = Future Value / (1 + Discount Rate)^n

Where:

Present Value is the value of the money today

Future Value is the value of the money in the future

Discount Rate is the rate of interest used to discount the future value to today's value

n is the number of periods

In this case, the future value of the bonds is the face value of $250,000, and the discount rate is the annual market rate of interest of 8%. The number of periods is the number of semi-annual periods, which is 10 because there are 5 years and 2 semi-annual payments per year.

Therefore, the present value of the bonds is:

Present Value = $250,000 / (1 + 0.08 / 2)^10 = $232,156

The issuance price of the bonds is the present value of the bonds, which is $232,156.