JTD Corporation issued $800,000 of 20-year, 12% bonds on January 1, 2006, when the market rate of interest was 10%. Interest is payable annually on December 31. Use the present values tables shown via the textbook link above.
a. Calculate the price of the bonds on January 1, 2006, the date the bonds were issued
To calculate the price of the bonds on January 1, 2006, we need to find the present value of the bond's cash flows. Here's how you can do it:
Step 1: Determine the cash flows
The bond pays interest annually, so the cash flows will consist of the annual interest payments and the principal payment at maturity. In this case, the bond has a maturity of 20 years and a face value of $800,000. The annual interest payment can be calculated by multiplying the face value by the annual coupon rate of 12%:
Annual Interest Payment = Face Value x Coupon Rate
= $800,000 x 0.12
= $96,000
Step 2: Use the present value tables
To calculate the present value of the bond's cash flows, we need to use the present value tables provided in your textbook or any other reliable resource. Look for the table that corresponds to the interest rate of 10% and the number of years remaining until each cash flow occurs.
Step 3: Calculate the present value of interest payments
We need to find the present value of the annual interest payments for 20 years. Refer to the present value table and locate the row that corresponds to a 20-year term and the column that corresponds to a 10% interest rate. The intersection value will give you the present value factor. Multiply this factor by the annual interest payment to find the present value of the interest payments:
Present Value of Interest Payments = Present Value Factor x Annual Interest Payment
Step 4: Calculate the present value of the principal payment
Since the principal payment will be received at the end of 20 years, we need to find the present value of the face value of $800,000. Use the same process as in Step 3 to find the present value factor for 20 years and 10%. Then, multiply this factor by the face value to get the present value of the principal payment.
Step 5: Calculate the price of the bonds
Finally, calculate the price of the bonds by summing the present values of the interest payments and the principal payment:
Price of the Bonds = Present Value of Interest Payments + Present Value of Principal Payment
By following these steps, you will be able to calculate the price of the bonds on January 1, 2006, using the present value tables provided.