On January 1, 2012, White Water issues $500,000 of 6% bonds, due in 20 years, with interest payable semiannually on June 30 and December 31 each year.
Assuming the market interest rate on the issue date is 5%, the bonds will issue at $562,757.
To explain how the bonds were issued at $562,757, let's break down the process:
1. Determine the bond's face value: The face value, also known as the par value, is the amount stated on the bond certificate that the issuer agrees to repay at maturity. In this case, the face value of the bonds is $500,000.
2. Calculate the bond's interest payments: The bonds carry a 6% interest rate, which is stated as an annual rate. Since interest is payable semiannually, we need to calculate the interest payment for each period. To do this, divide the annual interest rate by 2:
Annual Interest Rate = 6%
Semiannual Interest Rate = 6% / 2 = 3%
3. Determine the number of periods: The bonds have a term of 20 years, and interest is payable semiannually. Therefore, the total number of periods is 20 years multiplied by 2 (for the semiannual payments), which equals 40 periods.
4. Calculate the present value of the bond: The present value of the bond is computed by discounting the future cash flows (interest payments and face value) using the market interest rate. In this case, the market interest rate is 5%.
To calculate the present value of the interest payments, we need to discount each payment by the market interest rate. Since the interest payments are semiannual, we discount them for each period. Then we sum up all the discounted interest payments.
To calculate the present value of the face value, we apply the same discounting method but only for the final payment at maturity.
5. Add the present value of the interest payments and the present value of the face value to get the issue price: The issue price is the sum of the present values of the interest payments and the face value.
By following these steps and performing the necessary calculations, you can arrive at the issue price of $562,757.