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 calculate the issue price of the bonds, we need to use the present value formula. The formula is:
PV = C * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value (issue price)
C = Coupon payment per period
r = Market interest rate per period
n = Number of periods
In this case, the bonds have a face value of $500,000 and a coupon rate of 6%. The coupon payment per period can be calculated as follows:
Coupon Payment = Face Value * Coupon Rate / 2
Since the interest is payable semiannually, we divide the coupon rate by 2. Thus:
Coupon Payment = $500,000 * 6% / 2 = $15,000
Next, let's determine the number of periods. Since the bonds have a maturity of 20 years and interest is payable semiannually, we have a total of 40 coupon payment periods.
Now, we'll calculate the present value using the formula. The market interest rate is 5%, which we also divide by 2 since the interest is paid semiannually. Thus:
PV = $15,000 * (1 - (1 + 5%/2)^(-40)) / (5%/2)
Simplifying this calculation, we have:
PV = $15,000 * (1 - (1.025)^(-40)) / (0.025)
Evaluating the expression, we find:
PV ≈ $562,757
Therefore, the issue price of the bonds is approximately $562,757.