Alliant Corporation sold $100,000,000 face value 8% bonds. The bonds mature in 20 years and pay interest semiannually. The going market rate of interest on bonds of similar risk is 6%. How much will Aliant receive upon the sale of the bonds
To calculate how much Alliant Corporation will receive upon the sale of the bonds, we need to use the present value formula. The present value represents the current worth of future cash flows. In this case, the future cash flows are the periodic interest payments and the principal payment upon maturity.
The formula to calculate the present value of a bond is:
PV = C x [1 - (1 + r)^(-n)] / r + M / (1 + r)^n
where:
PV = Present value (the amount Alliant Corporation will receive upon selling the bonds)
C = Periodic interest payment (in this case, semiannual interest payment)
r = Market interest rate per period (in this case, semiannual rate)
n = Number of periods (20 years, so 20 * 2 = 40 periods)
M = Face value of the bond
Let's plug in the values:
PV = [($100,000,000 x 8% / 2) x (1 - (1 + 6% / 2)^(-40))] / (6% / 2) + $100,000,000 / (1 + 6% / 2)^40
Now, we can solve this equation to find the present value, which represents the amount Alliant Corporation will receive upon selling the bonds.