a. To calculate the total corporate value, we need to find the present value of each free cash flow and add them up. The formula for the present value of a future cash flow is:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.
Using this formula, we can calculate the present value of each free cash flow:
PV1 = $20.00 / (1 + 0.14)^1 = $17.54 million
PV2 = $48.00 / (1 + 0.14)^2 = $33.19 million
PV3 = $54.00 / (1 + 0.14)^3 = $33.13 million
Next, we need to calculate the present value of all future free cash flows beyond year 3, using the formula:
PV4 = FCF4 / (r - g)
Where FCF4 is the free cash flow in year 4, r is the discount rate, and g is the growth rate. Since the free cash flows are expected to continue growing at 12.5%, we can use this as the growth rate. We don't know the exact value of FCF4, but we can estimate it by using the free cash flow in year 3 and assuming that it will continue to grow at the same rate. Therefore:
FCF4 = FCF3 x (1 + g) = $54.00 x (1 + 0.125) = $61.13 million
Now we can calculate the present value of all future free cash flows beyond year 3:
PV4 = $61.13 million / (0.14 - 0.125) = $611.25 million
Finally, we can calculate the total corporate value by adding up the present values of all free cash flows:
Total corporate value = PV1 + PV2 + PV3 + PV4 = $97.01 million
Therefore, the firm's total corporate value is $97.01 million.
b. To calculate the stock price, we need to subtract the value of the debt from the total corporate value, and divide by the number of shares outstanding:
Stock price = (Total corporate value - Value of debt) / Number of shares outstanding
Using the total corporate value from part (a), the value of the debt is $1,500 million, and the number of shares outstanding is