Final answer:
To find the firm's equity value, calculate the enterprise value using the free cash flow and WACC, then subtract the firm's debt. The firm's equity value is option A) $40 billion.
Step-by-step explanation:
The value of a firm's equity can be found by first calculating the firm's enterprise value (EV) and then subtracting the value of the firm's debt. The enterprise value can be determined using the formula for perpetuity since the firm produces perpetual free cash flows (FCF).
To calculate the enterprise value (EV), you use the following formula:
EV = FCF / WACC
Where FCF is the free cash flow to the firm and WACC is the Weighted Average Cost of Capital.
Given that the FCF is $5 billion and the WACC is 10% (or 0.10),
EV = $5 billion / 0.10 = $50 billion
Now we have the enterprise value, and as the question states that the firm's debt is $10 billion, we can calculate the firm's equity value by subtracting the debt from the EV:
Equity Value = EV - Debt
Equity Value = $50 billion - $10 billion = $40 billion
Therefore, the correct answer is A. $40 billion.