If a firm expects free cash flow equal to $50 million (at time t + 1) and that cash flow is expected to grow at 3% forever, what is the firm's terminal value given a WACC of 9.5%?单项选择题
A
$679.81 million
B
$715.54 million
C
$769.23 million
D
$803.03 million

Question

If a firm expects free cash flow equal to $50 million (at time t + 1) and that cash flow is expected to grow at 3% forever, what is the firm's terminal value given a WACC of 9.5%?

BlackTom AI · Accepted Answer

Using the Gordon Growth Model (perpetuity growth formula): TV = FCF1 / (WACC − g).

1) Relevant knowledge points and concepts
- Terminal value for a firm with cash flows that grow at a constant rate forever is computed with the Gordon Growth Model (also called the perpetuity growth formula).
- The formula requires the next-period free cash flow (FCF1), the weighted average cost of capital (WACC) as the discount rate, and the constant growth rate g. It is valid only if g < WACC.

2) Complete reasoning process step by step
- We are given FCF at time t+1 = $50 million, growth rate g = 3% (0.03), and WACC = 9.5% (0.095).
- Plug these values into the formula TV = FCF1 / (WACC − g).

3) Calculations with intermediate steps
- Compute the denominator: WACC − g = 0.095 − 0.03 = 0.065 (6.5%).
- Divide the cash flow by this difference: TV = 50 / 0.065.
- 50 / 0.065 = 769.2307692307693... (in millions of dollars).
- Rounded to two decimals: $769.23 million.

4) Why the correct answer is correct
- The calculation follows the standard perpetuity growth formula exactly using the provided inputs. Because g (3%) is less than WACC (9.5%), the formula is valid and produces a finite terminal value. The arithmetic yields $769.23 million, matching the correct option.

5) Why the other options are incorrect
- $679.81 million, $715.54 million, and $803.03 million do not equal 50 / (0.095 − 0.03). Each corresponds to a different denominator (i.e., an implied WACC − g other than 0.065). Since the problem specifies WACC = 9.5% and g = 3%, those alternatives are inconsistent with the formula and given inputs.

6) Conclusion and confirmation
- Therefore, applying TV = 50 / (0.095 − 0.03) gives a terminal value of $769.23 million, which confirms the provided correct answer ($769.23 million).

If a firm expects free cash flow equal to $50 million (at time t + 1) and that cash flow is expected to grow at 3% forever, what is the firm's terminal value given a WACC of 9.5%?单项选择题

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