Kale Inc. forecasts the free cash flows (in millions) shown below. Assume the firm has zero non-operating assets. If the weighted average cost of capital is 11.0% and FCF is expected to grow at a rate of 5.0% after Year 2, then what is the firm’s total corporate value (in millions)? Do not round intermediate calculations.

Year

1

2

Free Cash flow

-$50

$100

Question

Kale Inc. forecasts the free cash flows (in millions) shown below.  Assume the firm has zero non-operating assets. If the weighted average cost of capital is 11.0% and FCF is expected to grow at a rate of 5.0% after Year 2, then what is the firm’s total corporate value (in millions)? Do not round intermediate calculations.

Year

1

2

Free Cash flow

-$50

$100

​

BlackTom AI · Accepted Answer

We start by identifying the cash flows and the growth assumption:
- Year 1 FCF = -50
- Year 2 FCF = 100
- After Year 2, FCF grows at g = 5% per year
- WACC = 11% and there are zero non-operating assets, so the firm’s value is the PV of all future FCFs.

First, compute the value at the end of Year 2 (the point just after Year 2 cash flow) of the perpetually growing FCF stream starting in Year 3. The Year 3 FCF is FCF2 × (1 + g) = 100 × 1.05 = 105. The terminal value at t = 2 is
Terminal value at t=2 = FCF3 / (WACC − g) = 105 / (0.11 − 0.05) = 105 / 0.06 = 1,750.

Next, discount all cash flows back to t = 0 using the WACC (11%). The present values are:
- PV of Year 1 FCF = −50 / (1 + 0.11) = −50 / 1.11 ≈ −45.05
- PV of Year 2 FCF = 100 / (1 + 0.11)^2 = 100 / 1.2321 ≈ 81.13
- PV of Terminal value = 1,750 / (1 + 0.11)^2 = 1,750 / 1.2321 ≈ 1,420.87

Sum these present values to obtain total corporate value:
Total value ≈ −45.05 + 81.13 + 1,420.87 ≈ 1,456.95.

Since the problem asks for the value in millions and instructs not to round intermediate calculations, the final aggregate value rounds to approximately 1,456 million when carried to the nearest million.

Now, evaluate the provided answer choices:
- $1,675: This overstates the terminal value or discounts; it does not align with the present-value sum we computed.
- $1,515: This is higher than our PV sum, suggesting a larger terminal value or smaller discounting error than our calculation.
- $1,558: Again, higher than the PV result; it would require a larger terminal value or lower discount rate than given.
- $1,617: This would demand substantial adjustments inconsistent with the given FCFs and growth, making it unlikely.
- $1,456: This matches the approximate total PV of all cash flows under the stated assumptions, including the Year 1 loss, Year 2 gain, and the perpetuity growth starting after Year 2.

Therefore, option $1,456 is the value consistent with the cash flows, growth, and discount rate provided.

fin_221_120251_242735 Submit: Test 3 (Chapters 7, 8, and 9)

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