📖 自由现金流估值：FCFE

Equity Investments

I. Lesson Focus

II. The Problem

Imagine you are analyzing a high-growth technology company that currently pays no dividends yet generates substantial operating cash flows while making heavy capital expenditures. The dividend discount model (DDM) cannot be used because dividends are zero, and you prefer not to value the entire firm and then subtract net debt. The Free Cash Flow to Equity (FCFE) model allows you to directly estimate the intrinsic value of equity and determine whether the current market price is overvalued or undervalued. This is one of the most important “non-dividend” valuation tools in the Equity Investments section of the CFA exam.

III. Definition and Calculation of Free Cash Flow to Equity (FCFE)

Free Cash Flow to Equity (FCFE) is the cash flow available to equity investors after the company has met all operating expenditures, paid interest and principal on debt, and made the capital expenditures required to maintain or expand operations.

The most commonly used formula (starting from net income) is:

$$ \text{FCFE} = \text{NI} - \text{Net Capital Expenditure} - \text{Change in Working Capital} + \text{Net Borrowing} $$

Where: - NI = Net Income - Net Capital Expenditure = CapEx – Depreciation - Change in Working Capital = increase in non-cash working capital - Net Borrowing = new debt issued – debt principal repaid

An alternative formula converting from FCFF is:

$$ \text{FCFE} = \text{FCFF} - \text{Int}(1-t) + \text{Net Borrowing} $$

Important point: FCFE is a levered cash flow (after debt service), so it is discounted at the required equity return to obtain equity value directly. It cannot be used to value the entire firm.

IV. Differences Among FCFE, FCFF, and Dividends

Exam trap: Many candidates incorrectly use “FCFE = CFO – CapEx” as the complete formula; this omits the net change in debt (Net Borrowing).

V. FCFE Valuation Models

1. Single-Stage (Gordon Growth) Model

Assumes FCFE grows at a constant perpetual rate g:

$$ V_0 = \frac{\text{FCFE}_1}{r_e - g} = \frac{\text{FCFE}_0(1+g)}{r_e - g} $$

where $r_e$ is the required return on equity (usually from CAPM).
Conditions: company in stable growth, g sustainable and less than $r_e$.

2. Two-Stage FCFE Model (Most Frequently Tested)

Divides the future into a high-growth period (n years) and a stable-growth period.

$$ V_0 = \sum_{t=1}^{n} \frac{\text{FCFE}_t}{(1+r_e)^t} + \frac{V_n}{(1+r_e)^n} $$

Terminal value at time n:

$$ V_n = \frac{\text{FCFE}{n+1}}{r_e - g{\text{stable}}} $$

In practice, growth in the high-growth phase is often estimated as: $g = \text{Retention Ratio} \times \text{ROE}$.

VI. Practical Steps to Forecast FCFE

1. Forecast revenue and profit margins to obtain NI.
2. Forecast CapEx, depreciation, and ΔWC to obtain net capital expenditure and working-capital change.
3. Forecast net borrowing (often based on a target D/E ratio).
4. Compute each period’s FCFE.
5. Select the appropriate model and discount at $r_e$.

Worked Cases

Case 1: Single-Stage FCFE Valuation (Basic)

XYZ Corp. reported 2023 net income of CNY 120 million, net capital expenditure CNY 45 million, working-capital increase CNY 15 million, and net borrowing CNY 30 million. Required equity return is 12%, perpetual growth rate is 4%. Calculate current equity value (in millions).

Solution:
FCFE₀ = 120 – 45 – 15 + 30 = 90
FCFE₁ = 90 × 1.04 = 93.6
V₀ = 93.6 / (0.12 – 0.04) = 93.6 / 0.08 = 1,170 million

Case 2: Two-Stage FCFE Model (High-Frequency Exam Topic)

ABC Corp. has the following FCFE forecasts (in millions):
FCFE₁ = 80, FCFE₂ = 110, FCFE₃ = 140.
From year 4 onward, stable growth g = 5%, $r_e$ = 11%. Shares outstanding = 50 million.

Solution:
Terminal value at t=3: V₃ = (140 × 1.05) / (0.11 – 0.05) = 147 / 0.06 = 2,450
V₀ = 80/1.11 + 110/1.11² + 140/1.11³ + 2,450/1.11³
≈ 72.07 + 89.35 + 102.55 + 1,794.07 ≈ 2,058 million
Per-share value = 2,058 / 50 ≈ 41.16

Case 3: Deriving FCFE from Financial Statements and Valuing

A company reports (in thousands): NI = 850, depreciation = 180, CapEx = 420, ΔWC = 95, new long-term debt = 150, debt repaid = 80. $r_e$ = 13%, g = 6%.

Solution:
Net CapEx = 420 – 180 = 240
Net Borrowing = 150 – 80 = 70
FCFE = 850 – 240 – 95 + 70 = 585
V₀ = 585 × 1.06 / (0.13 – 0.06) = 620.1 / 0.07 ≈ 8,860

Traps

Key Formulas

• FCFE = NI – Net CapEx – ΔWC + Net Borrowing
• FCFE = FCFF – Int(1–t) + Net Borrowing
• Single-stage: $V_0 = \frac{FCFE_1}{r_e - g}$
• Two-stage: $V_0 = \sum_{t=1}^{n}\frac{FCFE_t}{(1+r_e)^t} + \frac{FCFE_{n+1}/(r_e-g_n)}{(1+r_e)^n}$
• Sustainable growth: g = b × ROE (b = retention ratio)
• When all FCFE is paid as dividends, FCFE value = DDM value

Practice Questions

Q1. Which of the following is most likely added when calculating FCFE?
A. Depreciation
B. Net borrowing
C. Capital expenditure
D. Increase in working capital

Q2. Given FCFF = 500, interest expense = 80, tax rate = 25%, and net borrowing = –30, FCFE is closest to:
A. 410
B. 440
C. 470
D. 500

Q3. In a single-stage FCFE model, if g increases from 4% to 5% while $r_e$ = 10% and all else constant, the equity value will:
A. Increase
B. Decrease
C. Remain unchanged
D. Cannot be determined

Q4. In a two-stage FCFE model, the terminal value should be calculated using the:
A. High-growth rate
B. Stable-growth rate
C. Historical average growth rate
D. Risk-free rate

Q5. A company pays no dividends but generates positive FCFE. The most appropriate valuation method is:
A. DDM
B. FCFE model
C. P/E multiple
D. EV/EBITDA

Q6. When calculating FCFE, the repayment of long-term debt principal:
A. Increases FCFE
B. Decreases FCFE
C. Has no effect
D. Depends on the tax rate

Q7. If a company conducts large share repurchases, its FCFE will most likely:
A. Increase significantly
B. Decrease significantly
C. Approach zero
D. Be unrelated to the repurchase amount

Q8. Which statement about FCFE and FCFF is correct?
A. FCFE is always greater than FCFF
B. FCFE reflects the impact of leverage
C. FCFF subtracts debt principal repayment
D. Both cash flows use the same discount rate

Answers

Takeaways

• FCFE is the cash flow available to equity holders after operating needs, interest, and net debt service.
• The core formula must include +Net Borrowing; omitting it severely understates value.
• Use the single-stage model for stable-growth companies and the two-stage model for high-growth firms transitioning to stability.
• FCFE valuation is especially useful for non-dividend-paying, cash-flow-positive growth companies.
• Always apply the stable growth rate (not the high-growth rate) when calculating terminal value.
• FCFE valuation directly yields intrinsic equity value; no further subtraction of net debt is required.