📖 FCFE vs FCFF 比较

Equity Investments

I. Lesson Focus

This lesson compares Free Cash Flow to the Firm (FCFF) and Free Cash Flow to Equity (FCFE). Candidates must master the definitions, alternative calculation methods from net income, EBIT, or CFO, the precise adjustments required for each, the appropriate discount rates, and when to select one cash flow measure over the other in equity valuation. The material emphasizes numerical adjustments, two-stage modeling, and common formula traps tested in the CFA Level I curriculum.

II. The Problem

You are valuing a leveraged company and realize that free-cash-flow models overcome the dividend discount model’s limitation when a firm pays no dividends. However, you must immediately decide whether to forecast and discount FCFF to obtain total firm value (then subtract net debt for equity value) or to forecast FCFE and discount it directly to obtain equity value. The starting points, subtracted items, and discount rates differ materially; using the wrong metric or discount rate can produce valuation errors exceeding 30%. This lesson resolves the choice between FCFF and FCFE with clear formulas, numerical examples, and decision rules.

III. Core Concepts: Definitions and Economic Meaning

FCFF (Free Cash Flow to the Firm) is the cash flow available to all capital providers (debt and equity) after the firm has met its operating needs and made necessary investments in fixed and working capital. It represents the cash that would be available to investors if the firm had no debt.

FCFE (Free Cash Flow to Equity) is the cash flow available to common shareholders after operating needs, fixed-capital and working-capital investments, and net debt payments (after interest and principal) have been satisfied. It is the residual cash truly belonging to equity investors.

The fundamental link is:
FCFE = FCFF − After-tax interest + Net borrowing.

IV. Formula Comparison

1. Starting from Net Income (most frequently examined)

$$ FCFF = NI + NCC + Int(1-t) - FCInv - WCInv $$ $$ FCFE = NI + NCC - FCInv - WCInv + Net\ Borrowing $$ where NCC = non-cash charges (primarily depreciation and amortization), Int(1-t) = after-tax interest expense, FCInv = fixed-capital investment (Capex minus proceeds from asset sales), WCInv = working-capital investment, and Net Borrowing = new debt issuances minus debt repayments.

2. Starting from EBIT

$$ FCFF = EBIT(1-t) + Dep - FCInv - WCInv $$ $$ FCFE = FCFF - Int(1-t) + Net\ Borrowing $$

3. Starting from CFO (CFA examiners’ favorite)

$$ FCFF = CFO + Int(1-t) - FCInv $$ $$ FCFE = CFO - FCInv + Net\ Borrowing $$

V. Discount Rates and Valuation Model Alignment

• FCFF is always discounted at the WACC to produce enterprise value (EV). Equity value is then EV minus net debt.
• FCFE is always discounted at the required equity return (r_e) to produce equity value directly.

Constant-growth models:
$$ EV_0 = \frac{FCFF_1}{WACC - g} $$ $$ Equity\ Value_0 = \frac{FCFE_1}{r_e - g} $$

VI. Selection Criteria and Decision Logic

1. When the firm’s capital structure (debt/equity) is expected to remain stable, the FCFF model is more robust.
2. When leverage is expected to change significantly (e.g., deleveraging after a high-growth phase), the FCFE model better captures varying net borrowing.
3. Complex debt structures or unstable interest tax shields favor FCFF.
4. Analysts seeking a direct per-share equity value often prefer FCFE.
5. In acquisition valuation, FCFF is almost universally used because the buyer values the entire cash-flow-generating capability of the business.

Worked Cases

Case 1: Basic Calculation from Net Income

XYZ Corp. 2024 data (USD millions):
NI = 120, Depreciation = 45, Interest = 25, tax rate = 30%, Capex = 80, WCInv = 15, new long-term debt = 40, debt repayment = 10.

FCFF = 120 + 45 + 25(1−0.3) − 80 − 15 = 120 + 45 + 17.5 − 80 − 15 = 87.5
FCFE = 120 + 45 − 80 − 15 + (40−10) = 120 + 45 − 80 − 15 + 30 = 100

Conclusion: FCFE exceeds FCFF because the firm’s net borrowing of 30 added cash available to shareholders.

Case 2: Adjustment from CFO (High-Frequency Exam Style)

Given: CFO = 185, Interest = 32, tax rate = 25%, FCInv = 95, Net Borrowing = 18.

FCFF = 185 + 32(1−0.25) − 95 = 185 + 24 − 95 = 114
FCFE = 185 − 95 + 18 = 108

Common mistake: candidates forget to add back after-tax interest when moving from CFO to FCFF.

Case 3: Two-Stage FCFF Valuation

ABC Corp. has FCFF₁ = 80 million, expected growth of 12% for three years, then perpetual growth of 4%. WACC = 9.5%, net debt = 220 million, shares outstanding = 50 million.

Step 1: Explicit forecast
Year 1: 80
Year 2: 80 × 1.12 = 89.6
Year 3: 89.6 × 1.12 = 100.352

Step 2: Terminal value at end of Year 3
TV₃ = (100.352 × 1.04) / (0.095 − 0.04) = 104.366 / 0.055 ≈ 1,897.56

Step 3: Present value of enterprise
PV = 80/1.095 + 89.6/1.095² + (100.352 + 1,897.56)/1.095³ ≈ 73.06 + 74.72 + 1,480.85 ≈ 1,628.63 million

Equity value = 1,628.63 − 220 = 1,408.63 million
Per-share value = 1,408.63 / 50 ≈ 28.17

A consistent FCFE model with appropriately higher equity discount rate and corresponding FCFE series should theoretically yield the same equity value when capital-structure assumptions are stable.

Traps

Key Formulas

• FCFF = NI + NCC + Int(1−t) − FCInv − WCInv
• FCFE = NI + NCC − FCInv − WCInv + Net Borrowing
• FCFE = FCFF − Int(1−t) + Net Borrowing
• FCFF = CFO + Int(1−t) − FCInv
• FCFE = CFO − FCInv + Net Borrowing
• Enterprise Value = FCFF₁ / (WACC − g)
• Equity Value = FCFE₁ / (r_e − g)
• Use FCFF for firm valuation; use FCFE for direct equity valuation

Practice Questions

Q1. Which of the following is least likely a correct adjustment when calculating FCFF?
A. Adding after-tax interest to net income
B. Subtracting capital expenditures from CFO
C. Subtracting net borrowing from EBIT(1−t)

Q2. A company reports net income of $150 million, depreciation of $40 million, interest of $30 million (tax rate 25%), capital expenditures of $90 million, working-capital investment of $20 million, and net borrowing of $25 million. FCFE is closest to:
A. $107.5 million
B. $132.5 million
C. $82.5 million
D. $157.5 million

Q3. When a firm plans to significantly reduce financial leverage over the next five years, which valuation approach is most appropriate?
A. Constant-growth FCFF model
B. Two-stage FCFE model
C. Dividend discount model
D. None of the above

Q4. Given CFO = 220, interest expense = 40, tax rate = 30%, and net fixed-capital investment = 85, FCFF equals:
A. 163
B. 203
C. 175
D. 143

Q5. Which statement correctly describes the relationship between FCFF and FCFE?
A. FCFE is always greater than FCFF
B. FCFE = FCFF − after-tax interest + net borrowing
C. When net borrowing equals zero, FCFE equals FCFF
D. FCFF is discounted at the cost of equity

Q6. For an all-equity firm with no debt, the relationship between FCFF and FCFE is:
A. FCFF > FCFE
B. FCFF = FCFE
C. FCFF < FCFE
D. Cannot be determined

Q7. When valuing equity using an FCFE model, the appropriate discount rate is the:
A. WACC
B. After-tax cost of debt
C. Required return on equity
D. Risk-free rate

Q8. An analyst incorrectly discounts an FCFE series at the WACC. The most likely result is:
A. Overestimation of equity value
B. Underestimation of equity value
C. The same value obtained from an FCFF model
D. No effect on value

Answers

Takeaways

• FCFF is the cash flow available to all capital providers; FCFE is the residual cash flow available to equity investors after debt obligations.
• Always add back after-tax interest for FCFF and add net borrowing for FCFE.
• Discount FCFF at WACC to obtain enterprise value; discount FCFE at r_e to obtain equity value directly.
• Choose FCFF when capital structure is stable; choose FCFE when leverage is expected to change materially.
• When starting from CFO, add Int(1−t) for FCFF but not for FCFE.
• Theoretical values from both approaches should reconcile when assumptions are consistent; material differences usually indicate calculation errors or inconsistent assumptions.