7.3 Free Cash Flow Valuation: FCFF and FCFE Modeling

7.3 Free Cash Flow Valuation: FCFF and FCFE Modeling

Core Insight: Free cash flow valuation represents the gold standard of absolute corporate valuation in financial analysis. Unlike dividends, free cash flow measures the actual cash generated by operations after funding necessary capital investments and working capital requirements, making it invariant to discretionary dividend payout policies.

1. FCFF vs. FCFE: Conceptual Foundation

2. Computing Free Cash Flow to the Firm (FCFF)

FCFF can be calculated from four different accounting entry points. All four equations are mathematically equivalent:

                      ┌──────────────────────────────────────────────┐
                      │  Four Equivalent Paths to Calculating FCFF   │
                      └──────────────────────┬───────────────────────┘
             ┌───────────────────────────────┼───────────────────────────────┐
             ▼                               ▼                               ▼
┌─────────────────────────┐     ┌─────────────────────────┐     ┌─────────────────────────┐
│     From Net Income     │     │        From CFO         │     │        From EBIT        │
│  NI + NCC + Int(1 - t)  │     │    CFO + Int(1 - t)     │     │   EBIT(1 - t) + Dep     │
│     - FCInv - WCInv     │     │         - FCInv         │     │     - FCInv - WCInv     │
└─────────────────────────┘     └─────────────────────────┘     └─────────────────────────┘
                                             │
                                             ▼
                                ┌─────────────────────────┐
                                │       From EBITDA       │
                                │  EBITDA(1-t) + Dep(t)   │
                                │     - FCInv - WCInv     │
                                └─────────────────────────┘

1. From Net Income (NI)

$\text{FCFF} = \text{NI} + \text{NCC} + \text{Int}(1 - t) - \text{FCInv} - \text{WCInv}$

Where:

• $\text{NI}$ = Net income available to common shareholders.
• $\text{NCC}$ = Non-Cash Charges (depreciation, amortization, restructuring charges, impairment of goodwill, deferred tax liabilities).
• $\text{Int}(1 - t)$ = After-tax interest expense added back because interest is a return to debt capital providers.
• $\text{FCInv}$ = Fixed Capital Investment (Gross Capex minus proceeds from asset sales, or $\Delta \text{Gross PP&E}$).
• $\text{WCInv}$ = Working Capital Investment ($\Delta \text{Non-cash Current Assets} - \Delta \text{Non-interest-bearing Current Liabilities}$, excluding cash and notes payable/short-term debt).

2. From Cash Flow from Operations (CFO)

Under US GAAP, CFO includes net income, non-cash charges, and working capital changes, but subtracts interest expense:

$\text{CFO} = \text{NI} + \text{NCC} - \text{WCInv}$

$\text{FCFF} = \text{CFO} + \text{Int}(1 - t) - \text{FCInv}$

IFRS vs. US GAAP Accounting Nuance: Under US GAAP, interest paid is strictly classified under Operating Cash Flow (CFO). Under IFRS, interest paid can be classified under Operating or Financing Cash Flow (CFF). If an IFRS firm classifies interest paid under CFF, no after-tax interest adjustment is needed: $\text{FCFF} = \text{CFO} - \text{FCInv}$.

3. From Operating Earnings (EBIT)

$\text{FCFF} = \text{EBIT}(1 - t) + \text{Dep} - \text{FCInv} - \text{WCInv}$

4. From Operating Cash Earnings (EBITDA)

$\text{FCFF} = \text{EBITDA}(1 - t) + \text{Dep}(t) - \text{FCInv} - \text{WCInv}$

Where $\text{Dep}(t)$ is the depreciation tax shield ($t \times \text{Depreciation}$). Note that non-depreciation non-cash charges must also be adjusted if material.

3. Computing Free Cash Flow to Equity (FCFE)

FCFE represents residual cash flow remaining after operating expenses, fixed capital reinvestment, working capital changes, and net debt repayments.

1. From FCFF

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

Where $\text{Net Borrowing} = \text{New Debt Issued} - \text{Debt Principal Repaid}$.

2. From Net Income

$\text{FCFE} = \text{NI} + \text{NCC} - \text{FCInv} - \text{WCInv} + \text{Net Borrowing}$

3. From Cash Flow from Operations (CFO)

$\text{FCFE} = \text{CFO} - \text{FCInv} + \text{Net Borrowing}$

4. Forecasting FCFE with a Target Debt Ratio ($DR$)

When projecting future cash flows for a firm that maintains a constant target capital structure (Debt-to-Assets ratio $DR = \frac{D}{D+E}$), net debt borrowing automatically finances a constant portion of net capital expenditures and working capital:

$\text{Net Borrowing} = DR \times (\text{FCInv} - \text{Dep}) + DR \times (\text{WCInv})$

Substituting this into the FCFE equation eliminates the need to forecast explicit balance sheet debt line items:

$\text{FCFE} = \text{NI} - (1 - DR)(\text{FCInv} - \text{Dep}) - (1 - DR)(\text{WCInv})$

• $(1 - DR)$ represents the equity-funded portion of capital expenditures and working capital expansion.
• $(\text{FCInv} - \text{Dep})$ represents net new capital investment above asset replacement.

5. Comprehensive Free Cash Flow Formulas Summary

6. Multistage Free Cash Flow Valuation & Terminal Value

Total Enterprise Value ($V_{\text{firm}}$) is the present value of explicit forecast FCFF plus the present value of the terminal enterprise value:

$V_{\text{firm}} = \sum_{t=1}^n \frac{\text{FCFF}_t}{(1 + \text{WACC})^t} + \frac{\text{Terminal Value}_n}{(1 + \text{WACC})^n}$

$\text{Terminal Value}_n = \frac{\text{FCFF}_{n+1}}{\text{WACC} - g} = \frac{\text{FCFF}_n (1 + g)}{\text{WACC} - g}$

Non-Operating Assets and Debt Claims

To bridge from Enterprise Value to Equity Value per share:

$\text{Total Equity Value} = V_{\text{firm}} + \text{Cash and Marketable Securities} + \text{Non-Operating Assets} - \text{Market Value of Debt} - \text{Preferred Stock}$

$\text{Value per Share} = \frac{\text{Total Equity Value}}{\text{Diluted Number of Common Shares}}$

7. Comprehensive Worked Example: Multi-Year FCFF/FCFE Model and Share Valuation

Scenario: Global Dynamics Corp (GDC) has the following financial projections for Year 1:

• Revenue = $1,000.0M
• EBITDA = $300.0M
• Depreciation & Amortization (Dep) = $60.0M
• Operating Income (EBIT) = $240.0M
• Interest Expense = $40.0M
• Earnings Before Taxes (EBT) = $200.0M
• Marginal Tax Rate ($t$) = 25.0%
• Net Income (NI) = $200.0M \times (1 - 0.25) = $150.0\text{M}$
• Capital Expenditures (FCInv) = $90.0M
• Working Capital Investment (WCInv) = $20.0M
• Net Borrowing = +$15.0M
• Cash & Liquid Investments = $150.0M
• Market Value of Debt = $600.0M
• Shares Outstanding = 100.0M shares
• WACC = 8.0%, Cost of Equity $r_e = 10.0%$, Perpetual FCFF Growth Rate $g = 3.0%$
• Year 2 FCFF is projected to grow by 10.0% over Year 1, after which FCFF grows at perpetual rate $g = 3.0%$.

Step 1: Calculate Year 1 FCFF (Reconciling all 4 Methods)

1. From NI: $\text{FCFF}_1 = 150.0 + 60.0 + [40.0 \times (1 - 0.25)] - 90.0 - 20.0 = 150.0 + 60.0 + 30.0 - 90.0 - 20.0 = $130.0\text{M}$
2. From CFO: $\text{CFO}_1 = 150.0 + 60.0 - 20.0 = $190.0\text{M} \implies \text{FCFF}_1 = 190.0 + 30.0 - 90.0 = $130.0\text{M}$
3. From EBIT: $\text{FCFF}_1 = [240.0 \times (1 - 0.25)] + 60.0 - 90.0 - 20.0 = 180.0 + 60.0 - 90.0 - 20.0 = $130.0\text{M}$
4. From EBITDA: $\text{FCFF}_1 = [300.0 \times (1 - 0.25)] + [60.0 \times 0.25] - 90.0 - 20.0 = 225.0 + 15.0 - 90.0 - 20.0 = $130.0\text{M}$

Step 2: Calculate Year 1 FCFE

$\text{FCFE}_1 = \text{FCFF}_1 - \text{Int}(1 - t) + \text{Net Borrowing} = 130.0 - 30.0 + 15.0 = \$115.0\text{M}$

$\text{Verification from NI: } \text{FCFE}_1 = 150.0 + 60.0 - 90.0 - 20.0 + 15.0 = \$115.0\text{M}$

Step 3: Multi-Year Enterprise Valuation

• Year 1 FCFF = $130.0M
• Year 2 FCFF = $130.0M \times 1.10 = $143.0\text{M}$
• Terminal Value at $t = 2$: $\text{TV}_2 = \frac{\text{FCFF}_2 \times (1 + g)}{\text{WACC} - g} = \frac{143.0 \times 1.03}{0.08 - 0.03} = \frac{147.29}{0.05} = \$2,945.80\text{M}$

Step 4: Discount Cash Flows to Present ($t = 0$)

$\text{PV}(\text{FCFF}_1) = \frac{130.0}{1.08} = \$120.37\text{M}$

$\text{PV}(\text{FCFF}_2) = \frac{143.0}{(1.08)^2} = \$122.60\text{M}$

$\text{PV}(\text{TV}_2) = \frac{2,945.80}{(1.08)^2} = \$2,525.55\text{M}$

$\text{Total Firm Enterprise Value } (V_{\text{firm}}) = 120.37 + 122.60 + 2,525.55 = \$2,768.52\text{M}$

Step 5: Bridge to Equity Value Per Share

$\text{Total Equity Value} = V_{\text{firm}} + \text{Cash} - \text{Debt} = 2,768.52 + 150.0 - 600.0 = \$2,318.52\text{M}$

$\text{Intrinsic Value per Share} = \frac{\$2,318.52\text{M}}{100.0\text{M shares}} = \$23.19$