CFA Level II · CFA Level II Exam

Free Cash Flow Valuation: formula sheet

Full chapter guide

Key formulas

FCFF from net income: FCFF = NI + NCC + Int(1 – t) – FCInv – WCInv; NCC is non-cash charges such as depreciation. FCInv is fixed capital investment (capex less proceeds from asset sales). WCInv is investment in working capital.
FCFF from CFO: FCFF = CFO + Int(1 – t) – FCInv; This form applies when interest paid is already deducted in CFO. US GAAP always puts interest paid in CFO, so you add back after-tax interest. IFRS allows interest paid in either operating or financing activities, so check the classification. If interest paid is in financing, CFO is before the interest outflow, but taxes paid in CFO already include the interest tax shield. You must remove that shield: FCFF = CFO – Int × t – FCInv.
FCFF from EBIT: FCFF = EBIT(1 – t) + Dep – FCInv – WCInv; Use when the vignette gives operating income.
FCFF from EBITDA: FCFF = EBITDA(1 – t) + Dep(t) – FCInv – WCInv; Depreciation enters only through its tax shield.
FCFE from FCFF: FCFE = FCFF – Int(1 – t) + Net borrowing; Net borrowing = new debt issued – debt repaid.
FCFE from net income: FCFE = NI + NCC – FCInv – WCInv + Net borrowing; Interest is already deducted in net income, so do not subtract it again.
FCFE from CFO: FCFE = CFO – FCInv + Net borrowing; Use this form only when CFO is already after interest paid (always the case under US GAAP, and under IFRS when interest is classified in operating activities). CFO already reflects working capital changes. If interest paid is classified in financing (IFRS), first deduct the full interest paid, not the after-tax amount, because the taxes in CFO already include the interest tax shield: FCFE = CFO – Int – FCInv + Net borrowing.
Valuation by discounting: Firm value = Σ FCFF ÷ (1 + WACC)^t; Equity value = Σ FCFE ÷ (1 + r)^t; FCFF uses WACC. FCFE uses the cost of equity r. Equity value from FCFF = firm value – market value of debt (and preferred stock).
FCFF from net income: FCFF = NI + NCC + Int(1 − t) − FCInv − WCInv; NCC is non-cash charges, mainly depreciation and amortization. Add back losses and subtract gains on asset sales, since the cash is in investing flows.
FCFF from EBIT: FCFF = EBIT(1 − t) + Dep − FCInv − WCInv; EBIT is before interest, so no interest adjustment is needed. Dep means depreciation and amortization.
FCFF from EBITDA: FCFF = EBITDA(1 − t) + Dep × t − FCInv − WCInv; Depreciation is added back only for its tax shield, because EBITDA already excludes the charge.
FCFF from CFO: FCFF = CFO + Int(1 − t) − FCInv; Working capital change and non-cash charges are already in CFO. Add back Int(1 − t) only when interest paid was deducted in CFO (US GAAP, or IFRS if classified as operating). Under IFRS, if interest paid is classified in financing, CFO is already before interest, so do not add it back.
FCFE from FCFF: FCFE = FCFF − Int(1 − t) + Net borrowing; Net borrowing = debt issued − debt repaid. It can be negative.
FCFE from net income: FCFE = NI + NCC − FCInv − WCInv + Net borrowing; Net income is already after interest, so no interest adjustment is needed.
FCFE from CFO: FCFE = CFO − FCInv + Net borrowing; The fastest route when CFO is given. This form applies when interest paid is already deducted in CFO (US GAAP, or IFRS if classified as operating). If under IFRS interest paid is classified in financing, subtract Int(1 − t) from CFO to get FCFE.
FCFF from FCFE: FCFF = FCFE + Int(1 − t) − Net borrowing; The same link as above, rearranged. Use it to check your answers.
FCFF from net income: FCFF = NI + NCC + Int(1 − t) − FCInv − WCInv; NCC is non-cash charges, FCInv is fixed capital investment, WCInv is working capital investment.
FCFE from FCFF: FCFE = FCFF − Int(1 − t) + Net borrowing; Net borrowing is new debt minus repayments.
FCFE with constant debt ratio: FCFE = NI − (1 − DR)(FCInv − Dep) − (1 − DR)WCInv; DR is the proportion of net new investment (FCInv − Dep + WCInv) financed with debt. Use when the debt financing ratio is held constant.
Retention rate: b = 1 − dividend payout ratio; Retention is the share of earnings kept in the business. Do not replace dividends with FCFE unless the vignette tells you to.
Fundamental growth (FCFF): g = reinvestment rate × ROIC, where reinvestment rate = (FCInv − Dep + WCInv) ÷ EBIT(1 − t); ROIC = EBIT(1 − t) ÷ invested capital.
Sustainable growth: g = b × ROE, with b = 1 − dividend payout ratio; ROE = NI ÷ beginning equity. This is the standard fundamental growth formula for equity.
DuPont ROE: ROE = net profit margin × asset turnover × leverage; DuPont shows what drives growth. Higher leverage lifts ROE and g, with more risk.
Single-stage FCFF firm value: Firm value₀ = FCFF₁ ÷ (WACC − g) = FCFF₀ × (1 + g) ÷ (WACC − g); Requires WACC > g. FCFF₁ is next year's cash flow. Check whether the vignette gives FCFF₀ or FCFF₁.
Firm value to equity value: Equity value = Firm value − Market value of debt − Preferred stock (+ non-operating assets if excluded); Use market value of debt where given. Use the same date as the firm value.
Single-stage FCFE equity value: Equity value₀ = FCFE₁ ÷ (r − g) = FCFE₀ × (1 + g) ÷ (r − g); r is the required return on equity. Requires r > g.
Value per share: Value per share = Equity value ÷ Shares outstanding; Use the share count the vignette specifies.
WACC: WACC = [E ÷ (D + E)] × rₑ + [D ÷ (D + E)] × r_d × (1 − t); Use target or market-value weights and the after-tax cost of debt.
FCFE from FCFF: FCFE = FCFF − Interest × (1 − t) + Net borrowing; Net borrowing is new debt issued minus debt repaid.
Multistage firm value (FCFF): Firm value = Σ FCFF(t) ÷ (1 + WACC)^t for t = 1 to n + TV(n) ÷ (1 + WACC)^n; Equity value = firm value − market value of debt − preferred stock (plus non-operating assets if not already included).
Multistage equity value (FCFE): Equity value = Σ FCFE(t) ÷ (1 + r)^t for t = 1 to n + TV(n) ÷ (1 + r)^n; r is the required return on equity.
Terminal value, Gordon growth (FCFF): TV(n) = FCFF(n+1) ÷ (WACC − g) = FCFF(n) × (1 + g) ÷ (WACC − g); Requires g < WACC. Use the long-run sustainable g, not the high-stage rate.
Terminal value, Gordon growth (FCFE): TV(n) = FCFE(n+1) ÷ (r − g) = FCFE(n) × (1 + g) ÷ (r − g); Requires g < r.
Terminal value, multiples: TV(n) = multiple × metric(n); For example EV/EBITDA × EBITDA(n) gives firm TV; P/E × EPS(n) gives equity TV. Match the multiple to firm or equity value.
Multiple implied by Gordon growth: Implied TV/FCFF(n) = (1 + g) ÷ (WACC − g); Use it to cross-check a multiple-based TV against a growth-based TV.
Constant-growth FCFF firm value: Firm value = FCFF1 ÷ (WACC − g); Requires WACC > g and a stable growth, stable capital structure.
Constant-growth FCFE equity value: Equity value = FCFE1 ÷ (r − g); r is the required return on equity.
Equity value from FCFF: Equity = Firm value (operating) + non-operating assets − debt − preferred stock; Use market or fair values of the claims. Do not include non-operating asset income in FCFF.
Multistage terminal value: TV at n = FCF(n+1) ÷ (r − g), or TV = multiple × metric at n; Discount TV back n periods along with the explicit-period flows.
Sensitivity method: Change one input, hold others constant, recompute value; Compare percentage change in value across inputs to rank importance.

Quick revision

FCFF is cash flow to all capital providers; discount it at WACC to get firm value.
FCFE is cash flow to equity holders; discount it at the cost of equity to get equity value.
Equity value = firm value − market value of debt (and adjust for other claims the vignette states).
FCFE = FCFF − interest × (1 − tax rate) + net borrowing.
FCFF = NI + non-cash charges + interest × (1 − tax rate) − FCInv − WCInv.
FCFF = EBIT × (1 − tax rate) + depreciation − FCInv − WCInv.
FCFE = CFO − FCInv + net borrowing.
Use changes in operating working capital only, and exclude cash and short-term debt.
Constant growth value = next-period cash flow ÷ (discount rate − g), and it requires g below the discount rate.
In multistage models, terminal value is found at the end of the explicit period and then discounted back.
Check the terminal value share of total value; a very high share signals a fragile result.
Sensitivity analysis changes one input at a time; value is typically most sensitive to the discount rate and the terminal growth rate.

Common mistakes

Adding back interest to net income when computing FCFE. Fix: FCFE starts from net income, which is already after interest. Only FCFF adds back Int(1 – t).
Adding back full interest instead of interest × (1 – t). Fix: Always use after-tax interest in FCFF formulas. The shield is handled in WACC for discounting.
Adding back pre-tax interest instead of Int(1 − t) when moving from net income or CFO to FCFF. Fix: Always write Int(1 − t) in the formula. Interest is added back after tax because the tax shield stays in the cash flow.
Adding the full depreciation to EBITDA(1 − t). Fix: With EBITDA, depreciation enters only as Dep × t, its tax shield. Check by converting EBITDA to EBIT: EBITDA − Dep = EBIT.
Treating FCFE as dividends when computing retention Fix: Retention is 1 − dividend payout ratio. Use FCFE-based growth only if the vignette defines it.
Applying ROE growth to FCFF Fix: FCFF uses reinvestment rate × ROIC. Sustainable growth for equity uses retention × ROE.
Discounting FCFF at the cost of equity, or FCFE at WACC. Fix: Match the rate to the claimants. FCFF goes with WACC. FCFE goes with cost of equity.
Forgetting to grow the time 0 cash flow by (1 + g). Fix: Ask whether the figure is current or next year. Use FCFF₀ × (1 + g) if current.
Using the high-growth rate in the terminal value formula. Fix: TV uses the stable growth rate that applies after year n. Label each rate by stage before calculating.
Computing TV with FCF(n) instead of FCF(n+1). Fix: Multiply FCF(n) by (1 + g) first, or check whether the vignette already gives FCF(n+1).

Exam tips

Look at where interest paid sits in the cash flow statement before using any CFO formula. It decides whether you add it back for FCFF or deduct it for FCFE.
When a question asks which measure is better, read the leverage story: changing or high leverage points to FCFF, stable leverage points to FCFE.
Cross-check with FCFE = FCFF – Int(1 – t) + net borrowing. It catches most arithmetic errors fast.
FCFF discounted gives firm value, so look for the debt subtraction step. Many wrong options skip it.
No negative marking, so always answer. Eliminate options that use the wrong discount rate first.
Find the starting line first. The choice of formula follows from it, and many wrong options come from using the wrong formula.
Write the tax rate beside every interest or EBIT figure before you calculate. Missing the tax adjustment is the most common lost point.
If the vignette gives both a balance sheet and a cash flow statement, take capex from investing flows and the working capital change from the balance sheet or the CFO reconciliation. Do not mix them.