ACCA Strategic Professional · Advanced Financial Management

Valuation and the use of free cash flows: formula sheet

Full chapter guide

Key formulas

FCFF from operating profit (EBIT): FCFF = EBIT × (1 − t) + depreciation − capital expenditure − increase in working capital; t is the tax rate. Use a decrease in working capital as an inflow. Depreciation here means all non-cash charges added back.
FCFF from net income: FCFF = net income + non-cash charges + interest × (1 − t) − capital expenditure − increase in working capital; Add back after-tax interest because FCFF is before payments to lenders.
FCFE from FCFF: FCFE = FCFF − interest × (1 − t) + net borrowing; Net borrowing = new debt raised − debt repaid.
FCFE from net income: FCFE = net income + non-cash charges − capital expenditure − increase in working capital + net borrowing; Net income is already after interest and tax, so do not deduct interest again.
Firm value: Value of firm = Σ FCFF ÷ (1 + WACC)^t, plus terminal value discounted; Equity value = firm value − market value of debt.
Equity value: Value of equity = Σ FCFE ÷ (1 + ke)^t, plus terminal value discounted; ke is the cost of equity. This gives equity value directly.
Constant-growth terminal value: TV at end of year n = CF(n+1) ÷ (r − g) = CF(n) × (1 + g) ÷ (r − g); Valid only when r > g and growth is expected to continue indefinitely. Use WACC for FCFF and ke for FCFE.
FCFF: FCFF = EBIT × (1 − t) + depreciation − capital expenditure − increase in working capital; Use tax on operating profit, not on profit after interest. Add back other non-cash charges too. Interest is not deducted.
FCFE: FCFE = FCFF − interest × (1 − t) + net new borrowing; Equivalent to profit after tax + depreciation − capex − increase in working capital + net new borrowing.
Present value of explicit cash flows: PV = Σ CFt ÷ (1 + r)^t; r is WACC for FCFF and cost of equity for FCFE.
Terminal value (constant growth): TVn = CFn × (1 + g) ÷ (r − g); Valid only when r > g. It gives the value at the end of year n. Discount it by (1 + r)^n.
Firm value to equity value: Equity value = PV of FCFF (incl. TV) − market value of debt + surplus cash or non-operating assets; Use the market value of debt where given, not the book value.
Sustainable growth: g = retention rate × return on new investment; Use it to test whether an assumed growth rate is supported by reinvestment.
Sustainable growth (Gordon's growth approximation): g = b × r; b = retention (reinvestment) rate, r = return on new investment, often ROE. Assumes r stays constant and the capital structure is unchanged.
Retention rate: b = 1 − (dividend ÷ earnings) = 1 − payout ratio; For free cash flow, reinvestment rate = net reinvestment ÷ after-tax operating profit.
Reinvestment rate for FCFF: Reinvestment rate = (Capex − Depreciation + Increase in working capital) ÷ NOPAT; NOPAT = operating profit × (1 − tax rate).
Growth in FCFF: g = Reinvestment rate × ROIC; ROIC = NOPAT ÷ invested capital. Use the return expected on new investment.
Historical growth rate: g = (Latest ÷ Earliest)^(1 ÷ n) − 1; n = number of years of growth between the two figures, not the number of figures.
Forecast cash flow: CF(t) = CF(0) × (1 + g)^t; Use different g values for different years if the question gives them.
Terminal value (growing perpetuity): TV at end of year n = CF(n+1) ÷ (k − g) = CF(n) × (1 + g) ÷ (k − g); Needs k > g. Discount TV by the year-n discount factor.
Net asset value: Equity value = Total assets − Total liabilities; Adjust assets to fair value or realisable value if the question gives figures. Exclude or adjust items as instructed.
P/E valuation: Equity value = Earnings attributable to ordinary shareholders × P/E ratio; Per share: EPS × P/E. Use a P/E from a comparable company, adjusted for risk, growth and gearing differences.
Earnings yield: Earnings yield = EPS ÷ Share price = 1 ÷ P/E; Value = Earnings ÷ earnings yield.
EV/EBITDA valuation: Enterprise value = EBITDA × EV/EBITDA multiple; Equity value = Enterprise value − Net debt; Net debt = debt − cash. Add back any other claims given, such as preference shares.
Dividend valuation model with growth: P0 = D0 × (1 + g) ÷ (Ke − g); Needs constant growth g, and Ke > g. The value is ex-dividend, so D0 is the dividend just paid.
Gordon growth estimate: g = b × r; b = proportion of earnings retained, r = return on new investment. Use it if the question gives these.
FCFF valuation: Enterprise value = Σ FCFFt ÷ (1 + WACC)^t + Terminal value ÷ (1 + WACC)^n; Terminal value with growth g = FCFF(n+1) ÷ (WACC − g). Equity value = EV − debt (+ cash if not netted).
FCFE valuation: Equity value = Σ FCFEt ÷ (1 + Ke)^t + Terminal value ÷ (1 + Ke)^n; FCFE = FCFF − interest × (1 − tax) + net new borrowing.
Free cash flow to the firm: FCFF = operating cash flow after tax − net investment in non-current assets − increase in working capital; Start from operating profit (EBIT) × (1 − t), add back depreciation, then deduct capital expenditure and working capital increases. Exclude interest.
Enterprise value: EV = Σ FCFF(t) ÷ (1 + WACC)^t + terminal value ÷ (1 + WACC)^n; Terminal value with growth g: FCFF(n+1) ÷ (WACC − g), where WACC > g.
Enterprise value to equity value: Equity value = EV + surplus cash and non-operating assets − market value of debt − preference shares − other prior claims; Use the market (or PV) value of debt where given, not the book value. Only deduct items the question treats as claims.
Free cash flow to equity: FCFE = FCFF − interest × (1 − t) + net new borrowing; Discount FCFE at the cost of equity to get equity value directly. No debt deduction is needed.
Equity value per share: Value per share = equity value ÷ number of shares in issue; Check whether options or convertibles dilute the share count.

Quick revision

FCFF is the cash available to all capital providers after tax and reinvestment; discount it at the WACC.
FCFE is the cash available to equity holders after debt servicing and reinvestment; discount it at the cost of equity.
Firm value from FCFF less the value of debt gives equity value.
Discounting FCFE gives equity value directly, with no debt deduction.
Terminal value is often a large share of total value, so check it carefully.
A constant growth terminal value uses the next year's cash flow divided by (discount rate − growth).
Long-run growth should be realistic and should not exceed the growth of the economy in which the firm operates.
Reinvestment is needed to support growth, so do not assume high growth with no capital expenditure.
The discount rate must match the cash flow: WACC for FCFF, cost of equity for FCFE.
P/E and other multiples are quick but depend on a comparable company and market conditions.
Asset-based values may ignore future earning power and intangible assets.
Always state the main assumptions and say how sensitive the value is to them.

Common mistakes

Discounting FCFE at WACC, or FCFF at the cost of equity Fix: FCFF belongs to all capital providers, so use WACC. FCFE belongs to shareholders, so use ke. Write the rate next to the cash flow.
Deducting interest in FCFF Fix: For FCFF, work from EBIT, or add back interest × (1 − t) to net income. Leave financing out of FCFF.
Discounting FCFF at the cost of equity, or FCFE at WACC. Fix: Write the pairing at the top of your answer: FCFF with WACC gives firm value, FCFE with cost of equity gives equity value.
Forgetting to deduct debt after valuing FCFF. Fix: Treat the FCFF total as firm value. Always subtract the market value of debt before stating equity value or a share price.
Using the payout ratio instead of the retention rate in g = b × r. Fix: Always compute b = 1 − payout first. Write it down as a separate line.
Forgetting to multiply by (1 + g) when using the growth perpetuity formula. Fix: The formula needs the next cash flow: CF(0) × (1 + g) ÷ (k − g). Check which year the question's figure belongs to.
Applying an EV/EBITDA multiple and treating the result as equity value. Fix: Always deduct net debt after applying the multiple. Write 'EV' on the line, then 'less net debt', then 'equity value'.
Discounting FCFF at the cost of equity, or FCFE at WACC. Fix: Match the cash flow to the claim. FCFF goes with WACC because it is before financing. FCFE goes with Ke because it belongs to shareholders.
Deducting debt from an equity-based (FCFE) valuation. Fix: Check the cash flow type first. FCFE discounted at the cost of equity already gives equity value. Only FCFF needs the bridge.
Double counting cash or investment income. Fix: Keep non-operating items out of FCFF, then add their value once in the bridge.

Exam tips

State at the start which measure you are using and why. This earns marks for judgement.
Show every line of the free cash flow build-up. Marks are given for each correct adjustment, even if the final figure is wrong.
Always match the rate to the cash flow: FCFF with WACC, FCFE with ke. Write this beside your discounting.
Do not stop at the number. Comment on growth assumptions, the reliability of forecasts and sensitivity. These earn the professional skills marks for analysis and commercial acumen.
If the answers from FCFF and FCFE differ, say so and explain possible causes, such as changing gearing or inconsistent inputs.
Read the requirement first. If it asks for equity value, check whether the data gives FCFF with WACC or FCFE with cost of equity, and pick the route that matches.
Show the cash flow build-up line by line. Marks are given for each correct element, even when the final value is wrong.
Always comment on the terminal value share, the growth assumption and sensitivity. Section A cases and Section B questions reward these points as technical and professional skills marks.