CMA Final · Strategic Performance Management and Business Valuation

Economic Efficiency of the Firm - Performance Analysis: formula sheet

Full chapter guide

Key formulas

EVA: EVA = NOPAT − Capital charge; Positive EVA means value created; negative means value destroyed.
Capital charge: Capital charge = WACC × Invested capital; Use the capital figure the question specifies, usually opening capital employed.
NOPAT: NOPAT = EBIT × (1 − tax rate); EBIT is operating profit before interest and tax. Do not deduct interest.
EVA by spread: EVA = (ROIC − WACC) × Invested capital; ROIC = NOPAT ÷ Invested capital. Useful as a cross-check.
WACC: WACC = Ke × We + Kd × (1 − t) × Wd; Weights are of equity and debt in total capital.
Cost of equity (CAPM): Ke = Rf + β × (Rm − Rf); Use when the question gives beta and market data.
Invested capital: Invested capital = Equity + Debt (or Net fixed assets + Net working capital); Both routes should agree. Adjust for items such as capitalised R&D if told.
MVA (firm view): MVA = Market value of firm − Capital invested; Market value of firm = market value of equity + market value of debt.
MVA (equity view): MVA = Market value of equity − Equity capital invested; Use when the question deals only with shareholders' wealth.
Market value of equity: Market value of equity = Market price per share × Number of shares; Use the number of shares outstanding.
EVA: EVA = NOPAT − (WACC × Capital employed); A one-year measure of value creation.
MVA–EVA link: MVA = Σ EVAt ÷ (1 + WACC)^t, for t = 1 to ∞; MVA equals the present value of expected future EVAs. For a constant perpetual EVA, MVA = EVA ÷ WACC.
Return on Investment (ROI): ROI = (Divisional profit ÷ Capital employed) × 100; State which profit (before or after tax, before or after divisional interest) and which capital base (opening, closing or average) you use.
Residual Income (RI): RI = Divisional profit − (Capital employed × Required rate of return); The deduction is called the capital charge or notional interest. Profit must be before interest on that capital.
Project acceptance under ROI: Accept if project ROI > division's current ROI (manager's view); This can conflict with the company's view, which is to accept if project return > cost of capital.
Project acceptance under RI: Accept if project profit − (project investment × required rate) > 0; Equivalent to project return > required rate, so it supports goal congruence.
Capital employed (common form): Capital employed = Total assets − Current liabilities; Use the base given in the question. Net book value or gross value may be specified.
Gross cash flow: Gross cash flow = Net operating profit after tax + Depreciation and amortisation (+ other non-cash charges, as given); Some questions add rental or interest items. Follow the data given and state what you include.
Gross investment: Gross investment = Gross (undepreciated) fixed assets + Working capital (+ other operating assets, as given); Use original cost, not net book value. Adjust for inflation only if the question asks.
CFROI as an IRR: Gross investment = Σ [Gross cash flow ÷ (1 + CFROI)^t] for t = 1 to n + Terminal value ÷ (1 + CFROI)^n; Solve for CFROI by trial and error, then interpolate.
Terminal value: Terminal value = Non-depreciating assets (land, working capital) recoverable at end of asset life; Depreciable assets are taken as having nil value at the end of life.
Decision rule: CFROI > cost of capital: value created; CFROI < cost of capital: value destroyed; Compare like with like. If CFROI is real, use a real cost of capital.
Interpolation: IRR = Lower rate + [NPV at lower rate ÷ (NPV at lower rate − NPV at higher rate)] × (Higher rate − Lower rate); Choose two trial rates that give NPVs of opposite sign.
Incremental sales: Sales(t) = Sales(t-1) × (1 + g); g is the sales growth rate. Sales for each forecast year build on the previous year.
Operating cash flow (Rappaport): OCF(t) = Sales(t) × P × (1 − T) − (Sales(t) − Sales(t-1)) × (f + w), where Sales(t) = Sales(t-1) × (1 + g); P is the operating profit margin and T is the cash tax rate. Both apply to the sales of year t. The investment charge is based only on the change in sales, using the incremental fixed capital rate f and working capital rate w.
Incremental investment: Incremental investment(t) = (Sales(t) − Sales(t-1)) × (f + w); f and w are the incremental fixed capital and working capital rates, each as a proportion of the increase in sales.
Present value of forecast cash flows: PV = Σ OCF(t) ÷ (1 + k)^t, for t = 1 to n; k is the WACC and n is the value growth duration.
Residual value: Residual value = NOPAT(n) ÷ k, and PV of residual value = [NOPAT(n) ÷ k] × 1 ÷ (1 + k)^n; This assumes no value growth after year n and no incremental investment, so NOPAT(n) is the perpetual cash flow. State the assumption you use.
Corporate value: Corporate value = PV of cash flows over forecast period + PV of residual value + marketable securities; This is the value of the whole firm.
Shareholder value: Shareholder value = Corporate value − Market value of debt; Add marketable securities before deducting debt.
Shareholder value added: SVA = Shareholder value at end of period − Shareholder value at start, adjusted for dividends and new capital; In strategy comparison, value added = value with the strategy − value without it.
Total shareholder return (single period): TSR = (P₁ − P₀ + D) ÷ P₀ × 100; P₀ is opening price, P₁ closing price, D dividends received in the period.
Components of TSR: TSR = Capital gain yield + Dividend yield = (P₁ − P₀) ÷ P₀ + D ÷ P₀; Use this to show what drove the return.
Multi-year annualised TSR: Annualised TSR = [(Ending value ÷ Opening value)^(1/n) − 1] × 100; Ending value includes dividends (reinvested or added, state your assumption). n is the number of years.
Economic profit: Economic profit = NOPAT − (Capital employed × WACC); NOPAT is operating profit after tax. Use opening or average capital consistently.
Spread: Spread = ROCE (after tax) − WACC; Economic profit = Spread × Capital employed.
Return on capital employed: ROCE = EBIT ÷ Capital employed × 100; Use NOPAT for the after-tax version when comparing with WACC.
Return on equity: ROE = Profit after tax ÷ Shareholders' equity × 100; Compare with the cost of equity.
Dividend yield and P/E: Dividend yield = DPS ÷ Market price; P/E = Market price ÷ EPS; Both use the market price, so they change with the share price.

Quick revision

A firm creates value only when return on capital exceeds the cost of capital.
EVA = NOPAT − (WACC × capital employed).
Positive EVA means value is created; negative EVA means value is destroyed.
MVA = market value of the firm's capital − capital invested.
Residual income = divisional operating profit − (required rate of return × divisional investment).
ROI = operating profit ÷ investment, and it can make managers reject projects that are good for the firm.
Residual income and EVA charge for capital; ROI does not.
CFROI is a cash-based return that is compared with the cost of capital.
Shareholder value analysis links operating value drivers to the value of the firm.
TSR combines share price change and dividends over a period.
Always state your assumptions about capital and adjustments before computing.
End with a clear recommendation, not just a number.

Common mistakes

Deducting interest while computing NOPAT. Fix: Start from EBIT, or add back interest to profit before tax, then apply the tax rate.
Using the pre-tax cost of debt in WACC. Fix: Always multiply the cost of debt by (1 − t) before weighting.
Subtracting equity capital from the market value of the whole firm. Fix: Keep both sides on the same basis: firm value with total capital, or equity value with equity capital.
Using book value of equity instead of market price × shares. Fix: Market value of equity always comes from the market price.
Deducting the capital charge from profit that is already after interest on the same capital. Fix: Use profit before interest on the capital being charged. Check the question's wording before the capital charge step.
Mixing capital bases, such as profit with closing capital in one part and average capital in another. Fix: Choose one base as stated, write it down, and use it for ROI and RI throughout.
Using net book value of assets as the investment. Fix: CFROI uses gross investment: original cost before depreciation, plus working capital.
Forgetting to add back depreciation to get gross cash flow. Fix: Add depreciation and other non-cash charges to operating profit after tax. Say so in your first line.
Using accounting profit instead of operating cash flow Fix: Start with operating profit, deduct tax on it, then deduct incremental fixed and working capital investment. Depreciation is already inside operating profit, so do not treat it as a separate cash item unless the question says so.
Charging incremental investment on total sales instead of the increase in sales Fix: Multiply the rate by the change in sales over the previous year. Check the wording: 'incremental' means on additional sales.

Exam tips

Write the formula line first. Step marks are given even if a later figure is wrong.
Show WACC working separately, with the after-tax cost of debt visible.
In MCQs, check whether the question gives profit after interest or EBIT before you pick NOPAT.
In descriptive answers, give at least two advantages and two limitations, each in a short line with a reason.
Limitations to remember: depends on accounting data and adjustments, uses book capital, is an absolute figure that favours large units, and may encourage short-term focus.
In MCQs, check whether the question gives market value of debt. If not, the equity view or book debt is usually intended.
Write the formula first, then substitute. Marks are given for method.
For theory questions, state the difference between EVA and MVA in three points: period, basis and applicability.