ACCA Strategic Professional · Strategic Business Leader

Financial analysis and decision-making techniques: formula sheet

Full chapter guide

Key formulas

Gross profit margin: Gross profit ÷ Revenue × 100; Shows pricing power and direct cost control.
Operating profit margin: Profit from operations ÷ Revenue × 100; Includes overheads, so it shows overall cost control.
Return on capital employed (ROCE): Profit before interest and tax ÷ (Total equity + Non-current liabilities) × 100; Measures return on long-term funds. Define capital employed the same way each year.
Asset turnover: Revenue ÷ Capital employed; ROCE = operating margin × asset turnover.
Current ratio: Current assets ÷ Current liabilities; A short-term liquidity measure. Do not quote a universal ideal.
Quick ratio: (Current assets − Inventory) ÷ Current liabilities; Excludes inventory as it is the least liquid current asset.
Inventory days: Inventory ÷ Cost of sales × 365; Use average inventory if the question gives both years.
Receivables days: Trade receivables ÷ Credit revenue × 365; Use total revenue if credit sales are not given, and say so.
Payables days: Trade payables ÷ Cost of sales × 365; Use credit purchases if given.
Gearing (debt to equity): Debt ÷ Equity × 100; One of several definitions. State yours and use it consistently.
Interest cover: Profit before interest and tax ÷ Finance costs; Shows how easily profit covers interest.
Net present value: NPV = Σ [CFt ÷ (1 + r)^t] − initial investment; CFt is the net cash flow in year t and r is the cost of capital. Accept if NPV > 0.
Internal rate of return (interpolation): IRR ≈ L + [NPV_L ÷ (NPV_L − NPV_H)] × (H − L); L and H are two discount rates, one giving a positive NPV and one a negative NPV. The result is an estimate. Accept if IRR > cost of capital.
Payback period: Payback = full years before recovery + (unrecovered cost at start of year ÷ cash flow in that year); Assumes cash flows arise evenly through the year. Uses cumulative cash flows.
Accounting rate of return: ARR = average annual accounting profit ÷ initial investment × 100%; An alternative uses average investment = (initial cost + residual value) ÷ 2. State which you use.
Annuity of a constant cash flow: PV = cash flow × annuity factor; Use the factor from the tables ACCA provides for the rate and number of years.
Decision rules: NPV > 0 accept; IRR > r accept; payback ≤ target accept; ARR ≥ target accept; Payback and ARR targets are set by management.
Expected value: EV = Σ (probability × outcome); Probabilities must add up to 1. EV is a long-run average, so it may not match any single real outcome.
Sensitivity (percentage change): Sensitivity % = NPV ÷ PV of the variable being tested × 100; This is the percentage fall in that variable that makes NPV exactly zero. The smaller the percentage, the more sensitive the project.
Sensitivity margin of safety: Margin = (NPV ÷ PV of the variable) × 100; Use the present value of the cash flows of that variable only, for example sales revenue over the project life.
Standard deviation of outcomes: σ = √[ Σ p × (x − EV)² ]; Measures spread around the EV. Use it to compare projects with similar EVs.
Expected NPV decision rule: Accept if expected NPV > 0; A risk-neutral decision rule. Also consider the spread and the decision-maker's risk appetite.
Net asset value per share: (Total assets − Total liabilities) ÷ Number of shares; Use fair values for assets where the scenario gives them, not book values.
P/E valuation: Value of equity = Earnings after tax × P/E ratio; Value per share = EPS × P/E ratio; Use a P/E from a similar company. Adjust it down for an unquoted or riskier firm.
Earnings yield valuation: Value = Earnings ÷ Earnings yield; Earnings yield is the inverse of the P/E ratio.
Dividend valuation model (no growth): P₀ = D ÷ Ke; D is the annual dividend expected from now on, Ke is the cost of equity.
Dividend growth model: P₀ = D₀(1 + g) ÷ (Ke − g); Gives ex-dividend value. D₀ is the dividend just paid. Needs Ke greater than g.
Cost of equity from dividend growth: Ke = [D₀(1 + g) ÷ P₀] + g; Rearrangement of the growth model.
Gordon growth estimate of g: g = b × r; b is the proportion of earnings retained, r is the return on new investment.
Discounted cash flow value: Value = Σ [FCF_t ÷ (1 + r)^t] + Terminal value ÷ (1 + r)^n; Terminal value with constant growth = FCF_(n+1) ÷ (r − g). Discount at the WACC for firm value.
Equity value from enterprise value: Equity value = Enterprise value − Market value of debt (plus surplus cash); Enterprise value comes from DCF of free cash flows to the firm.
Economic Value Added: EVA = NOPAT − (WACC × Capital employed); NOPAT is net operating profit after tax. Accounting adjustments, such as adding back R&D, are sometimes made.
Market Value Added: MVA = Market value of the firm (debt + equity) − Capital invested; Positive MVA means wealth has been created. It is cumulative, not annual.
WACC: WACC = [E ÷ (E + D)] × Ke + [D ÷ (E + D)] × Kd × (1 − t); Use market values for E and D. Kd is the pre-tax cost of debt. t is the tax rate.
Cost of equity (dividend growth model): Ke = [D0 × (1 + g) ÷ P0] + g; P0 is the ex-dividend share price. D0 is the dividend just paid.
Cost of equity (CAPM): Ke = Rf + β × (Rm − Rf); Rm − Rf is the market risk premium. Beta reflects systematic risk.
Post-tax cost of irredeemable debt: Kd = [Interest × (1 − t)] ÷ Market value of debt; For redeemable debt, use the IRR of the cash flows instead.
M&M with tax (proposition 1): Vg = Vu + D × t; Geared value equals ungeared value plus the tax shield on permanent debt. It assumes perfect markets, ignoring distress costs.
Gearing ratio (market value): Debt ÷ (Debt + Equity) or Debt ÷ Equity; State which version you use.
Suitability: Suitability = fit with strategic position, objectives, strengths and environment; Ask: does it solve the problem or use the opportunity in the scenario?
Acceptability: Acceptability = returns + risk + stakeholder reaction + ethics; Financial return belongs here, but so do shareholder, employee, regulator and community views.
Feasibility: Feasibility = funding + people and skills + technology + time + legal and operational ability; Look for resource gaps in the scenario.
Balanced scorecard perspectives: Financial | Customer | Internal business process | Innovation and learning; Use it as a checklist to test whether an option supports all four, not only finance.
Decision rule for finance: Accept if NPV > 0 (at the right cost of capital), then test the non-financial factors; A positive NPV is necessary evidence, not a full decision.

Quick revision

Ratios only mean something when compared with a trend, a competitor or a target.
Check how a ratio is defined and apply the same definition each year.
NPV: accept a project if it is positive when discounted at the appropriate rate.
IRR is the discount rate at which NPV is zero. Compare it with the required return.
Payback ignores cash flows after the payback point and, in its simple form, the time value of money.
ARR uses accounting profit, not cash, so it can conflict with NPV.
Sensitivity analysis shows how far one input can change before the decision flips.
Valuation gives a range, not a single true value. State your assumptions.
Cost of capital reflects the risk of the investment and how it is financed.
Debt is usually cheaper than equity but raises financial risk.
Non-financial factors include stakeholders, ethics, fit with strategy and feasibility.
Always end with a clear recommendation, reasons and the main risks.

Common mistakes

Listing calculated ratios with little or no comment. Fix: For each ratio write what changed, why (using the case), and what it means. Aim for more analysis than arithmetic.
Calculating every possible ratio. Fix: Select ratios that test the specific issues in the scenario and the requirement.
Including depreciation or sunk costs in cash flows for NPV. Fix: Use cash flows only. Remove depreciation and past costs, and include only incremental future cash.
Discounting the initial outlay. Fix: Treat the initial investment as year 0 with a factor of 1.000.
Treating risk and uncertainty as the same thing. Fix: Define both at the start. Risk has known probabilities. Uncertainty does not.
Presenting the expected value as the result that will happen. Fix: Say that EV is a long-run average. Show the range of outcomes and the chance of a loss, especially for a one-off decision.
Using the dividend growth model with D₀ instead of D₀(1 + g). Fix: Check whether the dividend given is the one just paid. If so, multiply by (1 + g) first.
Applying a quoted company's P/E to an unquoted company without adjustment. Fix: State that unquoted shares are less liquid and riskier. Reduce the P/E, often by a stated discount, and explain why.
Using book values for the weights. Fix: Use market values of shares and debt unless the question gives no choice. Say so if you must use book values.
Forgetting to adjust debt for tax. Fix: Multiply the pre-tax cost of debt by (1 − t) before weighting.

Exam tips

Choose ratios to fit the scenario. A weak answer calculates everything; a strong answer calculates what supports a point.
Quote case facts when explaining a movement, such as a new product, price war or acquisition. This earns application and professional skills marks.
State your formula where definitions differ and keep it consistent. Markers reward clear, reasonable assumptions.
Link ratios to strategy: does the financial position support the proposed strategy, or limit it?
Keep limitations specific to the data and finish with a clear conclusion for the stated audience.
Show a short working table. Markers give credit for correct method even if one figure is wrong.
State your assumptions in one line each, such as end-of-year cash flows and the cost of capital used.
Always compare methods when they disagree. NPV and IRR can conflict for mutually exclusive projects, and NPV is preferred.