Models for the valuation of shares: formula sheet

Key formulas

Net asset value (book)

Net assets = Total assets − Total liabilities

Value per share = net assets ÷ number of ordinary shares. Remove preference shares from net assets first if they rank ahead of ordinary shares.

Net realisable value basis

Equity value = Sale proceeds of assets − Liabilities − Costs of closure

Used for a break-up or liquidation view. Usually gives the lowest value for a going concern.

Price/earnings (P/E) method

Value of equity = Earnings × P/E ratio

P/E is taken from a similar quoted company. Earnings are the profit after tax and after preference dividends.

Earnings yield method

Value of equity = Earnings ÷ Earnings yield

Earnings yield = 1 ÷ P/E. Same information as P/E, shown as a percentage.

Dividend valuation model (constant growth)

P₀ = D₀(1 + g) ÷ (Ke − g)

D₀ is the dividend just paid. Needs Ke > g. The price is ex-dividend.

Discounted cash flow value

Value = Σ [Cash flow in year t ÷ (1 + r)ᵗ]

Discount future free cash flows at a rate that reflects the risk. Include a terminal value if the business continues.

Net asset value

Net asset value = Total assets − Total liabilities (including debt and preference shares)

Preference shares and long-term debt are deducted to leave the value attributable to ordinary shareholders.

Value per share

Value per share = Net asset value attributable to ordinary shareholders ÷ Number of ordinary shares

Use shares in issue, not the nominal value total.

Net book value basis

NBV of net assets = Carrying amounts of assets − Liabilities

Often exclude intangibles such as capitalised development or purchased goodwill if the question asks for tangible net assets.

Net realisable value basis

NRV of net assets = Estimated sale proceeds of assets − Selling and closure costs − Liabilities

Break-up basis. Include redundancy and liquidation costs if given.

Replacement cost basis

Replacement cost of net assets = Current cost of equivalent assets − Liabilities

Use the cost of equivalent assets in similar condition, not new ones, unless told otherwise.

P/E ratio

P/E = Market price per share ÷ EPS

Use the same earnings basis (usually after tax and after preference dividends) for EPS.

Share value by P/E

Value per share = EPS × P/E ratio

The P/E must come from a comparable company or be given in the question.

Value of equity

Equity value = Total earnings attributable to ordinary shareholders × P/E ratio

Divide by the number of shares for a value per share.

Earnings yield

Earnings yield = EPS ÷ Market price per share = 1 ÷ P/E

Express as a percentage.

Value using earnings yield

Value per share = EPS ÷ Earnings yield

Gives the same answer as EPS × P/E if the yield is 1 ÷ the P/E.

EPS

EPS = (Profit after tax − Preference dividends) ÷ Number of ordinary shares

Use the weighted average number of shares if the number changed in the year.

Free cash flow to the firm

FCFF = operating profit after tax + depreciation − capital investment − increase in working capital

Before interest. Tax is on operating profit. Use a working capital decrease as an inflow.

Free cash flow to equity

FCFE = FCFF − interest after tax + net new borrowing

Net new borrowing is new debt less repayments. It can be negative.

Terminal value (growing perpetuity)

TV at end of year n = FCF(n+1) ÷ (r − g) = FCF(n) × (1 + g) ÷ (r − g)

Needs r > g. Use WACC for FCFF and the cost of equity for FCFE. It gives a value at time n.

Enterprise value

Enterprise value = PV of FCFF at WACC (including terminal value)

Discount each year's FCFF and the terminal value.

Equity value from enterprise value

Equity value = enterprise value − market value of debt (and preference shares)

Use market value of debt where given. Add surplus cash if the question treats it separately.

Equity value from FCFE

Equity value = PV of FCFE at the cost of equity (including terminal value)

Divide by number of shares for value per share.

Weak form

Price = f(past prices and trading data)

Technical (chartist) analysis is of no use. Insiders and fundamental analysts could still gain.

Semi-strong form

Price = f(all public information)

Includes weak form. Fundamental analysis of public data cannot beat the market consistently. Insider information can.

Strong form

Price = f(all public and private information)

Includes semi-strong form. No one can earn consistent abnormal returns.

Abnormal return

Abnormal return = actual return − return expected for the risk taken

EMH says abnormal returns cannot be earned consistently using the information already in the price.

Net asset value per share

(Total assets − Total liabilities) ÷ Number of shares

Use fair values, not just book values, and be clear about whether intangibles are included.

P/E valuation

Value of equity = Earnings × P/E ratio; Share price = EPS × P/E

Use earnings attributable to ordinary shareholders and a P/E from a comparable company.

Earnings yield

Earnings yield = EPS ÷ Share price = 1 ÷ P/E

Value can be found as Earnings ÷ Earnings yield.

Dividend valuation model with growth

P0 = D0 × (1 + g) ÷ (ke − g)

Valid only if ke is greater than g and growth is constant. D0 is the dividend just paid.

Dividend growth rate

g = b × r

b is the proportion of earnings retained and r is the return on new investment. It is an estimate.

Discounted cash flow value

Value = Σ [FCF ÷ (1 + r)^t] + terminal value discounted

Free cash flow to equity is discounted at the cost of equity.

Quick revision

• Asset-based values rely on net assets, so they may ignore earnings power and unrecorded intangibles.
• Share value by P/E method = EPS × P/E ratio.
• Earnings yield = EPS ÷ share price, which is the inverse of the P/E ratio.
• A P/E from a comparable company should be adjusted for differences such as risk, size and growth.
• Dividend valuation model with constant dividend: P = D ÷ Ke.
• Dividend valuation model with constant growth: P0 = D1 ÷ (Ke − g), where D1 is next year's dividend.
• The constant growth formula needs Ke greater than g.
• Growth can be estimated from past dividends or from retention rate × return on retained funds.
• Free cash flow to equity is the cash available to shareholders after tax, reinvestment and debt servicing, and is discounted at the cost of equity.
• Weak form EMH: prices reflect past price data. Semi-strong: all public information. Strong: all information, including private.
• Every model depends on forecasts and assumptions, so treat results as a range, not an exact figure.
• If you are asked to comment, give a reason tied to the scenario, not just a definition.

Common mistakes

• Using book value of assets as if it were the market value of the business. Fix: Remember that book values are historic, often exclude internally generated goodwill and brands, and say so. Use revalued figures if the question gives them.
• Forgetting to deduct preference shares before valuing ordinary shares. Fix: Deduct preference shares and all liabilities from assets, or use earnings after preference dividends, before dividing by ordinary shares.
• Forgetting to deduct long-term debt or preference shares. Fix: Take the liabilities from the whole statement of financial position and ask whether anyone ranks ahead of ordinary shareholders.
• Using book values when the question gives market or realisable values. Fix: Underline the basis in the question and replace each affected asset before adding up.
• Using profit before tax or before preference dividends to calculate EPS. Fix: Always use profit after tax less preference dividends, then divide by ordinary shares.
• Multiplying earnings by the earnings yield instead of dividing. Fix: Remember: P/E multiplies, yield divides. A yield of 8% means a P/E of 12.5.
• Discounting FCFE at WACC, or FCFF at the cost of equity. Fix: FCFF belongs to all investors, so use WACC. FCFE belongs to shareholders only, so use the cost of equity. Write the pairing next to your first line.
• Deducting debt from a value based on FCFE. Fix: FCFE is already after interest and debt flows. The present value is equity value. Only deduct debt after discounting FCFF.
• Saying weak form means prices are weak or inaccurate. Fix: Weak refers to the small set of information in the price: past prices only.
• Treating the three forms as separate, not cumulative. Fix: Each form includes the previous one. If a market is semi-strong, it is also weak form.

Exam tips

• Read the purpose of the valuation first. Examiners often reward the answer that links the method to the situation, such as break-up value for a company in difficulty.
• In written parts, give one strength and one weakness for each method you mention. Short, specific points score better than long general ones.
• In objective tests, check whether the question wants total equity value or value per share, and whether the figures are before or after preference dividends.
• If a question says the methods give very different values, explain why: assets ignore earnings, and earnings-based methods ignore asset backing.
• Show your working in constructed response answers even when the arithmetic is short, so method marks are available.
• Read the basis word first. NBV, NRV and replacement cost need different figures from the same data.
• Always show the deduction of liabilities and costs as separate lines to earn method marks.
• For discussion parts, give at least one limitation tied to the scenario, such as unrecorded intangibles or ignoring future earnings.