ACCA Applied Skills · Financial Management

Nature and purpose of the valuation of business and financial assets: formula sheet

Full chapter guide

Key formulas

Share-for-share exchange ratio: Shares offered per target share = Offer value per target share ÷ Bidder's value per share; Use this to link valuation to a share-for-share offer. Both values should be on a consistent basis.
Market capitalisation: Market capitalisation = Number of shares in issue × Share price; Gives the market value of equity for a listed company. It is a starting point, not always the fair value.
Takeover premium: Premium % = (Offer price − Current market price) ÷ Current market price × 100; Shows how much extra a bidder pays over the pre-bid price to gain control.
Net asset value (NAV): NAV = Total assets (at chosen basis) − Total liabilities (including preference shares); This gives the value attributable to ordinary shareholders. Deduct preference shares at redemption or nominal value as the question says.
NAV per share: NAV per share = NAV attributable to ordinary shareholders ÷ Number of ordinary shares; Use the number of shares in issue, not the nominal value in ₹ or $.
Replacement cost basis: Value = Current cost of equivalent assets − Liabilities; Adjust for the age and condition of the asset if the question gives a reduced cost for used equipment.
Realisable value basis: Value = Net sale proceeds of assets − Liabilities − Costs of closure; Use for break-up or liquidation. Net proceeds are after selling costs.
Adjusted NAV: Adjusted NAV = Book NAV ± revaluations ± unrecorded assets/liabilities; Start from book NAV and adjust. This is often the fastest route.
P/E ratio: P/E = Market price per share ÷ EPS = Market capitalisation ÷ Total earnings; Use earnings after tax and after preference dividends, available to ordinary shareholders.
Equity value using P/E: Equity value = Total earnings × P/E = EPS × P/E × number of shares; EPS × P/E gives the value per share.
Earnings yield: Earnings yield = EPS ÷ Share price × 100% = 1 ÷ P/E × 100%; The inverse of the P/E.
Equity value using earnings yield: Equity value = Total earnings ÷ Earnings yield; Express the yield as a decimal, e.g. 12.5% = 0.125.
Adjusted P/E: Adjusted P/E = Comparator P/E × (1 − discount); Apply discounts for lower marketability, smaller size or higher risk. Increase it for superior growth.
Dividend valuation model, constant growth (ex-div): P0 = D0(1 + g) ÷ (Ke − g) = D1 ÷ (Ke − g); Valid when Ke > g. D1 is the dividend due in one year. P0 is the ex-div price.
Cost of equity from the model: Ke = D1 ÷ P0 + g = D0(1 + g) ÷ P0 + g; Use the ex-div price. Rearrangement of the same formula.
No-growth dividend: P0 = D ÷ Ke; Flat dividend forever (g = 0).
Historical dividend growth: g = (Dn ÷ D0)^(1 ÷ n) − 1; n is the number of years of growth between the two dividends.
Retention (Gordon) growth: g = b × r; b = proportion of earnings retained = 1 − payout ratio. r = return on reinvested funds, often ROCE or ROE as given.
Cum-div and ex-div price: Cum-div price = ex-div price + dividend about to be paid; Remove the imminent dividend from a cum-div price before using the model.
Free cash flow to the firm (FCFF): FCFF = operating cash flow after tax − net investment in non-current assets − increase in working capital; Before interest. Tax is normally the tax on operating profit. Use the data the question gives you; follow its definition of free cash flow.
Free cash flow to equity (FCFE): FCFE = FCFF − interest × (1 − tax rate) + net new borrowing (new borrowing less repayments); This is after interest and debt movements. Net new borrowing already nets repayments against new borrowing, so do not deduct repayments again. Equivalent to cash available to pay dividends.
Value of the firm: Firm value = Σ FCFF ÷ (1 + WACC)^t + terminal value discounted; Discount at WACC.
Value of equity from firm value: Equity value = firm value − market value of debt; Use market value of debt, not book value, if given.
Equity value from FCFE: Equity value = Σ FCFE ÷ (1 + Ke)^t + terminal value discounted; Discount at the cost of equity. No debt deduction needed.
Terminal value (growing perpetuity): TV at end of year n = CF(n+1) ÷ (r − g) = CF(n) × (1 + g) ÷ (r − g); Needs r > g. Discount TV by (1 + r)^n, the same factor as the year n cash flow.
Value per share: Value per share = equity value ÷ number of shares; Final step for share price questions.
Irredeemable debt value: MV = I ÷ Kd; I is the annual interest in $ and Kd is the investor's required pre-tax yield. Rearranged, Kd = I ÷ MV.
Redeemable debt value: MV = Σ [I ÷ (1 + Kd)^t] + R ÷ (1 + Kd)^n; R is the redemption value and n is the years to redemption. Use an annuity factor for the interest and a single discount factor for R.
Zero-coupon bond value: MV = R ÷ (1 + Kd)^n; There is no interest, so only the redemption amount is discounted.
Yield to maturity by interpolation: YTM ≈ L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L); Discount the cash flows at two rates L and H, compare each present value with the market price, and interpolate. The NPVs should have opposite signs.
Conversion value: Conversion value = P0 × (1 + g)^n × conversion ratio; P0 is the current share price, g is expected share price growth, n is years to conversion, and the ratio is the number of shares per bond. This is a value at the conversion date, not today.
Convertible bond value: Value ≈ PV of interest + PV of the higher of (redemption value, conversion value); Compare the conversion value with the redemption value at the conversion date, since both are year n amounts. Then discount the higher one at the straight-debt yield. If redemption is higher, this equals the floor value. The market price can sit above this because the option has value before the conversion date.
Irredeemable preference shares: MV = D ÷ Kp; D is the annual preference dividend and Kp is the required yield. Dividends are fixed and are not tax-deductible.
Redeemable preference shares: MV = Σ [D ÷ (1 + Kp)^t] + R ÷ (1 + Kp)^n; Same structure as redeemable debt, using dividends in place of interest.
Weak form efficiency: Price = reflects all past price and trading data; Charts and past price patterns give no abnormal return. Tests: no pattern in price changes.
Semi-strong form efficiency: Price = reflects all public information; Includes weak form. Only private information can help. Tests: prices adjust quickly to announcements.
Strong form efficiency: Price = reflects all public and private information; Includes semi-strong. Insiders cannot gain. Evidence generally rejects this form.
Abnormal return: Abnormal return = actual return − expected return for the risk taken; Used to test efficiency. In an efficient market, only new information causes abnormal returns.

Quick revision

Valuation is needed for takeovers, flotations, disposals, tax, and for judging performance.
Net asset value equals assets minus liabilities; it often ignores goodwill and intangible value.
Market value of equity using P/E equals earnings × P/E ratio.
Earnings yield is earnings ÷ market value, which is the reciprocal of the P/E ratio.
Dividend valuation model with no growth: P₀ = D ÷ Ke.
With growth: P₀ = D₁ ÷ (Ke − g), where D₁ is next year's dividend.
Cash flow valuation discounts forecast free cash flows at the appropriate cost of capital.
Value of a bond equals the present value of its interest and redemption payments at the investor's required return.
Irredeemable preference shares are valued as dividend ÷ required return.
Weak form efficiency means prices reflect past prices; semi-strong adds public information; strong adds all information.
Always comment on the reliability and assumptions behind your valuation.

Common mistakes

Saying a listed company never needs a valuation because it has a share price. Fix: State that the price reflects minority trades. A bidder buying control or facing a distorted market may need its own valuation.
Listing reasons without linking them to the scenario. Fix: Pick the reasons that match the event in the question and use details such as listed status or deal type.
Using book value when the question asks for replacement cost or realisable value. Fix: Underline the basis in the question and use only the figures given for that basis.
Forgetting to deduct preference shares before finding value per ordinary share. Fix: After total net assets, ask who ranks first. Deduct preference shares and any other prior claims.
Applying the comparator's P/E without adjusting for an unlisted target. Fix: Always read the scenario for listing status, size and risk. Reduce the P/E when the target is unlisted or smaller, and state the adjustment.
Using profit before tax or before preference dividends as earnings. Fix: Use profit attributable to ordinary shareholders: after interest, tax and preference dividends.
Using D0 instead of D1 in the formula. Fix: Always multiply by (1 + g) unless the question states the next dividend. Write D1 = D0(1 + g) as a separate line.
Using a cum-div price directly in the model. Fix: Underline cum-div or ex-div. Subtract the dividend about to be paid from a cum-div price first.
Discounting FCFF at the cost of equity, or FCFE at WACC. Fix: Match them: all investors' cash flow with WACC, shareholders' cash flow with the cost of equity.
Forgetting to deduct debt after valuing the firm with FCFF. Fix: Add a line 'less market value of debt' every time you use FCFF. Cash surplus, if given, may be treated as reducing net debt.

Exam tips

In Section C, tie each reason to the facts given. A generic list scores poorly.
In objective tests, check whether the company is listed and whether the price looks distorted. These clues usually decide the answer.
For share-for-share offers, always check that both values use the same basis before calculating the exchange ratio.
Write the premium as a percentage of the pre-bid market price, not of the offer price.
Keep written reasons short: event, who needs the value, why the market price is not enough.
Circle the basis in the question first. Marks are lost most often by using the wrong basis.
In Section C, set out assets, liabilities, preference shares and per-share value as separate lines. Method marks depend on layout.
For objective questions, check the sign of each adjustment. A fall in value reduces NAV.