Formulae Flashcards by gemma dinmore

Payback definition and decision rule

Time taken for cash inflows to equal cash outflows

Accept if payback < target

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ARR formula (initial investment)

(Average annual profit from investment ÷ initial investment) × 100

Profit = after depreciation

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ARR formula (average investment)

(Average annual profit from investment ÷ average investment) × 100

Average investment = (initial outlay + scrap value) ÷ 2

Profit = after depreciation

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ARR decision rule

Accept if ARR > target

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NPV definition and decision rule

Change in wealth of investor as a result of investing in project

Accept if NPV is positive (usually)

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IRR definition and decision rule

Cost of capital at which NPV = 0

Accept if IRR % > cost of capital (usually)

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IRR formula

a + (NPVa ÷ (NPVa - NPVb)) × (b - a)

a = lower discount rate giving NPVa
b = higher discount rate giving NPVb

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Discount formula

(1 + r) ^-n

r = cost of capital
n = years

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Fisher equation

(1 + m) = (1 + r) × (1 + i)

m = money (nominal) rate
r = real (effective) rate
i = general inflation rate

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EAC formula and decision rule

NPV of one cycle replacement ÷ cumulative DF for cycle length

Lowest EAC

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Sensitivity formula

(NPV of project ÷ PV of cash flows subject to uncertainty) × 100%

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CAPM formula (given in exam)

rj = rf + βj (rm - rf)

rj = expected return for security j
rf = risk-free rate
βj = beta of security j
rm = expected return on the market portfolio

When applied to shares rj = cost of equity capital (ke)

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Alpha value current return formula

Expected return ± alpha value

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Interest rate parity equation

Spot rate x ((1+if) ÷ (1+iuk)) = forward rate

if = overseas interest rate
iuk = domestic interest rate

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Dividend payout ratio formula

Dividend ÷ earnings after tax and pref divs

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Ex-rights price formulas

(Market value of shares pre-issue + rights proceeds + project NPV) ÷ number of shares ex-rights

PV of new total dividends ÷ number of shares ex-rights

If NPV not given, assume nil

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Dividend yield formula

(Dividend per share ÷ market price per share) × 100

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EPS formula

Profit distributable to ordinary shareholders ÷ number of ordinary shares issued

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Price-earning (P/E) ratio formula

Market price per share ÷ EPS

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Total shareholder return formula

Dividend yield + capital gain

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Annual interest on loan stock formula

Coupon rate × nominal value

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2 capital gearing formulas

Debt ÷ equity

Debt ÷ (debt + equity)

If book value include RE

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Interest cover formula

Earnings before interest and tax ÷ interest

Equity investors’ required rate of return formula - dividends remain constant

Ke = D0÷P0

Ke = equity investors’ required rate of return
D0 = dividend paid at time 0
P0 - ex-dividend market value of equity

Equity investors' required rate of return formula - dividends grow at constant rate (given in exam)

Ke = (D0(1+g) ÷ P0) + g Ke = cost of equity D0 = current dividend per ordinary shares g = annual dividend growth rate P0 - current ex-dividend price per ordinary share

Growth earnings retention (Gordon growth) model formula

g = r × b ``` g = growth in future dividends r = return on equity b = proportion of profits retained ```

CAPM cost of equity formula (given in exam)

ke = rf + βj (rm - rf) ``` ke = cost of equity rf = risk-free rate βj = beta of security j rm = expected return on the market portfolio ```

Cost of preference shares formula

kp = D ÷ P0 ``` D = constant annual dividend P0 = ex-div market value ```

Net of tax cost of debt formula

Pre-tax cost of debt × (1 - 0.17)

Cost of debt formula

kd = (interest × (1 - 0.17)) ÷ P0 ``` P0 = market price of bond ex-interest Interest = interest paid on bond kd = required return of debt holder ```

WACC formula

(MVe × ke) + (MVd × kd) __________________ MVe + MVd ``` MVe = MV of issued shares MVd = MV of debt ```

Income gearing formula

EBIT ÷ interest

Value of business formula

Post-tax earnings discounted to perpetuity @ WACC

βe formula (given in exam)

βe = βa (1 + (D(1-T)÷E)) ``` βe = beta of equity in geared firm βa = ungeared (asset) beta D = MV of debt E = MV of equity T = corporation tax rate ```

Maximum price formula

MV of combined businesses - MV of bidder before bid is made

Price-earning (P/E) ratio VALUE formula

PE ratio ÷ earnings

Enterprise value formula

Enterprise value multiple × EBITDA

Equity value formula

Enterprise value - market value of debt + cash

Dividend yield formula

(Dividend per share ÷ market price of shares) × 100

Present value of future dividends formula

d0 (1 + g) _______ ke - g ``` d0 = dividend at time 0 g = growth rate ke = cost of equity ```

Project worth formula

Traditional NPV + value of real options

APT formula

E(ri) = rf + (E(rA)-rf)βA + (E(rB)-rf)βB ``` (E(rA)-rf)βA = risk premium on factor A (E(rB)-rf)βB = risk premium on factor B ```

Number of contracts formula

MV of portfolio ÷ value of 1 contract

Hedge efficiency formula

(Gain on futures ÷ loss on portfolio) × 100%

Intrinsic value formula

Current share price - exercise price Out of money options = zero

Time value formula

Actual value - intrinsic value

Price of interest rate futures contract formula

Price = 100 - interest rate

Maturity mismatch number of futures contract formula

(Loan ÷ futures contract size) × (length loan ÷ 3 months)

Effective interest rate formula

(Net payments ÷ loan amount) × (inverse pro-ration)

Value of right to subscribe formula

Ex-rights price - subscription price

M+M formulas

``` Vg = Vu Vg = Vu + DT ``` ``` Vg = value of debt + value of equity in geared firm Vu = value of equity in equivalent ungeared firm DT = tax shield on debt (d=MV of debt) ```

Adjusted present value (APV) formula

Base case value + present value of tax shield

APV decision rule

Accept if positive

TERP

(MV shares pre issue + issue proceeds) ÷ (number of shares post issue)

Subscription price

Proceeds generated ÷ number of shares issued