Formulae Flashcards
Payback definition and decision rule
Time taken for cash inflows to equal cash outflows
Accept if payback < target
ARR formula (initial investment)
(Average annual profit from investment ÷ initial investment) × 100
Profit = after depreciation
ARR formula (average investment)
(Average annual profit from investment ÷ average investment) × 100
Average investment = (initial outlay + scrap value) ÷ 2
Profit = after depreciation
ARR decision rule
Accept if ARR > target
NPV definition and decision rule
Change in wealth of investor as a result of investing in project
Accept if NPV is positive (usually)
IRR definition and decision rule
Cost of capital at which NPV = 0
Accept if IRR % > cost of capital (usually)
IRR formula
a + (NPVa ÷ (NPVa - NPVb)) × (b - a)
a = lower discount rate giving NPVa b = higher discount rate giving NPVb
Discount formula
(1 + r) ^-n
r = cost of capital n = years
Fisher equation
(1 + m) = (1 + r) × (1 + i)
m = money (nominal) rate r = real (effective) rate i = general inflation rate
EAC formula and decision rule
NPV of one cycle replacement ÷ cumulative DF for cycle length
Lowest EAC
Sensitivity formula
(NPV of project ÷ PV of cash flows subject to uncertainty) × 100%
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)
Alpha value current return formula
Expected return ± alpha value
Interest rate parity equation
Spot rate x ((1+if) ÷ (1+iuk)) = forward rate
if = overseas interest rate iuk = domestic interest rate
Dividend payout ratio formula
Dividend ÷ earnings after tax and pref divs
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
Dividend yield formula
(Dividend per share ÷ market price per share) × 100
EPS formula
Profit distributable to ordinary shareholders ÷ number of ordinary shares issued
Price-earning (P/E) ratio formula
Market price per share ÷ EPS
Total shareholder return formula
Dividend yield + capital gain
Annual interest on loan stock formula
Coupon rate × nominal value
2 capital gearing formulas
Debt ÷ equity
Debt ÷ (debt + equity)
If book value include RE
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
