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FM > Formulae > Flashcards

Formulae Flashcards

1
Q

Payback definition and decision rule

A

Time taken for cash inflows to equal cash outflows

Accept if payback < target

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2
Q

ARR formula (initial investment)

A

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

Profit = after depreciation

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3
Q

ARR formula (average investment)

A

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

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

Profit = after depreciation

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4
Q

ARR decision rule

A

Accept if ARR > target

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5
Q

NPV definition and decision rule

A

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

Accept if NPV is positive (usually)

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6
Q

IRR definition and decision rule

A

Cost of capital at which NPV = 0

Accept if IRR % > cost of capital (usually)

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7
Q

IRR formula

A

a + (NPVa ÷ (NPVa - NPVb)) × (b - a)

a = lower discount rate giving NPVa
b = higher discount rate giving NPVb
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8
Q

Discount formula

A

(1 + r) ^-n

r = cost of capital
n = years
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9
Q

Fisher equation

A

(1 + m) = (1 + r) × (1 + i)

m = money (nominal) rate
r = real (effective) rate
i = general inflation rate
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10
Q

EAC formula and decision rule

A

NPV of one cycle replacement ÷ cumulative DF for cycle length

Lowest EAC

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11
Q

Sensitivity formula

A

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

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12
Q

CAPM formula (given in exam)

A

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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13
Q

Alpha value current return formula

A

Expected return ± alpha value

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14
Q

Interest rate parity equation

A

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

if = overseas interest rate
iuk = domestic interest rate
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15
Q

Dividend payout ratio formula

A

Dividend ÷ earnings after tax and pref divs

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16
Q

Ex-rights price formulas

A

(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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17
Q

Dividend yield formula

A

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

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18
Q

EPS formula

A

Profit distributable to ordinary shareholders ÷ number of ordinary shares issued

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19
Q

Price-earning (P/E) ratio formula

A

Market price per share ÷ EPS

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20
Q

Total shareholder return formula

A

Dividend yield + capital gain

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21
Q

Annual interest on loan stock formula

A

Coupon rate × nominal value

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22
Q

2 capital gearing formulas

A

Debt ÷ equity

Debt ÷ (debt + equity)

If book value include RE

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23
Q

Interest cover formula

A

Earnings before interest and tax ÷ interest

24
Q

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

A

Ke = D0÷P0

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

25
Q

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

A

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

26
Q

Growth earnings retention (Gordon growth) model formula

A

g = r × b

g = growth in future dividends
r = return on equity
b = proportion of profits retained
27
Q

CAPM cost of equity formula (given in exam)

A

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
28
Q

Cost of preference shares formula

A

kp = D ÷ P0

D = constant annual dividend
P0 = ex-div market value
29
Q

Net of tax cost of debt formula

A

Pre-tax cost of debt × (1 - 0.17)

30
Q

Cost of debt formula

A

kd = (interest × (1 - 0.17)) ÷ P0

P0 = market price of bond ex-interest
Interest = interest paid on bond
kd = required return of debt holder
31
Q

WACC formula

A

(MVe × ke) + (MVd × kd)
__________________
MVe + MVd

MVe = MV of issued shares
MVd = MV of debt
32
Q

Income gearing formula

A

EBIT ÷ interest

33
Q

Value of business formula

A

Post-tax earnings discounted to perpetuity @ WACC

34
Q

βe formula (given in exam)

A

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
35
Q

Maximum price formula

A

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

36
Q

Price-earning (P/E) ratio VALUE formula

A

PE ratio ÷ earnings

37
Q

Enterprise value formula

A

Enterprise value multiple × EBITDA

38
Q

Equity value formula

A

Enterprise value - market value of debt + cash

39
Q

Dividend yield formula

A

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

40
Q

Present value of future dividends formula

A

d0 (1 + g)
_______
ke - g

d0 = dividend at time 0
g = growth rate
ke = cost of equity
41
Q

Project worth formula

A

Traditional NPV + value of real options

42
Q

APT formula

A

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
43
Q

Number of contracts formula

A

MV of portfolio ÷ value of 1 contract

44
Q

Hedge efficiency formula

A

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

45
Q

Intrinsic value formula

A

Current share price - exercise price

Out of money options = zero

46
Q

Time value formula

A

Actual value - intrinsic value

47
Q

Price of interest rate futures contract formula

A

Price = 100 - interest rate

48
Q

Maturity mismatch number of futures contract formula

A

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

49
Q

Effective interest rate formula

A

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

50
Q

Value of right to subscribe formula

A

Ex-rights price - subscription price

51
Q

M+M formulas

A 
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)
52
Q

Adjusted present value (APV) formula

A

Base case value + present value of tax shield

53
Q

APV decision rule

A

Accept if positive

54
Q

TERP

A

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

55
Q

Subscription price

A

Proceeds generated ÷ number of shares issued

FM (3 decks)

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