Flashcards in Equations Deck (34):

1

## Working capital cycle

###
Operating cycle= inventory period + accounts receivable period.

Working capital cycle= inventory period + accounts receivable period - accounts payable period

2

## Inventory cycle

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Raw material days= (average raw materials/ average daily COGS) x 360

Work in progress days= (average WIP/ average daily COGS) x 360

Finished goods days= (average finished goods/ average daily COGS) x 360

3

## Debtor and creditor days

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Accounts payable days= (average creditors/ daily credit purchases) x 360

Accounts receivable days= (average debtors/ daily credit sales) x 360

4

## Modigliani - Miller propostion 2 (with taxes) for cost of geared equity

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rS = r0 + (r0 - rB)(1-Tc) Bg/Sg

Where r0 is the ungeared cost of equity capital, Bg is the value of debt for the geared company, rB is the cost of debt financing, rS is the cost of geared equity financing, and Tc is the corporate tax rate.

5

## Weighted average cost of capital

### WACC= (bank/value x rBANK x (1-tC)) + (public/value x rPUBLIC x (1-Tc)) + (preferred/value x rPREF) + (common/value x rCOMMON)

6

## Modigliani - Miller propostition 1 (with taxes) for value of a geared company

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Vg = Vu + TcBg

Where Vg is the value of the geared company, Vu is the value of the ungeared company. Tc is the corporate tax rate, and Bg is the value of the geared company's borrowings. This assumes cash flows in perpetuity.

7

## Expected return on share

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rS = D1/P0 + g or rS = D0(1+g)/P0 + g

Where: D1= dividend year 1, P0= share price currently, g= growth rate, D0= dividend year 0

8

## Security expected return

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rS = rF +Bequity x (rM - rF)

rF= risk free rate, rM= expected return on market portfolio, Bequity= beta of equity

9

## Publicly traded debt

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-calculate yield to maturity from market date

-use CAPM for public debt

Estimate Bdebt and apply to formula

rB = rF + Bdebt x (rM - rF)

10

## Not publicly traded debt

### Replace Bdebt x (rM - rF) with the risk-premium or spread quoted by the lender

11

## Project financed with debt and equity use weighted average cost of capital

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B= funds raised from selling debt

S= funds raised from selling shares or retained earnings

V= assets invested in the project = B + S

All figures are market values NOT book values

rWACC= [(B/B+S) x rB] + [(S/B+S) x rS]

12

## Impact of debt on expected return on equity capital

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Debt(Bg), Equity(Sg), Capital(Bg+Sg), Return on capital(ROC)

ROC= operating income/total capital = operating income/(Sg+Bg)

Operating income= ROC x (Sg+Bg)

13

## Return on equity

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-operating income less interest payments on borrowings

ROE= ROC x (Sg+Bg) -rBBg =ROC +(ROC-rB) Bg/Sg

rB is interest payment on debt

14

## Earnings per share for geared and ungeared firms

### EPS(u) = EBIT(1-Tc)/N(u) = (EBIT-rBBg)(1-Tc)/N(g) = EPS(g)

15

## Under MM analysis

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-expected cash flow given by earnings

-discount rate is expected cost of equity capital under no debt (r0)

Vu = Vg = Sg + Bg

16

## MM proposition 2 - deriving the cost of capital

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Value of ungeared firm (Vu)

Vu = X/r0

Value of geared firm (Vg)

X = r0Vg

X = r0(Sg+Bg)

17

## Expected return on equity increases with the firm's debt-to-equity ratio

### rS = r0 + Bg/Sg (r0 - rB)

18

## Impact of leverage or rWACC

### rWACC = [Sg/Bg+Sg x rS] + [Bg/Bg+Sg x rB]

19

## Cost of capital for an ungeared company

### rS = r0 + (r0 - rB)(1 -Tc) Bg/Sg

20

## Value of geared company

### Vg = Vu + TcBg

21

## Annual holding cost

### 1/2 x Q x Ch

22

## Annual ordering cost

### D/Q x C0

23

## Total annual cost

### 1/2 x Q x Ch + D/Q x C0

24

## Optimal order period

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EOQ/average daily demand = Q*/D/365

Q*= -/2DC0/Ch

25

## Multipliers and company value

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P = E(1 - b) x M(D) x Eb x M(Rt)

E= earnings per share

b= retentions ratio

M(Rt)= valuation multiplier to be applied to retentions

1-b= payout ratio

M(D)= valuation multiplier to be applied to dividends

26

## Litner's (1956) model

### ^Div = Div1 - Div0 = S x (zEPS1 - Div0)

27

## Geared weighted avergage cost of capital

### rWACC = (Sg/Vg0 x rS + (Bg/Sg) x rB x (1-Tc)

28

## Economic order quantity

### Q = (2 x D x Co/Ch)^1/2

29

## After-tax gain

### (Px - Po)(1 - Tcg) + D(1 - Tc)

30

## Gain if sold before sharegoes ex-dividend

### (Pb - Po)(1 - Tcg)

31

## Ex-dividend price

### Px = Pb - fall x D

32

## Sell after dividend net of tax income

### (Pa - Po)(1 - Tg) + D(1 - Tp)

33

## Value of firm's equity

### Sg = Vg - Bg

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