Equations Flashcards Preview

Business Finance > Equations > Flashcards

Flashcards in Equations Deck (34):

Working capital cycle

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


Inventory cycle

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


Debtor and creditor days

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


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

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.


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)


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

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.


Expected return on share

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


Security expected return

rS = rF +Bequity x (rM - rF)
rF= risk free rate, rM= expected return on market portfolio, Bequity= beta of equity


Publicly traded debt

-calculate yield to maturity from market date
-use CAPM for public debt
Estimate Bdebt and apply to formula
rB = rF + Bdebt x (rM - rF)


Not publicly traded debt

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


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

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]


Impact of debt on expected return on equity capital

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)


Return on equity

-operating income less interest payments on borrowings
ROE= ROC x (Sg+Bg) -rBBg =ROC +(ROC-rB) Bg/Sg
rB is interest payment on debt


Earnings per share for geared and ungeared firms

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


Under MM analysis

-expected cash flow given by earnings
-discount rate is expected cost of equity capital under no debt (r0)
Vu = Vg = Sg + Bg


MM proposition 2 - deriving the cost of capital

Value of ungeared firm (Vu)
Vu = X/r0
Value of geared firm (Vg)
X = r0Vg
X = r0(Sg+Bg)


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

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


Impact of leverage or rWACC

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


Cost of capital for an ungeared company

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


Value of geared company

Vg = Vu + TcBg


Annual holding cost

1/2 x Q x Ch


Annual ordering cost

D/Q x C0


Total annual cost

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


Optimal order period

EOQ/average daily demand = Q*/D/365
Q*= -/2DC0/Ch


Multipliers and company value

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


Litner's (1956) model

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


Geared weighted avergage cost of capital

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


Economic order quantity

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


After-tax gain

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


Gain if sold before sharegoes ex-dividend

(Pb - Po)(1 - Tcg)


Ex-dividend price

Px = Pb - fall x D


Sell after dividend net of tax income

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


Value of firm's equity

Sg = Vg - Bg


Theoretical ex-rights price

market value of shares prior to rights issue + cash raised from rights issue / number of shares after rights issue