Equations Flashcards
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
