Equations

Question 1

Working capital cycle

Answer 1

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

Question 2

Inventory cycle

Answer 2

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

Question 3

Debtor and creditor days

Answer 3

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

Question 4

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

Answer 4

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.

Question 5

Weighted average cost of capital

Answer 5

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

Question 6

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

Answer 6

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.

Question 7

Expected return on share

Answer 7

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

Question 8

Security expected return

Answer 8

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

Question 9

Publicly traded debt

Answer 9

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

Question 10

Not publicly traded debt

Answer 10

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

Question 11

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

Answer 11

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]

Question 12

Impact of debt on expected return on equity capital

Answer 12

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)

Question 13

Return on equity

Answer 13

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

Question 14

Earnings per share for geared and ungeared firms

Answer 14

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

Question 15

Under MM analysis

Answer 15

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

Question 16

MM proposition 2 - deriving the cost of capital

Answer 16

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

Question 17

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

Answer 17

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

Question 18

Impact of leverage or rWACC

Answer 18

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

Question 19

Cost of capital for an ungeared company

Answer 19

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

Question 20

Value of geared company

Answer 20

Vg = Vu + TcBg

Question 21

Annual holding cost

Answer 21

1/2 x Q x Ch

Question 22

Annual ordering cost

Answer 22

D/Q x C0

Question 23

Total annual cost

Answer 23

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

Question 24

Optimal order period

Answer 24

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

Q*= -/2DC0/Ch

Question 25

Multipliers and company value

Answer 25

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

Question 26

Litner’s (1956) model

Answer 26

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

Question 27

Geared weighted avergage cost of capital

Answer 27

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

Question 28

Economic order quantity

Answer 28

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

Question 29

After-tax gain

Answer 29

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

Question 30

Gain if sold before sharegoes ex-dividend

Answer 30

(Pb - Po)(1 - Tcg)

Question 31

Ex-dividend price

Answer 31

Px = Pb - fall x D

Question 32

Sell after dividend net of tax income

Answer 32

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

Question 33

Value of firm’s equity

Answer 33

Sg = Vg - Bg

Question 34

Theoretical ex-rights price

Answer 34

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