Key equations to remember for Corp Fin exam

for calculating portfolio volatility.

• First calculate variance = w1²σ1²+w2²σ2²+2w1w2pσ1σ2= ANS.

• square root the answer from above to get volatility.

• where P is correlation.

Equation for weight of portfolio that yields the lowest risk.

w1= σ2²-σ2σ1P/ σ2²-σ1²-2σ2σ1P. where P is correlation.

Equation for depreciation tax shield=

Depreciation expense (if straight line this is asset cost- salvage value/ useful life)* Tax rate = tax shield.

To calculate a free cash flow from Unlevered Net Income what do we need to add/ subtract?

• Add back depreciation.

• subtract increases in Net Working Capital (cash+inventory+receivables-payables)

• subtract capital expenditure.

Weighted average cost of capital equation?

WACC= E/E+D*re+ D/E+D*(1-τc)*rd.

Where E is equity, D is debt, re is expected return to equity, rd is return to debt, τc is corporate tax rate. WHEN corporate tax isn’t applicable we use same equation just remove corp. tax part. Note: that equation is same as Return on equity for Unlevered firm.

Cum-Dividend price (pre-dividend payment)

= Dividend ($2) + PV of future dividend which is calculated by dividing future dividend amount (e.g. $4.80) by Weighted Average Cost of Capital (0.12), in this case PV of future dividend would be $40. Value of stock would be $42.

Ex dividend price=

future dividend amount/ WACC. only difference between this and Cum dividend is that Cum dividend you add dividend.

Effective dividend Tax rate=

τD*=τD-τG/1-τg. Where τD is dividend tax rate and τG is capital gains tax rate.

How to calculate equity value per share:

= (Enterprise value +Cash - Debt)/ no. of shares outstanding.

Terminal value of a cash flow=

(1+gFCF)*FCFt/ rWACC- gFCF. (NOTE thta for normal discounting of cash flows we do 1+rwacc, here it is just rwacc.

equation for cost of capital using Beta

= risk free I.R. + Beta* market risk premium.

PV of interest tax shield when debt is perpetual

τc*D

Return to equity on a levered firm

Re= Ru+D/E*(ru-rd) where ru is return to equity on unvelevered firm and rd is return to debt.

A bank quotes 6% IR compounded every 2 months. What is the value of one dollar after a year

P (principal)*(1+r/n)^nt. where n is no. compounds per year and t is time in years so 1(1+0.06/6)^6×1= 1.0615

When compounding is continuous:

e^r-1 e.g. for 7% i.r. do e^0.07-1 = 7.25% this is the effective annual rate.

Accrued IR=

Coupon payment/2 *Days last payment/ days between payments. add to asked price to get invoice price.

equation for stock price using dividend=

Dividend/(re-g) where re is equity cost of capital

Equation for CAPM

CAPM for stock i = r+beta of stock i (E(Rm)-r). where E(Rm) is expected returns on market, and r= risk free i.r. calculating the CAPM shows us the expected return on stock.

Sharpe ratio for a market portfolio

E(RM)-r/σm

Price to earnings ratio=

share price/ earnings per share.

Forward Price to Earnings equation=

Dividend payout rate/ rE-g. where dividend payout rate = Dividend/ Earnings per share.

equation for Beta=

= covariance between stock i and market/ variance of market.

Variance equation (for market return, can be adapted to stock return just switch Rm for Ri) =

(Rm-Avg market return)²/n-1, note that average return can;t include negative numbers. if were comparing stock and market n-1 =1

Calculate covariance:

(Ri- average stock return)*(Rm-Average market return)/ n-1

Equation for alpha:

alpha = Actual return- risk free rate+beta*(market return- risk free rate)

share price (using eps)

earnings per share* price to earnings ratio

How to calculate effective dividend tax rate from size of dividend and change in price of stock?

(Dividend - fall in stock price)/ size of dividend.

e.g. if dividend was $3.08 and price of stock fell by $2.63 post payment. the effective dividend tax rate would be 3.08-2.63=0.45, 0.45/3.08 = 0.1461 or 14.61%.

Market-to-Book ratio for assets/ equity

For Equity: MV(equity)/BV(equity). For assets: BV(assets)-BV(equity)+MV (equity)/ BV of assets

Operating margin (think of this as profit margin) =

Operating income/ total sales

Accounts receivable days=

Accounts receivable/ Average daily sales.

Return on equity (simplified equation, note that other equation states return TO equity =

Net income/ BV of equity.

Rate of return on investing Co getting C1 in the future, where Co is cash flow invested today.

Co/c1 -1

Rate of return on a stock paying a dividend.

p1+D/ po -1

PV of a perpetuity

Cash flow (C)/ rate of interest r - g

PV of an annuity=

C*1/r*(1-1/(1-r)^t) in lecture 3

FV of an annuity =

c/r* (1+r^t-1)