Financial Formulas

Chapter 6

OCF = (Sales – Costs)(1 – T) + Depreciation*T

Include change in nwc, salvage value, opportunity cost, and ocf (not sales or costs or anything else, must be ocf) in calculations

EAC- find the npv, then plug npv in as pv and solve for pmt (fv=0)

Find ocf not including sales (so ocf for costs) and include salvage values (fv is still 0 even if salvage value)

Choose option with lower EAC

increase in nwc add in year 0 then subtact back at end

decrease in nwc --- subtract in year 0 then add back at the end

Salvage value net of tax = value* (1-T) – book value

Changes in nwc accounts: think of it like cash flows: so increase in asset is a neg cash flow and thus would be a negative when calculating nwc change

Chapter 16

Value of a firm = value of debt + value of equity

When there are no taxes ---- Value of levered Firm=Value of unlevered firm

When there are no taxes ---- Rs = R0 + (B / SL) (R0 - RB)

RB is the interest rate (cost of debt)

Rs is the return on (levered) equity (cost of equity)

R0 is the return on unlevered equity (cost of capital)

B is the value of debt

SL is the value of levered equity

When there are taxes ---- Value of levered firm = value of unlevered firm + Tax rate*the value of debt

Value of unlevered firm= EBIT(1- tax rate) / the return on unlevered equity

When there are taxes ---- RS = R0 + (B/S)×(1-TC)×(R0 - RB)

RB is the interest rate (cost of debt)

RS is the return on equity (cost of equity)

R0 is the return on unlevered equity (cost of capital)

B is the value of debt

S is the value of levered equity

Options- Ch 22 and 23

Delta: = Range in Option Price /(Range in Stock Price)

Value of call option= Max (the value of stock at expiry – exercise price, 0) ---- Payoff= value of option – call premium

Value of put option = Max (exercise price – the value of stock at expiry, 0) ---- Payoff = value of option – put premium

Stock price +Put option = PV(strike price)+Call option

Binomial options:

Call price = (prob * Call value upside+ (1-prob)* call value downside)/ (1+rate)^period in years

Risk Neutral Prob= (e^rt – d) / (u-d) --- u=upside stock price/original stock price  and d= downside stock price/ original stock price

For two step use the length of time for the first step for t in risk neutral prob

When given standard deviation of stock returns--- u= e ^ (std dev * sqrt (time in years)) ----- d=1/u

2 step call price = prob ^ 2 * call value double up + 2 * prob up * prob down * middle call option value + prob down^2 * call value double down

Chapter 21

Cash flows for buying--- upfront negative cf for the purchase and then there will be a depreication tax shield and possible savings

After tax savings= annual saving * (1 – tax rate)         Dep tax shield= dep exp * tax rate

Cash flow for lease ---- nothing up front and then lease payments and possible savings each year

Lease payments = payment * (1 – tax rate)       After tax savings = savings (1-tax rate)

To get net advantage of leasing--- pv of leasing – pv of buying

To get breakeven lease payment – find npv of buy (neg in year 0 then dep tax shield) and plug this in for pv and do TVM on calculator solving for payment with fv=0 --- this gives you the payment after tax--- once you do this divide by 1-tax rate in order to account for tax discount and get pre tax payment