BALANCE SHEET EQUATION:

Assets = Liabilities + Stokeholders’ equity

Net working capital = Currents assets – Current liabilities

[in case to have financial statement year1]

Dividends = (Dividends year1 / Net income year1) Net income
Addition to retained earnings = Net income – Dividends
[or ARE= Net income(1 – d) [d: payout ratio]]
Equity = Equity year1 + addition to retained earnings

INCOME STATEMENT:
Income = Revenue – expenses

Earnings per share = Net income / Total shares outstanding

Dividends per share = Dividends / Total shares outstanding

Taxes:
Average tax rate: tax bill / taxable income

CASH FLOW:
Cash flow from the firm’s assets = CF to the firm’s creditors + CF to equity investors

Cash flow to creditors = interest paid – net new borrowing

::: Net new borrowing = Long-term debts last year – Long-term debt begin

Cash flow to stockholders = dividends – [(common stock last year + APIS last year) – (common
stock begin + APIS begin)] (APIS: Additional paid-in surplus)
Cash flow = Operating cash flow - Capital spending - Addition to net working capital
Operating cash flow = earnings before interest and taxes + depreciation – taxes
Capital spending = Acquisitions of fixed taxes – sales of fixed taxes
Or Capital spending = Ending net fixed assets – beginning of fixed assets + depreciation
Addition to net working capital (change in net working capital) = net working capital last year –
net working capital begin

RATIO ANALYSIS
Current ratio = current assets / current liabilities
Quick ratio = Current assets – Inventory / Current liabilities
Total debt ratio = Total assets – Total equity / Total assets

Debt-equity ratio = Total debt / Total equity

Equity multiplier = Total assets / Total equity; (Total assets = total equity + total debt)
Or Equity multiplier = 1 + Debt-equity ratio

Time interest earned ratio = EBIT / Interest

Cash coverage ratio = EBIT + (depreciation and amortization) / Interest

Inventory turnover = Cost of goods sold / Inventory

Days’ sales in inventory = 365 days / inventory turnover

Receivables turnover = Sales / Accounts receivable

Days’ sales in receivables = 365 days / receivables turnover

[big picture ratio: for every dollar in assets, the company generated TAT in sales]
Total assets turnover (TAT) = Sales / Total assets
PROFITABILITY MEASURES
Profit margin = Net income / Sales
EBITDA margin = EBITDA / Sales
Capital intensity ratio = Total assets / Sales

Return on Assets (ROA) = Net income / Total assets

Return on Equity (ROE) = Net income / Total Equity
or ROE = ROA x Equity multiplier
Dupont identity: ROE = Profit margin x Total assets turnover x Equity multiplier

MARKET VALUE MEASURES

Earnings per share (EPS) = Net income / Shares outstanding
Price-earnings ratio (PE) = Price per share / Earnings per share

Market-to-book ratio = Market value per share / Book value per share
where Book value per share = total equity / shares outstanding

Enterprise value = Market capitalization + Market value of interest bearing debt – Cash

Internal growth rate = ROA x b / 1 – ROA x b ; (b: plowback or retention)

b = Addition to retained earnings / Net income
or b = 1 – Dividend payout ratio = 1 – (cash dividends / net income)
Sustainable growth rate = ROE x b / 1 – ROE x b

External financial need (EFN) = Increment expected in assets - Increment expected in liabilities
and equity

Payout ratio = dividend / net income;

[payout ratio= (dividends y1 / net income y1)
VALUATION
Present value of investment: PV = CF1 / 1 + r; [CF1: cash flow date 1, r: rate of return]
Net present value of investment: cost or benefit of a decision
NPV = - cost + PV of next year sale

Compound interest:
Future value of an investment: FV = Co x (1+r)^t;
[Co: cash to invest, r: rate of investment, t:periods]

Discounting: compute Co (or it’s PV bellow)

Present value of investment: PV = Ct / (1+r)^t
Periods: compute t

Interest rate: r = (FV / Co)^1/t – 1

Simple interest:
FVsimple = Co + (t x (Co x r))

Effective annual rate:

EAR = (1 + r/m)^m – 1 ; r: annual percentage rate
Annual percentage rate = interest rate per period x number of periods in a year

Future value of compounding: FV = Co x (1+r/m)^mT

Continuous compounding: FV = Co x e^rT

Present value of Perpetuity: PV = C / r ; [r: relevant interest rate]

Present value of Growing Perpetuity: PV = C / r – g ; [g: rate of growth per period, r: appropriate
discount rate]

Present value of Annuity: PV = C [1/r – (1/r(1+r) ^T)]

Or PV = C [1 – (1/(1+r)^T)] / r

Future value of Annuity: PV = C [((1+r) ^T – 1)/r]

Growing Annuity: PV = C [(1 – ((1+g) / (1+r))^T) / r – g]

Present value of a firm:

Net cash flows: NPV = - Cost + C x PVIFA(r, T) ;
PVIFA(r, T) = [1 – 1/(1+r)^T]/r

NET PRESENT VALUE

[Net present value of investment: cost or benefit of a decision]
NPV = - cost + PV of the cash flows of the project
PV = CF1 / 1 + r; [CF1: cash flow date 1, r: rate of return]
*If NPV > 0, accept it

Payback method:
Payback period = # of complete period + (Cost – cashflow1 – cashflown…) / cashflow next
period needed to complete investment
For annuity: Payback period = Cost / annual cash flow
Discounted payback period:
1. PV = Cashflow / (1+r)^t ; r: discount rate , t: period
2. Apply payback period method with the new cashflows.

Internal rate of return (IRR): NPV = 0. Compute r.

*If IRR=>RR, accept it

Profitability index (PI) = PV of cash flows subsequent to initial investment / Initial Investment
*If PI > 1, accept it

CAPITAL INVESTMENT DECISIONS

Net working capital = Current assets – Current liabilities

Income before taxes (taxable income) = Sales revenue - Operating costs - Depreciation
Net income = Income before taxes – tax expense; (tax expense: tax rate x taxable income)

Total cash flow of investment = Cost asset + Opportunity cost + Change in net working capital
Cash flow for operations = Sales revenues + Operating cost + Taxes
Total cash flow of the project = Cash flow for operations + Total cash flow of investment

Salvage value:
If book value = 0: After-tax salvage value = Salvage value x (1 – tax rate)
Tax liability = tax rate x (sales price – book value)
After-tax salvage value = sales price – Tax liability

Net book value = Cost – Accumulated Depreciation

Or After-tax salvage value = market value + (Book value – Market value) x tax rate
Gain on sale = salvage value – net book value
Tax due = gain on sale x tax rate
-so: after tax cash flow = salvage value – tax due

Depreciation (straight-line method):

Annual depreciation expense = (cost of the asset – salvage value) / useful life of the asset
Straight line depreciation rate = Annual depreciation expense / (cost of the asset – salvage value)

Real interest rate = [(1+Nominal interest rate) / (1+inflation rate)] -1

*For very low interest rate and inflation: Real interest rate = Nominal interest rate - inflation rate

Net Present value = - Cost + OFC ; (OFC: Operating Cash Flow)

Bottom up approach:
OFC = (Sales – Costs) x (1 – tc) + (Depreciation x tc);
[sales-cost=savings or pretax operation costs; tc: corporate tax rate]

Also: OFC = [(Priceunit – Costunit) x Units – Fixed cost] x (1 – tax rate) + (Deprecia. x tax rate)

Using top-down approach: OFC = Sales – Cash cost – Taxes

Also: Operating cash flow (OCF) = Net income + Depreciation

NET PRESENT VALUE OF A PROJECT = - Cost + [OFC x PVIFA(r,T)]

EAC = NPV of a project / PVIFA(r,T)

SENSITIVITY ANALYSIS

Revenues:
Number of assets sold per year = market share x market size per year

Annual sales revenues = Number of assets sold per year x Price per unit

Costs:
Variable cost per year = Variable cost per unit x Number of assets sold per year
Total cost before taxes per year = Variable cost per year + Fixed cost per year

Net accounting Profit = (Revenues – Variable cost -Fixed cost – Depreciation ) x (1 – tax rate
Contribution margin = Net income + Depreciation + Fixed costs
Or Contribution margin = Sales price – Variable cost

Aftertax profit = (Sales price – Variable cost) x (1 – tax rate)

Accounting profit break-even point:

Fixed cost + Depreciation / Sales price – Variable cost

Equivalent annual cost (EAC) = Initial investment / T-year annuity factor at return tax
= Initial investment / PVIFA (r, T)

Present value break-even point:

[EAC + (Fixed costs x (1 – taxrate)) – (Depreciation x taxrate)] / (Sales price – Variable cost) x
(1 – tax rate)

MONTE CARLO SIMULATION

Revenues = Market size x Market share x Price per unit
Costs = Fixed manufacturing costs + Variable manufacturing costs + Marketing costs + Selling
costs
Initial investment = Cost of patent + Test marketing costs + Cost of production facility

Go to market now: NPV = Csuccess (Prob. Of success) + Cfailure (Prob. Of failure)

-Test marketing first (or Research option):
NPV = Co + {[ Csuccess (Prob. Of success)] + [Cfailure (Prob. Of failure)}/ (1 + R)^t
-Focus group and consulting firm:
NPV = Co + Csuccess (Prob. Of success) + Cfailure (Prob. Of failure)

BOND VALUATION

Coupon rate = Coupon value / Par value

Total Bond Value = Present value of face value + Annuity present value of coupons
Total Bond Value = F / (1+r)^T + C x PVIFA (r, T)

Effective annual rate = (1 + r)^t – 1 ; t:period in a year(2)

Real and nominal rate: R: nominal rate; r: real rate; h: inflation
Approximate rate: R = r + h
Exact: 1 + R = (1 + r) x (1 + h)

Break-even tax: corporate bond rate x (1 – m) = muni rate

Invoice price = Clean price + Accrued interest

Promised yield (y) = (Price in one year / Current price of corporate bond) - 1
Aftertax yield tax on treasury bond = (1 – tax bracket) x treasury bond selling rate

STOCK VALUATION

Dividend per share : [g = growth rate]

Year 1=Do (1+g)
Year 2= Do (1+g)^2
Year n= Do (1+g)^n

Price of a share: [R = rate of return]

Case 1: Constant dividend: Po = Do / R
Case 2: Dividends growth at a constant rate: Po = D1 / R – g
*or general: Pn = Dn+1 / R – g

Firm’s growth rate: g = retention ratio x Return on retained earnings (ROE)

[retention ratio = Retained earnings / Earnings]

R = Dividend yield + Capital gains yield = Div/Po + g