Finance Cheat Sheet

Cash Flow from Assets
= Cash Flow to Creditors + Cash Flow to Stockholders
= Operating Cash Flow (OCF) - Net Capital Spending (NCS) - Additions to Net Working Capital (NWC)

Cash Flow to Creditors
= - (Net New Borrowing)

Cash Flow to Equityholders
= Dividends Paid - (Net New Equity Raised) = (dividends – equity issued) – (interest – new LT debt)

Operating Cash Flow
= Net Income + Depreciation

Net Capital Spending
= End. Net Fixed Assets - Beg. Net Fixed Assets + Depreciation

Additions to Net Working Capital
= End. NWC - Beg. NWC

NWC = Current Assets - Current Liabilities

Personal Tax on Dividends
1. Grossed-up dividends = gross-up factor (1.25) x dividends
2. Gross federal tax = federal tax rate x grossed-up dividends
3. Federal dividend tax credit = federal dividend tax credit rate x grossed-up dividends
4. federal dividend tax = gross federal dividend tax – federal dividend tax credit

Ch 4: Time Value of Money

Future Value = I * (1+r)t

Present Value
= future value after t periods / (1+r)t
r = (FVPV )1/n – 1
Rule of 72: time for investment to double is 72/r
Interest rate on a perpetuity = cash payment / present value
= C / PV

PV of a perpetuity = cash payment / interest rate
= C / r

PV of a delayed perpetuity
= (cash payment / interest rate) x [1 / (1+r)t]

PV of a t-year annuity
= C [1/r – 1/(r(1+r)t) ]

PV annuity due
= 1 + [1/r – 1/(r(1+r)t-1)]

FV of annuity
= cash payment x (1+r)t
= C x {[1/r – 1/r(1+r)t] x (1+r)t}
= C x {[(1+r)t – 1] / r}

PV of a perpetual stream of payments growing at a constant rate
= C / (r-g)

PV of a finite stream of payments growing at a constant rate
= [C / (r-g)] x {1-[(1+g) / (1+r)]T}

Real future value of investment
= [$1000 x (1 + nominal interest rate)] / (1 + inflation rate)

1 + real interest rate
= (1 + nominal interest rate) / (1 + inflation rate)

Real interest rate =(approximately) nominal interest rate – inflation rate

1+EAR = (1 + annual rate)
= (1 + monthly rate)12
= (1+(APR/m))m

Monthly interest rate
= APR / 12

Per period rate
= (1+EAR)1/m -1

APR = m × per period rate

Ch 5 : Bonds Valuation

PV of a bond (bond price)
= PV (coupons) + PV (face value)
= coupon x [1/r – 1/r(1+r)t] + face value / (1+r)t

Coupon rate
= coupon / face value

Current yield
= annual coupon payment / bond price

Rate of Return
= (coupon income + price change) / investment

Effective annual equivalent: rate of return on a 2 year bond
= [1 + (coupon income + price change) / investment] ½

Price
= face value / (C+YTM) maturity

Ch 17: Ratios

Leverage Ratios
Long-term debt ratio
= long-term debt / (long-term debt + equity)
Debt-equity ratio
= long-term debt / equity
Total debt ratio
= total liabilities / total assets
Times interested earned
= EBIT / interest payments
Cash coverage ratio
= (EBIT + depreciation) / interest payments
Fixed charge coverage ratio
= (EBIT + depreciation) / interest payments + (debt payments) / (1 - tax rate)

Liquidity Ratios
NWC to assets
= net working capital / total assets
Current ratio
= current assets / current liabilities
Quick ratio
= (cash + marketable securities + receivables) / current liabilities

Interval Measure
= (cash + marketable securities + receivables) / average daily expenditures from operations

Efficiency Ratios
Total asset turnover
= sales / average total assets
Average collection period
= average receivables / average daily sales
Inventory turnover
= cost of goods sold / average inventory
Days’ sales in inventories
= average inventory / (cost of goods sold / 365)
Average payment period
= average payables / average daily expenses

Profitability Ratios
Gross profit margin
= (sales - cost of goods sold) / sales
Operating profit margin
= (EBIT - taxes) / sales
Net profit margin
= (net income + interest) / sales
Return on assets
= (net income + interest) / average total assets
Return on equity
= net income / average equity
Payout ratio
= dividends / earnings
Plowback ratio
= 1 - payout ratio
Growth in equity from plowback
= plowback ratio x ROE

Market Based Ratios
Price-earnings ratio
= stock price / earnings per share

Market to book ratio
= stock price / book value per share
= Market EquityBook Equity
Book value per share
= shareholder's equity/number of common shares outstanding

DuPont System
ROA
= asset turnover x profit margin
= sales/assets x (net income + interest) / sales
ROE
= leverage ratio x ROA x “debt burden”
= leverage ratio x asset turnover x profit margin x “debt burden”
= assets/equity x sales/assets x (net income + interest)/sales x net income/(net income + interest)

EVA = residual income
= income earned – income required
= income earned – [cost of capital x investment]

Dividends = eps * payout ratio

Ch 6: Stocks Valuation
Expected return = r = (DIV1 + P1 – P0)/P0

After-tax rate of return = (DIV1 – dividend tax)/P0 + (capital gain – capital gains tax)/P0

Price today = P0 = (DIV1 + P1)/P0
P0 = PV of (DIV1, DIV2…) = DIV1/(1 + r) + DIV2/(1 + r)2 + … + (DIVt + Pt)/(1 + r)2

Stock price = PV (all future dividends per share)

P0 = DIV1/r
Value of a no-growth stock = P0 = EPS1/r

Constant-growth DDM P0 =DIV1/r-g = DIV0* (1+g) / r-g

Expected rate of return = r = DIV1/P0 + g = dividend yield + growth rate
Non-constant growth:
P0 = DIV1/(1 + r) = DIV2/(1 + r)2 + … + DIVH/(1 + r)H + PH/(1 + r)H
PV of a growing annuity
= C1/(r-g) x {1- [(1-g)/(1+r)]t}
EPS = stock price/earnings
Terminal price = Pt = DIVt+1/(r – g)
Sustainable growth rate = g = return on equity x plowback ratio

Payout ratio = dividends/earnings

Plowback ratio = 1-payout ratio



Ch 7: NPV

NPV = PV – required investment

PV = C1/(1 + r) + C2/(1 + r)2 + … + Ct/(1 + r)t, last year to add CF sold for

NPV = C0 + C1/(1 + r) + C2/(1 + r)2 + … + Ct/(1 + r)t

PV = cash flow x annuity factor = C x [(1/r) - 1/r(1 + r)t]

Rate of return = profit/investment = (C1 – investment)/investment = (C1 + C0)/(-C0)

NPV = C0 + C1/(1 + IRR) + C2/(1 + IRR)2 + … + Ct/(1 + IRR)t

Book rate of return = book income/book assets

Equivalent annual cost = present value of costs/annuity factor
Profitability index = NPV/initial investment

Ch 8: Capital Budgeting

Incremental CF = CF with project = CF without project

Net working capital = ST assets – ST liabilities

Total project cash flows = CF from investment in plant and equipment + CF from investment in WC + CF from operations (incl. OCF & CCA tax shield)

CF O = revenues – cash expenses – taxes paid = net profit + depreciation = (revenues – cash expenses) x (1 – tax rate) + (depreciation x tax rate)

Depreciation tax shield = depreciation x tax rate = CCA tax shield

Taxable income = revenues – expenses – CCA

PV of CCA tax shield
= [CdTc/(r + d)][(1 + 0.5r)/(1 + r)] – [SdTc/(r + d)][1/(1 + r)t]
C = capital cost of an asset acquired at beginning of year 1
D = CCA rate for asset class to which asset belongs
UCC = undepreciated capital cost in year t after deducting CCA for the year
Tc = firm’s tax rate
r = discount rate
S = salvage amount from sale of asset at end of year t

PV of CCA tax shields = PV of perpetual tax shield on asset acquired in year 1 - in year t

PV = S/(1 + r)t

PV of CCA tax shield = 1/(1 + r)t x SdTc/(r + d)

CCA tax shield = CCA x tax rate

NPV = total PV excluding CCA tax shields + PV of CCA tax shield

Financial projections*
= Capital investment + Working capital + Change in working capital + Revenues + Expenses + CCA of equipment + Pretax Profit + Tax (35%) + Profit after tax

Cash flows*
= Capital investment + Change in working capital + Cash flows from operations (excl. CCA tax shield) + total cash flows (excl. CCA tax shield) + Discount factor + Present value (excl. CCA tax shields)+ Total PV (excl. CCA tax shields)

OCF (excl. CCA tax shield)
= Revenues – Expenses = Profit before tax – tax at 35%

Profitability index = NPV / -Co

Ch 10: Risk, Return of Capital

Percentage return = (capital gain + dividend) / initial share price

Dividend yield = dividend / initial share price

Percentage capital gain = capital gain / initial share price

1 + real rate of return = (1 + nominal rate of return) / (1 + inflation rate)

Portfolio rate of return = (fraction of portfolio in first asset x rate of return on first asset) / (fraction of portfolio in second asset x rate of return on second asset)

Correlation b/w x & y = (covariance b/w x & y) / (STD of x * STD of y)

Portfolio STD = ơp = sqrt(x2sơ2s + x2gơ2g + 2xsxgρsg ơs ơg)

Ch 11: CAPM

Beta of stock j = βj = (ρj,m)(ơj) / ơm or cov(rj, rm) / ơ2m = change in the rate of the return of stock j / change in the rate of return of the market

Beta of portfolio = (fraction of portfolio in 1st stock x beta of 1st stock) / (fraction of portfolio in 2nd stock x beta of 2nd stock)

Risk premium on any asset
= r – rf = β (rm-rf)

Market risk premium = rm - rf

Expected return on stock = risk-free interest rate + (beta x market risk premium) = r = rf + β(rm-rf)

rf = (required return – βrm) / 1-β

r = (DIV + capital gain) / price

fair price = (DIV + expected price) / 1+r

Variance = proportion * (estimated return – expected return)2 + …

Ch 12: WACC

Company cost of capital = weighted avg of debt and equity returns

After-tax cost of debt = pretax cost x (1-tax rate) = rdebt x (1-Tc)

WACC = [D/V x (1-Tc) rdebt] + (E/V x requity) + (P/V x rpreferred)

NPV = investment + (after-tax cash flow/rate of return)

requity = DIV1/P0 + g

rpreferred = dividend / price of preferred

stock’s beta = (expected return on stock – risk-free rate) / expected market risk premium

debt’s beta = (expected return on debt – risk-free rate) / expected market risk premium

βequity = βassets + (βassets – βdebt) D/E or βassets x (1+ D/E)

βlevered¬ = βu + (βu - βdebt)(1-Tc)D/E or βu x [1+(1-Tc)x D/E]