Finance Equations and Calculations
Asset Ratios
Inventory turnover = Sales or cost of goods sold/ Inventory
Days’ sales in inventory=(Ending Inventory × 365 days)/ Cost of goods sold
Accounts receivable turnover = Credit sales /Accounts receivable
Average collection period (ACP)=(Accounts receivable × 365 days /Credit sales)=365 days /Accounts receivable turnover
Accounts payable turnover = Cost of goods sold /Accounts payable
Average payment period (APP)=Accounts payable × 365 days /Cost of goods sold=365 days/ Accounts payable turnover
Fixed asset turnover = Sales/ Net fixed assets
Sales to working capital = Sales/ Working capital
Total asset turnover = Sales/ Total assets
Liquidity Ratios
Current ratio = Current assets/ Current liabilities
Quick ratio (acid-test ratio) = Current assets – Inventory/ Current liabilities
Cash ratio = Cash and marketable securities /Current liabilities
Current ratio using Inventory: Current ratio – Quick ratio=Inventory. Add inventory result to current assets and to current liabilities and then divide to calculate a new current ratio.
Debt Management Ratios
Debt ratio = Total debt/ Total assets
Debt-to-equity = Total debt/ Total equity
Equity multiplier = Total assets/ Total equity or Total assets/ Common stockholders’ equity
Times interest earned = EBIT/ Interest
Profitability Ratios
Gross profit margin = Sales − Cost of goods sold/ Sales
Operating profit margin = EBIT/ Sales
Profit margin=Net income available to common stockholders /Sales
Basic earnings power (BEP) = EBIT/ Total assets
Return on assets (ROA)=Net income available to common stockholders /Total assets
Return on equity (ROE)=Net income available to common stockholders/ Common stockholders’ equity
Dividend payout=Common stock dividends /Net income available to common stockholders
Market Value Ratios
Market-to-book ratio = Market price per share /Book value per share
Price-earnings (PE) ratio = Market price per share/ Earnings per share
Other
Assets = Liabilities + Equity
Percentage formula: to find X if P of it is Y. Use the formula Y/(1-0.30)=X
Net working capital = Current assets − Current liabilities
Earnings per share (EPS) = Net income available to common stockholders /Total shares of common stock outstanding
Dividends per share (DPS) =Common stock dividends paid /Number of shares of common stock outstanding
Book value per share (BVPS) =Common stock + Paid-in surplus + Retained earnings /Number of shares of common stock outstanding
Market value per share (MVPS) =Market price of the firm’s common stock
GDP = PCE + GP + GPDI + NE.
Treasury securities are 0 DRP.
Approximate return - Rule of 72 is the approximate number of years to double an investment. It calculated by dividing 72 by the annual rate of return.
FCF===[EBIT (1 − Tax rate) + Depreciation] − [ΔGross fixed assets + ΔNet operating working capital][NOPAT + Depreciation] − Investment in operating capital Operating cash flow − Investment in operating capital
ROA: Net income available to common stockholders +Profit margin + Total asset turnover
ROE: ROA×Equity multiplier or Total assets/Common stockholders’ equity
Retention ratio (RR)=Addition to retained earnings/Net income available to common stockholders
Retention ratio (RR)=Addition to retained earnings Net income available to common stockholders. For the Retention ratio: (1 – payout ratio).
If you know the retention ratio and net income and want the dividend payout:
ratio is (1 - the retention ratio) * net income
Internal growth rate= ROA × RR1 − (ROA × RR)
Sustainable growth rate= ROE × RR1 − (ROE × RR)
Future value in 1 year = FV1 =PV × (1 + i )
Future value in N years = FVN = PV × (1 + i)N
Future value in N periods =FVN =PV × (1 + i period 1 ) × (1 + i period 2 ) × (1 + i period 3 ) × …× (1 + i period N )
Present value of next period’s cash flow = PV = FV1 /(1 + i )
Present value of cash flow made in N years: PV = FV / (1 + i)N
Present value with different discount rates: =PV = FVN(1+iperiod 1) × (1 + i period 2) × (1 + iperiod 3) × ...×(1 + iperiod N)
NOTE: If you use Excel for FV or PV, make sure to add negative sign for the amount.
Bond price =PV of annuity (PMT, i, N) + PV (FV, i, N)
NOTE: Bond price will be $1000.00 for all questions/problems in this course.
Constant growth model: P0=D0(1 + g)/i − g= D1/i – g
Constant Growth Assumption: Annual Dividend*(1+ Expected Growth%)/(Required return%- Expected Growth%)
Expected return: i=Dividend yield + Capital gain or D1P0+ g
P/E=Current stock price/Per-share earnings for last 12 months
Dollar return: Capital gain or loss + Income; (Ending value – Beginning value) + Income
Percentage return:(Ending value – Beginning value + Income Beginning value)* 100%
Total risk = Firm−specific risk + Market risk
Rate of return will be calculated as: (Expected Price + Dividend - Current Price) / Current Price
Required return = Risk-free rate + Risk premium
Expected return=Rf+β(RM−Rf)
Free Cash Flow: Operating cash flow−Investment in operating capital=[EBIT(1−Tax rate)+Depreciation]−[ΔGross fixed assets + ΔNet operating working capital]
Depreciation: (Depreciable basis−Ending book value)/Life of asset
Payback Decision Rule: Accept project if calculated payback ≤ Maximum allowable payback; Reject project if calculated payback > Maximum allowable payback
NPV Decision Rule: Accept the project if the NPV is positive and reject the project if the NPV is NPV is negative. If a conflict in ranking occurs, the decision rule is to accept the project with the highest positive NPV instead of the project with the highest IRR that is greater than the hurdle rate.
IRR Decision Rule: Accept project if IRR ≥ Cost of capital; Reject project if IRR < Cost of capital
Operating cycle: Days’ sales in inventory + Average collection period; (Inventory × 365/Cost of goods sold) + (Accounts receivable × 365/Credit sales)
Cash cycle: Operating cycle − Average payment period; Operating cycle – (Accounts payable × 365)/Cost of goods sold
Average payment period (APP): Operating cycle−Cash cycle
Payables turnover = 365/APP
Dividends = Net income − Retained earnings necessary to fund positive NPV projects
Simple dividend payout ratio: dividends/net income
Current Yield when only % and price are known: %/price
Value of the stock: $Dividend/Required return%
Stock price: P/E * earnings per share
Market capitalization: Shares * Stock price
% Equity + % Debt will always equal 100%
Estimated Yield to Maturity Formula: (Annual Interest Payment) + (Face Value - Current Price)/(Years to Maturity)/(Face Value + Current Price)/2
WACC = WdKd + WpKp + WeKe
Weight of Debt*Cost of Debt+Weight of Equity*Return on Equity
Sample input in Excel: =0.4*(0.06)+0.6*(0.17)