FIN 331 Formula Sheet Financial Statements and Cash Flows Assets = Liabilities + Shareholders' equity Stockholders’ equity = Paid-in capital + Retained earnings Sales revenues − Expenses = Net income NWC = Current assets – Current liabilities NOWC = (Current assets – Excess cash) – (Current liabilities – Notes payable) Operating income (or EBIT) = Sales revenues − Operating costs Total debt = Short-term debt + Long-term debt Total liabilities = Total debt + Accounts payable + Accruals FCF = (EBIT (1 – T) + Depreciation) – (Capital expenditures + NOWC) Financial Statements and Ratios Current ratio Current assets / Current liabilities Quick ratio (Current assets - Inventories) / Current liabilities Cash ratio Cash / Current liabilities Inventory turnover Sales / Inventories Days sales in inventory 365 / Inventory turnover Days sales outstanding (DSO) Receivables / (Annual sales / 365) Fixed asset turnover Sales / Net fixed assets Total asset turnover Sales / Total assets Total debt to total capital ratio Total debt / (Total debt + Equity) Total liabilities to assets Total liabilities / Total assets Debt to equity ratio Total Debt / Equity Times interest earned (TIE) EBIT / Interest charges EBITDA coverage (EBITDA + Lease payments) / (Interest + Principal payments + Lease payments) Operating Margin Operating Income (EBIT) / Sales Profit Margin Net Income / Sales Return on total assets (ROA) Net income / Total assets Return on common equity (ROE) Net income / Common equity Return on invested capital (ROIC) EBIT (1 – T) / (Debt + Equity) Basic earning power (BEP) EBIT / Total assets Earnings Per Share (EPS) Net income / Shares outstanding Price/Earnings Ratio (P/E) Price per share / Earnings per share Market/Book Ratio (M/B) Market price per share / Book value per share Enterprise value (EV) MV of Equity + MV of liabilities – Cash and Equivalents Equity Multiplier Total Assets / Total equity ROE = ROA × Equity Multiplier = Profit Margin × Total Asset Turnover × Equity Multiplier Time Value of Money Future value = 𝐹𝑉𝑁=𝑃𝑉(1 + 𝐼)𝑁 Present value = 𝑃𝑉=𝐹𝑉𝑁(1 + 𝐼)𝑁⁄ 𝐹𝑉𝐴𝑁=𝑃𝑀𝑇 [(1 + 𝐼)𝑁− 1𝐼] 𝐹𝑉𝐴𝑑𝑢𝑒=𝐹𝑉𝐴𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦(1 + 𝐼) 𝑃𝑉𝐴𝑁=𝑃𝑀𝑇 [1 − 1/(1 + 𝐼)𝑁𝐼] 𝑃𝑉𝐴𝑑𝑢𝑒=𝑃𝑉𝐴𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦(1 + 𝐼) PV of a perpetuity = 𝑃𝑀𝑇𝐼 PV=∑𝐶𝐹𝑡(1 + 𝐼)𝑡𝑁𝑡=0 Periodic rate (𝐼𝑃𝐸𝑅)= 𝐼𝑀 Effective annual rate (EFF%)= (1 +𝐼𝑁𝑂𝑀𝑀)𝑀− 1FIN 331 Formula Sheet Interest Rates Quoted interest rate (r) = r* + IP + DRP + LP + MRP = rRF + DRP + LP + MRP Bonds Valuation 𝐵𝑜𝑛𝑑′𝑠 𝑉𝑎𝑙𝑢𝑒= 𝑉𝐵=∑𝐼𝑁𝑇(1 + 𝑟𝑑)𝑡𝑁𝑡=1+𝑀(1 + 𝑟𝑑)𝑁 𝑉𝐵=∑𝐼𝑁𝑇/2(1 + 𝑟𝑑/2)𝑡2𝑁𝑡=1+𝑀(1 + 𝑟𝑑/2)2𝑁 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑐𝑎𝑙𝑙𝑎𝑏𝑙𝑒 𝑏𝑜𝑛𝑑=∑𝐼𝑁𝑇(1 + 𝑟𝑑)𝑡𝑁𝑡=1+𝐶𝑎𝑙𝑙 𝑝𝑟𝑖𝑐𝑒(1 + 𝑟𝑑)𝑁 Accrued interest = Coupon payment ×𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑠𝑖𝑛𝑐𝑒 𝑙𝑎𝑠𝑡 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑖𝑛 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 Dirty price = Clean price + Accrued interest Invoice price = Quoted price + Accrued interest Risk and Rates of Return Expected rate of return = ∑𝑃𝑖𝑁𝑖=1× 𝑟𝑖 𝜎=√∑(𝑟𝑖− 𝑟)2𝑁𝑖=1𝑃𝑖 Coefficient of variation= CV=𝜎𝑟 Sharpe ratio=(𝑅𝑒𝑡𝑢𝑟𝑛− 𝑅𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒)𝜎 𝑟𝑃=∑𝑤𝑖𝑟𝑖𝑁𝑖=1 𝛽𝑃=∑𝑤𝑖𝛽𝑖𝑁𝑖=1 𝑟𝑖=𝑟𝑅𝐹+ (𝑟𝑀− 𝑟𝑅𝐹)𝛽𝑖 Stocks Valuation P0=∑Dt(1 + rs)t∞t=1 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑔𝑟𝑜𝑤𝑡ℎ:P0= 𝐷0(1 + 𝑔)𝑟𝑆− 𝑔=𝐷1𝑟𝑆− 𝑔 𝑍𝑒𝑟𝑜 𝑔𝑟𝑜𝑤𝑡ℎ:P0=𝐷𝑟𝑆 𝐻𝑜𝑟𝑖𝑧𝑜𝑛 𝑣𝑎𝑙𝑢𝑒= PN= 𝐷𝑁+1𝑟𝑆− 𝑔 𝑁𝑜𝑛𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑔𝑟𝑜𝑤𝑡ℎ:P0= D1(1 + rs)1+D2(1 + rs)2+ ⋯+DN(1 + rs)N+PN(1 + rs)N 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛= 𝑟𝑠=𝐷1𝑃0+ 𝑔 𝑉𝑃=𝐷𝑃𝑟𝑃 𝑟𝑃=𝐷𝑃𝑉𝑃 𝑀𝑉 𝑜𝑓 𝑐𝑜𝑚𝑝𝑎𝑛𝑦′𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠= FCF1(1+WACC)1+FCF2(1+WACC)2+ ⋯+FCFN(1+WACC)N+VN(1+WACC)N; Where VN= 𝐹𝐶𝐹𝑁+1𝑊𝐴𝐶𝐶−𝑔𝐹𝐶𝐹 Cost of Capital 𝑊𝐴𝐶𝐶=𝑤𝑑𝑟𝑑(1 − 𝑇) + 𝑤𝑃𝑟𝑃+ 𝑤𝐶𝑟𝑆 After-tax cost of debt = 𝑟𝑑(1 − 𝑇) 𝐶𝑜𝑠𝑡 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 𝑓𝑟𝑜𝑚 𝑛𝑒𝑤 𝑠𝑡𝑜𝑐𝑘= 𝑟𝑒=𝐷1𝑃0(1 − 𝐹)+ 𝑔 Capital Budgeting 𝑁𝑃𝑉=𝐶𝐹0+𝐶𝐹1(1 + 𝑟)1+𝐶𝐹2(1 + 𝑟)2+ ⋯+𝐶𝐹𝑁(1 + 𝑟)𝑁=∑𝐶𝐹𝑡(1 + 𝑟)𝑡𝑁𝑡=0 𝑁𝑃𝑉=𝐶𝐹0+𝐶𝐹1(1 + 𝐼𝑅𝑅)1+𝐶𝐹2(1 + 𝐼𝑅𝑅)2+ ⋯+𝐶𝐹𝑁(1 + 𝐼𝑅𝑅)𝑁=∑𝐶𝐹𝑡(1 + 𝐼𝑅𝑅)𝑡𝑁𝑡=0=0 Payback=No.of years prior to full recovery +Unrecovered cost at start of yearCash flow during full recovery
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