Formulas, Finanzas

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Assets = Liabilities + Shareholders’ equity Revenues – Expenses = Income Cash flow from assets = Cash flow to bondholders + Cash flow to shareholders Current ratio = Current assets/Current liabilities Quick ratio = Current assets – Inventory Current liabilities

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[3.1] [3.2] [3.3] [3.4] [3.5] [3.6]

Cash ratio = Cash/Current liabilities Net working capital to total assets = Net working capital/Total assets Interval measure = Current assets/Average daily operating costs Total debt ratio = [Total assets – Total equity]/Total assets = [$3,588 – 2,591]/$3,588 = .28 Debt/equity ratio = Total debt/Total equity = $.28/$.72 = .39 Equity multiplier = Total assets/Total equity = $1/$.72 = 1.39 Long-term debt ratio = Long-term debt Long-term debt + Total equity = $457/[$457 + 2,591] = $457/$3,048 = .15

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Times interest earned ratio = EBIT/Interest = $691/$141 = 4.9 times Cash coverage ratio = [EBIT + Depreciation]/Interest = [$691 + 276]/$141 = $967/$141 = 6.9 times Inventory turnover = Cost of goods sold/Inventory = $1,344/$422 = 3.2 times Days’ sales in inventory = 365 days/Inventory turnover = 365/3.2 = 114 days Receivables turnover = Sales/Accounts receivable = $2,311/$188 = 12.3 times Days’ sales in receivables = 365 days/Receivables turnover = 365/12.3 = 30 days NWC turnover = Sales/NWC = $2,311/($708 – $540) = 13.8 times

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Fixed asset turnover = Sales/Net fixed assets = $2,311/$2,880 = .80 times Total asset turnover = Sales/Total assets = $2,311/$3,588 = .64 times Profit margin = Net income/Sales = $363/$2,311 = 15.7% Return on assets = Net income/Total assets = $363/$3,588 = 10.12% Return on equity = Net income/Total equity = $363/$2,591 = 14% P/E ratio = Price per share/Earnings per share = $157/$11 = 14.27 times Market-to-book ratio = Market value per share/Book value per share = $157/($2,591/33) = $157/$78.5 = 2 times ROE = Net income/Sales × Sales/Assets × Assets/Equity = Profit margin × Total asset turnover × Equity multiplier Dividend payout ratio = Cash dividends/Net income = $44/$132 = 331⁄3% EFN = Increase in total assets – Addition to retained earnings = A(g) – p(S)R × (1 + g) EFN = – p(S)R + [A – p(S)R] × g EFN = –p(S)R + [A –p(S)R] × g g = pS(R)/[A –pS(R)] = .132($500)(2/3)/[$500 – .132($500)(2/3)] = 44/[500 – 44] = 44/456 = 9.65% ROA × R Internal growth rate = 1 – ROA × R EFN = Increase in total assets – Addition to retained earnings – New borrowing = A(g) – p(S)R × (1 + g) – pS(R) × (1 + g)[D/E] EFN = 0 g* = ROE × R/[1 – ROE × R]

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[4.7]

g* =

p(S/A)(1 + D/E) × R 1 – p(S/A)(1 + D/E) × R

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[4A.1]

EFN = Increase in total assets – Addition to retained earnings – New borrowing = A(g) – p(S)R × (1 + g) – pS(R) × (1 + g)[D/E] ROE = p(S/A)(1 + D/E) ROE × R g* = 1 – ROE × R

[4A.2]

Future value = $1 × (1 + r)t PV = $1 × [1/(1 + r)t] = $1/(1 + r)t PV × (1 + r)t = FVt PV = FVt /(1 + r)t = FVt × [1/(1 + r)t] Annuity present value = C × =C× 1 – Present value factor r 1 – [1/(1 + r) t ] r

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[6.1]

Annuity due value = Ordinary annuity value × (1 + r) EAR = [1 + (Quoted rate/m)]m – 1 EAR = eq – 1 Bond value = C × (1 – 1/(1 + r)t)/r + F/(1 + r)t 1 + R = (1 + r) × (1 + h) 1 + R = (1 + r) × (1 + h) R=r+h+r×h R≈r+h NPV = (co – cN)/cN × $1,000 – CP

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[7C.1]

OCF = EBIT + D – Taxes = (S – C – D) + D – (S – C – D) × Tc = $200 + 600 – 80 = $720 OCF = (S – C – D) + D – (S – C – D) × Tc = (S – C – D) × (1 – Tc) + D = Project net income + Depreciation = $120 + 600 = $720

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[10.2]

OCF = (S – C – D) + D – (S – C – D) × Tc = (S – C) – (S – C – D) × Tc = Sales – Costs – Taxes = $1,500 – 700 – 80 = $720 OCF = (S – C – D) + D – (S – C – D) × Tc = (S – C) × (1 – Tc) + D × Tc S – VC = FC + D P × Q – v...
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