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Lecture

Basic Equations

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Department
Finance
Course
FIN 300
Professor
Sirajum Sarwar
Semester
Fall

Description
Assets = Liabilities + Shareholders’equity [2.1] Revenues – Expenses = Income [2.2] Cash flow from assets = Cash flow to bondholders [2.3] + Cash flow to shareholders Current ratio = Current assets/Current liabilities [3.1] Current assets – Inventory Quick ratio = ▯▯▯ Current liabilities [3.2] Cash ratio = Cash/Current liabilities [3.3] Net working capital to total assets = Net working capital/Total assets [3.4] Interval measure = Current assets/Average daily operating costs [3.5] Total debt ratio = [Total assets – Total equity]/Total assets [3.6] = [$3,588 – 2,591]/$3,588 = .28 Debt/equity ratio = Total debt/Total equity [3.7] = $.28/$.72 = .39 Equity multiplier = Total assets/Total equity [3.8] = $1/$.72 = 1.39 Long-term debt ratio = ▯▯▯▯ Long-term debt [3.9] Long-term debt + Total equity = $457/[$457 + 2,591] = $457/$3,048 = .15 Times interest earned ratio = EBIT/Interest [3.10] = $691/$141 = 4.9 times Cash coverage ratio = [EBIT + Depreciation]/Interest [3.11] = [$691 + 276]/$141 = $967/$141 = 6.9 times Inventory turnover = Cost of goods sold/Inventory [3.12] = $1,344/$422 = 3.2 times Days’sales in inventory = 365 days/Inventory turnover [3.13] = 365/3.2 = 114 days Receivables turnover = Sales/Accounts receivable [3.14] = $2,311/$188 = 12.3 times Days’sales in receivables = 365 days/Receivables turnover [3.15] = 365/12.3 = 30 days NWC turnover = Sales/NWC [3.16] = $2,311/($708 – $540) = 13.8 times Fixed asset turnover = Sales/Net fixed assets [3.17] = $2,311/$2,880 = .80 times Total asset turnover = Sales/Total assets [3.18] = $2,311/$3,588 = .64 times Profit margin = Net income/Sales [3.19] = $363/$2,311 = 15.7% Return on assets = Net income/Total assets [3.20] = $363/$3,588 = 10.12% Return on equity = Net income/Total equity [3.21] = $363/$2,591 = 14% P/E ratio = Price per share/Earnings per share [3.22] = $157/$11 = 14.27 times Market-to-book ratio = Market value per share/Book value per share [3.23] = $157/($2,591/33) = $157/$78.5 = 2 times ROE = Net income/Sales × Sales/Assets × Assets/Equity [3.24] = Profit margin × Total asset turnover × Equity multiplier Dividend payout ratio = Cash dividends/Net income [4.1] = $44/$132 1 = 33 ⁄% EFN = Increase in total assets –Addition to retained earnings [4.2] = A(g) – p(S)R × (1 + g) EFN = – p(S)R + [A– p(S)R] × g [4.3] EFN = –p(S)R + [A –p(S)R] × g [4.4] 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 [4.5] EFN = Increase in total assets –Addition to retained earnings [4.6] – New borrowing = A(g) – p(S)R × (1 + g) – pS(R) × (1 + g)[D/E] EFN = 0 g* = ROE × R/[1 – ROE × R] [4.7] p(S/A)(1 + D/E) × R g* = ▯▯▯ [4.8] 1 – p(S/A)(1 + D/E) × R EFN = Increase in total assets –Addition to retained earnings [4A.1] – New borrowing = A(g) – p(S)R × (1 + g) – pS(R) × (1 + g)[D/E] ROE = p(S/A)(1 + D/E) [4A.2] g* = ▯▯ ROE × R 1 – ROE × R t Future value = $1 × (1 + r) [5.1] PV = $1 × [1/(1 + r) ] = $1/(1 + r) t [5.2] t PV × (1 + r) = FV t [5.3] PV = FV /(t + r) = FV × [t/(1 + r) ] t Annuity present value = C × ▯▯▯– Present value factor [6.1] ▯ ▯ r 1 – [1/(1 + r) ] = C × ▯▯▯ r Annuity due value = Ordinary annuity value × (1 + r) [6.1] EAR = [1 + (Quoted rate/ m)] – 1 [6.2] q EAR = e – 1 [6.3] Bond value = C × (1 – 1/(1 + r) )/r + F/(1 + r) t [7.1] 1 + R = (1 + r) × (1 + h) [7.2] 1 + R = (1 + r) × (1 + h) [7.3] R = r + h + r × h R ≈ r + h [7.4] NPV = (c o c )Nc N $1,000 – CP [7C.1] OCF = EBIT + D – Taxes [10.1] = (S – C – D) + D – (S – C – D) × T c = $200 + 600 – 80 = $720 OCF = (S – C – D) + D – (S – C – D) × T c [10.2] = (S – C – D) × (1 – T c + D = Project net income + Depreciation = $120 + 600 = $720 OCF = (S – C – D) + D – (S – C – D) × T c [10.3] = (S – C) – (S – C – D) × T c = Sales – Costs – Taxes = $1,500 – 700 – 80 = $720 OCF = (S – C – D) + D – (S – C – D) × T [10.4] c = (S – C) × (1 – T c + D × T c S – VC = FC + D P × Q – v × Q = FC + D [11.1] (P – v) × Q = FC + D Q = (FC + D)/(P – v) OCF = [(P – v) × Q – FC – D] + D [11.2] = (P – v) × Q – FC Q = (FC + OCF)/(P – v) [11.3] Total dollar return = Dividend income + Capital gain (or loss) [12.1] Total cash if stock is sold = Initial investment + Total return [12.2] = $3,700 + 518 = $4,218 Var(R) = (1/(T – 1)) [(R 1 R ▯ ) + . . . + (RT– ▯ ) ] [12.3] Risk premium = Expected return – Risk-free rate [13.1] = E(R ) – R U f = 20% – 8% = 12% E(R) = ∑ O × P [13.2] j j j σ = ∑ [O – E(R)] × P 2 [13.3] j j j 2 σ = ▯▯ σ E(R P = x 1 E(R ) 1 x × 2(R ) + 2 . . +x × EnR ) n [13.4] 2 2 2 2 2 σ P = x L L+ x Uσ U + 2x L CURR L,UσLσ U [13.5] σ = ▯σ ▯2 P p Total return = Expected return + Unexpected return [13.6] R = E(R) + U Announcement = Expected part + Surprise [13.7] R = E(R) + Systematic portion + Unsystematic portion. [13.8] Total risk = Systematic risk + Unsystematic risk [13.9] E(R i = R f [E(R )M– R ] f ß i [13.10] R = E(R) + ß F + ß F + ß F + ▯ [13.11] I I GNP GNP r r E(R) = R F E[(R ) 1 R ]ß F E1(R ) – R2]ß F 2 [13.12] + E[(R 3 – R Fß +3. . . E[(R )K– R ]F K σ 2 = x σ 2 + x σ 2 + 2x x CORR σ σ [13
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