FORMULA SHEET [3.2] 63

Transcription

1 FORMULA SHEET Assets = Liabilities + Shareholders equity [2.1] 26 Revenues - Expenses = Income [2.2] 30 Cash flow from assets = Cash flow to bondholders + Cash flow to shareholders [2.3] 32 Current ratio = Current assets/current liabilities [3.1] 61 Current assets Inventory Quick ratio = Current liabilities [3.2] 63 Cash ratio = (Cash + Cash equivalents)/current liabilities [3.3] 63 Net working capital to total assets = Net working capital/total assets [3.4] 63 Interval measure = Current assets/average daily operating costs [3.5] 63 Total debt ratio = [Total assets - Total equity]/total assets [3.6] 64 Debt/equity ratio = Total debt/total equity [3.7] 64 Equity multiplier = Total assets/total equity [3.8] 64 Long-term debt Long-term debt ratio = Long-term debt + Total equity [3.9] 64 Times interest earned ratio = EBIT/Interest [3.10] 65 Cash coverage ratio = [EBIT + Depreciation]/Interest [3.11] 65 Inventory turnover = Cost of goods sold/inventory [3.12] 65 Days sales in inventory = 365 days/inventory turnover [3.13] 65 Receivables turnover = Sales/Accounts receivable [3.14] 66 Days sales in receivables = 365 days/receivables turnover [3.15] 66 NWC turnover = Sales/NWC [3.16] 67 Fixed asset turnover = Sales/Net fixed assets [3.17] 67 Total asset turnover = Sales/Total assets [3.18] 67 Profit margin = Net income/sales [3.19] 67 Return on assets = Net income/total assets [3.20] 68 Return on equity = Net income/total equity [3.21] 68 P/E ratio = Price per share/earnings per share [3.22] 69 Market-to-book ratio = Market value per share/book value per share [3.23] 69 Dividend payout ratio = Cash dividends/net income [4.1] 90 EFN = Increase in total assets - Addition to retained earnings = A(g) - p(s)r (1 + g) [4.2] 96 EFN = -p(s)r + [A - p(s)r] g [4.3] 96 EFN = -p(s)r + [A - p(s)r] g g = ps(r)/[a - ps(r)] [4.4] 98 Internal growth rate = ROA R 1 ROA R [4.5] 98 Ross_FormulaSheet_4th.indd :27

2 2 Formula Sheet EFN* = Increase in total assets - Addition to retained earnings - New borrowing = A(g) - p(s)r (1 + g) - p(s)r (1 + g)[d/e] EFN* = 0 [4.6] 98 g* = ROE R/[1 - ROE R] [4.7] 98 p ( S/A )( 1 + D/E ) R g* = 1 p ( S/A )( 1 + D/E ) R [4.8] 100 Future value = $1 (1 + r) t [5.1] 112 PV = $1 [1/(1 + r) t ] = $1/(1 + r) t [5.2] 120 PV (1 + r) t = FV t PV = FV t /(1 + r) t = FV t [1/(1 + r) t ] [5.3] 121 Annuity present value = C ( 1 Present value factor r ) = C { 1 1/(1 + r ) t r } [6.1] 136 Annuity FV factor = (Future value factor - 1)/r = ((1 + r) t - 1)/r [6.2] 140 Annuity due value = Ordinary annuity value (1 + r) [6.3] 142 Perpetuity present value Rate = Cash flow PV r = C [6.4] 142 Annuity present value factor = (1 - Present value factor)/r = (1/r) (1 - Present value factor) [6.5] 142 PV = C r g [6.6] 144 PV = C r g [ 1 ( 1 + g 1 + r ) t ] [6.7] 145 EAR = [1 + (Quoted rate/m)] m - 1 [6.8] 146 EAR = e q - 1 [6.9] 149 Bond value = C (1-1/(1 + r) t )/r + F/(1 + r) t [7.1] R = (1 + r) (1 + h) [7.2] R = (1 + r) (1 + h) R = r + h + r h [7.3] 185 R r + h [7.4] 185 P 0 = (D 1 + P 1 )/(1 + r) [8.1] 197 P 0 = D/r [8.2] 198 P 0 = D (1 + g) 0 r g = D 1 r - g [8.3] 199 P t = D (1 + g) t r g = D t+1 r g [8.4] 200 (r - g) = D 1 /P 0 r = D 1 /P 0 + g [8.5] 203 OCF = EBIT + D - Taxes = (S - C - D) + D - (S - C - D) T C [10.1] 263 Ross_FormulaSheet_4th.indd :27

3 Formula Sheet 3 OCF = (S - C - D) + D - (S - C - D) T C = (S - C - D) (1 - T C ) + D = Project net income + Depreciation [10.2] 264 OCF = (S - C - D) + D - (S - C - D) T C = (S - C) - (S - C - D) T C = Sales - Costs - Taxes [10.3] 264 OCF = (S - C - D) + D - (S - C - D) T C = (S - C) (1 - T C ) + D T C [10.4] 264 PV tax shield on CCA = [IdT ] c [1 +.5k] d + k 1 + k - S dt n c d + k 1 (1 + k ) n [10.5] 267 S - VC = FC + D P Q - v Q = FC + D (P - v) Q = FC + D Q = (FC + D)/(P - v) [11.1] 299 OCF = [(P - v) Q - FC - D] + D = (P - v) Q - FC [11.2] 301 Q = (FC + OCF)/(P - v) [11.3] 302 Total dollar return = Dividend income + Capital gain (or loss) [12.1] 318 Total cash if stock is sold = Initial investment + Total return [12.2] 319 Var(R) = (1/(T - 1)) [ ( R 1 - R ) ( R T - R ) 2 ] [12.3] 328 Geometric average return = [(1 + R 1 ) (1 + R 2 ) (1 + R T )] 1/T - 1 [12.4] 333 Risk premium = Expected return - Risk-free rate = E(R U ) - R f [13.1] 348 E(R) = ΣR j P j j where R j = value of the jth outcome P j = associated probability of occurrence = the sum over all j [13.2] 348 Σ j σ 2 = Σ[R j - E(R)] 2 P j j σ = σ 2 [13.3] 349 E(R P ) = x 1 E(R 1 ) + x 2 E(R 2 ) + + x n E(R n ) [13.4] 352 σ 2 P = x2 L σ2 L + x2 U σ2 U + 2x L x U CORR L,U σ L σ U σ P = σ 2 P [13.5] 355 Total return = Expected return + Unexpected return R = E(R) + U [13.6] 359 Announcement = Expected part + Surprise [13.7] 360 R = E(R) + Systematic portion + Unsystematic portion [13.8] 361 Total risk = Systematic risk + Unsystematic risk [13.9] 364 E(R i ) = R f + [E(R M ) - R f ] β i [13.10] 374 R = E(R) + β I F I + β GNP F GNP + β r F r + ε [13.11] 377 Ross_FormulaSheet_4th.indd :27

4 4 Formula Sheet E(R) = R F + E[(R 1 ]β 1 + E[(R 2 ]β 2 + E[(R 3 ]β E[(R K ]β K [13.12] 378 σ 2 P = x2 L σ2 L + x2 U σ2 U + 2x L x U CORR L,U σ L σ U [13A.1] 384 N N σ 2 P xj σ ij i=1 j=1 [13A.2] 385 δσ 2 p δx 2 N = 2 xj σ i2 = 2 [ x 1 COV ( R 1,R 2 ) + x 2 σ x 3 COV ( R 3,R 2 ) + + x N COV ( R N,R 2 ) ] [13A.3] 385 j=1 β 2 = COV(R 2,R M ) σ 2 (R M ) = (D 1 /P 0 ) + g [13A.4] 386 [14.1] 389 = R f + β E [R M - R f ] [14.2] 391 R P = D/P 0 V = E + D m [14.3] 394 [14.4] % = E/V + D m /V [14.5] 395 WACC = (E/V) + (P/V) R P + (D m /V) R D (1 - T C ) [14.6] 396 f A = (E/V) f E + (D m /V) f D [14.7] 403 β Portfolio = β Levered firm = Debt Debt + Equity β + Equity Debt Debt + Equity β Equity Equity β Unlevered firm = Debt + Equity β Equity Equity β Unlevered firm = Equity + (1 - T C ) Debt β Equity [14A.1] 417 [14A.2] 417 [14A.3] 418 Number of new shares = Funds to be raised/subscription price [15.1] 440 Number of rights needed to buy a share of stock = Old shares/new shares [15.2] 441 Ro = (Mo - S)/(N + 1) where M o = common share price during the rights-on period S = subscription price N = number of rights required to buy one new share [15.3] 442 M e = M o - R o [15.4] 444 R e = (M e - S)/N Percentage change in EPS Degree of financial leverage = Percentage change in EBIT DFL = EBIT EBIT - Interest [15.5] 444 [16.1] 458 [16.2] 458 Ross_FormulaSheet_4th.indd :27

5 Formula Sheet 5 u V u = EBIT/ = V L = E L + D L where V u = Value of the unlevered firm V L = Value of the levered firm EBIT = Perpetual operating income u = Equity required return for the unlevered firm E L = Market value of equity D L = Market value of debt [16.3] 462 = R A + (R A - R D ) (D/E) [16.4] 463 β E = β A (1 + D/E) [16.5] 464 Value of the interest tax shield = (T C R D D)/R D = T C D [16.6] 467 V L = V U + T C D [16.7] 467 = R U + (R U - R D ) (D/E) (1 - T C ) [16.8] 468 V L = V U + [ 1 - (1 - T ) (1 - T ) C S 1 - T b ] D [16A.1] 487 Net working capital + Fixed assets = Long-term debt + Equity [18.1] 520 Net working capital = (Cash + Other current assets) - Current liabilities [18.2] 520 Cash = Long-term debt + Equity + Current liabilities - Current assets (other than cash) - Fixed assets [18.3] 520 Operating cycle = Inventory period + Accounts receivable period [18.4] 522 Cash cycle = Operating cycle - Accounts payable period [18.5] 522 Cash collections = Beginning accounts receivable + 1/2 Sales [18.6] 534 Accounts receivable = Average daily sales ACP [20.1] 574 Cash flow (old policy) = (P - v)q [20.2] 579 Cash flow (new policy) = (P - v)q [20.3] 579 PV = [(P - v)(q - Q)]/R [20.4] 580 Cost of switching = PQ + v(q - Q) where PQ = present value in perpetuity of a one-month delay in receiving the monthly revenue of PQ [20.5] 580 NPV of switching = -[PQ + v(q - Q)] + (P - v)(q - Q)/R [20.6] 580 NPV = 0 = -[PQ + v(q - Q)] + (P - v)(q - Q)/R [20.7] 580 NPV = -v + (1 - π)p /(1 + R) [20.8] 583 NPV = -v + (1 - π)(p - v)/r [20.9] 584 Score = Z = 0.4 [Sales/Total assets] EBIT/Total assets [20.10] 587 Total carrying costs = Average inventory Carrying costs per unit = (Q/2) CC [20.11] 594 Total restocking cost = Fixed cost per order Number of orders = F (T/Q) [20.12] 594 Total costs = Carrying costs + Restocking costs = (Q/2) CC + F (T/Q) [20.13] 594 Ross_FormulaSheet_4th.indd :27

6 6 Formula Sheet Carrying costs = Restocking costs (Q*/2) CC = F (T/Q*) [20.14] 595 Q* 2 = 2T F CC [20.15] 595 Q* = 2T F CC [20.16] 595 (E[S 1 ] - S 0 )/S 0 = h FC [21.1] 614 E[S 1 ] [1 + (h FC )] [21.2] 614 E[S t ] [1 + (h FC )] t [21.3] 615 F 1 /S 0 = (1 + R FC )/(1 + R CDN ) [21.4] 617 (F 1 - S 0 )/S 0 = R FC [21.5] 617 F 1 )] [21.6] 617 F t )] t [21.7] 617 E[S 1 ] )] [21.8] 618 E[S t ] )] t [21.9] 618 R CDN = R FC - h FC [21.10] 618 NPV = V B * - Cost to Firm A of the acquisition [23.1] 668 C 1 = 0 if (S 1 - E) 0 [25.1] 717 C 1 = S 1 - E if (S 1 - E) > 0 [25.2] 717 S 0 [25.3] if S 0 - E < 0 S 0 - E if S 0 - E 0 [25.4] 718 S 0 = + E/(1 + R f ) - E/(1 + R f ) [25.5] 720 Call option value = Stock value - Present value of the exercise price - E/(1 + R f ) t [25.6] 720 N(d 1 ) - E/(1 + R f ) t N(d 2 ) [25A.1] 745 d 1 = [ln(s 0 /E) + (R f + 1/2 σ 2 _ ) t]/[σ _ t ] d 2 = d 1 - σ t [25A.2] 746 Ross_FormulaSheet_4th.indd :27

7 Formula Sheet 7 Online Appendix 4A EFN = Increase in total assets - Addition to retained earnings - New borrowing = A(g) - p(s)r (1 + g) - ps(r) (1 + g)[d/e] [4B.1] 4 ROE = p(s/a)(1 + D/E) [4B.2] 4 Appendix 7B NPV = (c o - c N )/c N $1,000 - CP [7B.1] 3 Appendix 19A Opportunity costs = (C/2) R [19A.1] 2 Trading costs = (T/C) F [19A.2] 2 Total cost = Opportunity costs + Trading costs = (C/2) R + (T/C) F [19A.3] 3 C* = (2T F)/R [19A.4] 3 C* = L + (3/4 F σ 2 /R) 1/3 [19A.5] 5 U* = 3 C* - 2 L [19A.6] 5 Average cash balance = (4 C* - L)/3 [19A.7] 5 Appendix 20A Net incremental cash flow = P Q (d - π) [20A.1] 3 NPV = -PQ + P Q (d - π)/r [20A.2] 3 Ross_FormulaSheet_4th.indd :27