Fundamentals of Corporate Finance Seventh Canadian Edition

Transcription

1 Fundamentals of Corporate Finance Seventh Canadian Edition by Ross, Westerfield, Jordan, and Roberts Formula Sheet page # Assets 5 Liabilities 1 Shareholders equity [2.1] 26 Revenues 2 Expenses 5 Income [2.2] 30 Cash flow from assets 5 Cash flow to bondholders 1 Cash flow to shareholders [2.3] 32 Current ratio 5 Current assets/current liabilities [3.1] 64 Current assets 2 Inventory Quick ratio 5 Current liabilities [3.2] 66 Cash ratio 5 Cash 1 Cash equivalents/current liabilities [3.3] 66 Net working capital to total assets 5 Net working capital/total assets [3.4] 66 Interval measure 5 Current assets/average daily operating costs [3.5] 66 Total debt ratio 5 [Total assets 2 Total equity]/total assets [3.6] 67 Debt/equity ratio 5 Total debt/total equity [3.7] 67 Equity multiplier 5 Total assets/total equity [3.8] 67 Long-term debt Long-term debt ratio 5 Long-term debt 1 Total equity [3.9] 67 Times interest earned ratio 5 EBIT/Interest [3.10] 68 Cash coverage ratio 5 [EBIT 1 Depreciation]/Interest [3.11] 68 Inventory turnover 5 Cost of goods sold/inventory [3.12] 68 Days sales in inventory days/inventory turnover [3.13] 68 Receivables turnover 5 Sales/Accounts receivable [3.14] 69 Days sales in receivables days/receivables turnover [3.15] 69 NWC turnover 5 Sales/NWC [3.16] 70 Fixed asset turnover 5 Sales/Net fixed assets [3.17] 70 Total asset turnover 5 Sales/Total assets [3.18] 70 Profit margin 5 Net income/sales [3.19] 70 Return on assets 5 Net income/total assets [3.20] 71 Return on equity 5 Net income/total equity [3.21] 71 P/E ratio 5 Price per share/earnings per share [3.22] 72 Market-to-book ratio 5 Market value per share/book value per share [3.23] 72 ROE 5 Net income/sales 3 Sales/Assets 3 Assets/Equity [3.24] 74 5 Profit margin 3 Total asset turnover 3 Equity multiplier

2 2 Formula Sheet Dividend payout ratio 5 Cash dividends/net income [4.1] 95 EFN 5 Increase in total assets 2 Addition to retained earnings [4.2] A1g2 2 p1s2r g2 EFN 5 2p(S)R 1 [A 2 p(s)r] 3 g [4.3] 101 EFN 5 2p(S)R 1 [A 2 p(s)r] 3 g [4.4] 102 g 5 ps(r)/[a 2 ps(r)] Internal growth rate 5 ROA 3 R 1 2 ROA 3 R [4.5] 102 EFN * 5 Increase in total assets 2 Addition to retained earnings [4.6] New borrowing 5 A(g) 2 p(s)r 3 (1 1 g) 2 ps(r) 3 (1 1 g)[d/e] EFN * 5 0 g* 5 ROE 3 R/[1 2 ROE 3 R] [4.7] 103 p1s/a211 1 D/E2 3 R g* p1s/a211 1 D/E2 3 R [4.8] 105 Future value 5 $1 3 (1 1 r) t [5.1] 119 PV 5 $1 3 [1/(1 1 r) t ] 5 $1/(1 1 r) t [5.2] 127 PV 3 (1 1 r) t 5 FV t [5.3] 129 PV 5 FV t /(1 1 r) t 5 FV t 3 [1/(1 1 r) t ] Annuity present value 5 C 3 a 5 C 3 e 1 2 Present value factor b [6.1] 145 r 1 2 1/11 1 r2t f r Annuity FV factor 5 1Future value factor 2 12/r [6.2] r2 t 2 12/r Annuity due value 5 Ordinary annuity value 3 (1 1 r) [6.3] 152 Perpetuity present value 3 Rate 5 Cash flow [6.4] 152 PV 3 r 5 C Annuity present value factor Present value factor2/r [6.5] /r Present value factor2 PV 5 C [6.6] 154 PV 5 C c 1 2 a1 1 g t 1 1 r b d [6.7] 155 EAR 5 [1 1 (Quoted rate/m)] m 2 1 [6.8] 157 EAR 5 e q 2 1 [6.9] 160 Bond value 5 C 3 (1 2 1/(1 1 r) t )/r 1 F/(1 1 r) t [7.1] R 5 (1 1 r) 3 (1 1 h) [7.2] R 5 (1 1 r) 3 (1 1 h) [7.3] 198 R 5 r 1 h 1 r 3 h R < r 1 h [7.4] 198

3 Formula Sheet 3 P 0 5 (D 1 1 P 1 )/(1 1 r) [8.1] 211 P 0 5 D/r P 0 5 D g2 0 P t 5 D g2 t 5 D 1 5 D t11 [8.2] 212 [8.3] 213 [8.4] D 1 /P 0 [8.5] 217 r 5 D 1 /P 0 1 g OCF 5 EBIT 1 D 2 Taxes [10.1] S 2 C 2 D2 1 D 2 1S 2 C 2 D2 3 T c OCF 5 1S 2 C 2 D2 1 D 2 1S 2 C 2 D2 3 T c [10.2] S 2 C 2 D T c 2 1 D 5 Project net income 1 Depreciation OCF 5 1S 2 C 2 D2 1 D 2 1S 2 C 2 D2 3 T c [10.3] S 2 C2 2 1S 2 C 2 D2 3 T c 5 Sales 2 Costs 2 Taxes OCF 5 1S 2 C 2 D2 1 D 2 1S 2 C 2 D2 3 T c [10.4] S 2 C T c 2 1 D 3 T c PV tax shield on CCA 5 3IdTc k4 3 2 S n dtc d 1 k 1 1 k d 1 k 3 1 [10.5] 286 n 11 1 k2 S 2 VC 5 FC 1 D [11.1] 321 P 3 Q 2 v 3 Q 5 FC 1 D (P 2 v) 3 Q 5 FC 1 D Q 5 (FC 1 D)/(P 2 v) OCF 5 31P 2 v2 3 Q 2 FC 2 D4 1 D [11.2] P 2 v2 3 Q 2 FC Q 5 (FC 1 OCF)/(P 2 v) [11.3] 324 Total dollar return 5 Dividend income 1 Capital gain (or loss) [12.1] 341 Total cash if stock is sold 5 Initial investment 1 Total return [12.2] 342 Var 1R2 5 11/1T R 1 2 R2 2 1 p 1 1R T 2 R2 2 4 [12.3] 350 Geometric average return R R p R T 24 1/T 2 1 [12.4] 356 Risk premium 5 Expected return 2 Risk-free rate [13.1] E1R U 2 2 R f E1R2 5 o j R j 3 P j [13.2] 372 where R j 5 value of the jth outcome P j 5 associated probability of occurrence 5 the sum over all j o j

4 4 Formula Sheet s 2 5 o j 3R j 2 E1R P j [13.3] 373 s 5 2s 2 E1R P 2 5 x 1 3 E1R x 2 3 E1R p 1 x n 3 E1R n 2 [13.4] 375 s 2 P 5 x2 L s2 L 1 x2 U s2 U 1 2x L x U CORR L Us L s U [13.5] 378 s P 5 2s 2 P Total return 5 Expected return 1 Unexpected return [13.6] 382 R 5 E(R) 1 U Announcement 5 Expected part 1 Surprise [13.7] 383 R 5 E(R) 1 Systematic portion 1 Unsystematic portion [13.8] 384 Total risk 5 Systematic risk 1 Unsystematic risk [13.9] 387 E(R i ) 5 R f 1 [E(R M ) 2 R f ] 3 b i [13.10] 398 R 5 E(R) 1 b I F I 1 b GNP F GNP 1 b r F r 1 e [13.11] 401 E(R) 5 R F 1 E[(R 1 ]b 1 1 E(R 2 ]b 2 [13.12] E[(R 3 ]b E[(R K ]b K s 2 P 5 x2 L s2 L 1 x2 U s 2 U 1 2x L x U CORR L, U s L s U [13A.1] 408 s 2 P on i51 on j51 x j s ij [13A.2] 409 ds 2 P dx o N x s 5 23x COV1R, R 2 1 x j51 j i s2 1 x COV 1R, R 2 [13A.3] p 1 x N COV1R N, R 2 24 b 2 5 COV1R, R 2 2 M s 2 1R M 2 [13A.4] D 1 /P g [14.1] R f 1 b E 3 3R M 2 R f 4 [14.2] 416 R P 5 D/P 0 V 5 E 1 D [14.3] 419 [14.4] % 5 E/V 1 D m /V [14.5] 420 WACC 5 1E/V P/V2 3 R P 1 1D m /V2 3 R D T C 2 [14.6] 421 f A 5 1E/V2 3 f E 1 1D m /V2 3 f D [14.7] 428 b Portfolio 5 b Levered firm 5 Debt Debt 1 Equity 3 b Debt 1 Equity b Unlevered firm 5 Debt 1 Equity 3 b Equity Equity b Unlevered firm 5 Equity T C 2 3 Debt 3 b Equity Equity Debt 1 Equity 3 b Equity [14A.1] 442 [14A.2] 442 [14A.3] 442 Number of new shares 5 Funds to be raised/subscription price [15.1] 465 Number of rights needed to buy a share of stock 5 Old shares/new shares [15.2] 466

5 Formula Sheet 5 R o 5 (M o 2 S)/(N 1 1) [15.3] 467 where M o 5 common share price during the rights-on period S 5 subscription price N 5 number of rights required to buy one new share M e 5 M o 2 R o [15.4] 468 R e 5 (M e 2 S)/N [15.5] 468 Percentage change in EPS Degree of financial leverage 5 Percentage change in EBIT DFL 5 EBIT EBIT 2 Interest [16.1] 483 [16.2] 483 V u 5 EBIT/u 5 V L 1 E L 1 D L [16.3] 487 where V u 5 Value of the unlevered firm V L 5 Value of the levered firm EBIT 5 Perpetual operating income u 5 Equity required return for the unlevered firm E L 5 Market value of equity D L 5 Market value of debt 5 R A 1 (R A 2 R D ) 3 (D/E) [16.4] 487 b E 5 b 3 (1 1 D/E) A [16.5] 489 Value of the interest tax shield 5 (T C 3 R D 3 D)/R D [16.6] T C 3 D V L 5 V U 1 T C 3 D [16.7] R U 1 (R U 2 R D ) 3 (D/E) 3 (1 2 T C ) [16.8] 493 V L 5 V U 1 c T T 2 C S d 3 B 11 2 T b 2 [16A.1] 512 Net working capital 1 Fixed assets 5 Long-term debt 1 Equity [18.1] 549 Net working capital 5 (Cash 1 Other current assets) [18.2] Current liabilities Cash 5 Long-term debt 1 Equity 1 Current liabilities [18.3] Current assets (other than cash) 2 Fixed assets Operating cycle 5 Inventory period 1 Accounts receivable period [18.4] 551 Cash cycle 5 Operating cycle 2 Accounts payable period [18.5] 551 Cash collections 5 Beginning accounts receivable 1 1/2 3 Sales [18.6] 563 Average daily float 5 Average daily receipts 3 Weighted average delay [19.1] 588 Accounts receivable 5 Average daily sales 3 ACP [20.1] 604 Cash flow (old policy) 5 (P 2 v)q [20.2] 609 Cash flow (new policy) 5 (P 2 v)q9 [20.3] 609

6 6 Formula Sheet PV 5 [(P 2 v)(q9 2 Q)]/R [20.4] 610 Cost of switching 5 PQ 1 v(q9 2 Q) [20.5] 610 where PQ 5 present value in perpetuity of a one-month delay in receiving the monthly revenue of PQ NPV of switching 5 2[PQ 1 v(q9 2 Q)] 1 (P 2 v)(q9 2 Q)/R [20.6] 610 NPV [PQ 1 v(q9 2 Q)] 1 (P 2 v)(q9 2 Q)/R [20.7] 611 NPV 5 2v 1 (1 2 p)p9/(1 1 R) [20.8] 613 NPV 5 2v 1 (1 2 p)(p 2 v)/r [20.9] 614 Score 5 Z [Sales/Total assets] EBIT/Total assets [20.10] 617 Total carrying costs 5 Average inventory 3 Carrying costs per unit [20.11] (Q/2) 3 CC Total restocking cost 5 Fixed cost per order 3 Number of orders [20.12] F 3 (T/Q) Total costs 5 Carrying costs 1 Restocking costs [20.13] (Q/2) 3 CC 1 F 3 (T/Q) Carrying costs 5 Restocking costs (Q*/2) 3 CC 5 F 3 (T/Q*) [20.14] 625 Q* 2 5 2T 3 F CC Q* 5 B 2T 3 F CC [20.15] 625 [20.16] 625 (E[S 1 ] 2 S 0 )/S 0 5 h FC [21.1] 646 E[S 1 ] 3 [1 1 (h FC )] [21.2] 646 E[S t ] 3 [1 1 (h FC )] t [21.3] 646 F 1 /S 0 5 (1 1 R FC )/(1 1 R CDN ) [21.4] 649 (F 1 2 S 0 )/S 0 5 R FC [21.5] 649 F 1 )] [21.6] 649 F t )] t [21.7] 649 E[S 1 ] )] [21.8] 650 E[S t ] )] t [21.9] 650 R CDN 5 R FC 2 h FC [21.10] 650 NPV 5 V B * 2 Cost to Firm A of the acquisition [23.1] 702 C if (S 1 2 E) # 0 [25.1] 752 C 1 5 S 1 2 E if (S 1 2 E). 0 [25.2] 752 # S 0 [25.3] 752 $ 0 if S 0 2 E, 0 [25.4] 753 $ S 0 2 E if S 0 2 E $ 0

7 Formula Sheet 7 S E/(1 1 R f ) [25.5] E/(1 1 R f ) Call option value 5 Stock value 2 Present value of the exercise price [25.6] E/(1 1 R f ) t 3 N(d 1 ) 2 E/(1 1 R f ) t 3 N(d 2 ) [25A.1] 782 d 1 5 3ln1S 0 /E2 1 1R f 1 1/2 3s t4/ 3s 32t4 [25A.2] 782 d 2 5 d 1 2 s31t Appendix 4A Online EFN 5 Increase in total assets 2 Addition to retained earnings 2 New borrowing [4B.1] 4 5 A(g) 2 p(s)r 3 (1 1 g) 2 ps(r) 3 (1 1 g)[d/e] ROE 5 p(s/a)(1 1 D/E) [4B.2] 4 Appendix 7B NPV 5 (c o 2 c N )/c N 3 $1,000 2 CP [7B.1] 3 Appendix 19A Opportunity costs 5 (C/2) 3 R [19A.1] 2 Trading costs 5 (T/C) 3 F [19A.2] 2 Total cost 5 Opportunity costs 1 Trading costs [19A.3] 3 5 (C/2) 3 R 1 (T/C) 3 F C* 5 212T 3 F2/R [19A.4] 3 C* 5 L 1 (3/4 3 F 3 s 2 /R) 1/3 [19A.5] 5 U* C* L [19A.6] 5 Average cash balance 5 (4 3 C* 2 L)/3 [19A.7] 5 Appendix 20A Net incremental cash flow 5 P9Q 3 (d 2 p) [20A.1] 3 NPV 5 2PQ 1 P9Q 3 (d 2 p)/r [20A.2] 3