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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 fl ow from assets 5 Cash fl ow to bondholders 1 Cash fl ow to shareholders [2.3] 32 Current ratio 5 Current assets/Current liabilities [3.1] 64 Quick ratio 5 Current assets 2 Inventory 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 ratio 5 Long-term debt 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 5 365 days/Inventory turnover [3.13] 68 Receivables turnover 5 Sales/Accounts receivable [3.14] 69 Days’ sales in receivables 5 365 days/Receivables turnover [3.15] 69 NWC turnover 5 Sales/NWC [3.16] 70 Fixed asset turnover 5 Sales/Net fi xed assets [3.17] 70 Total asset turnover 5 Sales/Total assets [3.18] 70 Profi t 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 Profi t margin 3 Total asset turnover 3 Equity multiplier ros69760_formulasheet_001-007.in1 Page 1 3/25/10 7:14:13 PM user-f467 /Volumes/203/MHRL033/ros69760/0070969760/ros69760_pagefiles 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] 101 5 A1g2 2 p1S2R 3 11 1 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] 103 2 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 g* 5 p1S/A2 11 1 D/E2 3 R 1 2 p1S/A2 11 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 FVt [5.3] 129 PV 5 FVt /(1 1 r)t 5 FVt 3 [1/(1 1 r)t] Annuity present value 5 C 3 a1 2 Present value factorr b [6.1] 145 5 C 3 e 1 2 1/ 11 1 r2tr f Annuity FV factor 5 1Future value factor 2 12/r [6.2] 150 5 1 11 1 r2t 2 12/r Annuity due value 5 Ordinary annuity value 3 (1 1 r) [6.3] 152 Perpetuity present value 3 Rate 5 Cash fl ow [6.4] 152 PV 3 r 5 C Annuity present value factor 5 11 2 Present value factor2/r [6.5] 152 5 11/r2 3 11 2 Present value factor2 PV 5 C r 2 g [6.6] 154 PV 5 C r 2 g c 1 2 a 1 1 g 1 1 r bt d [6.7] 155 EAR 5 [1 1 (Quoted rate/m)]m 2 1 [6.8] 157 EAR 5 eq 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] 180 1 1 R 5 (1 1 r) 3 (1 1 h) [7.2] 197 1 1 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 ros69760_formulasheet_001-007.in2 Page 2 3/25/10 7:14:15 PM user-f467 /Volumes/203/MHRL033/ros69760/0070969760/ros69760_pagefiles Formula Sheet 5 Ro 5 (Mo 2 S)/(N 1 1) [15.3] 467 where Mo 5 common share price during the rights-on period S 5 subscription price N 5 number of rights required to buy one new share Me 5 Mo 2 Ro [15.4] 468 Re 5 (Me 2 S)/N [15.5] 468 Degree of financial leverage 5 Percentage change in EPS Percentage change in EBIT [16.1] 483 DFL 5 EBIT EBIT 2 Interest [16.2] 483 Vu 5 EBIT/REu 5 VL 1 EL 1 DL [16.3] 487 where Vu 5 Value of the unlevered fi rm VL 5 Value of the levered fi rm EBIT 5 Perpetual operating income REu 5 Equity required return for the unlevered fi rm EL 5 Market value of equity DL 5 Market value of debt RE 5 RA 1 (RA 2 RD) 3 (D/E) [16.4] 487 bE 5 bA 3 (1 1 D/E) [16.5] 489 Value of the interest tax shield 5 (TC 3 RD 3 D)/RD [16.6] 491 5 TC 3 D VL 5 VU 1 TC 3 D [16.7] 491 RE 5 RU 1 (RU 2 RD) 3 (D/E) 3 (1 2 TC) [16.8] 493 VL 5 VU 1 c 1 2 11 2 TC2 3 11 2 TS2 11 2 Tb2 d 3 B [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] 549 2 Current liabilities Cash 5 Long-term debt 1 Equity 1 Current liabilities [18.3] 549 2 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 fl oat 5 Average daily receipts 3 Weighted average delay [19.1] 588 Accounts receivable 5 Average daily sales 3 ACP [20.1] 604 Cash fl ow (old policy) 5 (P 2 v)Q [20.2] 609 Cash fl ow (new policy) 5 (P 2 v)Q9 [20.3] 609 ros69760_formulasheet_001-007.in5 Page 5 3/25/10 7:14:25 PM user-f467 /Volumes/203/MHRL033/ros69760/0070969760/ros69760_pagefiles 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 5 0 5 2[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 5 0.4 3 [Sales/Total assets] 1 3.0 3 EBIT/Total assets [20.10] 617 Total carrying costs 5 Average inventory 3 Carrying costs per unit [20.11] 623 5 (Q/2) 3 CC Total restocking cost 5 Fixed cost per order 3 Number of orders [20.12] 624 5 F 3 (T/Q) Total costs 5 Carrying costs 1 Restocking costs [20.13] 624 5 (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 [20.15] 625 Q* 5 B 2T 3 F CC [20.16] 625 (E[S1] 2 S0)/S0 5 hFC 2 hCDN [21.1] 646 E[S1] 5 S0 3 [1 1 (hFC 2 hCDN)] [21.2] 646 E[St] 5 S0 3 [1 1 (hFC 2 hCDN)]t [21.3] 646 F1/S0 5 (1 1 RFC)/(1 1 RCDN) [21.4] 649 (F1 2 S0)/S0 5 RFC 2 RCDN [21.5] 649 F1 5 S0 3 [1 1 (RFC 2 RCDN)] [21.6] 649 Ft 5 S0 3 [1 1 (RFC 2 RCDN)]t [21.7] 649 E[S1] 5 S0 3 [1 1 (RFC 2 RCDN)] [21.8] 650 E[St] 5 S0 3 [1 1 (RFC 2 RCDN)]t [21.9] 650 RCDN 2 hCDN 5 RFC 2 hFC [21.10] 650 NPV 5 VB* 2 Cost to Firm A of the acquisition [23.1] 702 C1 5 0 if (S1 2 E) # 0 [25.1] 752 C1 5 S1 2 E if (S1 2 E) . 0 [25.2] 752 C0 # S0 [25.3] 752 C0 $ 0 if S0 2 E , 0 [25.4] 753 C0 $ S0 2 E if S0 2 E $ 0 ros69760_formulasheet_001-007.in6 Page 6 3/25/10 7:14:25 PM user-f467 /Volumes/203/MHRL033/ros69760/0070969760/ros69760_pagefiles Formula Sheet 7 S0 5 C0 1 E/(1 1 Rf) [25.5] 755 C0 5 S0 2 E/(1 1 Rf) Call option value 5 Stock value 2 Present value of the exercise price [25.6] 756 C0 5 S0 2 E/(1 1 Rf)t C0 5 S0 3 N(d1) 2 E/(1 1 Rf)t 3 N(d2) [25A.1] 782 d1 5 3 ln1S0/E2 1 1Rf 1 1/2 3 s22 3 t 4/ 3s 3 2t 4 [25A.2] 782 d2 5 d1 2 s 3 1t Online Appendix 4A 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 (co 2 cN)/cN 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 s2/R)1/3 [19A.5] 5 U* 5 3 3 C* 2 2 3 L [19A.6] 5 Average cash balance 5 (4 3 C* 2 L)/3 [19A.7] 5 Appendix 20A Net incremental cash fl ow 5 P9Q 3 (d 2 p) [20A.1] 3 NPV 5 2PQ 1 P9Q 3 (d 2 p)/R [20A.2] 3 ros69760_formulasheet_001-007.in7 Page 7 3/25/10 7:14:26 PM user-f467 /Volumes/203/MHRL033/ros69760/0070969760/ros69760_pagefiles