Fundamentals of Corporate Finance



Fundamentals of Corporate Finance | |

|Seventh Canadian Edition |

|by Ross, Westerfield, Jordan, and Roberts |

|Formula Sheet |

| | |page # |

|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] |64 |

|[pic] |[3.2] |66 |

|Cash ratio = Cash + Cash equivalents/Current liabilities |[3.3] |66 |

|Net working capital to total assets = Net working capital/Total assets |[3.4] |66 |

|Interval measure = Current assets/Average daily operating costs |[3.5] |66 |

|Total debt ratio = [Total assets − Total equity]/Total assets |[3.6] |67 |

|Debt/equity ratio = Total debt/Total equity |[3.7] |67 |

|Equity multiplier = Total assets/Total equity |[3.8] |67 |

|[pic] |[3.9] |67 |

|Times interest earned ratio = EBIT/Interest |[3.10] |68 |

|Cash coverage ratio = [EBIT + Depreciation]/Interest |[3.11] |68 |

|Inventory turnover = Cost of goods sold/Inventory |[3.12] |68 |

|Days’ sales in inventory = 365 days/Inventory turnover |[3.13] |68 |

|Receivables turnover = Sales/Accounts receivable |[3.14] |69 |

|Days’ sales in receivables = 365 days/Receivables turnover |[3.15] |69 |

|NWC turnover = Sales/NWC |[3.16] |70 |

|Fixed asset turnover = Sales/Net fixed assets |[3.17] |70 |

|Total asset turnover = Sales/Total assets |[3.18] |70 |

|Profit margin = Net income/Sales |[3.19] |70 |

|Return on assets = Net income/Total assets |[3.20] |71 |

|Return on equity = Net income/Total equity |[3.21] |71 |

|P/E ratio = Price per share/Earnings per share |[3.22] |72 |

|Market-to-book ratio = Market value per share/Book value per share |[3.23] |72 |

|ROE = Net income/Sales × Sales/Assets × Assets/Equity |[3.24] |74 |

|= Profit margin × Total asset turnover × Equity multiplier | | |

|Dividend payout ratio = Cash dividends/Net income |[4.1] |95 |

|EFN = Increase in total assets − Addition to retained earnings |[4.2] |101 |

|= A(g) − p(S)R × (1 + g) | | |

|EFN = −p(S)R + [A − p(S)R] × g |[4.3] |101 |

|EFN = −p(S)R + [A − p(S)R] × g |[4.4] |102 |

|g = pS(R)/[A − pS(R)] | | |

|[pic] |[4.5] |102 |

|EFN* = Increase in total assets − Addition to retained earnings |[4.6] |103 |

|− 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] |103 |

|[pic] |[4.8] |105 |

|Future value = $1 × (1 + r)t |[5.1] |119 |

|PV = $1 × [1/(1 + r)t] = $1/(1 + r)t |[5.2] |127 |

|PV × (1 + r)t = FVt |[5.3] |129 |

|PV = FVt/(1 + r)t = FVt × [1/(1 + r)t] | | |

|[pic] |[6.1] |145 |

|Annuity FV factor = (Future value factor − 1)/r |[6.2] |150 |

|= ((1 + r)t − 1)/r | | |

|Annuity due value = Ordinary annuity value × (1 + r) |[6.3] |152 |

|Perpetuity present value × Rate = Cash flow |[6.4] |152 |

|PV × r = C | | |

|Annuity present value factor = (1 − Present value factor)/r |[6.5] |152 |

|= (1/r) × (1 − Present value factor) | | |

|[pic] |[6.6] |154 |

|[pic] |[6.7] |155 |

|EAR = [1 + (Quoted rate/m)]m − 1 |[6.8] |157 |

|EAR = eq − 1 |[6.9] |160 |

|Bond value = C × (1 − 1/(1 + r)t)/r + F/(1 + r)t |[7.1] |180 |

|1 + R = (1 + r) × (1 + h) |[7.2] |197 |

|1 + R = (1 + r) × (1 + h) |[7.3] |198 |

|R = r + h + r × h | | |

|R ( r + h |[7.4] |198 |

|P0 = (D1 + P1)/(1 + r) |[8.1] |211 |

|P0 = D/r |[8.2] |212 |

|[pic] |[8.3] |213 |

|[pic] |[8.4] |214 |

|(r − g) = D1/P0 |[8.5] |217 |

|r = D1/P0 + g | | |

|OCF = EBIT + D − Taxes |[10.1] |281 |

|= (S − C − D) + D − (S − C − D) ( Tc | | |

|OCF = (S − C − D) + D − (S − C − D) ( Tc |[10.2] |282 |

|= (S − C − D) ( (1 − Tc) + D | | |

|= Project net income + Depreciation | | |

|OCF = (S − C − D) + D − (S − C − D) ( Tc |[10.3] |282 |

|= (S − C) − (S − C − D) ( Tc | | |

|= Sales − Costs − Taxes | | |

|OCF = (S − C − D) + D − (S − C − D) ( Tc |[10.4] |282 |

|= (S − C) ( (1 − Tc) + D ( Tc | | |

|[pic] |[10.5] |286 |

| S − VC = FC + D |[11.1] |321 |

|P × Q − v × Q = FC + D | | |

|(P − v) × Q = FC + D | | |

|Q = (FC + D)/(P − v) | | |

|OCF = [(P − v) ( Q − FC − D] + D |[11.2] |323 |

|= (P − v) ( Q − FC | | |

|Q = (FC + OCF)/(P − v) |[11.3] |324 |

|Total dollar return = Dividend income + Capital gain (or loss) |[12.1] |341 |

|Total cash if stock is sold = Initial investment + Total return |[12.2] |342 |

|[pic] |[12.3] |350 |

|[pic] |[12.4] |356 |

|Risk premium = Expected return − Risk-free rate |[13.1] |372 |

|= E(RU) − Rf | | |

|[pic] |[13.2] |372 |

|where | | |

| Rj = value of the jth outcome | | |

| Pj = associated probability of occurrence | | |

|[pic] = the sum over all j | | |

|[pic] |[13.3] |373 |

|[pic] |[13.4] |375 |

|[pic] |[13.5] |378 |

|Total return = Expected return + Unexpected return |[13.6] |382 |

|R = E(R) + U | | |

|Announcement = Expected part + Surprise |[13.7] |383 |

|R = E(R) + Systematic portion + Unsystematic portion |[13.8] |384 |

|Total risk = Systematic risk + Unsystematic risk |[13.9] |387 |

|E(Ri) = Rf + [E(RM) − Rf] × βi |[13.10] |398 |

|R = E(R) + βIFI + βGNPFGNP + βrFr + ε |[13.11] |401 |

|E(R) = RF + E[(R1) − RF]β1 + E(R2) − RF ]β2 |[13.12] |401 |

|+ E[(R3) − RF]β3 + . . . E[(RK) − RF]βK | | |

|σ2P = x2Lσ2L + x2Uσ2U + 2xLx UCORRL, UσLσU |[13A.1] |408 |

|[pic] |[13A.2] |409 |

|[pic] |[13A.3] |409 |

|[pic] |[13A.4] |409 |

|RE = (D1/P0) + g |[14.1] |414 |

|RE = Rf + βE × [RM − Rf ] |[14.2] |416 |

|RP = D/P0 |[14.3] |419 |

|V = E + D |[14.4] |420 |

|100% = E/V + Dm/V |[14.5] |420 |

|WACC = (E/V) × RE + (P/V) × RP + (Dm /V) × RD × (1 − TC) |[14.6] |421 |

|fA = (E/V) × fE + (Dm/V) × fD |[14.7] |428 |

|[pic] |[14A.1] |442 |

|[pic] |[14A.2] |442 |

|[pic] |[14A.3] |442 |

|Number of new shares = Funds to be raised/Subscription price |[15.1] |465 |

|Number of rights needed to buy a share of stock = Old shares/New shares |[15.2] |466 |

|Ro = (Mo − S)/(N + 1) |[15.3] |467 |

|where | | |

|Mo = common share price during the rights-on period | | |

|S = subscription price | | |

|N = number of rights required to buy one new share | | |

|Me = Mo − Ro |[15.4] |468 |

|Re = (Me − S)/N |[15.5] |468 |

|[pic] |[16.1] |483 |

|[pic] |[16.2] |483 |

|Vu = EBIT/REu = VL + EL + DL |[16.3] |487 |

|where | | |

| Vu = Value of the unlevered firm | | |

|VL = Value of the levered firm | | |

|EBIT = Perpetual operating income | | |

|REu = Equity required return for the unlevered firm | | |

|EL = Market value of equity | | |

|DL = Market value of debt | | |

|RE = RA + (RA − RD) × (D/E) |[16.4] |487 |

|βE = βA × (1 + D/E) |[16.5] |489 |

|Value of the interest tax shield = (TC × RD × D)/RD |[16.6] |491 |

|= TC × D | | |

|VL = VU + TC × D |[16.7] |491 |

|RE = RU + (RU − RD) × (D/E) × (1 − TC) |[16.8] |493 |

|[pic] |[16A.1] |512 |

|Net working capital + Fixed assets = Long-term debt + Equity |[18.1] |549 |

|Net working capital = (Cash + Other current assets) |[18.2] |549 |

|− Current liabilities | | |

|Cash = Long-term debt + Equity + Current liabilities |[18.3] |549 |

|− Current assets (other than cash) − Fixed assets | | |

|Operating cycle = Inventory period + Accounts receivable period |[18.4] |551 |

|Cash cycle = Operating cycle − Accounts payable period |[18.5] |551 |

|Cash collections = Beginning accounts receivable + 1/2 × Sales |[18.6] |563 |

|Average daily float = Average daily receipts × Weighted average delay |[19.1] |588 |

|Accounts receivable = Average daily sales × ACP |[20.1] |604 |

|Cash flow (old policy) = (P − v)Q |[20.2] |609 |

|Cash flow (new policy) = (P − v)Q( |[20.3] |609 |

|PV = [(P − v)(Q( − Q)]/R |[20.4] |610 |

|Cost of switching = PQ + v(Q( − Q) |[20.5] |610 |

|where PQ = present value in perpetuity of a one-month | | |

|delay in receiving the monthly revenue of PQ | | |

|NPV of switching = −[PQ + v(Q( − Q)] + (P − v)(Q( − Q)/R |[20.6] |610 |

|NPV = 0 = −[PQ + v(Q( − Q)] + (P − v)(Q( − Q)/R |[20.7] |611 |

|NPV = −v + (1 − π)P(/(1 + R) |[20.8] |613 |

|NPV = −v + (1 − π)(P − v)/R |[20.9] |614 |

|Score = Z = 0.4 × [Sales/Total assets] + 3.0 × EBIT/Total assets |[20.10] |617 |

|Total carrying costs = Average inventory × Carrying costs per unit |[20.11] |623 |

|= (Q/2) × CC | | |

|Total restocking cost = Fixed cost per order × Number of orders |[20.12] |624 |

|= F × (T/Q) | | |

|Total costs = Carrying costs + Restocking costs |[20.13] |624 |

|= (Q/2) × CC + F × (T/Q) | | |

|Carrying costs = Restocking costs (Q*/2) × CC = F × (T/Q*) |[20.14] |625 |

|[pic] |[20.15] |625 |

|[pic] |[20.16] |625 |

|(E[S1] − S0)/S0 = hFC − hCDN |[21.1] |646 |

|E[S1] = S0 × [1 + (hFC − hCDN)] |[21.2] |646 |

|E[St] = S0 × [1 + (hFC − hCDN)]t |[21.3] |646 |

|F1/S0 = (1 + RFC)/(1 + RCDN) |[21.4] |649 |

|(F1 − S0)/S0 = RFC − RCDN |[21.5] |649 |

|F1 = S0 × [1 + (RFC − RCDN)] |[21.6] |649 |

|Ft = S0 × [1 + (RFC − RCDN)]t |[21.7] |649 |

|E[S1] = S0 × [1 + (RFC − RCDN)] |[21.8] |650 |

|E[St] = S0 × [1 + (RFC − RCDN)]t |[21.9] |650 |

|RCDN − hCDN = RFC − hFC |[21.10] |650 |

|[pic] |[23.1] |702 |

|C1 = 0 if (S1 − E) ( 0 |[25.1] |752 |

|C1 = S1 − E if (S1 − E) > 0 |[25.2] |752 |

|C0 ( S0 |[25.3] |752 |

|C0 ( 0 if S0 − E < 0 |[25.4] |753 |

|C0 ( S0 − E if S0 − E ( 0 | | |

|S0 = C0 + E/(1 + Rf) |[25.5] |755 |

|C0 = S0 − E/(1 + Rf) | | |

|Call option value = Stock value − Present value of the exercise price |[25.6] |756 |

|C0 = S0 − E/(1 + Rf)t | | |

|C0 = S0 × N(d1) − E/(1 + Rf)t × N(d2) |[25A.1] |782 |

|[pic] |[25A.2] |782 |

|Online |

|Appendix 4A | | |

|EFN = Increase in total assets − Addition to retained earnings − New borrowing |[4B.1] |4 |

|= A(g) − p(S)R × (1 + g) − pS(R) × (1 + g)[D/E] | | |

|ROE = p(S/A)(1 + D/E) |[4B.2] |4 |

|Appendix 7B | | |

|NPV = (co − cN)/cN × $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 |[19A.3] |3 |

|= (C/2) × R + (T/C) × F | | |

|[pic] |[19A.4] |3 |

|C* = L + (3/4 × F × σ2/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 |

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