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
/ [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
/ [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
= Profit margin ´ Total asset turnover ´ Equity multiplier / [3.24] / 74
Dividend payout ratio = Cash dividends/Net income / [4.1] / 95
EFN = Increase in total assets - Addition to retained earnings
= A(g) - p(S)R ´ (1 + g) / [4.2] / 101
EFN = -p(S)R + [A - p(S)R] ´ g / [4.3] / 101
EFN = -p(S)R + [A - p(S)R] ´ g
g = pS(R)/[A - pS(R)] / [4.4] / 102
/ [4.5] / 102
EFN* = Increase in total assets - Addition to retained earnings
- New borrowing
= A(g) - p(S)R ´ (1 + g) - pS(R) ´ (1 + g)[D/E]
EFN* = 0 / [4.6] / 103
g* = ROE ´ R/[1 - ROE ´ R] / [4.7] / 103
/ [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
PV = FVt/(1 + r)t = FVt ´ [1/(1 + r)t] / [5.3] / 129
/ [6.1] / 145
Annuity FV factor = (Future value factor - 1)/r
= ((1 + r)t - 1)/r / [6.2] / 150
Annuity due value = Ordinary annuity value ´ (1 + r) / [6.3] / 152
Perpetuity present value ´ Rate = Cash flow
PV ´ r = C / [6.4] / 152
Annuity present value factor = (1 - Present value factor)/r
= (1/r) ´ (1 - Present value factor) / [6.5] / 152
/ [6.6] / 154
/ [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)
R = r + h + r ´ h / [7.3] / 198
R » r + h / [7.4] / 198
P0 = (D1 + P1)/(1 + r) / [8.1] / 211
P0 = D/r / [8.2] / 212
/ [8.3] / 213
/ [8.4] / 214
(r - g) = D1/P0
r = D1/P0 + g / [8.5] / 217
OCF = EBIT + D - Taxes
= (S - C - D) + D - (S - C - D) ´ Tc / [10.1] / 281
OCF = (S - C - D) + D - (S - C - D) ´ Tc
= (S - C - D) ´ (1 - Tc) + D
= Project net income + Depreciation / [10.2] / 282
OCF = (S - C - D) + D - (S - C - D) ´ Tc
= (S - C) - (S - C - D) ´ Tc
= Sales - Costs - Taxes / [10.3] / 282
OCF = (S - C - D) + D - (S - C - D) ´ Tc
= (S - C) ´ (1 - Tc) + D ´ Tc / [10.4] / 282
/ [10.5] / 286
S - VC = FC + D
P ´ Q - v ´ Q = FC + D
(P - v) ´ Q = FC + D
Q = (FC + D)/(P - v) / [11.1] / 321
OCF = [(P - v) ´ Q - FC - D] + D
= (P - v) ´ Q - FC / [11.2] / 323
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
/ [12.3] / 350
/ [12.4] / 356
Risk premium = Expected return - Risk-free rate
= E(RU) - Rf / [13.1] / 372
/ [13.2] / 372
where
Rj = value of the jth outcome
Pj = associated probability of occurrence
= the sum over all j
/ [13.3] / 373
/ [13.4] / 375
/ [13.5] / 378
Total return = Expected return + Unexpected return
R = E(R) + U / [13.6] / 382
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] ´ bi / [13.10] / 398
R = E(R) + bIFI + bGNPFGNP + brFr + e / [13.11] / 401
E(R) = RF + E[(R1) - RF]b1 + E(R2) - RF ]b2
+ E[(R3) - RF]b3 + . . . E[(RK) - RF]bK / [13.12] / 401
s2P = x2Ls2L + x2Us2U + 2xLx UCORRL, UsLsU / [13A.1] / 408
/ [13A.2] / 409
/ [13A.3] / 409
/ [13A.4] / 409
RE = (D1/P0) + g / [14.1] / 414
RE = Rf + bE ´ [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
/ [14A.1] / 442
/ [14A.2] / 442
/ [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
/ [16.1] / 483
/ [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
bE = bA ´ (1 + D/E) / [16.5] / 489
Value of the interest tax shield = (TC ´ RD ´ D)/RD
= TC ´ D / [16.6] / 491
VL = VU + TC ´ D / [16.7] / 491
RE = RU + (RU - RD) ´ (D/E) ´ (1 - TC) / [16.8] / 493
/ [16A.1] / 512
Net working capital + Fixed assets = Long-term debt + Equity / [18.1] / 549
Net working capital = (Cash + Other current assets)
- Current liabilities / [18.2] / 549
Cash = Long-term debt + Equity + Current liabilities
- Current assets (other than cash) - Fixed assets / [18.3] / 549
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 - p)P¢/(1 + R) / [20.8] / 613
NPV = -v + (1 - p)(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
= (Q/2) ´ CC / [20.11] / 623
Total restocking cost = Fixed cost per order ´ Number of orders
= F ´ (T/Q) / [20.12] / 624
Total costs = Carrying costs + Restocking costs
= (Q/2) ´ CC + F ´ (T/Q) / [20.13] / 624
Carrying costs = Restocking costs (Q*/2) ´ CC = F ´ (T/Q*) / [20.14] / 625
/ [20.15] / 625
/ [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
/ [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 ³ 0 if S0 - E 0
C0 ³ S0 - E if S0 - E ³ 0 / [25.4] / 753
S0 = C0 + E/(1 + Rf)
C0 = S0 - E/(1 + Rf) / [25.5] / 755
Call option value = Stock value - Present value of the exercise price
C0 = S0 - E/(1 + Rf)t / [25.6] / 756
C0 = S0 ´ N(d1) - E/(1 + Rf)t ´ N(d2) / [25A.1] / 782
/ [25A.2] / 782
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 = (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
= (C/2) ´ R + (T/C) ´ F / [19A.3] / 3
/ [19A.4] / 3
C* = L + (3/4 ´ F ´ s2/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 - p) / [20A.1] / 3
NPV = -PQ + P¢Q ´ (d - p)/R / [20A.2] / 3
Stephen A. Ross
FormulaSheet
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