Formula Sheet Finance

Formulas (Brooks’ Financial Management) 1. Pct Change = [L(Later) – E(Earlier)] / E = (L/E) – 1 2. Pct = Decimal * 100; Decimal = Pct / 100 3. Order of Operations: “PEMDAS” 4. For (S / O): [ (S/O)] / S > 0; [ (S/O)] / O<0: % (S/O) ≈ % S-% O 5. For Normal Distribution: Mean +/- σ ≈ 68%; Mean +/- 2σ ≈ 95%; Mean +/- 3σ ≈ 99+% 6. Total return (%) = income return (%) + capital gain (%) 7. Capital gain (loss) = percent 8. FVn = PV0(1 + r) in price of asset n 9. PV0 = FVn / (1 + r)n 10. n = ln (FV/PV) / ln (1 + r) [Rule of 72: n (yrs.) ≈ 72 / r (annual %)] 11. r = (FVn/PV0)(1/n) – 1 [Rule of 72: r (annual %) ≈ 72 / n (yrs.)] 12. FVAn = PMT [((1 + r)n - 1) / r] 13. PVAt = PMT(t+1) [(1 - 1/(1 + r)n) / r] 14. PVPt = PMT(t+1) / r 15. Periodic Interest Rate, r = APR / m 16. EAR = (1 + APR/m)m - 1 17. r (Approximate) ≈ r* + h 18. r = r* + inf + dp + mp 19. Bond Price (PB) = Coupon PMT [(1 - 1/(1 + r)n) / r] + Par / (1 + r)n (See #s 13 and 9 above) 20. Current Yield = Annual Coupon PMT / PB 21. YTM = (Par/PB)(1/n) – 1 (See #11 above) 22. YTM ≈ (Coupon + (Par –PB)/n) / [.4 Par + .6 PB] (Approximation Formula) 23. Profit = ending value + distributions-original cost 24. HPR = (profit or loss)/ original cost 25. Simple annual return = HPR/n; 26. Compound annual return = (1 + HPR)(1/n) - 1 27. [CAPM] Re = E (ri) = rf + βi [E(rm) - rf] 28. Reward-to-Risk Ratio (Treynor Index) = [(E(ri) - rf)/ βi] (See #16 above) 29. Div(t+1) = Divt(1 + x) where x may or may not be equal to g 30. Pt = Div(t+1) / (r – g) (“Growing Perpetuity”) 31. P0 = Div1/ (1+r)1 + …+ (Divt + Pt)/(1+r)t 32. Pt = Div(t+1) / r (See #14 above) 33. r = (Div1/P0) + g 34. Assets liabilities + owners’ equity 35. Retained earnings = net income - distributed earnings (dividends) 36. Retained earnings + dividends = net income 37. Revenue - operating expenses = earnings before interest and taxes 38. Net income = revenues – expenses 39. ∆ NI (any expense item) = - ∆ Expense (1 – T) 40. ∆ Cash (any expense item except depreciation) = - ∆ Expense (1 – T) 41. ∆ Cash (depreciation only) = ∆ Expense * T 42. Cash flow from assets = cash flow to creditors + cash flow to owners 43. Cash flow from assets = operating cash flow – net capital spending – change in net working capital 44. Operating cash flow = EBIT + depreciation – taxes 45. Net Capital Spending = purchase of new capital equipment – sale of existing capital equipment 46. Net capital spending = ∆ gross fixed assets = ∆ net fixed assets + depreciation 47. Net working capital = current assets – current liabilities 48. net working capital = ∆ current assets - ∆ current liabilities 49. Cash flow to creditors = interest expense - ∆ L. T. liabilities 50. Cash flow to owners = dividends - ∆ common stock 51. Break-even EBIT: Solve for EBIT in (EBIT -InterestNL)/SharesNL = (EBIT - InterestL)/SharesL 52. Current ratio = current assets / current liabilities 53. Cash coverage ratio = (EBIT + depreciation) / interest expense 54. Total asset turnover = sales / total assets 55. Gross profit = sales – COGS; Gross profit margin = (sales – COGS) / sales 56. Net profit = revenue – costs; Net profit margin = net income / sales 57. Return on assets = net income / total assets 58. Return on equity = net income / total owners’ equity 59. Earnings per share (EPS) = net income / number of outstanding shares 60. Price – earnings ratio = market price per share / earnings per share 61. Market to book ratio = market price per share / book value of equity per share 62. Return on equity = (net income / sales) * (sales / total assets) * (total assets / total equity) 63. Annual straight-line depreciation = (equipment cost + installation cost – residual value)/ years of useful life 64. CF Salvage = SP – (SP – BV) T 65. BV = Original Cost – Accumulated Depreciation 66. WACC = (E*Re + D*Rd*(1 – T))/V = (E/V)*Re + (D/V)*Rd*(1 – T) where V = E + D 67. NPV = CF0* + CF1/ (1 + r)1 + CF2/(1 + r)2 +…+ CFn/(1 + r)n [* NOTE ERROR WITH TERM IN TEXTBOOK!] 68. IRR: $0 = CF0 + CF1/ (1 +IRR)1 + CF2/(1 + IRR)2 +…+ CFn/(1 + IRR)n