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# Finance Formula

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• 1. BA 640 Formula Chapter 6 Risk and Return 1) Rate of return = Amount received - Amount invested Amount invested n k = ∑ k i Pi ˆ 2) Expected rate of return Pi = Probability , ki = Rate of return i =1 Calculator 1) Selecting Mode LR : MODE 5 2) Clear Data : CST EXE AC 3) Insert return before : -22 ALFHA Nj 0.1 MAR …… SHIFT 1 EXE ; DT x ∑ (k )P n 2 = −k ˆ σ = Variance = σ 2 3) Risk or Standard deviation i i i =1 Calculator 1) Insert return before : -22 ALFHA Nj 0.1 MAR …… SHIFT 2 EXE ; DT xσ n CV = Risk / Return = σ/x 4) Coefficient of variation 5) Beta coefficient ( β ) Calculator insert Mkt. before : 25.7 ALFHA CFj 40 MAR …… SHIFT 8 EXE β , DT 6) Correlation ( r ) Calculator insert Mkt. before : 25.7 ALFHA CFj 40 MAR …… SHIFT 9 EXE ( -1 < r < 1 ) , DT r ∑ (k )P n 2 n = − kp ˆ ∑ wi kˆi σp ˆ 7) Expected return on a portfolio k p = , Risk on a portfolio pi i i =1 i =1 8) Security Market Line (SML) : ki = kRF + (RPM)bi Required return = Risk-free return + Premium for risk Required return on stock i = Risk-free rate of return + (Market risk premium)(Stock i ‘ s beta) Chapter 9 Bonds and Their Valuation CF CF CF + + .....+ n 1 2 (1+ k) (1+ k) (1+ k)n 1) PV = Calculator 1) Selecting Mode FIN : MODE 4 1 2 SHIFT AC EXE AC 2) Clear Data : 3) PV = 10 n 10 i% 100 PMT 1000 FV COMP PV EXE 2) Yield to maturity (YTM) or kd = 10 n -887 PV 90 PMT 1000 FV COMP i% EXE Chapter 10 Stock and Their Valuation D1 D2 D3 D∞ P= + + +. . . + ˆ (1+ ks )1 (1+ ks )2 (1+ ks )3 (1+ ks )∞ 1) Stock Value = PV of Dividends 0 ˆ D (1 + g ) = D1 P0 = 0 D1 3) k s = +g ˆ ks − g ks − g 2) If g is constant, then P0 = Actual dividend yield + Actual capital gains yield 3) k s D D ps V ps = k ps = ps or 4) V ps k ps kS = kRF + (kM - kRF) bFirm 5) Use the SML to calculate kS ; 1) After-tax component cost of debt = kd ( 1-T ) Chapter 11 The cost of Capital D = ps 2) The cost of preferred stock k ; ps Pn
• 2. WACC = wdkd (1-T) + wpskps + wceks 3) Weighted Average Cost of Capital (WACC) ; ˆ ks = k s = kRF + RP = D1 / P0 + expected g 4) 5) ks = Bond yield + Risk premium 6) g = (Retention rate)(ROE) = (1.0 – Payout rate)(ROE) = b(ROE) Chapter 13 The Basics of Capital Budgeting : Evaluating Cash Flows 1) Payback period = Year before full recovery + Unrecovered cost at start of year Cash flow during year 2) Net Present Value (NPV) : Sum of PVs of inflows and Outflows = PV inflow – PV outflow n n CFt CF t ∑ NPV = ∑ = − CF0 NPV (1 + k )t (1 + k )t or t=0 t =1 Calculator -100 CFj 10 CFj 60 CFj 80 10 i% COMP NPV EXE n CF t ∑ (1 + IRR = =0 )t 3) Internal Rate of Return (IRR) : NPV =0 ; IRR t=0 Calculator -100 CFj 10 CFj 60 CFj 80 10 i% COMP IRR EXE TV 4) Modify Internal rate of return (MIRR) : PV costs = PV terminal value : PV costs = (1 + MIRR ) n Chapter 8 Time Value of Money FVn = PV (1 + i ) n ⎛1⎞ n FV ⎜ ⎟ n or PV = = FV 1) (1 + i )n n ⎝1+ i⎠ mn ⎛ ⎞ mn ⎛ ⎞ i i = PV ⎜ 1 + Nom ⎟ = ⎜ 1 + Nom ⎟ − 1 .0 FV or Effective annual rate 2) n ⎝ m⎠ ⎝ m⎠ Chapter 14 Cash Flow Estimate and Risk Analysis 1) Net Proceeds from sales (NP) = MV + Tax ; MV = Market value = MV + Tax rate ( MV-BV) ; BV = Book value 2) Net operating working capital (NOWC) = All current assets that _ All current liabilities that do not pay interest do not pay interest = Operating current assets – operating current liabilities 3) Operating capital = (Net operating working capital) – (Net plant and equipment) 4) NOPAT = Net operating profit after taxes = EBIT(1-Tax rate) 5) Operating cash flow (OCF) = NOPAT + Depreciation = EBIT(1-Tax) + Depreciation = (Sales – CGS – Operating Expense – depreciation)(1-Tax) + Depreciation = (Sales – CGS – Operating Expense)(1-Tax) + (Depreciation x Tax) 6) Free cash flow (FCF) = Operating cash flow - Gross investment in operating capital = NOPAT – Net investment in operating capital 7) Free cash flow (FCF) = EBIT(1-Tax) + Depreciation + ∆NWC + ∆CAPEX 8) EBIT = Sales – CGS – Operating Expense – depreciation = Sales – Variable Cost – Fixed Cost