Finance Formula Sheet

Introduction to Finance Formula Sheet (2.1) Accounting identity: assets ≡liabilities+ owners' equity (2.2) Net working capital: NWC =current assets - current liabilities (2.3) Net income: net income = revenues - expenses (2.4) Earnings before interest and taxes: EBIT =revenues - operating expenses (2.5) Operating cash flow: OCF = EBIT + depreciation - taxes (2.6) Change in retained earnings: ΔRE = net income - distributed earnings (2.7) Cash flow from assets: CF from assets ≡ CF to creditors + CF to owners (3.2) Future value of a lump sum: FV=PV× (1+r )n (3.3) Present value of a lump sum: (3.4) Interest rate: (3.5) Number of periods: (4.3) Future value of an annuity: (4.4) Present value of an annuity: (4.8) Present value of a perpetuity: (4.9) Annuity payment: (4.10) Number of periods: PV=FV× FV 1 = n ( 1+r ) n ( 1+r ) 1/n r= ( FVPV ) n= ln ( FV/ PV ) ln ( 1+r ) −1 [( 1+r )n −1 ] FV=PMT× r [1−1 / ( 1+r )n ] PV=PMT× PV= r PMT r PMT= FV = PV [ (1+r )n−1 ] /r [ 1−1/ ( 1+r )n] /r ( ) ( FV×r PV×r ln 1− PMT PMT n= =− ln ( 1+ r ) ln ( 1+r ) ln 1+ APR m (5.1) Periodic interest rate: (5.2) Effective annual rate: (5.4) Fisher effect: ( 1+r )= ( 1+r ) × (1+h) (5.6) Nominal interest rate: r=r ¿ +h+ ( r ¿×h ) (5.11) Nominal interest rate: ¿ r=r +h+dp + mp r= ( EAR= 1+ APR m −1 m ) ¿ 1 ) Introduction to Finance (6.1) Formula Sheet Bond value: 1 +coupon × bond price= par value × n ( 1+r ) 1− 1 ( 1+r )n r 1 n ( 1+r ) (6.2) Zero-coupon bond value: (7.2) Value of preferred stock: (7.5) Value of common stock (infinite horizon): pric e 0= Di v 0 × (1+ g ) r−g (7.6) Value of common stock (infinite horizon): pric e 0= Div 1 r−g (7.8) Value of common stock (finite horizon): price 0= (7.9) Expected rate of return for common stock: r= Div 0 × ( 1+g ) +g price 0 (7.10) Expected rate of return for preferred stock: r= dividend price (8.1) Profit: profit =ending value+ distributions −original cost (8.2) Return: (8.3) Holding period return: (8.4) Simple annual return: (8.5) Effective annual rate: (8.6) Variance: bond price= par value × price= dividend r pricen (1+r ) return= HPR= n + [ ( )] Div 0 × ( 1+g) 1+g × 1− r −g 1+r n loss profit or orginal cost original cost profit/ ( loss ) original cost APR= HPR n HPR = profit cost variance ( X) = ∑ ( X i−average ) 2=σ 2 n−1 √ variance= √ σ 2=σ (8.7) Standard deviation: standard deviation= (8.8) Expected payoff: expected payoff=∑ payof f i ×probabilit y i (8.9) Variance: σ 2 =∑ (payoff i −expected payoff ¿ (8.10) Portfolio beta: n β p=∑ wi ×β i i=1 2 )2 ׿ probability i Introduction to Finance (8.11) CAPM: (9.1) Net present value: (9.2) Equivalent annual annuity: (9.3) Internal rate of return: (9.4) Profitability index: (11.1) Net present value: Formula Sheet E (r i ) =r f + [E ( r m )−r f ]×β i CF1 CF 2 CF 3 CF n + + +. ..+ ( 1+ r )1 ( 1+r )2 ( 1+r )3 (1+r )n NPV=−CF0 + EAA= NPV PVIFA $ 0=−CF 0 + PI= CF1 CF2 CF 3 CF n + + +...+ ( 1+r ) 1 (1+r )2 ( 1+r )3 (1+r ) n present value of benefits present value of costs n NPV=−investment + ∑ t=1 (11.2) cash flow t (1+WACC)t Cost of debt: 1 +coupon × net price= par value × n ( 1+R d ) (11.3) Net price of preferred stock: (11.4) Cost of preferred stock: (11.5) Cost of equity: net price= R ps= 1− 1 (1+R d ) n Rd dividend R ps dividend price Re =E ( r i )=r f + [ E (r m ) −r f ] ×β i r (¿¿ i)=r f + β( E ( r m )−r f ) Re =E ¿ (11.6) Cost of retained earnings: Re = Div 0 × ( 1+ g ) P0 +g Di v 0 × ( 1+ g) +g P0 × ( 1−F ) (11.7) Cost of new equity: (11.8) After-tax cost of debt: after-tax cost of debt=R d × ( 1−T c ) (11.9) Weighted average cost of capital: WACC adj = Re = 3 E PS D ×Re + ×R ps+ ×Rd × ( 1−T c ) V V V