Corporate Finance formula

N u m b e r

Time Value of

Money Formula For:

Annual Compounding Compounded (m) Times per Year Continuous Compounding

1 Future Value of a Lump Sum. ( FVIFi,n ) ) +1 ( VP = VF ni ⎟

⎠⎞

⎜⎝⎛

mi nm

+1PV=FV )PV(=FV ine

2 Present Value of a Lump Sum. ( PVIFi,n ) ) +1 ( FV = PV -ni ⎟

⎠⎞

⎜⎝⎛

mi nm

+1 FV = PV-

) FV( =PV -ine

3 Future Value of an Ordinary Annuity ( FVIFAi,n )

⎥⎦

⎤⎢⎣

⎡ 1 -)+1 ( =FVA

iiPMT

n ( )⎥⎦

⎤⎢⎣

⎡ −+=

mimiPMT

nm

/1)/(1 FVA

4 Future Value Annuity Due FV Annuity Due = FVA*(1+ i ) FV Annuity Due = FVA*(1+ ieffective )

5 Present Value of an Ordinary Annuity. ( PVIFAi,n )

⎥⎦

⎤⎢⎣

⎡i

iPMTn) +1 (-1 =PVA

-

( )

⎥⎦

⎤⎢⎣

⎡mi

miPMTnm

/ )/( +1 - 1 =PVA

-

6 Present Value Annuity Due PV Annuity Due = PVA*(1+ i ) PV Annuity Due = PVA*(1+ ieffective )

7 Present Value of a Perpetuity. i

PMT= perpetuityPV

]1)1[(PV /1 perpetuity

−+= mi

PMT

8 Continuous growing perpetuity PV=PMT /(i-g)

9 Effective Annual Rate given the APR. APR = EAR 1 -+1 = EAR ⎟

⎠⎞

⎜⎝⎛

mi m

1 - = EAR e i

10 Bond price PV = PV (coupons) + PV (face value)

11 Rate of return

12 Current yield

13 Real and nominal rate of return

14 Expected return

15 Dividend Yield

16 Constant Growth Dividend Discount Model

17 Dividend Discounted Model

18 Equivalent annual cost (EAC)

19 Estimating Expected Rates of Return with Constant Growth

Dividend

20 Growth rate g = ROE X plowback ratio

21 Return on Equity

22 Present Value of Growth Opportunity

23 P/E ratio P/E = P0/ EPS

24 NPV PV – (required investment)

25 NPV(A+B) NPV (A+B) = NPV (A) + NPV (B)

26 Percentage return

27 Variance σ2

28 Standard deviation σ

29 General Cost of capital

30 Cost of capital with only Debt and Equity

31 After-tax Cost of Capital: WACC

32 Covariance of asset 1 and asset 2

33 Two assets portfolio variance

34 N assets portfolio variance

35 Beta for one asset i : βi

36 General portfolio β

37 Portfolio β with only Debt and Equity

38 CAPM model r = rf + β (rm – rf ) where rm is the market return and rf is the risk free rate

39 Risk premium ( r - rf ) r - rf = β (rm – rf ) where rm is the market return and rf is the risk free rate

40 Expected return on preferred stock

41 Arbitrage Pricing Theory Return = α + b1(rfactor1) + b2(rfactor2) + b3(rfactor3) + …+ noise

42 Fama-French three-factor model r- rf =bmarket(rmarket factor)+bsize(rsize factor)+ bbook-to-market(r book-to-market factor)

i = the nominal or Annual Percentage Rate n = the number of periods

m = the number of compounding periods per year EAR = the Effective Annual Rate ln = the natural logarithm, the logarithm to the base e e = the base of the natural logarithm ≈ 2.71828

PMT = the periodic payment or cash flow Perpetuity = an infinite annuity g = continuous growth rate DIV=dividend

EPS= earns per share P0= current price

NPV= net present value R = return

= mean of x Rm market portfolio return Rf risk free return ρ12 correlation between asset 1 and 2