Corporate Finance formula

Corporate Finance formula Time Value of Money Formula For:

Annual Compounding

Compounded (m) Times per Year

nm

1

Future Value of a Lump Sum. ( FVIFi,n )

F V = P V ( 1 + i )n

2

Present Value of a Lump Sum. ( PVIFi,n )

-n

3

Future Value of an Ordinary Annuity ( FVIFAi,n )

⎡ ( 1 + i )n - 1 ⎤ FVA = PMT ⎢ ⎥ i ⎣ ⎦

⎡ (1 + (i / m) )nm − 1⎤ FVA = PMT ⎢ ⎥ i/m ⎣ ⎦

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 )

⎡1 - ( 1 + i )- n ⎤ PVA = PMT ⎢ ⎥ i ⎣ ⎦

⎡1 - ( 1 + (i / m) )- nm ⎤ PVA = PMT ⎢ ⎥ i/m ⎣ ⎦

6

Present Value Annuity Due

PV Annuity Due = PVA*(1+ i )

PV Annuity Due = PVA*(1+ ieffective )

7

Present Value of a Perpetuity.

PVperpetuity =

8

Continuous growing perpetuity

PV=PMT /(i-g)

9

Effective Annual Rate given the APR.

EAR = APR

PV = FV ( 1 + i )

PMT i

i ⎞ ⎛ PV = FV ⎜1 + ⎟ ⎝ m⎠

PVperpetuity =

FV = PV( )in - nm

11

Rate of return

12

Current yield

13

Real and nominal rate of return

14

Expected return

)

-in

i ⎞ ⎛ EAR = ⎜ 1 + ⎟ - 1 m⎠ ⎝ PV = PV (coupons) + PV (face value)

EAR =

e

Bond price

PV = FV(

PMT [(1 + i )1/ m − 1] m

10

e

i ⎞ ⎛ FV = PV ⎜1 + ⎟ ⎝ m⎠

Continuous Compounding

e

N u m b e r

i

-1

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

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

g = ROE X plowback ratio

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

42

Fama-French three-factor model

Return = α + b1(rfactor1) + b2(rfactor2) + b3(rfactor3) + …+ noise

r- rf =bmarket(rmarket factor)+bsize(rsize factor)+ bbook-to-market(r book-to-market factor)

i = the nominal or Annual Percentage Rate m = the number of compounding periods per year ln = the natural logarithm, the logarithm to the base e PMT = the periodic payment or cash flow g = continuous growth rate

n = the number of periods EAR = the Effective Annual Rate e = the base of the natural logarithm ≈ 2.71828 Perpetuity = an infinite annuity DIV=dividend

EPS= earns per share

P0= current price

NPV= net present value

R = return

= mean of x Rf risk free return

Rm market portfolio return ρ12 correlation between asset 1 and 2