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Formula Sheet...

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Formula sheet Present value calculations:

Future Value: FVn  C0 (1 r )

n

Present Value of Single cash flow and Discount Factor: 1 (1  r)n Cn PV0  n  DFn  Cn (1 r ) DFn 

Constant Perpetuity:

PV0 =

C1 r

Perpetuity with constant growth rate:

PV0 =

C1 rg

Constant Annuity: PV0 

C1  1  1  r  (1  r) N 

Annuity with constant growth rate: N C1   1  g   PV0  1     r  g   1 r  

Notations: Ct – cash flow at time t, r – discount rate, N – number of periods, g – growth rate

Interest rates Equivalent Annual Rate and Annual Percentage Rate: k

APR   1 EAR   1 k  

where k is the compounding frequency (number of periods) within the year. Capital budgeting: NPV formula:

NPV  CF0 

CF1 CF2 CFN   ...  2 (1 r) N (1 r ) (1 r )

Bond valuation: Coupon payment:

Coupon =

Coupon rate  Face value No. of coupon payments per year

Price of N-period zero-coupon bond:

P

FV (1+ YTMN ) N

Yield to Maturity: 1  

 FV  N   YTM N   1   P  Price of a coupon bond: P

 FV Coupon  1  1 N  N YTM  (1  YTM )  (1 YTM )

Notations: FV – face value, YTM – yield to maturity, N – number of periods

Stock valuation:

Stock price from Dividend Discount Model:  Div1 Div2 DivN  PN Divt     ...  2 N t (1 rE ) (1 rE ) (1 rE ) t 1 (1 rE )

P0 

Gordon Growth Model: Constant dividend growth: Div 0 (1  g ) Div1  rE  g (rE - g )

P0 

Dividend Discount Model with constant long-term growth: Div1 Div 2 Div N Div N 1 1   ...  N  N  2 (1  rE ) (1  rE ) (1 rE ) (1 rE ) ( rE - g) Div1 Div 2 Div N 1 (1  g )Div N    ...    N N 2 (1  rE ) (1  rE ) (1 rE ) (1 rE ) (rE - g )

P0 

Enterprise Value: Enterprise Value = Market Value of Equity + Debt Value - Cash

Discounted Free Cash Flow Model:

EV0  PV(Future Free Cash Flow) 

FCF1 FCF 2 FCFN FCFN 1 1 ...   N  N  2  (1  rWACC ) (1  rWACC ) (1  rWACC ) (1  rWACC ) (rWACC - g FCF )



FCF1 FCF 2 FCFN 1 (1  g FCF )FCFN   ...    N N 2 (1  rWACC ) (1  rWACC ) (1  rWACC ) (1  rWACC ) (rWACC - g FCF )

Stock price from discounted free cash flow model: P0  

EV0 + Cash 0 - Debt 0 Shares Outstanding0 PV(Future Free Cash Flow) + Cash 0 - Debt 0 Shares Outstanding 0

Notations: EVt – Enterprise Value at time t, Divt – Dividend at time t, FCFt – Free Cash Flow at time t, g – growth rate, rE – Expected Return on Equity, rWACC – Weighted Average Cost of Capital, N – number of periods

Risk and Return: Average annual return: R 

1 T

 R1



 R2 



1 T R T t 1 t

Variance of realized return: Var (R ) 

1 T  1

T

 R

t  1

t

 R

2

Correlation between two stocks i and j: Corr (R i,R j) 

Cov (Ri ,Rj ) SD (R i ) SD (R j )

Variance of a 2-stock portfolio: 2 2 Var (R P )  x i Var (Ri )  x jVar (R j )  2x ix jCov (R i ,R j )

CAPM: Mkt E[RPortfolio ]  r f  Portfolio (E[R Mkt]  r f )...