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 
 DFn  Cn
(1  r ) n
DFn 
Constant Perpetuity:
PV0 =
C1
r
Perpetuity with constant growth rate:
PV0 =
C1
rg
Present Value of Constant Annuity:
PV0 
C1 
1 
1 

r  (1  r ) N 
Future Value of a Constant Annuity:
FVN 
C1
(1  r ) N  1
r 
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 
EAR  1 
 1
k 

where k is the compounding frequency (number of periods) within the year.
Equivalent n-month rate:
Equivalent n-month rate  (1  r )n/12 1
where r is the EAR in annualised terms.
Capital budgeting:
NPV formula:
NPV  CF0 
CFN
CF1
CF2

 ... 
2
(1  r ) (1  r )
(1  r ) N
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+YTM N ) N
Yield to Maturity:
1
 
 FV  N 
YTM N  
 1
 P 
Price of a coupon bond:
P
Coupon 
1
1 
YTM  (1  YTM ) N

FV

N
 (1  YTM )
Notations: FV – face value, YTM – yield to maturity, N – number of periods
Stock valuation:
Gordon Growth Model: Constant dividend growth:
Div0 (1  g )
Div1

rE  g
(rE - g )
P0 
Dividend Discount Model with constant long-term growth:
P0 

DivN
DivN 1
Div1
Div2
1

 ... 


2
N
N
(1  rE ) (1  rE )
(1  rE )
(1  rE )
(rE - g )
DivN
(1  g )DivN
Div1
Div2
1

 ... 


2
N
N
(1  rE ) (1  rE )
(1  rE )
(1  rE )
(rE - g )
Enterprise Value:
Enterprise Value = Market Value of Equity + Debt Value - Cash
Discounted Free Cash Flow Model:
EV0  PV(Future Free Cash Flow)

FCFN
FCFN 1
FCF1
FCF2
1

 ... 


2
N
N
(1  rWACC ) (1  rWACC )
(1  rWACC )
(1  rWACC )
( rWACC - g FCF )

FCFN
(1  g FCF ) FCFN
FCF1
FCF2
1

 ... 


2
N
N
(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 Outstanding 0
PV(Future Free Cash Flow) + Cash 0 - Debt 0
Shares Outstanding 0
Earnings growth rate:
Earnings growth rate  Retention Rate  Return on New Investments
 (1  Dividend Payout Ratio)  Return on New Investments
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  L  RT  
1 T
 Rt
T t 1
Variance of realized return (unbiased estimator):
Var (R) 
1
T  1
T
 R
t 1
t
 R
2
Standard error:
Standard Error = Standard deviation /√𝑇
Correlation between two stocks i and j:
Corr (Ri ,R j ) 
Cov(Ri ,R j )
SD(Ri ) SD(R j )
Variance of a 2-stock portfolio:
Var (RP )  xi2Var (Ri )  x 2jVar (R j )  2 xi x j Cov(Ri ,R j )
Beta of investment i with portfolio P:
𝛽𝑖𝑃 =
𝑆𝐷(𝑅𝑖 ) × 𝐶𝑜𝑟𝑟(𝑅𝑖 , 𝑅𝑃 )
𝑆𝐷(𝑅𝑝 )
CAPM:
Mkt
E[RPortfolio ]  rf   Portfolio
(E[RMkt ]  rf )