This document provides definitions and formulas for various corporate finance and portfolio management, derivatives, alternative investments, equity and fixed income concepts. Some of the key concepts defined include net present value, internal rate of return, weighted average cost of capital, capital asset pricing model, dividend discount model, bond yields, option pricing, and financial statement ratios such as return on equity, profit margins, and liquidity ratios.

1. Corporate Finance and Portfolio management
1. Net Present Value n
n
2
2
1
1
0
r)(1
CF
......
r)(1
CF
r)(1
CF
CFNPV






Invest if : NPV > 0 Do not invest if: NPV< 0
2. Internal Rate of Return 0
IRR)(1
CFn
0t
t
t



Invest if: IRR > r Do not invest if: IRR< r
3. Average Accounting Rate of Return (AAR)=
book valueAverage
incomenetAverage
4. Profitability Index PI=
InvesmentInitial
NPV
1
InvesmentsInitial
flowscashfutureofPV

Invest if: PI > 1.0 Do not invest if: PI< 1.0
5. Cost of Capital eeppdd rwrwt)(1rw(WACC) 
where wd = target debt proportion in total capital
rd = the before-tax marginal tax rate t = the company’s marginal tax rate
wp = target preferred stock proportion in total capital
rp = the marginal cost of preferred stock re = the marginal cost of equity
we = target common stock proportion in total capital
6. Capital Asses Pricing Model Approach   FMiFi RREβR)E(R 
where
β I = the return correlation of stock i to changes in the market return
E(RM) = the expected return on the market E(RM)-RF = the expected market risk premium
7. Dividend Discount Model Approach V0 =
   
......
r1
D
r1
D
e
2
e
1




where
V0 = the intrinsic value of a share Dt = the share’s dividend at the end of period t
re = the cost of equity
8.
gr
D
P
e 
 1
0
9. g
P
D
re 
0
1

2. 10.




















E
D
t)(11
1
ββ equityasset
11. Country equity premium= Sovereign yield spread


















currencymarkettdevelopmentheof
termsinmarketbondsoverignthe
ofdevationstandardAnnualized
indexequityof
deviationstandardAnnualized
12. The cost of preferred stock is the preferred stock dividend divided by the current
preferred stock price :
p
p
p
P
D
r 
13. We can estimate the growth rate in the dividend discount
model by using published forecasts of analysts or by the sustainable growth rate:
14. Current Ratio =
abilitiesCurrent li
sestsCurrent as
15. Quick Ratio =
abilitiesCurrent li
ceivablesntsle invesmem marketabShort-terCash Re
16. Accounts receivable turnover =
ceivablesAverage re
esCredit Sal
17. Inventory turnover =
ventoryAverage in
ods soldCost of go
18. Number of days of receivables =
on credity's salesAverage da
eceiveableAccounts r
=
365redit /Sales on c
eceivableAccounts r
19. No. of days of inventory =
soldt of goodsy'sAverage da
Inventory
cos
=
365ods sold /Cost of go
Inventory
20. Operating cycle = Number of days of inventory + Number of days of receivables
21. Net operating cycle = Number of days of inventory + Number of days of receivables - Number
of days of payables
ROE
EPS
D
1g 







3. 22. Money Market yield = 











maturitytodaysofNumber
360
pricePurchase
pricePurchase-valueFace
23. Bond Market yield = 











maturitytodaysofNumber
365
pricePurchase
pricePurchase-valueFace
24. Discount- basis yield = 











maturitytodaysofNumber
360
valueFace
pricePurchase-valueFace
25. Cost of trade credit = 1
1
1 perioddiscountbeyond
daysofNumber
365







 











Discount
Discount
26. Return on equity =
equityrs'shareholdeAverage
assetstotalAverage
assetstotalAverage
Revenues
Revenues
incomeNet
equityrs'shareholdeAverage
incomeNet


27. Standard Deviation = 

n
1i
i
2
ii
2
P)]E(R[Rσ
28. rij=
ji
ijCov

where rij= the correlation coefficient of returns
i = the standard deviation of Rit j = the standard deviation of Rjt
29. 212,121
2
2
2
2
2
1
2
1 2  rwwwwport 
Derivatives and Alternative Investments
1. FRA payoff formula (from the perspective of the party going )
Notional Principal =
 


























360
rateunderlyinginDays
xpriationaterateUnderlying1
360
rateunderlyinginDays
ratecontractForwardexpirationatrategUnderliyin
2. Minimum and Maximum Values of Options
Option Minimum value Maximum Value
European call 00 c 00 Sc 
American call 00 C 00 SC 
European put 00 p T
rXp )1/(0 
American put 00 P XP 0

4. 3. Put-call parity = c0 + X/ (1+r)T
=p0 +s0
4. Appraisal price =
ratecapMarket
NOI
Equity and Fixed income
1. Dividend Discount Model (DDM)
       









k
D
k
D
k
D
k
D
1
......
111
Vj 3
3
2
21
  

n
t
t
t
k
D
1 1
2. Present value of Free Cash Flows to Equity
  

n
t
t
j
j
k
FCFE
V
1 1
2. Justified/ Fundamental (P/E)
gk
ED
E
Pi

 11
1
/
4. (Shareholders’ equity)- (Total value of equity claims that are senior to common stock) = Common
shareholders’ equity
5. (Common shareholders’ equity)/ (Number of common stock shares outstanding) = Book value per
share
6. Coupon rate = Yield required by market Price = Par value
Coupon rate < Yield required by market  Price < Par value (discount)
Coupon rate > Yield required by market  Price > Par value (premium)
7. Price of callable bond = Price of option-free bond – Price of embedded call option
8. Price of putable bond = Price of option- free bond + Price of embedded put option
9. Taxable-equivalent yield =
ratetaxMarginal-1
ldexempt yieTax 
10. Present value of an annuity =  















i
i1
1
1
paymentAnnuity
periodsofno.
11. Valuing a Zero- Coupon Bond 2
1 
 rsno. of yea
i
alueMaturity v
Where i is the semiannual discount rate
12. Current yield =
Price
interestcoupandollarAnnual

5. 13. Yield on an annual-pay basis














 1
2
basisequivalent-bondaonYield
1
2
14. Spread for life =
 














Price
100
marginQuoted
Maturity
Price100100
15. Z-spread = OAS + Option cost
16.
 
 
1
1
1
1











t
m
m
tm
tm
mt
z
z
f
17. Effective duration =
  decimalinyieldinChangepriceInitial2
riseyieldsifPrice-declineyieldsifPrice
18. Macaulay duration =
  







 Pricek
PVCFn.....PVCF2PVCF1
Yield/k1
1 n21
19. Modified duration=
 Yield/k1
durationMacaulay

20. Portfolio Duration = kk DwDwDwDw  .....332211
Financial Reporting and Analysis
1. Assets = Liabilities + Owners’ equity Revenue – Expenses = Net income (loss)
2. Basic EPS
goutstandinsharesofnumberaverageWeighted
dividendsPreferred-incomeNet

3. Diluted EPS =
ersioned at convbeen issucould have
atshares thNew commondingouts
resber of shaverage numWeighted a
videndseferred die debtconvertibl
rest onAfter taxNet income









tan
Pr
int
4. Diluted EPS =
 
excersiceuponreceivedcashwith
purchasedbeenhavecouldthatShares
excersiceoptionatissuedbeenhavecould
thatsharesNewgoutstandin
sharesofnumberaverageWeighted
dividendsPreferredNetincome




6. 5. Net profit margin =
Revenue
incomeNet
6. Gross profit margin=
Revenue
profitGross
7. FCFF= NI + NCC + Int (1-Tax rate)- FCInv – WCInv
8. FCFF = CFO + Int (1-Tax rate) - FCInv
9. FCFF = CFO- FCInv + Net borrowing – Net debt repayment
10. Definitions of commonly Used Activity Ratios
Activity Ratios Numerator Denominator
Inventory Turnover Cost of goods sold Average inventory
Days of inventory on hand (DOH) Number of days in period Inventory turnover
Receivables turnover Revenue Average receivables
Days of sales outstanding(DSO) Number of days in period Receivables turnover
Payables turnover Purchases Average trade payables
Number of days payables Number of days in period Payables turnover
Working capital turnover Revenue Average working capital
Fixed asset turnover Revenue Average net fixed assets
Total asset turnover Revenue Average total assets
11. Definitions of commonly Used Liquidity Ratios
Liquidity Ratios Numerator Denominator
Current ratio Current assets Current liabilities
Quick ratio Cash + Short-term marketable investments + Receivables Current liabilities
Cash ratio Cash + Short-term marketable investments Current liabilities
Defensive
interval ratio
Cash + Short-term marketable investments + Receivables Daily cash
expenditures
Additional Liquidity Measures
Cash Conversion cycle (net
operating cycle)
DOH + DSO – Number of days of payables
12. Definitions of commonly Used Solvency Ratios
Solvency Ratios Numerator Denominator
Debt Ratios
Debt-to-assets ratioa
Total debtb
Total assets
Debt-to-capital ratio Total debtb
Total debtb
+ Total shareholders’ equity
Debt-to-equity ratio Total debtb
Total shareholders’ equity
Financial leverage ratio Average total assets Average total equity
Coverage Ratios
Interest coverage EBIT Interest payments
Fixed charge coverage EBIT + Lease payments Interest payments + Lease payments

7. 13. Definitions of commonly Used Profitability Ratios
Profitability Ratios Numerator Denominator
Return on Sales10
Gross profit margin Gross profit Revenue
Operating profit margin Operating income11
Revenue
Pretax margin EBT (earnings before tax but after interest) Revenue
Net profit Income Net Income Revenue
Return on Investment
Operating ROA Operating income Average total assets
ROA Net income Average total assets
Return on total capital EBIT Short and long -term debt and equity
ROE Net income Average total equity
Return on common equity Net income-preferred dividends Average common equity
14. ROE = Net profit margin * Asset turnover * leverage
15. ROE = Tax burden * Interest burden * EBIT margin * Asset turnover * Leverage
Quantitative analysis
1. Population Mean: calculated as
Where there are N members in the population and each observation is Xi i =1, 2, …N.
Sum of all the deviations is zero.
2. Sample Mean: calculated as
3. Weighted Mean: calculated as
4. Geometric Mean: calculated as
Where there are n observations and each observation is Xi.
5. Mean Absolute Deviation: is the average of the data’s absolute deviations from the mean.
6. Population Variance: is the average of the population’s squared deviations from the mean.
The population standard deviation is simply the square root of the population variance.
7. Sample Variance: is the average of the sample data’s squared deviations from the sample mean.
The sample standard deviation is


N
i
iX X
N 1
1



n
i
iX
n
X
1
1


n
i
iiweighted XwX
1
n
n
XXXXG ...321 


n
i
i XX
n
MAD
1
1
 

N
i
iX
N 1
22 1

 
 



n
i
i XX
n
s
1
22
1
1

8. 8. Covariance describes the co-movement between 2 random numbers, given as :
Cov(X1, X2) = σ12
9. Correlation coefficient is a unit-less number, which gives a measure of linear dependence between
two random variables. ρ(X1, X2) = Cov(X1, X2) / σ1σ2
10. Portfolio Expected Return:
E(rp) = wA rA + (1-wA )rB
Portfolio Variance:
OR
11. Coefficient of variation
12. Sharpe measure
13. Addition Rule
Used to Get Compound Probabilities for Union of Events: P(A OR B) = P(A U B) = P(A) + P(B) - P(A ∩ B)
For Mutually Exclusive Events: P(A OR B) = P(A U B) = P(A) + P(B)
14. Sum Rule & Bayes’ Theorem
Out of a group of 100 patients being treated for chronic back trouble, 25% are chosen at random to
receive a new, experimental treatment as opposed to the more usual muscle relaxant-based therapy
which the remaining patients receive. Preliminary studies suggest that the probability of a cure with the
standard treatment is 0.3, while the probability of a cure from the new treatment is 0.6.
15. Discrete Probability Distributions
Probability distribution for a Binomial random variable is given by:
16. Normal Distribution Random Variable
General Normal random variable X ~ N (μ, σ2
)
X can be standardized to a Standard Normal random variable.
Resulting variable has mean zero and variance equal to 1.
YX
YX
XYEYXCov
YXEYXCov




)(),(
)])([(),(
     BAAABAAAr rrCovwwwwp
,121 22222
 
    BAABAABAAAr wwwwp
  121 22222
X
s
CV 
p
fp rr
SM

)( 

)()/()()/()()()( ccc
APABPAPABPBAPBAPBP  
)()/()()/(
)()/(
)/( cc
APABPAPABP
APABP
BAP


xnx
x
n
ppCxXP 
 )1()(



X
Z

9. 17. Confidence Intervals
The standard error of the mean (sx) is given by:
18. Errors in Estimation
Type I and Type II Errors
Type I error occurs if the null hypothesis is rejected when it is true
Type II error occurs if the null hypothesis is not rejected when it is false
Significance Level
-> Significance level
The upper-bound probability of a Type I error
1 -  ->confidence level
The complement of significance level
19. The sample variance for a pooled estimater is given as
20. Hypothesis Tests for Variances
n
s
sx 
2
)1()1(
21
2
22
2
112



nn
snsn
s