CFA l 1 Formula Sheet December 2015

7/24/2019 CFA l 1 Formula Sheet December 2015

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FinQuiz Formula Sheet CFA Level I 2015

• r MM = (r BD) !

!HbI "HxTI OQ GyI *(IH7T(a zMxx

$T(byH7I $(MbI

• r MM =

pqd (rs

pqd/ G (rs (Rule: r MM>

r BD

)

10. Bond Equivalent Yield = BEY =

Semiannual Yield ! 2

Reading 7: Statistical Concepts & Market

Returns

1. Range = Max Value – Min Value

2. Class Interval = i ={/B

| where

• i = class interval

•

H = highest value

• L = lowest value, k = No. of classes.

3. Absolute Frequency = Actual No of

Observations (obvs) in a given class

interval

4. Relative Frequency =K}7OxTGI !(I~TILba

*OGHx 1O OQ V}•7

5.

Cumulative Absolute Frequency = Add upthe Absolute Frequencies

6.

Cumulative Relative Frequency = Add up

the Relative Frequencies

7. Arithmetic Mean =FT. OQ O}•7 ML JHGH}H7I

1OPOQ O}•7 ML GyI JHGH}H7I

8. Median = Middle No (when observations

are arranged in ascending/descending

order)

•

For Even no of obvs locate

median at mean of

L

l and€L'l

l‚X9>:>X=9

• For Odd no. of obvs locate

median atL'&

l position

9.

Mode = obvs that occurs most frequently

in the distribution

10. Weighted Mean = ƒ„ 8 2M ƒMLM\& =

(w1X1+ w2X2+….+ wnXn)

11. Geometric Mean = GM = ƒ& ƒl m ƒLn

with Xi"0 for i = 1,2,…n.

12. Harmonic Mean = H.M = ƒ{ 8L

%

…†

n†‡%

13.

Population Mean = µ =ˆ†

n†

1 where N is the

number of observations in the entire

population and X i is the ith observation

14. Sample Mean = ƒ 8ˆ†

n†

L where n =

number of observation in the sample

15. Measures of Location:

• Quartiles =

hM7G(M}TGMOL

‰

• Quintiles =

hM7G(M}TGMOL

v

• Deciles =

hM7G(M}TGMOL

&d,

• Position of a percentile = Ly =

= , + a

&dd

16.

Mean Absolute Deviation = MAD =

[̂/ˆn†‡%

L

17. Population Var = !2 =

ˆ†/Š ‹#†‡%

1

18. Population S.D = Œl=ˆ†/Š ‹#

†‡%

1

19. Sample Var = s2 =ˆ†/ˆ ‹n

†‡%

L/&

20.

Sample S.D = s = ˆ†/ˆ ‹n

†‡%L/&

21. Semi-var =ˆ†/ˆ ‹

L/&!O( Hxx ˆ†ˆ

22.

Semi-deviation (Semi S.D) =

94Ž>;5>;=Y4 =ˆ†/ˆ ‹

L/&!O( Hxx ˆ†ˆ

23. Target Semi-var =ˆ†/z ‹

L/&!O( Hxx ̂ †z

where B = Target Value

24. Target Semi-Deviation =

:;54: 94Ž>;5>;=Y4 =

ˆ†/z ‹

L/&!O( Hxx ˆ†z




25. Coefficient of Variation = CV =F

ˆ

where s= sample S.D and ƒ = sample

mean

26.

Sharpe Ratio = )IHL $O(GQOxMO N/)IHL NQ NFPh OQ $O(GQOxMO N

27.

Excess Kurtosis = Kurtosis – 3

28. Geometric Mean R #

‘5>:3Ž4:>Y ]4;= Z ?"H(MHLbI OQ N

l

Reading 8: Probability Concepts

1.

Empirical Prob of an event E = P(E) =$(O} OQ I•ILG ’

*OGHx $(O}

2. Odds for event E =$(O} OQ ’

&/$(O} OQ ’

3. Odds against event E =&/$(O} OQ ’

$(O} OQ ’

4. Conditional Prob of A given that B has

occurred = P(A“B) =$ Kz

$ z" P(B) $ 0.

5. Multiplication Rule (Joint probability that

both events will happen):

P(A and B) = P(AB) = P(A“B) ! P(B)

P(B and A) = P(BA) = P(B“A) ! P(A)

6. Addition Rule (Prob that event A or B will

occur):

P(A or B) = P(A) + P(B) – P(AB)

P(A or B) = P(A) + P(B) (when events are

mutually exclusive because P(AB) = 0)

7.

Independent Events:

• Two events are independent if:

P(B“A) = P(B) or if P(A“B) =

P(A)

• Multiplication Rule for two

independent events = P(A & B) =

P(AB) = P(A)! P(B)

• Multiplication Rule for three

independent events = P(A and B

and C) = P(ABC) = P(A) ! P(B)

! P(C)

8.

Complement Rule (for an event S) = P(S)

+ P(SC) = 1 (where S

C is the event not S)

9.

Total Probability Rule:

P(A) = P(AS) + P(ASC) = P(A“S)!P(S) +

P(A“SC)!P(SC)

P(A) = P(AS1) + P(AS2) +….+ P(ASn) =

P(A“S1)!P(S1) + P(A“S2)!P(S2)… +

P(A“Sn)!P(Sn)

(where S1, S2, …,Sn are mutually exclusive

and exhaustive scenarios)

10. Expected R = E(wiR i) = wiE(R i)

11. Cov (R i R j) = ” ZM ? ”ZM Z ? ”Z

Cov (R i R j) = Cov (R j R i)

Cov (R, R) = !2 (R)

12. Portfolio Var = !2 (R p) =

2M2iX ZMZL\&

LM\&

!2 (R p) = 2&

lŒl Z& + 2llŒl Zl +

2pl

Œl

Zp + 22&2liX Z&– Zl +22&2piX Z&– Zp +

22l2piX Zl– Zp

13.

Standard Deviation (S.D) = Œl Z$

14. Correlation (b/w two random variables R i,

R j) = — ZMZ 8 RO• N†N˜

™N†0™N˜

15.

Bayes’ Formula =

@ ”4=:“š42 ›=eX5Ž;:>X= 8

$ 1I„ fLQO(.HGMOL“’•ILG

$ 1I„ fLQO(.HGMOL 0

@ @5>X5 ‚5XœP Xe ”4=:

16. Multiplication Rule of Counting = n

factorial = = = n (n-1)(n-2)(n-3)…1.

17. Multinomial Formula (General formula for

labeling problem) = L

L%L‹mLž

18.

Combination Formula (Binomial Formula)

= i(L =

L

( =

L

L/( (

where n = total no. of objects and r = no.

of objects selected.

19. Permutation = @(L =

L

L/(




Reading 9: Common Probability Distributions

1. Probability Function (for a binomial

random variable) p(x) = p(X=x) =L

Ÿ ‚

Ÿ

+ ? ‚

L/Ÿ

= 8

L

L/Ÿ Ÿ ‚

Ÿ

+ ?‚ L/Ÿ (for x = 0,1,2….n)

• x = success out of n trials

• n-x = failures out of n trials

•

p = probability of success

• 1-p = probability of failure

• n = no of trials.

2. Probability Density Function (pdf) = f(x)

=&

}/H

k X:3452>94

eX5 ; ¡ œ =

F(x) =Ÿ/H

}/H eX5 ; ¢ ¡ ¢ œ(cumulative

distribution)

3. Normal Density Funct = e ¡ 8&

™ l£4¡‚

/€Ÿ/Š‹

l™‹ ¤¥¦ ? § ¢ ¡ ¢ , §

4. Estimations by using Normal Distribution:

•

Approximately 50% of all obsv fall in

the interval ¨ ©l

pŒ

• Approx 68% of all obvs fall in the

interval ¨ © Œ


interval ¨ ©ªŒ


interval ¨ ©«Œ

• More precise intervals for 95% of the

obvs are ¨ © +P¬Œ and for 99% of the

observations are ¨ © ªP®¯ŒP

5. Z-Score (how many S.Ds away from the

mean the point x lies) ° 8

9:;=<;5< =X5Ž;± 5;=<XŽ ;5>;œ±4 8

ˆ/Š

™ (when X is normally distributed)

6. Roy’s Safety-Frist Criterion = SF Ratio =’ NE /N²

™E

7. Sharpe Ratio = =’ NE /N³

™E

8. Value at Risk = VAR = Minimum $ loss

expected over a specified period at a

specified prob level.

9. Mean (µL) of a lognormal random variable

= exp (µ + 0.50%2)

10. Variance (%L2) of a lognormal random

variable = exp (2µ+ %2) ! [exp (%2) – 1].

11.

Lognormal Price = ST = S0exp (r 0,T)

Where, exp = e and r 0,t = Continuously

compounded return from 0 to T

12. Price relative = End price / Beg price =

St+1/ St=1 + R t, t+1

where,

Rt, t+1 = holding period return on the stock

from t to t + 1.

13. Continuously compounded return

associated with a holding period from t to t

+ 1:

r t, t+1= ln(1 + holding period return) or

r t, t+1 = ln(price relative) = ln (S t+1 / St) = ln

(1 + R t,t+1)

14. Continuously compounded return

associated with a holding period from 0 to

T:

r 0,T= ln (ST / S0) or 5d–* 8 5*/&–* ,5*/l–*/& , ´ , 5d–&

Where,

r T-I, T = One-period continuously

compounded return

15. When one-period continuously

compounded returns (i.e. r 0,1) are IID

random variables.

” 5d–* 8 ” 5*/&–* , ” 5*/l–*/& ,

´ , ” 5d–& 8 ¨ ̂And

A;5>;=Y4 8 Œl 5d–* 8 Œ l^

S.D. = % (r 0,T) = % ^




16. Annualized volatility = sample S.D. of

one period continuously compounded

returns ! ^

Reading 10: Sampling and Estimation

1.

Var of the distribution of the sample mean

=™‹

L

2. S.D of the distribution of the sample mean

=™‹

L

3. Standard Error of the sample mean:

• When the population S.D (!) is known

= Œˆ 8

™

L • When the population S.D (!) is not

known = 9ˆ 87

L where s = sample

S.D estimate = 9;Ž‚±4 ;5>;=Y4 8

9l 23454 9l =ˆ†/ˆ ‹n

†‡%

L/&

4. Finite Population Correction Factor = fpc

=1/L

1/& where N= population size

5.

New Adjusted Estimate of Standard Error

= (Old estimated standard error ! fpc)

6.

Construction of Confidence Interval (CI) =

Point estimate ± (Reliability factor !

Standard error)

• CI for normally distributed population

with known variance = ƒ © °Hwl™

L

• CI for normally distributed population

with unknown variance = ƒ © °HwlF

L

where S = sample S.D.

7. Student’s t distribution

µ = ƒ © :HwlF

L

8. Z-ratio =n

X z

!

µ "

=

9. t-ratio =

n s

X t

µ !

=

Reading 11: Hypothesis Testing

1. Test Statistic =µ¶·¸¹ºµ»¶»¼½»¼¾ / ¿À¸Á»Âº½¼ÃºÄÅ¶¹ÆºÁÇ¸Á¸ ¶̧È¶·º»ºÈ

½»¶ÉÄ¶ÈÄºÈÈÁÈÁÇ½¶·¸¹º½»¶»¼½»¼¾ Ê

*when Pop S.D is unknown, the standard

error of sample statistic is given by Ëˆ 8

F

L

*when Pop S.D is known, the standard

error of sample statistic is given by Œˆ 8

™

L

2. Power of Test = 1-Prob of Type II Error

3. ° 8ˆ/Šg

Ì

n

(when sample size is large or

small but pop S.D is known)

4. ° 8

ˆ/Šg

-n (when sample size is large but

pop S.D is unknown where s is sample

S.D)

5. :L/& 8ˆ/Šg

-

n

(when sample size is large or

small and pop S.D is unknown and

popsampled is normally or approximately

normally distributed)

6. Test Statistic for a test of diff b/wtwo pop

means (normally distributed, pop var

unknown but assumed equal)

t =ˆ%/ ‹̂ / Š%/Š‹

ÍÎ‹

n%'

ÍÎ‹

n‹

%w‹ where ËSl = pooled

estimator of common variance =

L%/& F%‹' L‹/& F‹

‹

L%' L‹/l where <e 8 =& , =l ?

ª.

7. Test Statistic for a test of diff b/w two pop

means (normally distributed, unequal and

unknown pop var)




t =ˆ%/ ‹̂ / Š%/Š‹

Í%‹

n%'

Í‹‹

n‹

%w‹ In this df calculated as

<e 8

Í%‹

n% '

Í‹‹

n‹

‹

Í%

‹

n%

‹

n%'

Í‹

‹

n‹

‹

n‹

8. Test Statistic for a test of mean differences

(normally distributed populations,

unknown population variances)

•

: 8J/ŠÏg

FJ

• sample mean difference = < 8

&

L<M

LM\&

• sample variance = ËJ

l 8J†/J ‹n

†‡%

L/&

• sample S.D = ËJ

l

• sample error of the sample mean

difference = 9J

8FÏ

L

8. Chi Square Test Statistic (for test

concerning the value of a normal

population’s variance) ! l

8 L/& 7‹

™g‹

where = ?+ 8 <e ;=< 9l

89;Ž‚±4 ;5>;=Y4 8

ˆ†/ˆ ‹n†‡%

L/&

9. Chi Square Confidence Interval for

variance

Lower limit = L =L/& F‹

! Ðw‹

‹ and Upper limit

= U =L/& F‹

! %ÑÐw‹

‹

10. F-test (test concerning differences between

variances of two normally distributed

populations) F =F%

‹

F‹‹

Ë&l 8 +9: 9;Ž‚±4 ;5 2>:3 =& Xœ9 Ò Ë&

l

8 ª=< 9;Ž‚±4 ;5 2>:3 =l Xœ9

<e& 8 =& ? + =ÓŽ45;:X5 <e

<el 8 =l ? + <4=XŽ>=;:X5 <e

11. Relation between chi-square and F-

distribution = j 8ˆ%

‹

.

ˆ‹‹

L

where:

•

ƒ&l is one chi-square random variable

with one m degrees of freedom

•

ƒll is another chi-square random

variable with one n degrees of

freedom

12. Spearman Rank Correlation = 57

8 + ? <M

lLM\&

= =l ? +

• For small samples rejection points for

the test based on 57are found using

table.

• For large sample size (e.g. n>30) t-test

can be used to test the hypothesis i.e.

: 8= ? ª &wl57

+ ? 57l &wl

Reading 12: Technical Analysis

1. Relative Strength Analysis =ÔÈ¼¾ºÁÇ¶½½º»

ÔÈ¼¾ºÁÇ»ÂºÕºÉ¾Â·¶ÈÖ×½½º»

2. Price Target for the

•

Head and Shoulders = Neckline –

(Head – Neckline)

• Inverse Head and Shoulders =

Neckline + (Neckline– Head)

3.

Simple Moving Average =ÔØ'ÔÙ'ÔÚmP'ÔÉ

Û

4.

Momentum Oscillator (or Rate of ChangeOscillator ROC):

• Momentum Oscillator Value M = (V-

Vx) 0+kk

(where V = most recent closing price

and Vx = closing price x days ago)

• Alternate Method to calculate M ="

"Ü0+kk

5.

Relative Strength Index = RSI = +kk ?

&dd

&'NF where

RS =ÝS byHLUI7 JT(MLU bOL7MJI(IJ SI(MOJ

hO„L byHLUI7 JT(MLU bOL7MJI(IJ SI(MOJ

6.

Stochastic Oscillator (composed of two

lines - %K and %D):




•

Þß 8 +kkR/B&‰

{&‰/B&‰ where:

C = latest closing price, L14 = lowest

price in last 14 days, H14 is highest

price in last 14 days

•

% D = Average of the last three % K values calculated daily.

7. Put/Call Ratio (Type of Sentiment

Indicators) =ÅÁ¹Æ·ºÁÇÔÆ»à¸»¼ÁÉ½áÈ¶ÄºÄ

ÅÁ¹Æ·ºÁÇâ¶¹¹à¸»¼ÁÉ½áÈ¶ÄºÄ

8. Short Interest Ratio (Type of Sentiment

Indicators) =µÂÁÈ»ãÉ»ºÈº½»

×äºÈ¶åºæ¶¼¹ÀáÈ¶Ä¼ÉåÅÁ¹Æ·º

9. Arms Index or TRIN i.e. Trading Index

(Type of Flow of funds Indicator) =

‘5Ž ›=<4¡ X5 ^Z›š 8

1OPOQ KJ•HL f77TI7 ç1OPOQ hIbxML f77TI7

"OxT.I OQ KJ•HL f77TI7ç"OxT.I OQ hIbxML f77TI7

Reading 13: Demand & Supply Analysis:

Introduction

1.

Slope of the demand curve =è éê ëìéíî

è éê ïðñêòéòó ôîõñêöîö

2. Slope of the supply curve =è éê ëìéíî

è éê ïðñêòéòó ÷ðøøùéîö

3. Consumer Surplus = Value that a

consumer places on units consumed –

Price paid to buy those units

• Area (for calculating Consumer

Surplus) = & (Base ! Height) = & [Qd

! (Price intercept – P1)]

4. Producer Surplus = Total revenue received

from selling a given amount of a good –

Total variable cost of producing that

amount

•

Total revenue = Total quantity sold !

Price per unit

• Area (for calculating Producer

Surplus) = & (Base ! Height) = &

{(Q0) ! (P0 – intercept point on y-

axis**)}

**where supply curve intersects y-axis

5.

Total Surplus = Consumer surplus +

Producer surplus

6.

Total Surplus = Total value to buyers –

Total variable cost

7. Society Welfare =Consumer surplus +

Producer surplus

8.

Own-Price Elasticity of Demand =

!!"

#$$%

&!!"

#$$%

&

'

'=

'

'=

xd

x

x

xd

x

xd

pd

Q

P

P

Q

P

Q E

x

%

%

9. Arc Elasticity of Demand =Þ è éê ïðñêòéòó ôîõñêöîö

Þ è éê ëìéíî

)(

)(

P%

Q%

2121

12

2121

12

P P

P P

QQ

QQ

+

!

+

!

="

"

10. Income Elasticity of Demand =Þ è éê ïðñêòéòó ôîõñêöîö

Þ è éê úêíûõî=

I

I

Q

Q

xd

xd

x

!

!

=

!

!

I%

Q% d

11. Cross Elasticity =Þ èéê ïðñêòéòó ôîõñêöîö ûü ýûûö þ

Þ è éê ëìéíî ûü ýûûö ÿ

Reading 14: Demand & Supply Analysis:

Consumer Demand

1. Marginal Utility =è éê !ûòñù "òéùéòó

è éê ïðñêòéòó #ûê$ðõîö

2.

Equation of Budget Constraint Line = (PX

! QX) + (PY ! QY)

3. Slope of Budget Constraint Line = ?ë…

ë%,

where X and Y is measured on the

horizontal and vertical axis, respectively.




4. Marginal Rate of Substitution =è éê ï%

è éê ï…=

&ñì'éêñù "òéùéòó ûü ýûûö þ

&ñì'éêñù "òéùéòó ûü ýûûö ÿ

Reading 15: Demand & Supply Analysis: The

Firm

1. Profit = Total revenue – Total cost

2.

Accounting Profit = Total Revenue –

Explicit Costs(or Accounting costs)

3. Economic Profit

• = Total Revenue – Explicit Costs –

Implicit Costs or

•

= Accounting Profit – Implicit Costsor

•

= Total Revenue – Total Economic

Costs

4. Economic costs = Explicit costs + Implicit

costs

5.

Normal Profit = Accounting Profit –

Economic Profit

6.

Accounting profit = Economic Profit + Normal Profit

7. Economic rent = (New “Higher” Price

after ( in Demand – Previous Price before

( in Demand) ! QS before ( in Demand

8.

Total Revenue (TR):

• = Price ! Quantity or

• = Sum of individual units sold !

Respective prices of individual Units

sold = ' (Pi ! Qi)

9.

Average Revenue (AR) =

!ûòñù )î*îêðî

ïðñêòéòó

10. Marginal Revenue (MR) =è éê !ûòñù )î*îêðî

è éê ïðñêòéòó

11. Total Variable Cost = Variable Cost per

unit ! Quantity Produced

12.

Total Cost = Total Fixed + Total Variable

13. Average total cost (ATC) =

!ûòñù #û$òïðñêòéòó ëìûöðíîö

= Avg. Fixed Cost + Avg.

Variable Cost

14. Marginal cost (MC) =è éê !ûòñù #û$ò

è éê ïðñêòéòó ëìûöðíîö

15. Marginal Variable Cost =è éê !ûòñù +ñìéñ,ùî #û$ò

è éê ïðñêòéòó ëìûöðíîö

16.

Marginal revenue (in perfect competition)

= Avg. Revenue = Price regardless of

Demand

17. Profit can be increased by increasing

output when MR> MC

18. Profit can be increased by decreasing

output when MR< MC

19. Break-even price: P = ATC ! Output

level where Price = Average Revenue =

Marginal Revenue = Average Total Cost

! where, Total Revenue = Total Cost.

20.

Firms earn Economic Profits when Price >

Average Total Cost

21. Profits occur when Total Revenue (TR) "

Total Cost (TC) & when Price = Marginal

revenue! firm will continue operating.

22. Losses are incurred when there are

Operating profits (Total Revenue "

Variable Cost) but Total Revenue < Total

Fixed Cost + Total Variable Cost ANDwhen Price = Marginal Revenue while

losses are < fixed costs! firm will

continue operating.

23. Losses are incurred when there are

Operating losses (Total Revenue <

Variable Cost) AND when losses=

fixed costs! firm will shut down.

24.

Average Product =

!ûòñù ëìûöðíò

ïðñêòéòó ûü -ñ,ûì

25. Marginal Product =è éê !ûòñù ëìûöðíò

è éê ïðñêéòó ûü -ñ,ûì =

è éê !ûòñù .ðòøðò

è éê /û ûü 0ûì1îì$




26. Least-cost optimization Rule:&ñì'éêñù ëìûöðíò ûü -ñ,ûì

ëìéíî ûü -ñ,ûì8

&ñì'éêñù ëìûöðíò ûü ë2ó$éíñù #ñøéòñù

ëìéíî ûü ë2óéíñù #ñøéòñù

27.

Profit is maximized when: MRP = Price or

cost of the input for each type of resource

that is used in the production process

28. Marginal Revenue product = Marginal

Product of an input unit ! Price of the

Product = Value of the input to firm =è éê !ûòñù )î*îêðî

è éê ïðñêòéòó ûü úêøðò îõøùûóîö

29. Surplus value or contribution of an input to

firm’s profit = MRP – Cost of an input

Reading 16: The Firm & Market Structures

1. In perfect competition, Marginal revenue =

Avg. Revenue = Price regardless of level

of Demand

2. Marginal Revenue = 3¦456 0 + ?

&

ëìéíî 7ùñ$òéíéòó ûü ôîõñêö 3. Concentration Ratio =

÷ðõ ûü $ñùî$ *ñùðî$ ûü ò2î ùñì'î$ò / üéìõ$

!ûòñù &ñì1îò ÷ñùî$

4.

Herfindahl-Hirshman Index = Sum of the

squares of the market shares of the top N

companies in an industry

Reading 17: Aggregate Output, Prices &

Economic Growth

1. Nominal GDP t = Prices in year t !

Quantity produced in year t

2. Real GDP t = Prices in the base year !

Quantity produced in year t

3. Implicit price deflator for GDP or GDP

deflator =*ñùðî ûü íðììîêò óì ûðòøðò ñò íðììîêò óì øìéíî$

*ñùðî ûü íðììîêò óì ûðòøðò ñò ,ñ$î óì øìéíî$ !

100

4. Real GDP = [Nominal GDP / (GDP

deflator ÷ 100)]

5. GDP deflator =/ûõéêñù ýôë

)îñù ýôë0+kk

6. GDP = Consumer spending on final good

&services + Gross private domestic invst +

Govt. spending on final goods &services +

Govt. gross fixed invst + Exp – Imp +

Statistical discrepancy

7.

Net Taxes = Taxes – Transfer payments

8.

GDP = National income + Capital

consumption allowance + Statistical

discrepancy

9. National Income = Compensation of

employees + Corp & Govt enterprise

profits before taxes + Interest income +

unincorporated business net income + rent

+ indirect business taxes less subsidies

10. Total Amount Earned by Capital = Profit +

Capital Consumption Allowance

11. PI = National income – Indirect business

taxes – Corp income taxes – Undistributed

Corp profits + Transfer payments

12. Personal disposable income (PDI) =

Personal income – Personal taxes OR GDP

(Y) + Transfer payments (F) – (R/E +

Depreciation) – direct and indirect taxes

(R)

13. Business Saving = R/E + Depreciation

14. Household saving = PDI - Consumption

expenditures - Interest paid by consumers

to business - Personal transfer payments to

foreigners

15.

Business sector saving = Undistributed

corporate profits + Capital consumption

allowance

16. Total Expenditure = Household

consumption (C) + Investments (I) +

Government spending (G) + Net exports

(X-M)

17. Private Sector Saving = Household Saving

+ Undistributed Corporate Profits +

Capital Consumption Allowance




18. GDP = Household consumption + Private

Sector Saving + Net Taxes

19. Domestic saving = Investment + Fiscal

balance + Trade balance

20. Trade Balance = Exports – Imports

21. Fiscal balance = Government Expenditure

– Taxes = (Savings – Investment) – Trade

Balance

22. Average propensity to consume (APC) =8''ìî'ñòî #ûê$ðõøòéûê

)îñù úêíûõî

23. Quantity theory of money equation:

Nominal Money Supply ! Velocity of

Money = Price Level ! Real Income or

Expenditure

24. % è in unit labor cost = % è in nominal

wages - % è in productivity

25. Economic growth = Annual % è in real

GDP

26.

Total Factor Productivity growth = Growthin potential GDP – [Relative share of labor

in National Income ! (Growth in labor) +

[Relative share of capital in National

Income ! (Growth in capital)]

27. Growth in potential GDP = Growth in

technology + (Relative share of labor in

National Income ! Growth in Labor) +

(Relative share of capital in National

Income ! Growth in capital]

28. Capital share =Corporate profits + net

interest income + net rental income +

(depreciation/ GDP)

29.

Labor share =7õøùûóîî #ûõøîê$ñòéûê

ýôë

Reading 18: Understanding Business Cycles

1. Price index at time t2 ="HxTI OQ GyI RO.7T.SGMOL zH7|IG HG G‹

"HxTI OQ GyI ROL7T.SGMOL zH7|IG HG G%0+kk

Inflation Rate =ëìéíî úêöî9 ñò òéõî ò‹

&dd? +

2. Fisher Index = ›‚ 0›: (where, IL =

Laspeyres index and I p = Paasche Index)

3.

;=>: ±;œX5 YX9: €;:i >=<>Y;:X5 8!ûòñù ùñ,ûì íûõøîê$ñòéûê øîì 2ûðì øîì <ûì1îì

.ðòøðò øîì 2ûðì øîì <ûì1îì

4. =6>¥54?@ ¥¤ A¥B6@ 8/ûõéêñù ýôë

&ûêîó ÷ðøøùó

Reading 19: Monetary & Fiscal Policy

1. Total Money created = New deposit/

Reserve Req

2. Money Multiplier =&

)î$îì*î )îC ûì ìî$îì*î ìñòéû

3. Narrow money = M1= notes and coins in

circulation + other very highly liquid

deposits

4.

Broad money = M2 = M1 + entire range of

liquid assets available to make purchases

5. M3 = M2 + other liquid assets

6. Quantity Theory of Money = M ! V = P !

Y where,

M = Quantity of money

V = Velocity of circulation of money

P = Average price level

Y = Real output

7. Neutral Rate = Trend Growth + Inflation

Target

8.

Impact of Taxes and Government

Spending: The Fiscal Multiplier

The net impact of the government sector

on AD:

•

G – T + B = Budget surplus or Budget

deficit

where, G = government spending , T

=taxes, B =transfer benefits

• Disposable income = National Income

– Net taxes = (1 – t) National Income

where, Net taxes = taxes – transfer

payments, t = net tax rate

9.

Fiscal Multiplier (in the absence of taxes)

= 1/(1 - MPC)

• MPS = 1 – MPC.




• Total increase in income and spending

= Fiscal multiplier ! G

10.

Fiscal Multiplier (in the presence of taxes)

•

MPC (with taxes) = MPC ! (1 - t)

• Fiscal multiplier =

&

&/)$R &/G

• Total ( in income and spending =

Fiscal multiplier ! G

• Initial ( in consumption due to

reduction in taxes = MPC ! tax cut

amount

• Total or cumulative effect of tax cut =

multiplier ! initial change in

consumption

11. Cumulative multiplier =íðõðùñòé*î îüüîíò ûê ìîñù ýôë û*îì ò2î ò<û óîñì$

Þ OQ Dh$

Reading 20: International Trade & Capital

Flows

1.

Terms of trade =ëìéíî ûü î9øûìò$

ëìéíî ûü éõøûìò$

2.

Terms of Trade (as an index number) =8*' øìéíî ûü î9øûìò$

8*' øìéíî ûü éõøûìò$

3. Net exports = Value of a country's exports

–imports

4. Net welfare effect = consumer’s surplus

loss + producer’s surplus gain + Govt.

revenue

5.

Closed Economy’s output = Y = C+I+G

6. Open Economy’s output = Y =

C+I+G+(X-M)

• Current Account Balance = X-M = Y-

C+I+G

7. Consumption = Income + transfers – taxes

– saving

C = Yd- S p =Y+R-T-S p And,

CA = S p- I+ Govt surplus (or Govt saving)= S p- I+ (T- G- R)

Restated differently, S p + Sg = I + CA

where, Sg = Govt savings

S p = I + CA – Sg

• Current Account Imbalance CA = Sp

+ Sg – I

Reading 21: Currency Exchange Rates

1.

E¥¦64FB G¦456 >6H6> 4B I¥A6J?45 5K¦¦6B5@ 8

Löwü 03ü

2.

M6N> 6O5PNBF6 ¦N?6€ôwü 8 €Lö ü 03ü w3ö 8

Lö ü 0€3ü w3ö

3.

M6N> QO5PNBF6 MN?6 öûõî$òéíwüûìîé'ê 8

Löwü 0 #ëúR

#ëúS

4.

TPNBF6 4B M6N> QO5PNBF6 ¦N?6 8

+ ,è÷SwR

÷SwR 0

&'èUR UR

&'èUSUS

? +

5. Direct Quote =&

úêöéìîíò ïðûòî

6. Points on a forward rate quote = Fwd X-

rate quote –Spot X-rate quote

7. Forward rate = Spot X-rate +Vûì<ñìö øûéêò$

&d–ddd

8. E¥¦WN¦I G¦6A4KAwI4J5¥KB? €4B Þ 8

$øûò þ/ìñòî'€üûì<ñìö øûéêò$w&d–ddd

$øûò þ/ìñòî? +

9. To convert spot rate into a forward quote

(when points are represented as %) = Spot

exchange rate ! (1 + % premium or

discount)

10. Arbitrage relationship is stated as follows:

•

+ , >J 8 Ë ³

Ï

+ , >Q&

!³Ï

•

In case of indirect quote, Arbitrage

relationship is: + , >J 8

+wËQwJ + , >Q jQwJ

•

j³

Ï

8 Ë ³

Ï

&'M³

&'MÏ

• Forward rate as a % of spot rate =

!³wÏ

F³wÏ8

&'M³

&'MÏ




11. Return on hedged foreign investment

(with a quoted forward rate) = ËQwJ + ,

>Q&

!³wÏ

12.

Expected % change in the spot rate =F[_%

F[? + 8 ÞèËG'& 8

M³/MÏ

&'MÏ

• Forward points: jQwJ ? ËQwJ 8

ËQwJ

M³/MÏ

&'MÏX Y (where Y is quoted

interest rate period)

13. Relationship between the trade balance and

expenditure/ saving decisions:

= Ex – Im = (Sav – Inv) + (T – G)

where T= taxes net of transfers

G= government expenditures)

14. Price elasticity of demand = ( =Þ í2ñê'î éê Cðñêòéòó

Þ í2ñê'î éê øìéíî = –

Þ è ï

Þ è ë

15. Expenditure (R) = Price ! Quantity = P !

Q

•

% ) in expenditure = % ) R = % ) P

+ % ) Q = (1- () % ) P

16. Basic idea of Marshall-Lerner condition =

ZŸ[Ÿ , Z) [) ? + \ k where,

*x=share of exports

(X=price elasticity of foreign demand for

domestic country exports

*M=share of imports

(M =price elasticity of domestic country

demand for imports

17.

Trade balance = Income (GDP) –

Domestic expenditure = Absorption

Reading 22: Financial Statement Analysis: An

Introduction

1. Gross Profit = Revenue – Cost of sales

2. Operating Profit or EBIT = Gross profit –

Operating costs + Other operating income

3.

Profit before tax = EBIT + non-operatingincome – Interest expense

4. Profit after tax = Profit before tax –

Income tax expense

Reading 23: Financial Reporting Mechanics

1.

Owner’s Equity = Contributed Capital +

R.E

2.

End R.E = Beg R.E + Net income –

Dividends

3.

Assets = Liabilities + Contributed Capital

+ Beg R.E + Revenue – Expenses –

Dividends

Reading 24: Financial Reporting Standards

Reading 25: Understanding Income Statements

1. Revenue recognized on Prorated basis =!ûòñù 8õûðêò ûü #û$ò

!éõî ûü ò2î íûêòìñíò

2. Revenue recognized under Percentage-of-

Completion Method = % of Total cost

spent by the firm ! Total Contract

Revenue

3. Revenue recognized when outcome cannot

be reliably measured

under IFRS, Revenue= Contract costs

incurred "#$%& '( )**+, #- &%.%#"%

&%/-&0%$ "#012 3-#0&430 15 3-6/2%0%

4. Revenue recognized under installment

method =ëìûüéò

÷ñùî$ 0 Cash receipt

5. Wgtd Avg cost per unit =!ûòñù #û$ò ûü ýûûö$ ñ*ñéùñ,ùî üûì ÷ñùî

!ûòñù ðêéò$ ñ*ñéùñ,ùî üûì ÷ñùî

6. COGS using Wghtd Avg Cost = No of

units sold ! Wghtd Avg cost per unit

7. COGS using LIFO = Total cost – Value of

ending inventory

8. Annual Depreciation Expense (using

Straight-Line Method) =#û$ò/)î$éöðñù +ñùðî

7$òéõñòîö "$îüðù -éüî




9. Annual Depreciation Expense (Declining

balance method) =&ddÞ

"$îüðù ùéüî ! Acceleration

factor (say 200% or 2) ! Net Book Value

10.

Basic EPS =/îò úêíûõî/ëìîüîììîö ôé*éöîêö$

0'2ò 8*' /û ûü $2ñìî$ ûðò$òñêöéê'

11. Diluted EPS for preferred stock =/îò úêíûõî

0'2ò 8*' /û ûü $2ñìî$ ûw$'/î< íûõõûê $2ñìî$ ò2ñò

<ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê

12. Diluted EPS for convertible debt =/îò úêíûõî '8! M ûê

íûê*îìòé,ùî öî,ò/ëìîüîìì ôé*0'2ò 8*' êû ûü $2ñìî$ ûw$'8ööéòéûêñù íûõõûê $2ñìî$

ò2ñò <ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê

13.

Diluted EPS using Treasury Stock Method=

€]6? ^B5¥A6 ? 3¦6¤ 6¦¦6I I4H4I6BIJ

_`FP? aHF ]¥P ¥¤ JPN¦6J ,

€]6W JPN¦6J N? ¥G?4¥B 6O6¦54J6 ?

LPN¦6J GK¦5PNJ6I W4?P

TNJP ¦6564H6I KG¥B 6O6¦54J6 0

€3¦¥G¥¦?4¥B ¥¤ b¦c

14. Net Profit Margin =/îò úêíûõî

)î*îêðî

15. Gross Profit Margin =ýìû$$ ëìûüéò

)î*îêðî

16. Comprehensive EPS = EPS + Other

Comprehensive Income per share

Reading 26: Understanding Balance Sheets

1. Percentage of A/C Receivable estimated to

be uncollectible =8ùùû<ñêíî üûì ôûð,òüðù 8w#

ýìû$$ ñõûðêò ûü 8w# )îíîé*ñ,ùî

2.

Net Identifiable Assets = Fair value ofidentifiable assets – Fair value of liabilities

& contingent liabilities

3.

Amortized cost of PPE = Historical cost –

Accumulated depreciation – Impairment

losses

4. Carrying value for PPE under revaluation

model

= Fair value at date of revaluation –

Accumulated depreciation (if any)

5.

Amortized cost of PPE = Historical cost –

Accumulated depreciation – Impairment

losses

6. Carrying value for PPE under revaluation

model

= Fair value at date of revaluation –

Accumulated depreciation (if any)

7. Deferred tax liability = Taxable income <

Reported Financial Statement Income

before taxes

8. Deferred tax liability = Actual income tax

payable in a period < Income tax expense

9. Vertical common-size balance-sheet =dñùñêíî $2îîò 8õûðêò

!ûòñù 8$$îò$

10.

Current ratio =#ðììîêò 8$$îò$

#ðììîêò -éñ,éùéòéî$

11. Quick (acid test) =#ñ$2'&ñì1îòñ,ùî $îíðìéòéî$')îíîé*ñ,ùî$


12. Cash ratio =#ñ$2'&ñì1îòñ,ùî $îíðìéòéî$


13.

Long-term debt-to-equity =!ûòñù ùûê'/òîìõ öî,ò

!ûòñù 7Cðéòó

14.

Debt-to-Equity = !ûòñù ôî,ò!ûòñù 7Cðéòó

15.

Total Debt =!ûòñù ôî,ò

!ûòñù 8$$îò$

16. Financial Leverage =!ûòñù 8$$îò$

!ûòñù 7Cðéòó

Reading 27: Understanding Cash Flow

Statements

1.

End Cash = Beg cash + Cash receipts

(from operating, investing, and financing

activities) – Cash payments (for operating,

investing, and financing activities)

2. End A/c Receivable = Beg A/c Receivable

+ Revenues – Cash collected from

customers




3. Cash received from customers = Revenue

– Increase in a/c receivable

4. Purchases from suppliers = COGS +

Increase in inventory

5. Cash paid to suppliers = Cogs + Increase

in inventory – Increase in a/c payable

6. End Inventory = Beg inventory +

Purchases – COGS

7. End a/c payable = Beg a/c payable +

Purchases – Cash paid to suppliers

8.

Cash paid to employees = Salary andwages expense – Increase in salary and

wages payable

9.

End salary and wages payable = Beg salary

and wages payable + Salary and wages

expense – cash paid to employees

10.

Cash paid for other operating expenses =

Other operating expenses – Decrease in

prepaid expenses – Increase in other

accrued liabilities

11. Cash paid for interest = Interest expense +

Decrease in interest payable

12. End Interest Payable = Beg interest

payable + Interest expense – Cash paid for

interest

13. Cash paid for income taxes = Income tax

expense – Increase in income tax payable

14. Historical cost of equipment sold = Beg

balance equipment + Equipment purchased

– End balance equipment

15. Accumulated Dep on equipment sold =

Beg. balance accumulated dep + Dep

expense – End. balance accumulated dep

16. Cash received from sale of equipment =

Historical cost of equipment sold –

Accumulated dep on equipment sold +

gain on sale of equipment

17. Dividends paid = Beg balance of R.E +

Net income – End balance of R.E

18.

FCFF = Net income + Non-cash charges +

Interest expense (1 – tax rate) – Cap exp –

WC expenditures

19.

FCFF = CFO + Interest expense (1 – Tax

rate) – Cap exp

20.

FCFE = CFO – Cap exp + Net borrowing

21. CF to revenue =#V.

/îò )î*îêðî

22.

Cash ROA =#V.

8*îìñ'î !ûòñù 8$$îò$

23. Cash ROE =#V.

8*îìñ'î $2ñìî2ûùöîì$eîCðéòó

24. Cash to income =#V.

.øîìñòéê' éêíûõî

25. Cash flow per share =

#V./ëìîüîììîö ôé*éöîêö$/û ûü íûõõûê $2ñìî$ ûw$

26. Debt Coverage =#V.

!ûòñù ôî,ò

27. Interest Coverage =#V.'úêòîìî$ò øñéö'!ñ9î$ øñéö

úêòîìî$ò øñéö

28. Reinvestment =#V.

#ñ$2 øñéö üûì ùûê'/òîìõ ñ$$îò$

29. Debt payment =#V.

#ñ$2 øñéö üûì -! öî,ò ìîøñóõîêò

30. Dividend payment =#V.

ôé*éöîêö$ øñéö

31.

Investing and Financing =#V.

#ñ$2 ûðòüùû<$ üûì éê*î$òéê' ñêö üéêñêíéê' ñíòé*éòéî$

Reading 28: Financial Analysis Techniques

1. Compound Growth Rate =

7êö +ñùðî

dî' +ñùðî

%

fg gR hijkgSl? +

2.

Combined ratio =-û$$î$ ñêö 79øîê$î$

/îò ëìîõéðõö 7ñìêîö

3. Operating ROA =.øîìñòéê' úêíûõî

8*' !ûòñù 8$$îò$




4. ROA = /îò úêíûõî

8*' !ûòñù 8$$îò$ or

ROA =/îò úêíûõî'úêòîìî$ò 79øîê$î &/!ñ9 ìñòî

8*' !ûòñù 8$$îò$

5. Effective Tax Rate =úêíûõî !ñ9

7ñìêéê'$ ,îüûìî !ñ9

6. Vertical common size income statement =úêíûõî $òñòîõîêò úòîõ

)î*îêðî

7.

Horizontal common size balance sheet =dñùñêíî $2îîò éòîõ éê ÿîñì l

dñùñêíî $2îîò éòîõ éê ÿîñì &

8. Inventory turnover =#û$ò ûü $ñùî$ ûì íû$ò ûü 'ûûö$ $ûùö

8*' úê*îêòûìó

9. Days of Inventory on Hand (DOH) =/û ûü ôñó$ éê øîìéûö

úê*îêòûìó !ðìêû*îì

10. Receivables Turnover =)î*îêðî

8*' )îíîé*ñ,ùî$

11. Days of Sales Outstanding (DSO)

=

/û ûü ôñó$ éê ëîìéûö

)îíîé*ñ,ùî$ òðìêû*îì

12. Avg A/c Receivable Balance = Avg Days’

Credit Sales ! DSO or

Avg A/c Receivable Balance =÷ñùî$

)îíîé*ñ,ùî$ !ðìêû*îì =

÷ñùî$mno

pqr

13. Payables turnover =ëðìí2ñî$

8*' òìñöî øñóñ,ùî$

14.

No of Days of Payables =/û ûü ôñó$ éê øîìéûö

ëñóñ,ùî$ !ðìêû*îì

15. WC Turnover =)î*îêðî

8*' 0#

16. Fixed Asset Turnover =)î*îêðî

8*' /îò Vé9îö 8$$îò$

17. Total Asset Turnover =)î*îêðî

8*' !ûòñù 8$$îò$

18. Pretax margin =7ñìêéê'$ ,îüûìî òñ9 ,ðò ñüòîì éêòîìî$ò

)î*îêðî

19. Return on Total Capital =7dú!

÷2ûìò ñêö ùûê' òîìõ öî,ò ñêö îCðéòó

20.

ROE =/îò úêíûõî

8*' !ûòñù 7Cðéòó

•

ROE = ROA ! Leverage

• ROE = Tax Burden ! Interest Burden

! EBIT Margin ! Total Asset

Turnover ! Leverage

21. Return on Common Equity =

/îò úêíûõî/ëìîüîììîö ôé*éöîêö$8*' #ûõõûê 7Cðéòó

22. Coefficient of Variation of Operating

Income =÷Pô ûü .øîìñòéê' úêíûõî

8*' .øîìñòéê' úêíûõî

23.

Coefficient of Variation of Net Income =÷Pô ûü /îò úêíûõî

8*' /îò úêíûõî

24. Coefficient of Variation of Revenues =÷Pô ûü )î*îêðî

8*' )î*îêðî

25.

Monetary Reserve Requirement (CashReserve Ratio) =

)î$îì*î$ 2îùö ñ$ #îêòìñù dñê1

÷øîíéüéîö ôîøû$éò -éñ,éùéòéî$

26. Liquid Asset Requirement =)îñöéùó &ñì1îòñ,ùî ÷îíðìéòéî$

÷øîíéüéîö ôîøû$éò -éñ,éùéòéî$

27. Net Interest Margin =/îò úêòîìî$ò úêíûõî

!ûòñù úêòîìî$ò 7ñìêéê' 8$$îò$

28.

Sales per Square Meter =)î*îêðî

!ûòñù )îòñéù ÷øñíî éê ÷Cðñìî &îòîì$

29. Average Daily Rate =)ûûõ )î*îêðî

/û ûü )ûûõ$ $ûùö

30.

Occupancy Rate =/û ûü )ûûõ$ ÷ûùö

/û ûü )ûûõ$ ñ*ñéùñ,ùî

31.

EBIT Interest Coverage =7dú!

ýìû$$ úêòîìî$ò

32. EBITDA Interest Coverage =7dú!ô8


33. FFO Interest Coverage =VV.'úêòîìî$ò ëñéö/.øîìñòéê' -îñ$î 8ösð$òõîêò$


34.

Return on Capital =7dú!

8*' #ñøéòñù =

7dú!

8*' €7Cðéòó'/ûê íðììîêò öîüîììîö òñ9î$'öî,ò




35. FFO to Debt =VV.

!ûòñù ôî,ò

36. Free Operating CF to Debt =#V./#ñø 79ø

!ûòñù ôî,ò

37.

Discretionary CF to Debt =#V./#ñø î9ø/ôé*éöîêö$ øñéö

!ûòñù öî,ò

38.

Net CF to Capital expenditures =VV./ôé*éöîêö$

#ñø î9ø

39. Debt to EBITDA =!ûòñù öî,ò

7dú!ô8

40. Total Debt to total debt plus Equity =

!ûòñù öî,ò!ûòñù öî,ò'7Cðéòó

41. Z-Score = 1.2 ! #8/#-

!8 + 1.4 !

)P7

!8 +

3.3 ! 7dú!

!8 + 0.6 !

&+ ûü $òûí1

d+ ûü ùéñ,éùéòéî$ + 1.0

! ÷ñùî$

!8

42. Segment margin =÷î'õîêò ëìûüéò €-û$$

÷î'õîêò )î*îêðî

43.

Segment turnover = ÷î'õîêò )î*îêðî÷î'õîêò 8$$îò$

44. Segment ROA =÷î'õîêò ëìûüéò €-û$$

÷î'õîêò 8$$îò$

45.

Segment Debt Ratio =÷î'õîêò -éñ,éùéòéî$

÷î'õîêò 8$$îò$

Reading 29: Inventories

1. NRV = Estimated Selling Price –

Estimated Costs of completion and

disposal

2.

Inventory amount net of valuation

allowance = Carrying amount of Inventory

– Write downs

3. (NRV – Normal Profit Margin) + MV +

NRV

Reading 30: Long-Lived Assets

1.

Dep Exp under Straight-line Method =ôîøìîíéñ,ùî #û$ò

7$òéõñòîö "$îüðù -éüî =

té$òûìéíñù #û$ò/7$òéõñòîö )î$éöðñù $ñù*ñ'î +ñùðî

7$òéõñòîö "$îüðù -éüî

2. Dep Exp under Units-of-Production

Method = Depreciable Cost ! ëìûöðíòéûê éê ò2î ëîìéûö

7$òéõñòîö ëìûöðíòé*î #ñøñíéòó

3. Carrying amount under cost model =

Historical Cost – Accumulated Dep or

Amortization

4.

Carrying amount under revaluation model= Fair value at the date of revaluation –

Any subsequent Accumulated Dep or

Amortization

5.

Impairment Loss (IFRS) = Recoverable

Amount – Net Carrying Amount

Where, Recoverable amount = Max [(Fair

value – Costs to sell); Value in Use)] and

Value in use = PV of Expected Future CFs

6.

Impairment Loss (US GAAP) = Asset’s

Fair Value – Carrying Amount …….If

Carrying amount > Undiscounted Expected

Future Cash Flows

Reading 31: Income Taxes

1. Deferred tax asset = Company’s taxable

income > Accounting profit

2.

Tax base of revenue received in advance =

Carrying amount – Any amount of revenuethat will not be taxed at a future date

3. Reported Effective Tax Rate =úêíûõî !ñ9 î9øîê$î

ëìî òñ9 éêíûõî ûì 8ííûðêòéê' ëìûüéò

4.

Deferred tax liability = Carrying amount

of asset > Tax base of asset

5. Deferred tax asset = Carrying amount of

asset < Tax base of asset

6. Deferred tax asset = Carrying amount of

liability > Tax base of asset

7.

Deferred tax liability = Carrying amount of

liability < Tax base of asset

8. Company’s tax expense (or credit)

reported on its income statement = Income




tax liability currently payable + è in

deferred tax asset / liability

Where,

• Income Tax liability currently

payable = Taxable income ! Tax

rate

•

èin deferred tax asset / liability =

Diff b/w the balance of the

deferred tax asset / liability for the

current period and the balance of

the previous period.

9. The company’s tax expense (or credit)

reported on its income statement = Taxes

payable + () Deferred tax liability - )

Deferred tax asset)Where,

• Income Tax liability currently

payable = Taxable income ! Tax

rate

• Deferred tax liability = (carrying

amount – tax base) ! tax rate

• Deferred tax asset = (tax base –

carrying amount) ! tax rate

10. Tax base of a liability = Carrying amount

of the liability – Amounts that will be

deductible for tax purposes in the future

Reading 32: Non-current (Long-term)

Liabilities

1. Annual Interest Payment = Face Value !

Coupon Rate

2. Sale proceeds of bond = Sum of PV of

Interest Payments + PV of Face value of

Bond

3.

When Face value - Sale proceed is > zero,

discount

4. When Face value – Sale proceed is < zero,

premium

5. Initial carrying amount = Face value – (+)

Discount (Premium)

6.

Total Interest Expense (in case of discount)

= Periodic interest payments +

Amortization of Discount7. Total Interest Expense (in case of

premium) = Periodic interest payments -

Amortization of Premium

8. Amount of Bonds payable reported on the

balance sheet = Historical cos t +/-

Cumulative amortization (or amortization

cost)

9. Amount of Bonds payable initially

reported on the balance sheet under IFRS =

Sales proceeds – Issuance costs

10.

Amount of Bonds payable initially

reported on the balance sheet under US

GAAP = Sales proceeds

11.

Bond interest expense under effective

interest rate method = Carrying value of

the bonds at the beginning of the period !

Effective interest rate

12. Bond Interest Payment under effective

interest rate method = Face value of the

bonds ! Contractual (coupon) rate

13. Amortization of the discount or premium

under effective interest rate method =

Bond interest expense – Bond interest

payment

14. Bond Discount/Premium Amortization

under Straight-line Method =dûêö ôé$íûðêò ûì øìîõéðõ

/û ûü úêòîìî$ò ëîìéûö$

15.

No of shares subscribed when warrants are

exercised =8''ìî'ñòî øìéêíéøñù ñõûðêò ûü öî,ò

ëñì *ñùðî ûü ñ ùûò

! shares subscribed per lot

16. Carrying amount of the leased asset =

Initial recognition amount – Accumulated

depreciation

17.

Accumulated depreciation = Prior year’s

accumulated depreciation + Current year’s

depreciation expense

18.

Interest expense = Lease liability at the beg

of the period ! interest rate implicit in the

lease

19. Sales revenue = lower of the fair value of

the asset and PV of the min lease payments




20. Cost of sales = Carrying amount of the

leased asset – PV of the estimated

unguaranteed residual value

21.

Interest Revenue = Lease receivable at the

beg of the period ! Interest rate

22. Net interest expense = Beg Net pension

liability ! Discount rate

23. Net Interest income = Beg Net Pension

asset ! Discount rate

24.

Reported pension expense (U.S. GAAP) =

Pension costs – Expected return on

Pension plan assets

25. Funded Status = PV of the Defined benefit

obligations – Fair value of the plan assets

Reading 33: Financial Reporting Quality

Reading 34: Financial Statement Analysis:

Applications

1.

Company’s sales = Projected market share

! Projected total industry sales

2. Forecast amount of profit for a given

period = Forecasted amount of sales !

Forecast of the selected profit margin

3. Retained CF (RCF) / Total debt =

€ûøîìñòéê' #V ,îüûìî 0# í2ñê'î$ u öé*éöîêö$

òûòñù öî,ò

4.

)îòñéêîö #V/#ñø î9ø

!ûòñù ôî,ò

5. Inventory value adjusted to FIFO basis =

End Inventory value under LIFO + End

LIFO reserve balance

6. COGS adjusted to a FIFO basis = COGS

under LIFO – (End LIFO reserve – Beg

LIFO reserve)

7. Useful life of the company’s overall asset

base that has passed =8ííðõðùñòîö ôîø

ýìû$$ ëë7

8. Avg age of the asset base =8ííðõðùñòîö ôîø

8êêðñù ôîø î9øîê$î

9.

Remaining useful life of the asset =/îò ëë7 €êîò ûü ñííðõðùñòîö öîø

8êêðñù öîø î9øîê$î

10. Avg depreciable life of the assets at

installation =ýìû$$ ëë7

8êêðñù ôîø î9øîê$î

11. % of asset base that is being renewed

through new capital investment =#ñøî9

ýìû$$ ëë7' #ñøî9

12.

Adjusted BV = Total stockholders’ equity

– Goodwill

13. Adjusted Price to BV ratio =ëìéíî õñì1îò íñøéòñùévñòéûê

8ösð$òîö d+

14. Tangible B.V = Total stockholders’ equity

– Goodwill – Other intangible assets15. Price to tangible BV ratio =

ëìéíî

!ñê'é,ùî d+

16. Adjusted debt-to-equity ratio =)îøûìòîö öî,ò'ë+ ûü ûøîìñòéê' ùîñ$î

)îøûìòîö 7Cðéòó

17. Adjusted debt-to-asset ratio =)îøûìòîö öî,ò'ë+ ûü ûøîìñòéê' ùîñ$î

)îøûìòîö 8$$îò' ë+ ûü ûøîìñòéê' ùîñ$î

18. Adjusted Asset Turnover ratio =

÷ñùî$)îøûìòîö 8*' òûòñù ñ$$îò$'ë+ ûü ûøîìñòéê' ùîñ$î

19.

PV of future operating lease payments* =ë+ ûü íñøéòñù ùîñ$î øñóõîêò$

"êöé$íûðêòîö /ûêíðììîêò #ñøéòñù -îñ$î øñóõîêò$

! Undiscounted Noncurrent Operating

Lease Payments

*If term structures of capital and operating

leases are assumed to be similar

20.

Interest expense = Interest ! PV of thelease payments

21. Depreciation expense estimated on

straight-line basis =ë+ ûü ò2î ùîñ$î øñóõîêò$

/û ûü óì$ ûü üðòðìî ùîñ$î øñóõîêò$

22. Adjusted Interest Coverage ratio =




Qw^x Ê , ¦6B? 6OG ÊÊ ?y6G 6OG ÊÊ

> 6OG6BJ6 Ê ,> 5¥J?J ÊÊ

* Unadjusted

**associated with the operating lease

obligations

Reading 35: Capital Budgeting

1.

Incremental CF = CF with a decision - CF

without that decision

2. NPV = PV of cash inflows - IO =

NPV =

t =1

n

!AT CFs at time t

1+ Req RoR( )t " IO

3. Avg Accounting RoR (AAR) =8*' /ú ñüòîì öîø Ò GHŸI7 ,îüûìî éêòîìî$ò

8*' d+ ûü úê*$ò

4. PI =ë+ ûü üðòðìî #V$

ú. = 1 +

/ë+

ú.

5. Value of a company = Value of company’s

existing invst + Net PV of all of

company’s future invst

Reading 36: Cost of Capital

1. WACC = wdr d (1 – t) + w pr p + wer e

2.

Debt-to-Equity Ratio conversion into

weight (i.e. Debt / (Debt + Equity) =piz{

|}~k{•

&'piz{

|}~k{•

3. Optimal Capital Budget is the point where

MC of capital = Marginal return from

investing

4.

After-tax cost of debt = Before-tax

Marginal Cost of Debt ! (1 – firm’s

marginal tax rate)

5. Preferred Stock Price per Share

=ëìîü ÷òûí1 ôé* øîì ÷2ñìî

#û$ò ûü ëìîü ÷òûí1

6. Expected Return on Stock I (under CAPM)

= E (R i) = R F + ,i [E (R M) – R F]

7. Expected Return on Stock I = E (R i) = R F +

,i1 (Factor risk premium)1 + ,i2 (Factor

risk premium)2+…..+,i j (Factor risk

premium) j

8. Cost of Equity = € 8 ô%

ëg, F

9. Expected Growth Rate of Dividends

g = (1 -ô

7ë÷) ! ROE

g = retention rate ! ROE

10. Company’s stock returns = Méò 8 N ,

‚Mõò

11.

Unlevered ƒ of Comparable Company =

ƒ"– íûõøñ 8„

…– †g‡hˆjˆz‰i

&' &/ò†g‡hˆjˆz‰i

p†g‡hˆjˆz‰i|†g‡hˆjˆz‰i

12. Levered ƒ of Project =

ŠB– S(O 8 ŠÝ– bO.S + , + ? :S(O

‹S(O

”S(O

13.

ŠH77IG 8 ŒŽ†[

&' &/G s

‘

14. ŠI~TMGa 8 ŠH77IG + , + ? : h

’

15.

Sovereign yield spread = Govt bond yield

(denominated in developed country’s

currency) – T.B yield on a similar maturity

bond in developed country

16.

Country equity premium = Sovereign yield

spread ! 8êê ÷Pô ûü 7Cðéòó éêöî9

8êê ÷Pô ûü $û*îìîé'ê ,ûêö &1ò éê

òîìõ$ ûü öî*îùûøîö õ1ò íðììîêíó

17. Cost of equity = K e= R F + ,[(E(R M)-R F) +

CRP]

18. Breakpoint =8õûðêò ûü íñøéòñù ñò <2éí2 $ûðìíîe$ íû$ò ûü íñø è

ëìûø ûü êî< íñø ìñé$îö üìûõ ò2î $ûðìíî

19. Cost of Capital when flotation costs are in

monetary terms= ¦î 8 ô%

ëg/V , F

20. When FC are in terms of % of the share

price: Cost of Equity = ¦î 8 ô%

ëg &/ü , F

21. If FC are not tax deductible: NPV = PV of

Cash Inflows – IO – (FC in % ! New

Equity Capital)




22. If FC are tax deductible: NPV = PV of

Cash Inflows – IO – [(FC in % ! New

Equity Capital) ! (1 – Marginal Tax Rate)]

23. Asset ƒ = (Debt ƒ ! Proportion of Debt) +

(Equity ƒ ! Proportion of Equity)

Reading 37: Measures of Leverage

1.

Contribution Margin (CM) = (# of units

sold) ! [(price per unit) - (variable cost per

unit)]

2. Per unit CM = Price per unit - Variable

cost per unit

3.

Operating income = CM – Fixed OperatingCosts

4. DOL =Þ è éê .øîìñòéê' úêíûõî 7dú!

Þ è éê "êéò$ ÷ûùö

or

DOL=#&

#&/ Vé9îö .øîìñòéê' #û$ò

5. DFL =Þ è éê /îò úêíûõî

Þ è éê .øîìñòéê' úêíûõîor

#&/ Vé9îö .ø #û$ò

#&/Vé9îö .ø #û$ò$/Vé9îö Véê #û$ò

6. DTL=Þ è éê /îò úêíûõî

Þ è éê /û ûü "êéò$ ÷ûùö = DOL ! DFL =

#&

#&/Vé9îö .ø #û$ò$/Vé9îö Véê #û$ò

7.

Break-even Revenue = (Variable cost per

unit ! Break-even Number of Units) +

Fixed Operating costs + Fixed Financial

Cost

8. Breakeven Number of units =Vé9îö .øîìñòéê' #û$ò$'Vé9îö Véêñêíéñù #û$ò$

ëìéíî øîì ðêéò/+ñìéñ,ùî íû$ò øîì ðêéò

Reading 38: Dividends & Share Repurchases:

Basics

1. Company’s payout for the year = Cash

dividends + Value of shares repurchased in

any given year

2. Dividend Payout ratio =#ûõõûê $2ñìî íñ$2 öé*éöîêö$

/îò úêíûõî ñ*ñéùñ,ùî òû íûõõûê $2ñìî$

3.

EPS after Stock Dividend = EPS before

Dividend ! ÷2ñìî$ ûw$ ,îüûìî ôé*éöîêö

÷2ñìî$ ûw$ ñüòîì ôé*éöîêö

4.

Stock Price after Stock Dividend = Stock

Price before Dividend ! EPS after

Dividend

5. Total Market Value after Stock Dividend =

Shares outstanding after Dividend ! Stock

price after Dividend

6.

Stock price after 2-for-1 stock split =÷òûí1 øìéíî ,îüûìî $òûí1 $øùéò

l

7. EPS after 2-for-1 stock split =7ë÷ ,îüûìî $òûí1 $øùéò

l

8.

DPS after 2-for-1 stock split =ôë÷ ,îüûìî $òûí1 $øùéò

l

9. EPS after buyback =7ñìêéê'$/8üòîì òñ9 #û$ò ûü Vðêö$

÷2ñìî$ .ðò$òñêöéê' ñüòîì dðó,ñí1

10.

Ex-dividend value of share = Stock price –Dividend per share

11. Market value of Equity after distribution of

cash dividends =

_€’ ûü $2ñìî$ ûw$ 0 €&+ $2ñìî u #ñ$2 öé*c

’ ûü $2ñìî$ ûw$

12. Post-repurchase share price =

’ûü $2ñìî$ ûw$ 0 €&+ $2ñìî u

<ûìò2 ûü ÷2ñìî ìîøðìí2ñ$îc

€ ’ ûü $2ñìî$ ûw$/’ ûü $2ñìî$ ìîøðìí2ñ$îö €íñê ,î ìîøðìí2ñ$î

Reading 39: Working Capital Management

1. Operating cycle = No of days of inventory

+ No of days of receivables

2. Net operating cycle = No of days of

inventory + No of days of receivables – No

of days payables

3. Money Market Yield =Vñíî *ñùðî/ëðìí2ñ$î øìéíî

ëðìí2ñ$î øìéíî 0

pqd

/û ûü öñó$ òû õñòðìéòó

4.

Bond Equivalent Yield =Vñíî *ñùðî/ëðìí2ñ$î øìéíî

ëðìí2ñ$î øìéíî0

pqv





5. Discount-basis Yield =Vñíî *ñùðî/ëðìí2ñ$î øìéíî

Vñíî +ñùðî0

pqd


6.

Wght Avg collection period = wghts !

Avg no of days to collect accounts within

each age category

Where, Weights = % of total receivables in

each category

7. Float Factor =8*' ôñéùó Vùûñò

8*' ôñéùó ôîøû$éò =

8*' ôñéùó Vùûñò“g{ˆ‰ ”‡g~{ gR –—i†˜l pihglk{iS

fg gR pˆ•l

Where, Float =Amount of money that is in

transit b/w payments (by customers) and

funds (usable by co)

8. Value of stretching payment = A/c payable

! Co's opportunity cost for ST funds

9.

Cost of Trade Credit = + ,

ôé$íûðêò

&/ôé$íûðêò

mno

? + where n = days beyond discount period

10. Cost of Line of Credit =úêòîìî$ò'#ûõõéòõîêò üîî

-ûñê 8õûðêò

11. Bankers Acceptance Cost =úêòîìî$ò

/îò øìûíîîö$ =

úêòîìî$ò

-ûñê ñõûðêò/úêòîìî$ò

12. Commercial Paper Cost

=úêòîìî$ò'ôîñùîìe$ íûõõé$$éûê'dñí1ðø íû$ò$

-ûñê ñõûðêò/úêòîìî$ò

13. Annualized cost = Cost ! 12

Reading 40: The Corporate Governance of

Listed Companies

Reading 41: Portfolio Management: An

Overview

1. NAV of bond mutual fund =€*ñùðî ûü îñí2 ,ûêö éê ò2î øûìòüûùéû

/û ûü $2ñìî$

2. New Shares that need to be created =8õûðêò òû ,î úê*î$òîö éê ò2î Vðêö

/8+ øîì $2ñìî ûì !ûòñù *ñùðî øîì $2ñìî ûü ñ &ðòðñù Vðêö

3. New NAV of the Fund = NAV or Total

value of a Mutual Fund + Amount to be

invested in the Fund

4. No of shares need to be retired =8õûðêò òû ,î <éò2öìñ<ê üìûõ ò2î Vðêö

/8+ øîì $2ñìî ûì !ûòñù *ñùðî øîì $2ñìî ûü ñ &ðòðñù Vðêö

Reading 42: Portfolio Risk & Return: Part I

1.

Total Return = Capital Gain (or Loss) +

Dividend Yield

2. Capital Gain =ë{/ë{Ñ%

ë{Ñ%

3. Dividend Yield =ô{

ë{Ñ%

4. 3-Yr HPR = [(1 + R 1) ! (1 + R 2) ! (1 +

R 3)]– 1

5. Arithmetic mean (AM) R = ZM 8N†%'N†‹'´'N†P™Ñ%'N†™

* 8

&

* ZMG

*G\&

6. Geometric R for n periods = MDM 8

+ , Z& + , Zl m + , ZL&

* ? +

7. IRR =#V ñò !éõî ò

&'ú)) { 8 k!

ò\d

8. Annualized Return (Ann R):

•

Ann R = (1 + Quarterly R) 4 – 1

• Ann R = (1 + Monthly R)12

– 1

• Ann R = (1 + Weekly R) 52 – 1

• Ann R = (1 + Daily R) 365 – 1

• Weekly R = (1 + Daily R) 5 – 1

• Weekly R = (1 + Annual R) 1/52 – 1

9. Portf R (for Two Assets) = (Wght of Asset

1 ! R of Asset 1) + (Wght of Asset 2 ! R

of Asset 2)

10. Gross R = R – Trading exp – other exp

directly related to the generation of returns.

11.

Net R = Gross R - All managerial and

administrative exp






15. Total Weight of Nonmarket securities in

portfolio should be proportional to =

„†¥†#†‡%

„†‹™†

‹#†‡%

16.

Information Ratio =8ùø2ñ ûü ÷îíðìéòó é

/ûê$ó$òîõñòéí )é$1 ûü ÷îíðìéòó é

17. Expected Return of Portfolio (under

Arbitrage Pricing Model) = Q Mø 8 M V ,

¦ ùƒø–ú , ´ , ¦ 1ƒø–1

18. Return on an Asset in excess of 1-Month

T-Bill Return (under four factor model) =

Q Méò 8 ¤é , ƒé–&§!¢¨xò ,

ƒé–÷&dL¢wò , ƒé–t&-©¢ªò , ƒé–"&ô«¢yò

Reading 44: Basics of Portfolio Planning &

Construction

1.

Investor’s Expected Utility from Portfolio

= U p = E (R p) – /%2 p

2. Tactical Asset Allocation (TAA) Return

contribution = Actual return of the

portfolio – Return that would have beenearned if the asset class weights were equal

to the policy weights

Reading 45: Market Organization & Structure

1. Total return to a Leveraged Stock Purchase

=)îõñéêéê' 7Cðéòó/ú.

ú.where,

Remaining Equity = IO – Purchase

commission + (-) Trading g(l) – Margin i

paid + Div received – Sales commission

paid

OR

Remaining Equity = Proceeds on sale –

Payoff loan – Margin i paid + Div received

– Sales commission paid

2. ROE (based on leverage alone)

= Leverage (in times) ! stock price return

(in %)

3.

Price of stock below which a margin call

will take place (P):

^B4?4N> AN¦F4B ¬ , €3 ? ^B4?4N> L? ¥5 3¦4563

8 ¢N4B?6BNB56 ¢N¦F4B M6K4¦6A6B? €Þ

4.

Total cost of placement to the issuing firm

in IPO ($)

= Gross proceeds received by the issuing

firm – Net proceeds received by the issuing

firm

5. Total cost of placement to the issuing firm

in IPO (%) =€ýìû$$ øìûíîîö$ ìîíîé*îö ,ó úV/

/îò øìûíîîö$ ìîíîé*îö ,ó úV

/îò øìûíîîö$ ìîíîé*îö ,ó úV

where IF = Issuing firm

6.

Max leverage ratio =&ddÞ

Þ ûü 7Cðéòó

7. Max leverage ratio for position financed by

min margin requirement =&

&éê õñì'éê ìîCðéìîõîêò

Reading 46: Security Market Indices

1. Value of a price return index =

VPRI = D

P n

N

i

ii!=1

For Single Period:

2.

% Change in value of Price return index

Portfolio = PR I = 0

01

PRI

PRI PRI

V

V V !

3. Price Return (Ind constituent security):PR I

=

0

01

i

ii

P

P P !

4.

Price return of the index: PR I =

!=

""#

$%%&

' ( N

i i

ii

i

P

P P w

1 0

01




5. Total return of Index Portfolio:

0

01

PRI

I PRI PRI

V

IncV V +!

6.

Total return of each security = TR i =

i

iii

P

Inc P P

0

01 +!

!=

""#

$%%&

' +(=

N

i i

iii

i

P

Inc P P wturnTotal

1 0

01Re

Over Multiple Time Periods:

7.

Value of Price Return index at time t =

VPRIT = VPRI0 (1 + PR I1) (1 + PR I2) … (1 +

PR IT)

8. Value of Total Return index at time t =

VTRIT = V TRI0 (1 + TR I 1) (1 + TR I 2) … (1 +

TR I T)

9. Weight of security i under price weighting

=ëìéíî ûü $îíðìéòó é

÷ðõ ûü ñùù øìéíî$ ûü íûê$òéòðîêò $îíðìéòéî$

10. Weight of security i under equal weighting

=&

/û ûü $îíðìéòéî$ éê ò2î éêöî9

11. Weight of security i under market-cap

weighting =/d ûü $2ñìî$ ûw$ ûü ÷é 0 ÷2ñìî øìéíî ûü ÷é

/û ûü $2ñìî$ ûw$ ûü ÷é 0 ÷2ñìî øìéíî ûü ÷éf®‡%

Where Si = Security i

12. Weight of Si under Float-Adjusted Mkt

Cap weighting =Vìñíòéûê ûü $2ñìî$ ûw$ õ1ò üùûñò 0 ûü $2ñìî$ ÷é 0

÷2ñìî øìéíî ûü $îíðìéòó é

€Vìñíòéûê ûü $2ñìî$ ûw$ &1ò üùûñò 0 ûü $2ñìî$ ûw$ ûü ÷é 0

÷2ñìî øìéíî ûü $îíðìéòó é

13. Fundamental weight on security i =Vðêöñõîêòñù $évî õîñ$ðìî ûü íûõøñêó éÊ

€Vðêöñõîêòñù $évî õîñ$ðìî ûü íûõøñêó éf®‡%

*Book value, cash flow, revenues, earnings,

dividends, & number of employees.

Reading 47:Market Efficiency

Reading 48: Overview of equity Securities

1. Equity security’s Total Return =÷ñùî ë ûü ñ $2ñìî/ëðì2ñ$î ë ûü ñ $2ñìî'íñ$2w$òûí1 ôé*

ëðìí2ñ$î øìéíî ûü ñ $2ñìî

2. ROE in yr t =/ú €üûì .ìöéêñìó ÷2ñìî2ûùöîì$ éê óì ò

8*' !ûòñù d+ ûü 7Cðéòó

OR

ROE =/ú €üûì .ìöéêñìó ÷2ñìî2ûùöîì$ éê óì ò

÷2ñìî2ûùöîì$eîCðéòó ñò ,î' ûü óì ò

3. MV of equity = Mkt price per share !

Shares O/s

4. BV of equity per share =!ûòñù ÷te$ îCðéòó

÷2ñìî$ ûw$

5. Price-to-book ratio =&ñì1îò øìéíî øîì $2ñìî

d+ ûü îCðéòó øîì $2ñìî

6. ROE = Net profit margin ! Asset turnover

! Financial leverage =/îò îñìêéê'$

/îò $ñùî$ 0

/îò $ñùî$

8*' òûòñù ñ$$îò$ 0

8*' òûòñù ñ$$îò$

8*' íûõõûê îCðéòó

Reading 49: Introduction to Industry &

Company Analysis

Reading 50: Equity Valuation: Concepts &

Basic Tools

1.

Value of a share of stock today =79øîíòîö öé*éöîêö éê óì ò

€&'ìîCðéìîö ).) ûê $òûí1{¯ò\&

If an investor intends to buy and hold a share

for 1 yr:

2. Value of a share of stock today =79øîíòîö ôé* éê & óì '79øîíòîö $îùùéê' øìéíî éê & óîñì

€&'ìîC )û) ûê $òûí1%

3. Value of a share of stock for n holding

periods or investment horizon =79øîíòîö ôé* éê óì ò

&'ìîC ) ûê $òûí1 { ,L

G\&

79øîíòîö øìéíî éê ê øîìéûö$&'ìîC ) ûê $òûí1

4. CFO = NI + Non-cash exp – Inv in WC

5.

FCFE = CFO – FCInv + Net Borrowing

6. Value of a share for a non-div-paying

stock =V#V7 éê óîñì ò

&'ìîC ) ûê $òûí1 {¯ò\&




7. ReqRoR on sharei = Current expected Rf

rate + Beta i [MRP]

8. Value of a pref stock (non-callable, non-

convertible) =

( ) ( )r

D

r

D

g r

g DV 000

0

0

011=

!

+

=

!

+

=

9. Value of a pref stock (non-callable, non-

convertible) with maturity at time n =

Ad 8‹d

€ + , 5 G ,

L

G\&

j

+ , 5 L

Gordon Growth Model:

10.

Value of a share of stock =( )r g

g r

D

g r

g DV <

!

=

!

+

= ,1

10

0

11. Sustainable dividend growth rate =

g = ROE ! b

where b = earnings retention rate = (1 -

Dividend payout ra tio)

Two-stage valuation model:

12.

Value of share today = V0 =

Ad 8‹d + , 7

G

€ + , 5 G ,

AL

€+ , 5L

L

G\&

AL 8‹L'&

5 ? B

‹L'& 8 ‹d€ + , 7L + , B

13. Justified P/E =ëd

7&8

ô%w7%

ì/' 8

ø

ì/'

14. EV = MV of stock + MV of debt – Cash

and cash Equivalents

15.

Asset-based value = Value of Assets –

Value of Liabilities

Reading 51: Fixed Income Securities: Defining

Elements

1. Inf adj Principal amount of a zero-coupon-

indexed bond

= [Par value ! (1 + CPI)]

2.

Inf adj coupon payment for an interest-

indexed bond

= [(coupon rate ! Par value) ! (1+CPI)]

3. Inf adj Principal amount of a capital-

indexed bond

= [Par value ! (1 + CPI)]

4. Inflation adjusted coupon payment for a

capital-indexed bond

= [Par value ! (1 + CPI)] ! coupon rate

Reading 52: Fixed Income Markets: Issuance,

Trading & Funding

Reading 53: Introduction to Fixed Income

Valuation

1. Amount of discount below par value =

Present value of deficiency

2. Present value of deficiency =#ûðøûê ìñòî/&ñì1îò öé$íûðêò ìñòî 0ëñì *ñùðî

&'&ñì1îò öé$íûðêò ìñòî {êò\&

3. Bond price =

PV = PMT

(1+ r)1 + PMT

(1+ r)2 + ...+ PMT + FV

(1+ r) N

4.

% Price change =/î< øìéíî/.ùö øìéíî

.ùö øìéíî

5. Bond price (given sequence of spot rates)

= PV =

PMT

(1+ Z 1)1 +

PMT

(1+ Z 2 )2 +...+

PMT + FV

(1+ Z N ) N

6. Full price of bond = Flat price of bond +

Accrued interest

7. Accrued interest = a^ 8G

*0@]^

8. Full price of a fixed-rate bond between

coupon payments = PVFull

=

PMT

(1+ r)1!t /T

+

PMT

(1+ r)2!t /T

+...+PMT + FV

(1+ r) N !t /T

9. Full price of a fixed-rate bond between

coupon payments

PV ! (1+ r)t /T

10. Interpolated yield (say for 3-year, given

market discount rates for 2 and 5 yrs) =

(Average yield for 2 year bonds) +p/l

v/l !




(average yield for 5 year bonds – average

yield for 2 year bonds)

11. 1+ APR

m

m

!

"

#$

%

&

m

= 1+ APR

n

n

!

"

#$

%

&

n

12. Current yield =÷ðõ ûü íûðøûê øñóõîêò$ ìîíîé*îö û*îì ò2î óîñì

Vùñò øìéíî

13. Price of Floating-rate note = PV=

( I +Qm)!FV

m

1+ I + DM

m

"

#$

%

&'1 +

( I +QM )!FV

m

1+ I + DM

m

"

#$

%

&'2 +...+

( I +QM )!FV

m+FV

1+ I + DM

m

"

#$

%

&' N

14. Price of Money Market Instrument (on a

discount-rate basis) =

PV = FV ! 1" Days

Year! DR

#

$%

&

'(

15. Market Discount Rate =

DR = Year Days( )! FV " PV

FV

#

$%

&

'(

16. Price of Money Market Instrument (on an

add-on rate basis)=

PV =FV

1+ Days

Yr! AOR

"

#$

%

&'

17. Add-on rate =

AOR =Yr

Days

!

"#

$

%&'

FV ( PV

PV

!

"#

$

%&

Relation b/w two spot rates and Implied

Forward Rate:

18. (1 + zA)A ! (1 + IFR A,B-A)B-A = (1 + zB)B

Z-spread over the benchmark spot curve:

Price of a bond =

PV =PMT

(1+ z1+ Z )

1 +

PMT

(1+ z2 + Z )

2 +...+

PMT + FV

(1+ z N + Z )

N

19. OAS = Z-spread – Option value (bps per

year)

20. G-spread = Yield-to-maturity on Corporate

bond – Yield-to-maturity on a government

bond

21. Interpolated Spread = I-spread = Yield to

maturity of the bond - Standard swap rate

in that currency of the same tenor

Reading 54: Introduction to Asset Backed

Securities

1. Loan-to-value ratio (LTV) =ëìûøîìòóe$ øðìí2ñ$î øìéíî

8õûðêò ûü &ûìò'ñ'î

2. Monthly CF for a MPS = Monthly CF of

underlying pool of mortgages - Servicing

fee - Other fees

3. Pass-through rate = Mortgage rate on the

underlying pool of mortgages – Servicing

Fee - Other fees

4.

SMM = Pre-pmt for month ÷ (Beg

mortgage balance for month – Scheduled

principal re-pmt for month)

5. CPR = 1 0 (1 0 SMM)12

6. CF Construction (Monthly CF for MPS):

• Net interest = (Beg mortgage

balance ! Pass-through rate) / 12

• Scheduled principal re-pmt =

Mortgage pmt – Gross i- pmt• Gross i- pmt = (Beg mortgage

balance ! WAC) / 12

• Pre-pmt for month = SMM !

(Beg mortgage balance for month

– Scheduled principal re-pmt for

month)

• Total principal re-pmt =

Scheduled principal re-pmt +

Prepayment

• Beg mortgage balance for the

following month = Beg mortgage

balance for the month – Total

Principal Pmt

• Projected CF for MPS = Net i-

pmt + Total principal re-pmt

7. DSC ratio =ëìûøîìòó°$ ñêêðñù /.ú

ôî,ò $îì*éíî




Reading 55: Understanding Fixed Income Risk

& Return

1. Interest-on-interest gain from

compounding = Future value of reinvested

coupons - Total amount of coupon payments

Where,

FV of Reinvested Coupons = [CR !(1+

RR)n-1] + [CR !(1+RR) n-2] +…+ [CR !(1+

RR)n-n]

Total Amount of Coupon Pmt = CR ! Par

value ! No of periods

RR = Re-invstmnt rate per period

CR = coupon rate

2. Realized RoR on Bond=

÷ðõ ûü )îéê*î$òîö #ûðøûê$'

)îöîõøòéûê ûü ëìéêíéøñù ñò &ñòðìéòó

dûêö ëìéíî

%

n

? +

3. Carrying value of bond (if bond purchased

below par) = Purchase price + Amortized

amount of Discount

4.

Carrying value of a bond (if bond purchased above par) = Purchase price –

Amortized amount of Premium

5. Amortized amount for 1st year = Bond

Price after 1-yr - Initial bond price

6. Capital g / (l) = Sale price of Bond after n

years – Carrying value of Bond after n

years

7.

Macaulay Duration =

MacDur = 1! t / T ( )

PMT

1+ r( )1!t /T

PV Full

"

#

$$$$

%

&

''''

+ 2! t / T ( )

PMT

1+ r( )2!t /T

PV Full

"

#

$$$$

%

&

''''

+...+ N ! t / T ( )

PMT + FV

1+ r( ) N !t /T

PV Full

"

#

$$$$

%

&

''''

(

)

**

+

**

,

-

**

.

**

OR

MacDur =1+ r

r!

1+ r + N " c! r( )#$ %&

c" 1+ r( ) N

!1#$

%&+ r

'

()

*)

+

,)

-)! (t /T )

8. Modified D =&ñíôðì

&'ì

9. Annualized Modified D =&ûöéüéîö ôðìñòéûê

ëîìéûöéíéó ûü øñóõîêò éê ñ óîñì

10. % 1 PVFull

= - AnnModDur ! 1Yield

11. Approx Modified D =

(PV ! )! (PV

+)

2" (#Yield )" (PV 0)

12. Approx Mac Dur = Approx Mod Dur ! (1

+ r)

13.

Effective D =(PV

! )! (PV

+)

2" (#Curve)" (PV 0)

14. Macaulay D for a Zero-coupon bond =1/G

*

15. Macaulay D for a Perpetual bond = (1+ r) /

r

16. Avg Mod D for the Portf =

¢¥I y ¥¤ w¥BI + 0&+ ûü dûêö &

!ûòñù &+ûü ëûìòü

+ ¢¥I y ¥¤ w¥BI ª 0&+ ûü dûêö l

!ûòñù &+ ûü ëûìòü +

…+ ¢¥I y ¥¤ w¥BI ] 0&+ ûü dûêö /

!ûòñù &+ ûü ëûìòü

17. Money D = Annualized Mod D ! Full

Bond Price

18. ) Full price of Bond (in currency units) # -

Money D ! è in annual YTM

19. PVBP =(PV

!

)!(PV

+)

2

20. Basis Point Value (BPV) = Money

duration ! 0.0001 (1 bp)

21. Bloomberg’s Risk Statistic = PVBP ! 100

22. %)PVFull

= (-AnnModDur ! )Yield) +&

l

0‘==iX=4¡>:± 0€èu>4±<l

23. Approx. Convexity Adjustment =

(PV !)+ (PV

+)![2" (PV 0 )]

(#Yield )2" (PV 0 )




24. Convexity of a zero coupon bond =

N ! (t /T )[ ]" N +1! (t /T )[ ](1+ r)

2

25.

Money Convexity vs Money Duration =)PV Full # - (MoneyDur ! )Yield) + [

&

l !

MoneyCon ! ()Yield)2]

26. Money Convexity of bond = Annual

Convexity ! Full Price

27. Effective Convexity =

PV !( )+ PV +

( )! 2" (PV 0)[ ]#$ %&

'Curve( )

2

" PV 0 )( )

28. Duration Gap = Bond’s Macaulay

Duration – Investment Horizon

Reading 56: Fundamentals of Credit Analysis

1. Expected Loss = Default Probability !

Loss Severity given Default

2.

Funds From Operations = NI +Dep +

Amor+ Deferred income taxes noncashitems

Where NI = Net Income

3. FCF Before Div = NI – Cap exp. – (+) Inc

(dec) in Non-cash WC – Non-recurring

items

4. FCF After Div = FCF Before Div – Div

5. Operating Profit Margin =.øîìñòéê' úêíûõî

)î*îêðî

6. EBITDA = Operating Income + Dep +

Amort

7.

FCF = CFO – Cap exp– Div

8. Capital expenditures = Additions to P&E +

Additions to product rights & intangibles –

Proceeds of sale of P&E

9. Total debt = ST debt + Current portion of

LT debt + LT debt

10.

Capital = Debt + Equity

11.

Yield on Corp Bond = Real Rf rate +Expected Inf rate + Maturity P + Liquidity

P+ Credit spread

12.

Yield spread = Liquidity P + Credit spread

13. Return impact for smaller spread )# % )

in price # -Modified Duration ! )Spread

14. Return impact for larger spread ) # % ) in

price # - (Modified D ! )Spread) +

&lConvexity ! ()Spread)2

15. Secured debt leverage =!ûòñù $îíðìîö öî,ò

7dú!ô8

16. Senior unsecured leverage =÷îíðìîö öî,ò'÷îêéûì ðê$îíðìîö öî,ò

7dú!ô8

17. Total Leverage =!ûòñù öî,ò

7dú!ô8

18.

Net Leverage =!ûòñù öî,ò/#ñ$2

7dú!ô8

Reading 57: Derivatives Markets andInstruments

1. Value of the contract to the ‘Long’ at

expiration = ST – F0(T)

2.

Value of the contract to the ‘Short’ at

expiration = F0(T) – ST

3. Margin % in stock market =&+ ûü ÷òûí1/&+ ûü ôî,ò

&+ ûü ÷òûí1

4. Margin Call:

• Long position: Price² that would

trigger a margin call = IM req – MM

req

• Short position: Price( that would

trigger a margin call = IM req – MM

req

5. TED spread = LIBOR – T-Bill rate

6. At expiration (for option Buyer):

• Value of Call option =

cT = Max (0, ST - X)

• Profit from Call option =

Max (0, ST - X) – c0

• Value of Put option = pT =

Max (0, X- ST)




• Profit from Put option =

Max (0, X- ST) – p0

7.

At expiration (for option Seller):

• Profit from Call option =

– Max (0, ST - X) + c0

• Profit from Put option =

– Max (0, X- ST) + p0

8. To eliminate arbitrage opportunity:

Forward Price should be = Spot Price

0 + , > 5;:4 Þ G

Reading 58: Basics of Derivative Pricing &

Valuation

1. Pricing of risky assets = S0 =7 €÷!

&'ì'³ “

2. Commodity = F 0, T = S0 e(r – 2)T where, 2 =

Convenience yield 0 Cost of carry

3. S0 =7 €÷“

&'ì'´ “ – 3 + 4

where, 3 (theta) = Present value of the

costs and 4 (gamma) = Present value of

benefits

4. Arbitrage and Derivatives = Underlying

asset + Opposite position in derivative =

Underlying payoff – Derivative payoff =

Rf return

5.

Pricing and Valuation of Forward

Contracts:

• At Expiration F0 ( T) = S0 (1 + r) T or

S0 = F0 (T) / (1 + r) T

•

Value of forward (long) during

contract life (where t < T) = Vt (T) =

St – F0 (T) / (1 + r)(T – t)

•

Value of forward (short) during

contract life (where t < T ) = Vt

(T) = F0 (T) / (1 + r) (T – t) - St

• Value of forward (long) at expiration

(where t = T) = VT (T) = ST - F0 (T)

•

Value of forward (long) at initiation

(where t = 0) = Vt (0, T) = S0 – F0 (T) /

(1 + r) T

= 0

• Forward price of an asset with benefits

and/or costs = (S0 – 4 + 3) (1 + r) T =

S0 (1 + r)T

– (4 - 3) (1+ r)T

• Value of Forward contract with

benefits and/or costs during the life of

the contract = St – (4 - 3) (1 + r) t - F0

(T) / (1 + r) (T – t)

6. FRAs: An example of 3 ! 9 FRA (read as

three by nine):

• Contract expires in 90 days

•

Underlying loan settled in 270 days

•

Underlying rate is 180-day LIBOR• For Synthetic FRA (take long position

in a 270-day Euro$ T.D and short

position in a 90-day Euro$ T.D

• For synthetic forward position in a 90-

day zero-coupon that begins in 30

days (buy 120-day & sell 30-day zero

coupon bonds)

7. Payoff of Call options:

• At expiration call option = c T = Max

(0, ST –X)

• Profit (call buyer) = Max (0, ST – X) –

c0

• Profit (call seller) = -Max (0, ST – X)

+ c0

8. Payoff of Put options:

•

p T = Max (0, X- ST)

• Profit (put buyer) = Max (0, X-ST) – p0

• Profit (put seller) = - Max (0, X – ST) +

p0

9.

Max Profit/Loss for Option writer/holder:

• Max profit of option seller/writer!

Option premium.

• Max loss of option seller/writer!

unlimited in case of calls; large in case

of puts (bounded by zero).

• Max loss of option holder!Option

premium

Put-Call Parity

10. Protective Put

•

Value PP = p0 + S0

• Payoff at expiration (put out-of-the-

money) = ST.

•

Payoff at expiration (put in-the-

money) = (X-ST) + ST = X.




11. Fiduciary Call

•

Value FC = c0 + X / (1+r) T

• Payoff at expiration (when call out-of-

the-money) = X.

• Payoff at expiration (call in-the-

money) = X + (ST – X) = ST.

12. Put-Call Parity (to avoid arbitrage) = c0 +

X / (1+r) T = p0 + S0

• Synthetic long position in a call =

T r

X S pc

)1(000

+

!+=

• Synthetic long position in a put =

p0= c

0!S

0+

X

(1+ r)T

• Synthetic long position in an

underlying = S 0 = c 0+

X

(1+ r)T ! p0

• Synthetic long position in a riskless

bond = X

(1+ r)T = p

0+S

0 ! c

0

13. Put-Call-Forward Parity = F0(T) / (1 + r) T

+ p0 = c0 + X/(1 + r) T

14.

Valuing a callable bond using Binomial

Model:

•

0

1

0

1 ,S

S d

S

S u

!+

==

• Value at time 0 = V0 = hS0 0 c0

• Value at time 1 will either V1

+ = hS1+ -

c1+ or V1- = hS1- - c1-

• If the portfolio was hedged, then V

+

would equal V-.

• Value of the call =

• Value of the put =

Reading 59: Risk Management Applications of

Option Strategies

1. For Call Option Buyer

• cT = max (0, ST –X)

• When ST + X"cT = 0

• When ST> X"cT = ST – X

• Value at expiration = cT

• Profit = cT – c0

•

Maximum profit = 5! no upper limit

• Maximum loss = c0

• Breakeven = ST* = X + c0

2. For Call Option Seller

• cT = max (0, ST –X)

•

When ST + X"cT = 0

• When ST> X"cT = ST –X

•

Value at expiration = -cT

• Profit = –cT+ c0

• Maximum profit = c0

• Maximum loss = 5! no upper limit

• Breakeven = ST* = X +c0

3. For Put Option Buyer

•

pT = max (0, X - ST)

• When ST< X" pT = X - ST

• When ST " X" pT = 0

•

Value at expiration = pT

• Profit = pT – p0

• Maximum profit = X – p0

• Maximum loss = p0

• Breakeven = ST* = X –p0

4. For Put Option Seller

• pT = max (0, X –ST)

• When ST< X" pT = X – ST

• When ST " X" pT = 0

•

Value at expiration = –pT

• Profit = –pT + p0

• Maximum profit = p0

• Maximum loss = X - p0

• Breakeven = ST* = X - p0




5. Covered Call = Long stock position +

Short call position

• Value at expiration = VT = ST – max

(0, ST – X)

• When ST + X"VT = ST

• When ST> X"VT = ST - ST +X = X

• Profit = VT – S0 + c0

• Maximum Profit = X – S0 + c0

•

Maximum Loss = S0 – c0

• Breakeven =ST* = S0 – c0

6. Protective Put = Long stock position +

Long Put position

• Value at expiration: VT = ST + max (0,

X - ST)

• When ST + X"VT = ST + X - ST = X

•

When ST> X"VT = ST

• Profit = VT – S0 - p0

• Maximum Profit = 5

•

Maximum Loss = S0 + p0 – X

• Breakeven =ST* = S0 + p0

Reading 60: Introduction to AlternativeInvestments

1. Total Return = Alpha R + Beta R

2. Asset Based Valuation = Co value = Co’s

assets value – Co’s liabilities value

Real Estate Valuation

3. Direct Cap Approach " Valuation of a

property =1Vf

RHSMGHxMµHGMOL NHGI where

NOI = Gross potential income –Estimated

vacancy losses – Estimated collective

losses – Insurance – Property Taxes –Utilities – Repairs, maintenance exp.

4.

Income Based Approach" FFO = NI +

Dep exp on R.E + Def Tax charges – Gains

from sales of R.E + losses from sale of R.E

5. AFFO = FFO – Recurring Cap exp

6. Asset based Approach" REIT’s NAV =

Estimated MV of REIT’s total assets –

Value of REIT’s total liabilities.

7. Pricing of Commodity Futures Contracts:

Futures price # Spot price (1 +r) + Storage

costs – Convenience yield

8. Roll yield = Spot price of a commodity –

Futures contract price or

Roll yield = Futures contract price with

expiration date ‘X’– Futures contract price

with expiration date ‘Y.

9.

Returns on a passive investment in

commodity futures

= Return on the collateral + RP or

convenience yield net of storage costs.

10. Sharpe ratio = (Investment return – Rf

return) / S.D. of return

11. Sortino Ratio = (Annualized RoR –

Annualized Rfe rate)/Downside Deviation

Documents

CFA l 1 Formula Sheet December 2015