cfa level 1, june, 2016 - formula sheet

8/16/2019 CFA Level 1, June, 2016 - Formula Sheet

http://slidepdf.com/reader/full/cfa-level-1-june-2016-formula-sheet 1/31



FinQuiz Formula Sheet CFA Level I 2016

• r MM = opf ( qr

opf/ G ( qr (Rule: r MM>

r BD)10. Bond Equivalent Yield = BDY =

Semiannual Yield ! 2

Reading 7: Statistical Concepts & MarketReturns

1. Range = Max Value – Min Value

2. Class Interval = i " z/B

{ where

• i = class interval• H = highest value• L = lowest value, k = No. of classes.

3. Absolute Frequency = Actual No ofObservations (obvs) in a given classinterval

4. Relative Frequency = K|7OwSGI !(I}SILa`

*OGHw 1O OP U|~7

5. Cumulative Absolute Frequency = Add upthe Absolute Frequencies

6. Cumulative Relative Frequency = Add upthe Relative Frequencies

7. Arithmetic Mean = FS. OP O|~7 ML JHGH|H7I

1O•OP O|~7 ML GxI JHGH|H7I

8. Median = Middle No (when observationsare arranged in ascending/descendingorder)

• For Even no of obvs locatemedian at L

k

• For Odd no. of obvs locate

median at L'&

k

9. Mode = obvs that occurs most frequentlyin the distribution

10. Weighted Mean = € 8 2 M € MLM[& =

(w1X1+ w 2X2+….+ w nXn)

11. Geometric Mean = GM = €& € k l € Lm

with X i" 0 for i = 1,2,…n.

12. Harmonic Mean = H.M = € z 8 L%

‚ ƒmƒ„%

13. Population Mean = µ =…ƒ

mƒ

1 with € M † j

for i = 1,2,.,.,n.

14. Sample Mean = € 8…ƒ

mƒ

L where n =

number of observation in the sample

15.

Measures of Location:• Quartiles = iM7G(M|SGMOL

‡

• Quintiles = iM7G(M|SGMOL

u

• Deciles = iM7G(M|SGMOL

&f,

• Percentiles = L y = = , + `

&ff

16. Mean Absolute Deviation = MAD =…Z/…m

ƒ„%

L

17. Population Var = !2 = …ƒ/ˆ ‰#

ƒ„%

1

18. Population S.D = Š k =…ƒ/ˆ ‰#

ƒ„%

1

19. Sample Var = s 2 = …ƒ/… ‰mƒ„%

L/&

20. Sample S.D = s =…ƒ/… ‰m

ƒ„%

L/&

21. Semi-var = …ƒ/… ‰

L/&!O( Hww …ƒ‹…

22. Semi-deviation (Semi S.D) =

94Œ> ;5>;=X4 = …ƒ/… ‰

L/&!O( Hww …ƒ‹…

23. Target Semi-var = …ƒ/y ‰

L/&!O( Hww …ƒ‹y

where B = Target Value

24. Target Semi-Deviation =:;5Ž4: 94Œ> ;5>;=X4 =

…ƒ/y ‰

L/&!O( Hww …ƒ‹y

25. Coefficient of Variation = CV = F…

where s= sample S.D and € = samplemean

26. Sharpe Ratio = )IHL $O(GPOwMO N/)IHL NP N

F•i OP $O(GPOwMO N

27. Excess Kurtosis = Kurtosis – 3




• 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)

=&

|/Hj

eW5 ; ¢ £ ¢ œ =

F(x) = Ÿ/H

|/H eW5 ; ¤ £ ¤ œ

3. Normal Density Funct = e £ 8&

™ k¥4£’ /cŸ/ˆd ‰

k™‰ ¦§¨ ? © ¤ £ ¤ , ©

4. Estimations by using Normal Distribution:

• Approximately 50% of all obsv fall in

the interval ª « k

oŠ

• Approx 68% of all obvs fall in theinterval ª « Š

• Approx 95% of all obvs fall in theinterval ª «¬Š

• Approx 99% of all obvs fall in theinterval ª « Š

• More precise intervals for 95% of theobvs are ª « +•®¯Š and for 99% of theobservations are ª « ¬•°±Š•

5. Z-Score (how many S.Ds away from themean the point x lies) ² 89:;=<;5< =W5Œ;³ 5;=<WŒ ;5>;œ³4 8

…/ˆ

™ (when X is normally distributed)

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

™E

7. Sharpe Ratio = = NE /N µ

™E

8. Value at Risk = VAR = Minimum $ lossexpected over a specified period at aspecified prob level.

9. Mean (µ L) 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. Log Normal Price = S T = S 0exp (r 0,T)Where, exp = e and r 0,t = Continuouslycompounded return from 0 to T

12. Price relative = End price / Beg price =St+1/ S t=1 + R t, t+1

where,

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

13. Continuously compounded returnassociated with a holding period from t to t+ 1:

r t, t+1= ln(1 + holding period return) orr t, t+1 = ln(price relative) = ln (S t+1 / S t) = ln(1 + R t,t+1)

14. Continuously compounded returnassociated with a holding period from 0 toT:

R 0,T= ln (S T / S 0) or 5f–* 8 5 */&–* ,5*/k–*/& , ¶ , 5 f–&

Where,r T-I, T = One-period continuouslycompounded returns

15. When one-period continuouslycompounded returns (i.e. r 0,1) are IIDrandom variables.

“ 5f–* 8 “ 5 */&–* , “ 5 */k–*/& ,

¶ , “ 5 f–& 8 ª] And

A;5>;=X4 8 Š k 5f–* 8 Š k ]

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

16. Annualized volatility = sample S.D. ofone period continuously compoundedreturns ! ]

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

= Š… 8 ™

L

• When the population S.D ( ! ) is notknown = 9… 8 7

L where s = sample

S.D estimate of s =

9;Œ’³4 ;5>;=X4 8

9k 23454 9 k =…ƒ/… ‰m

ƒ„%

L/&

4. Finite Population Correction Factor = fpc

= 1/L

1/& where N= population

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 populationwith known variance = £ « ² Hvk

™

L

•

CI for normally distributed populationwith unknown variance = £ « ² Hvk

F

L

where S = sample S.D.

7. Student’s t distribution

µ = € « : HvkF

L

8. Z-ratio = Z =

x ! µ

! / n

9. t-ratio = t =

x ! µ

s / n

Reading 11: Hypothesis Testing

1. Test Statistic =·¸¹º»¼ ·½¸½¾¿½¾À ÁÂºÃ½Ä¼¿¾Å¼Æ Ç¸»È¼ ÃÉ ºÃº º¸Ê¸¹¼½¼Ê

¿½¸ËÆ¸ÊÆ ¼ÊÊÃÊ ÃÉ ¿¸¹º»¼ ¿½¸½¾¿½¾ÀÌ

*when Pop S.D is unknown, the standarderror of sample statistic is give by Í … 8

F

L

*when Pop S.D is unknown, the standarderror of sample statistic is give by Š… 8 ™

L

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

3. ² 8 …/ˆ hÎm

(when sample size is large or

small but pop S.D is known)

4. ² 8 …/ˆ h-m

(when sample size is large but

pop S.D is unknown where s is sampleS.D)

5. : L/& 8 …/ˆ h-m

(when sample size is large or

small and pop S.D is unknown and pop

sampled is normally or approximatelynormally distributed)

6. Test Statistic for a test of diff b/w two popmeans (normally distributed, pop varunknown but assumed equal)

t = …%/… ‰ / ˆ %/ˆ ‰

Ï Ð‰

m%'

Ï Ð‰

m‰

%v‰ where Í Rk = pooled

estimator of common variance =L%/& F %

‰' L ‰/& F ‰‰

L%' L ‰/k where <e 8 = & , = k ?

¬.

7. Test Statistic for a test of diff b/wn two pop means (normally distribu ted, unequaland unknown pop var unknown)

t = …%/… ‰ / ˆ %/ˆ ‰

Ï %‰

m%'

Ï ‰‰

m‰

%v‰ In this df calculated as

<e 8

Ï %‰

m% '

Ï ‰‰

m‰

‰

Ï %‰

m%

‰

m%'

Ï ‰‰

m‰

‰

m‰

8. Test Statistic for a test of mean differences(normally distributed populations,unknown population variances)

• : 8 J/ˆ Ñh

FJ

• sample mean difference = < 8

&L

<MLM[&

• sample variance = Í Jk 8

J %/J ‰mƒ„h

L/&




• sample S.D = Í Jk

• sample error of the sample mean

difference = 9 < 8 FÑ

L

8. Chi Square Test Statistic (for testconcerning the value of a normal

population variance) € k 8 L/& F ‰

™h‰ where

= ?+ 8 <e ;=< Í k 8

9;Œ’³4 ;5>;=X4 8…ƒ/… ‰m

ƒ„h

L/&

9. Chi Square Confidence Interval forvariance

Lower limit = L = L/& F ‰

…Òv‰‰ and Upper limit

= U = = L/& F ‰

…%¡Òv‰‰

10. F-test (test concerning differences betweenvariances of two normally distributed

populations) F = F%‰

F‰‰

Í &k 8 +9: 9;Œ’³4 ;5 2>:3 = & Wœ9 Í&k 8

¬=< 9;Œ’³4 ;5 2>:3 = k Wœ9

<e& 8 = & ? + =ÓŒ45;:W5 <e<ek 8 = k ? + <4=WŒ>=;:W5 <e

11. Relation between Chi Square and F-

distribution = Ô 8…%

‰.

…‰‰

L where:

• €&k is one chi square random variable

with one m degrees of freedom

• € kk is another chi square random

variable with one n degrees offreedom

12. Spearman Rank Correlation = 57

8 + ?¯ <&

kLM[&

= =k ? +

• For small samples rejection points forthe test based on 57are found usingtable.

• For large sample size (e.g. n>30) t-testcan be used to test the hypothesis i.e.

: 8= ? ¬ &vk57

+ ? 5 7k &vk

Reading 12: Technical Analysis

1. Relative Strength Analysis =ÕÊ¾À¼ ÃÉ ̧ ¿¿¼½

ÕÊ¾À¼ ÃÉ ½Ä¼ Ö¼ËÀÄ¹¸Ê× Ø¿¿¼½

2. Price Target for the• Head and Shoulders = Neckline –

(Head – Neckline)• Inverse Head and Shoulders =

Neckline + (Neckline– Head)

3. Simple Moving Average = ÕÙ'Õ Ú'Õ Ûl•'Õ Ë

Ü

4. Momentum Oscillator (or Rate of ChangeOscillator ROC):

• Momentum Oscillator Value M = (V-Vx) 0+jj

(where V = most recent closing priceand V x = closing price x days ago)

• Alternate Method to calculate M ="

"0+jj

5. Relative Strength Index = RSI = +jj ?

&ff

&'NF where

RS = ÝR axHLTI7

iO L axHLTI7

6. Stochastic Oscillator (composed of twolines %K and %D):

• Þß 8 +jj Q/B&‡

z&‡/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) = ÇÃ»È¹¼ ÃÉ ÕÈ½ àº½¾ÃË¿ áÊ¸Æ¼Æ

ÇÃ»È¹¼ ÃÉ â¸»» àº½¾ÃË¿ áÊ¸Æ¼Æ

8. Short Interest Ratio (Type of Sentiment

Indicators) = ·ÄÃÊ½ ãË½¼Ê¼¿½ Øä¼Ê¸å¼ æ¸¾»Â áÊ¸Æ¾Ëå ÇÃ»È¹¼

9. Arms Index TRIN i.e. Trading Index (Typeof Flow of funds Indicator) = 5Œ ›=<4£ W5 ]Y›š 8

1O•OP KJ~HL g77SI7 ç1O•OP iIawML g77SI7

"OwS.I OP KJ~HL g77SI7ç"OwS.I OP iIawML g77SI7




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 aconsumer places on units consumed –Price paid to buy those units• Area (for calculating Consumer

Surplus) = & (Base ! Height) = & (Q0

! P0)

4. Producer Surplus = Total revenue receivedfrom selling a given amount of a good –Total variable cost of producing thatamount

• Total revenue = Total quantity sold ! Price per unit

• Area (for calculating Producer

Surplus) = & (Base ! Height) = & {(Q 0) ! (P0 – intercept point on y-axis**)}

**where supply curve intersects y-axis

5. Total Surplus = Consumer surplus +Producer surplus

6. Total Surplus = Total value – Totalvariable cost

7. Society Welfare = Consumer surplus +Producer surplus

8. Price Elasticity of Demand =Þ è éê ïðñêòéòó ôîõñêöîö

Þ è éê ëìéíî

)(

)(P%Q%

2121

12

2121

12

P P P P QQQQ

+

!

+

!

="

"

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

Þ è éê úêíûõî=

)(

)(I%Q%

2121

12

2121

12

I I I I QQQQ

+

!

+

!

="

"

10. 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 = (P X ! QX ) + (P Y ! QY)

3. Slope of Budget Constraint Line = è éê ï %

è éê ï ‚ =

ë ‚

ë %

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: TheFirm

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 Costs

or• = Total Revenue – Total Economic

Costs

4.

Economic costs = Explicit costs + Implicitcosts5. Normal Profit = Accounting Profit –

Economic Profit

6. Accounting profit = Economic Profit + Normal Profit




7. Economic rent = (New “Higher” Priceafter ( 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 Unitssold = ' (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 perunit ! Quantity Produced

12. Total Cost = Total Fixed + Total Variable

13. Average total cost (ATC) =! ûòñù # û $ò

ïðñêòéòó 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 = Demand

17. Profit can be increased by increasingoutput when MR> MC

18. Profit can be increased by decreasingoutput when MR< MC

19. Break-even price: P = ATC ! Outputlevel 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 = MarginalCost ! firm will continue operating.

22. Losses are incurred when there areOperating profits (Total Revenue " Variable Cost) but Total Revenue < TotalFixed Cost + Total Variable Cost ANDwhen Price = Marginal Cost while lossesare < fixed costs ! firm will continueoperating.

23. Losses are incurred when there areOperating losses (Total Revenue ( Variable Cost) AND when losses " fixedcosts ! 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 0 ûì 1 îì $

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

ëìéíî ûü - ñ , ûì8

& ñì ' éêñù ëìûöðíò ûü ë 2ó$éíñù # ñøéòñù

ëìéíî ûü ë 2 óéíñù # ñøéòñù

27. Profit is maximized when: MRP = Price orcost of the input for each type of resourcethat is used in the production process

28. Marginal Revenue product = MarginalProduct of an input unit ! Price of the

Product = Price of the input =è éê ! ûòñù ) î * îêðî

è éê ïðñêòéòó ûü úêøðò îõøùûóîö

29. Surplus value or contribution of an input tofirm’s profit = MRP – Cost of an input

Reading 16: The firm & Market Structures

1. In perfect competition, Marginal revenue =Avg. Revenue = Price = Demand

2. Marginal Revenue = 3 ¨456 0 + ?

&

ëìéíî 7 ùñ$òéíéòó ûü ôîõñêö

3. Concentration Ratio =÷ðõ ûü $ñùî $ *ñùðî $ ûü ò2 î ùñì ' î $ò &f üéìõ $

! ûòñù & ñì 1 îò ÷ñùî $




4. Herfindahl-Hirshman Index = Sum of thesquares of the market shares of the top Ncompanies 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 / GDPdeflator) ÷ 100]

5. GDP deflator = / ûõéêñù ýôë

) îñù ýôë0+jj

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 payments8. GDP = National income + Capital

consumption allowance + Statisticaldiscrepancy

9. National Income = Compensation ofemployees + 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 businesstaxes – Corp income taxes – UndistributedCorp 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 - Consumptionexpenditures - Interest paid by consumersto business - Personal transfer payments toforeigners

15. Business sector saving = Undistributedcorporate profits + Capital consumptionallowance

16. Total Expenditure = Householdconsumption (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 + PrivateSector Saving + Net Taxes

19. Domestic saving = Investment + Fiscal balance + Trade balance

20. Trade Balance = Exports – Imports

21. Fiscal balance = Government Expenditure – Taxes = (Savings – Inves tment) – TradeBalance

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

) îñù úêíûõî

23. Quantity theory of money equation: Nominal Money Supply ! Velocity ofMoney = Price Level ! Real Income orExpenditure

24. % è in unit labor cost = % è in nominalwages - % è in productivity

25. Economic growth = Annual % è in realGDP

26. Total Factor Productivity growth = Growthin potential GDP – [Relative share of laborin National Income ! (Growth in labor) +[Relative share of capital in NationalIncome ! (Growth in capital)]




27. Growth in potential GDP = Growth intechnology + (Relative share of labor in

National Income ! Growth in Labor) +(Relative share of capital in NationalIncome ! Growth in capital]

28. Capital share =Corporate profits + netinterest income + net rental income +(depreciation/ GDP)

29. Labor share = 7 õøùûóîî # ûõøîê $ñòéûê

ýôë

Reading 18: Understanding Business Cycles

1. Price index at time t 2 ="HwSI OP GxI QO.7S.RGMOL yH7{IG HG G ‰

"HwSI OP GxI QOL7S.RGMOL yH7{IG HG G %0+jj

Inflation Rate = ëìéíî úêöî 9 ñò òéõî òk

&ff? +

2. Fisher Index = ›’ 0› : (where, I L =Laspeyres index and I p = Paasche Index)

3. ; =>: ³;œW5 XW9: c;: d >=<>X;:W5 8! ûòñù ùñ, ûì íûõøîê $ñòéûê øîì 2ûðì øîì < ûì 1 îì

. ðòøðò øîì 2 ûðì øîì < ûì 1 îì

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 ) î C ûì ìî $îì * î ìñòéû

3. Narrow money = M1= currency held

outside banks + checking accounts +traveller’s check

4. Broad money = M2 = M1 + time deposits+ saving deposits

5. M3 = M2 + deposits with non-bank financial institution

6. Quantity Theory of Money = M ! V = P ! Y where,

M = Quantity of moneyV = Velocity of circulation of moneyP = Average price levelY = Real output

7. Neutral Rate = Trend Growth + InflationTarget

8. Impact of Taxes and GovernmentSpending: The Fiscal Multiplier

The net impact of the government sectoron AD:

• G – T + B = Budget surplus or Budgetdeficitwhere, G = government spending , T=taxes, B =transfer benefits

• Disposable income = Income – Nettaxes = (1 – t) 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 = &

&/)$Q &/G

• Total ( in income and spending =

Fiscal multiplier ! G• Initial ( in consumption due to

reduction in taxes = MPC ! tax cutamount

• Total or cumulative effect of tax cut =multiplier ! initial change inconsumption

11. Cumulative multiplier =íðõðùñòé * î îüüîíò ûê ìîñù ýôë û * îì ò 2 î ò < û óîñì $

Þ OP Di$

Reading 20: International Trade & CapitalFlows

1. Terms of trade = ëìéíî ûü î 9øûìò $ëìéíî ûü éõøûìò $

2. Terms of Trade (as an index number) =8*' øìéíî ûü î 9øûìò $8*' øìéíî ûü éõøûìò $




3. Net exports = Value of a country's (exports –imports)

4. Net welfare effect = consumer’s surplusloss + 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 = Y d - S p =Y+R-T-S p And,CA = S p- I+ Govt surplus (or Govt saving)= S p- I+ (T- G- R)S p + S g = I + CA

where, S g = Govt savingsS p = I + CA – S g

• Current Account Imbalance CA = Sp+ Sg – I

Reading 21: Currency Exchange Rates

1. E§¨ 64FB G̈ 456 >6H6> 4B I §A6J?45 5K̈ ¨ 6B5@ 8Lövü 0 3ü

2. M6N> 6O5PNBF6 ¨N?6côvüd 8 c Lö ü 0 3ü dv3ö 8

Lö ü 0c 3ü v3ö d

3. M6N> QO5PNBF6 MN?6 öûõî $òéívüûìîé ' ê 8

Lövü 0 #ëúR

# ëúS

4. TPNBF6 4B M6N> QO5PNBF6 ¨N?6 8

+ ,è÷ S vR

÷SvR 0

&'è UR UR

&'è USUS

? +

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 $

&f–fff

8. E§¨ WN̈I G̈ 6A4KAvI4J5§KB? c4B Þd 8

$øûò þ/ìñòî'cüûì < ñìö øûéêò $v&f–fffd

$øûò þ/ìñòî? +

9. To convert spot rate into a forward quote(when points are represented as %) = Spotexchange rate ! (1 + % premium ordiscount)

10. Arbitrage relationship is stated as follows:

• + , > J 8 Í µÑ

+ , > P&

! µÑ

• In case of indirect quote, Arbitragerelationship is: + , > J 8+vÍ PvJ + , > P ÔPvJ

• ÔµÑ

8 Í µÑ

&'Mµ

&'MÑ

• Forward rate as a % of spot rate =! µvÑ

FµvÑ8

&'Mµ

&'MÑ

11. Return on hedged foreign investment(with a quoted forward rate) = Í PvJ + ,

>P&

! µvÑ

12. Expected % change in the spot rate =FZ^%

FZ? + 8 ÞèÍ G'& 8

Mµ /MÑ

&'MÑ

• Forward points: ÔPvJ ? Í PvJ 8

Í PvJMµ /MÑ

&'MÑX Y (where Y is quoted

interest rate period)

13. Relationship between the trade balance andexpenditure/ saving decisions:= Ex – Im = (Sav – Inv) + (T – G)

where T= taxes net of transfersG= government expenditures)

14. Price elasticity of demand = ) =Þ í 2 ñê ' î éê Cðñêòéòó

Þ í 2 ñê ' 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 ) [ ) ? + † j where,




+ x=share of exports) X=price elasticity of foreign demand fordomestic country exports+ M=share of imports) M =price elasticity of domestic countrydemand for imports

17. Trade balance = Income (GDP) –Domestic expenditure = Absorption

Reading 22: Financial Statement Analysis: AnIntroduction

1. Gross Profit = Revenue – Cost of sales

2. Operating Profit or EBIT = Gross profit –Operating costs + Other operating income

3. Profit before tax = EBIT – 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 8 õûðêò ûü # û $ò

! éõî ûü ò 2 î íûêòìñíò

2. Revenue recognized under Percentage-of-Completion Method = % of Total costspent by the firm ! Total ContractRevenue

3. Revenue recognized when outcome cannot be reliably measured = Contract costsincurred

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 ofending inventory

8. Annual Depreciation Expense (using

Straight-Line Method) = # û $ò/ ) î $éöðñù + ñùðî7$ òéõñòîö "$ îüðù - éüî

9. Annual Depreciation Expense (Declining

balance method) = &ffÞ

"$ îüðù ùéüî ! Acceleration

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

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

0'2 ò 8*' / û ûü $2 ñìî $ ûðò $òñêöéê '

11. Diluted EPS for preferred stock =/ îò úêíûõî

0'2 ò 8*' / û ûü $2 ñìî $ ûv$' / î < íûõõûê $2 ñìî $ ò2 ñò< ûðùö 2 ñ* î , îîê é $$ðîö ñò íûê * îì $éûê

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

íûê * îìòé , ùî öî , ò/ëìîüîììîö ôé *0'2 ò 8*' ûü $2 ñìî $ ûv$' 8 öö

ò2 ñò < ûðùö 2ñ* î , îîê é $$ðîö ñò íûê * îì $éûê

13. Diluted EPS using Treasury Stock Method=

c/ îò úêíûõî/ëìîüîììîö öé *éöîêö $d\0'2 ò 8*' ûü $2 ñìî $'c

÷2ñìî $ øðìí 2 ñ$îö < éò2 # ñ$2 ìîíîé * îö ðøûê î 9îìíé $î d 0cëìûøûìòéûê ûü ÿìd ]

14. Net Profit Margin = / îò úêíûõî) î * îêðî

15. Gross Profit Margin =ýìû $$ ëìûüéò

) î * îêðî

16. Comprehensive EPS = EPS + OtherComprehensive Income per share

Reading 26: Understanding Balance Sheets




1. Percentage of A/C Receivable estimated to be uncollectible =

8 ùùû< ñêíî üûì ôûð , òüðù8 v#ýìû $$ ñõûðêò ûü 8 v# ) 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 – Impairmentlosses

4. Carrying value for PPE under revaluationmodel= Fair value at date of revaluation –Accumulated depreciation (if any)

5. Amortized cost of PPE = Historical cost –Accumulated depreciation – Impairmentlosses

6. Carrying value for PPE under revaluationmodel= 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 =^ ñùñêíî $2 îîò 8 õûðêò

! ûòñù 8$$ îò $

10. Current ratio = # ðììîêò 8$$ îò $# ðììîêò - éñ, éùéòéî$

11. Quick (acid test) =# ñ$2 ' & ñì 1 îòñ , ùî $îíðìéòéî $' ) îíîé *ñ , ùî $

# ðììîêò - éñ, éùéòéî$

12. Cash ratio = # ñ$2 ' & ñì 1 îòñ , ùî $îíðìéòéî $ # ðììîêò - éñ, éùéòéî$

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

! ûòñù 7Cðéòó

14. Debt-to-Equity = ! ûòñù ôî , ò

! ûòñù 7C ðéòó

15. Total Debt = ! ûòñù ôî , ò! ûòñù 8$$ îò $

16. Financial Leverage = ! ûòñù 8$$ îò $! ûòñù 7Cðéòó

Reading 27: Understanding Cash FlowStatements

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 fromcustomers

3. Cash received from customers = Revenue – Increase in a/c receivab le

4. Purchases from suppliers = COGS +Increase in inventory

5. Cash paid to suppliers = Cogs + Increasein 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 salaryand wages payable + Salary and wagesexpense – cash paid to employees

10. Cash paid for other operating expenses =Other operating expenses – Decrease in

prepaid expenses – Increase in otheraccrued liabilities

11. Cash paid for interest = Interest expense +Decrease in interest payable

12. End Interest Payable = Beg interest payable + Interest expense – Cash paid forinterest

13. Cash paid for income taxes = Income taxexpense – 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 + Depexpense – 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 – Taxrate) – 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 $2 ñìî 2 ûùöîì $_î Cðéòó

24. Cash to income = #V.. øîìñòéê ' éêíûõî

25. Cash flow per share =#V. /ëìîüîììîö ôé *éöîêö $/ û ûü íûõõûê $2 ñìî $ ûv$

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 =

7 êö + ñùðî^ î ' + ñùðî

%`a aR bcdeaSf ? +

2. Combined ratio = - û$$î $ ñêö 79 øîê $î $/ îò ëìîõéðõö 7 ñìêîö

3. Operating ROA = . øîìñòéê ' úêíûõî

8*' ! ûòñù 8$$ îò $

4. ROA = / îò úêíûõî

8*' ! ûòñù 8$$ îò $ or

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

8*' ! ûòñù 8$$ îò $

5. Effective Tax Rate = úêíûõî ! ñ97 ñìêéê '$ , îüûìî ! ñ9

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

) î * îêðî

7. Horizontal common size balance sheet =^ ñùñêíî $2 îîò éòîõ éê ÿîñì k

^ ñùñêíî $2 îîò 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 $! ðìêû * îì

=÷ñùî $

ghijkl

13. Payables turnover = ëðìí 2 ñî $

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 =7 ñìêéê '$ , îüûìî òñ 9 , ðò ñüòîì éêòîìî $ò

) î * îêðî

19. Return on Total Capital =7^ ú!

÷2 ûìò ñêö ùûê ' òîìõ öî , ò ñêö î Cðéòó

20. ROE = / îò úêíûõî

8*' ! ûòñù 7Cðéòó

• ROE = ROA ! Leverage• ROE = Tax Burden ! Interest Burden

! EBIT Margin ! Total AssetTurnover ! Leverage

21. Return on Common Equity =/ îò úêíûõî/ëìîüîììîö ôé *éöîêö $

8*' # ûõõûê 7Cðéòó

22. Coefficient of Variation of Operating

Income = ÷•ô ûü . øîìñòéê ' úêíûõî

8*' . øîìñòéê ' úêíûõî

23. Coefficient of Variation of Net Income =÷•ô ûü / îò úêíûõî

8*' / îò úêíûõî

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

8*' ) î * îêðî

25. Monetary Reserve Requirement (Cash

Reserve Ratio) = ) î $îì * î $ 2 îùö ñ $ # îêòìñù ^ ñê 1÷øîíéüéîö ôîøû $éò- éñ, éùéòéî$

26. Liquid Asset Requirement =

) îñöéùó & ñì 1 îòñ , ùî ÷îíðìéòéî $÷øîíéüéîö ôîøû $éò- éñ, éùéòéî$

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

! ûòñù úêòîìî $ò 7 ñìêéê ' 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 = 7^ ú!ýìû $$ úêòîìî $ò

32. EBITDA Interest Coverage = 7^ ú! ô 8ýìû $$ úêòîìî $ò

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

ýìû $$ úêòîìî $ò

34. Return on Capital = 7^ ú!8*' # ñøéòñù

=7^ ú!

8*' c7Cðéòó' / ûê íðììîêò öîüîììîö òñ 9î $'öî , òd

35. FFO to Debt = VV.! ûòñù ôî , ò

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

! ûòñù ôî , ò

37. Discretionary CF to Debt =#V. / # ñø î 9ø/ôé *éöîêö $ øñéö

! ûòñù öî , ò

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

# ñø î 9ø

39. Debt to EBITDA = ! ûòñù öî , ò

7^ ú! ô 8

40. Total Debt to total debt plus Equity =! ûòñù öî , ò

! ûòñù öî , ò' 7Cðéòó

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

+ 1.4 ! ) •7!8

+

3.3 ! 7^ ú!!8

+ 0.6 ! &+ ûü $òûí 1^+ ûü ùéñ, éùéòéî$

+ 1.0

! ÷ñùî $!8

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

÷î ' õîêò ) î * îêðî

43. Segment turnover = ÷î ' õîêò ) î * îêðî

÷î ' õîêò 8$$ îò $

44. Segment ROA = ÷î ' õîêò ëìûüéò c - û $$d÷î ' õîêò 8$$ îò $

45. Segment Debt Ratio = ÷î ' õîêò - éñ, éùéòéî$÷î ' õîêò 8$$ îò $

Reading 29: Inventories




1. NRA = Estimated Selling Price –Estimated Costs of completion anddisposal

2. Inventory amount net of valuationallowance = Carrying amount of Inventory

– Write downs

3. (NRA – Normal Profit Margin) ( MV ( NRA

Reading 30: Long-Lived Assets

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

7$ òéõñòîö "$ îüðù - éüî =

n é$òûìéíñù # û $ò/ 7$ òéõñòîö ) î $éöðñù $ñù*ñ ' î + ñùðî7$ òéõñòîö "$ îüðù - éüî

2. Dep Exp under Units-of-ProductionMethod = Depreciable Cost !

ëìûöðíòéûê éê ò 2 î ëîìéûö

7$ òéõñòîö ëìûöðíòé * î # ñøñíéòó

3. Carrying amount under cost model =Historical Cost – Accumulated Dep orAmortization

4.

Carrying amount under revaluation model= Fair value at the date of revaluation –Any subsequent Accumulated Dep orAmortization

5. Impairment Loss (IFRS) = RecoverableAmount – Net Carrying Amount

Where, Recoverable amount = Max [(Fairvalue – Costs to sell); Value in Use)] andValue in use = PV of Expected Future CFs

6. Impairment Loss (US GAAP) = Asset’sFair Value – Carrying Amount …….IfCarrying amount > Undiscounted ExpectedFuture Cash Flows

Reading 31: Income Taxes

1. Deferred tax asset = Company’s taxableincome > 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 î 9øîê $î

ëìî òñ 9 éêíûõî ûì 8 ííûðêòéê ' ëìûüéò

4. Deferred tax liability = Carrying amountof asset > Tax base of asset

5. Deferred tax asset = Carrying amount ofasset < Tax base of asset

6. Deferred tax asset = Carrying amount ofliability > Tax base of asset

7. Deferred tax liability = Carrying amount ofliability < Tax base of asset

8. Company’s tax expense (or credit)reported on its income statement = Income

tax liability currently payable + è indeferred tax asset / liabilityWhere,

• Income Tax liability currently payable = Taxable income ! Taxrate

• è in deferred tax asset / liability =Diff b/w the balance of thedeferred tax asset / liability for thecurrent period and the balance ofthe 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 ! Taxrate

• Deferred tax liability = (carryingamount – tax base) ! tax rate

• Deferred tax asset = (tax base –carrying amount) ! tax rate

10. Tax base of a liability = Carrying amountof the liability – Amounts that will bedeductible 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 ofInterest Payments + PV of Face value ofBond

3. When Face value - Sale proceed is > zero,discount

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

5. Bond payable = 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 cost +/-Cumulative amortization (or amortizationcost)

9. Amount of Bonds payable initiallyreported on the balance sheet under IFRS =Sales proceeds – Issuance costs

10. Amount of Bonds payable initiallyreported on the balance sheet under USGAAP = Sales proceeds

11. Bond interest expense under effectiveinterest rate method = Carrying value of

the bonds at the beginning of the period ! Effective interest rate

12. Bond Interest Payment under effectiveinterest rate method = Face value of the

bonds ! Contractual (coupon) rate

13. Amortization of the discount or premiumunder effective interest rate method =Bond interest expense – Bond interest

payment

14. Bond Discount/Premium Amortizationunder Straight-line Method =^ ûêö 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 – Accumulateddepreciation

17. Accumulated depreciation = Prior year’saccumulated depreciation + Current year’s

depreciation expense

18. Interest expense = Lease liability at the begof the period ! interest rate implicit in thelease

19. Sales revenue = lower of the fair value ofthe asset and PV of the min lease payments

20. Cost of sales = Carrying amount of theleased asset – PV of the estimatedunguaranteed residual value

21. Interest Revenue = Lease receivable at the beg of the period ! Interest rate

22. Net interest expense = Beg Net pensionliability ! Discount rate

23. Net Interest income = Beg Net Pensionasset ! Discount rate

24. Reported pension expense = 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 =cûøîìñòéê ' #V , îüûìî 0# í 2 ñê ' î $ o öé*éöîêö $d

òûòñù öî , ò

4. ) îòñéêîö #V/ # ñø î 9ø! ûòñù ôî , ò




5. Inventory value adjusted to FIFO basis =End Inventory value under LIFO + EndLIFO reserve balance

6. COGS adjusted to a FIFO basis = COGSunder LIFO – (End LIFO reserve – BegLIFO reserve)

7. Useful life of the company’s overall asset

base that has passed = 8 ííðõðùñòîö ôîø

ýìû $$ ëë 7

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

8 êêðñù ôîø î 9øîê $î

9. Remaining useful life of the asset =/ îò ëë 7 cêîò ûü ñííðõðùñòîö öîød

8 êêðñù öîø î 9øîê $î

10. Avg depreciable life of the assets at

installation = ýìû $$ ëë 7

8 êêðñù ôîø î 9øîê $î

11. % of asset base that is being renewedthrough new capital investment =

# ñøî 9

ýìû $$ ëë 7 ' # ñøî 9

12. Adjusted BV = Total stockholders’ equity – Goodwill

13. Adjusted Price to BV ratio =ëìéíî õñì 1 îò íñøéòñùé pñòéûê

8 ö mð $òîö ^+

14. Tangible B.V = Total stockholders’ equity – Goodwill – Other intangible assets

15. Price to tangible BV ratio = ëìéíî

! ñê ' é, ùî ^+

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 $! ûòñù # ñøéòñù - îñ $î øñóõîêò $! Total Future

Operating Lease Payments

20. Interest expense = Interest ! PV of thelease payments

21. Depreciation expense estimated onstraight-line basis =

ë + ûü ò2 î ùîñ $î øñóõîêò $/ û ûü óì $ ûü üðòðìî ùîñ $î øñóõîêò $

22. Adjusted Interest Coverage ratio =Qqrs , ¨ 6B? 6OGÌ ? t6G 6OGÌ

>GN@A6B?J, > 6OG6BJ6Ì

* associated with the operating leaseobligations

Reading 35: Capital Budgeting

1. Incremental CF = CF with a decision - CFwithout 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 u òñ9î $ , îüûìî éêòîìî $ò

8*' ^+ ûü úê*$ò

4. PI = ë + ûü üðòðìî #V$ú.

= 1 + / ë +ú.

5. Value of a company = Value of company’sexisting invst + Net PV of all ofcompany’s future invst

Reading 36: Cost of Capital

1. WACC = w dr d (1 – t) + w pr p + w er e

2. Debt-to-Equity Ratio conversion intoweight (i.e. Debt / (Debt + Equity) =

jcvwxyzew{

&'jcvw

xyzew{

3. Optimal Capital Budget is the point whereMC of capital = Marginal return frominvesting

4. After-tax cost of debt = Before-taxMarginal Cost of Debt ! (1 – firm’smarginal tax rate)




5. Preferred Stock Price per Share

=ëìîü ÷òûí 1 ôé * øîì ÷ 2 ñìî

# û $ò ûü ëìîü ÷òûí 1

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 (Factorrisk premium) 2+…..+ , i j (Factor risk

premium) j

8. Cost of Equity = | } 8 ô %

ë h, F

9. Expected Growth Rate of Dividends

g = (1 -ô

7 ë÷ ) ! ROEg = retention rate ! ROE

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

11. Unlevered • of Comparable Company =

• " – íûõøñ 8€ –‚aƒb„d„v…c

&' &/ò ‚aƒb„d„v…cj ‚aƒb„d„v…cx ‚aƒb„d„v…c

12. Levered • of Project =

†B– R(O” 8 †Ý– aO.R + , + ? : R(O”‡ R(O”

“ R(O”

13. †H77IG 8 ˆ ‰Š‹ƒZŒ

&' &/G r

14. †I}SMG` 8 †H77IG + , + ? : i

15. Sovereign yield spread = Govt bond yield(denominated in developed country’scurrency) – T.B yield on a similar maturity

bond in developed country

16. Country equity premium = Sovereign yield

spread ! 8 êê ÷•ô ûü 7Cðéòó éêöî 98 êê ÷•ô ûü $û * îìîé ' ê , ûêö &1 ò éêòîìõ $ ûü öî * îùûøîö õ 1ò íðììîêíó

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

18. Breakpoint =8 õûðêò ûü íñøéòñù ñò <2 éí 2 $ûðìíî _$ íû $ò ûü íñø è

ëìûø ûü êî < íñø ìñé $îö üìûõ ò 2 î $ûðìíî

19. Cost of Capital (hen flotation costs are in

monetary terms = ¨ î 8 ô %

ë h / V , F

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

price: Cost of Equity = ¨ î 8 ô %

ë h / V , F

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

Cash Inflows – IO – (FC in % ! NewEquity Capital)

22. If FC are tax deductible: NPV = PV ofCash Inflows – IO – [(FC in % ! NewEquity Capital) ! (1 – Marginal Tax Rate)]

23. Asset • = (Debt • ! Proportion of Debt) +(Equity • ! Proportion of Equity)

Reading 37: Measures of Leverage

1. Contribution Margin (CM) = (# of unitssold) ! [(price per unit) - (variable cost perunit)]

2. Per unit CM = Price per unit - Variablecost per unit

3. Operating income = CM – Fixed OperatingCosts

4. DOL = Þ è éê . øîìñòéê ' úêíûõî 7^ ú!Þ è éê " êéò$ ÷ûùö

or

DOL= #&#& / Vé9îö . øîìñòéê ' # û $ò

5. DFL = Þ è éê / îò úêíûõî

Þ è éê . øîìñòéê ' úêíûõî or

#& / Vé9îö . ø # û $ò

#& / Vé9îö . ø úêíûõî/ Vé9îö Véê # û $ò

6. DTL= Þ è éê / îò úêíûõî

Þ è éê / û ûü " êéò$ ÷ûùö = DOL ! DFL =

#&#& / Vé9îö . ø úêíûõî/ Vé9îö Véê # û $ò

7. Break-even Revenue = (Variable cost perunit ! Break-even Number of Units) +Fixed Operating costs + Fixed FinancialCost

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 = Cashdividends + Value of shares repurchased inany given year

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

/ îò úêíûõî ñ *ñéùñ, ùî òû íûõõûê $2 ñìî $

3. EPS after Dividend = EPS before Dividend

! ÷2 ñìî $ ûv$ , îüûìî ôé *éöîêö

÷2 ñìî $ ûv $ ñüòîì ôé *éöîêö

4. Stock Price after Dividend = Stock Price before Dividend ! EPS after Dividend

5. Total Market Value after Dividend =Shares outstanding after Dividend ! Stock

price after Dividend

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

k

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

k

8. DPS after 2-for-1 stock split =ôë÷ , îüûìî $òûí 1 $øùéò

k

9. EPS after buyback =7 ñìêéê '$ / 8 üòîì òñ 9 # û $ò ûü Vðêö $÷2ñìî $ . ðò$òñêöéê ' ñüòîì ^ ðó , ñí 1

10. Ex-dividend value of share = Stock price –

Dividend per share

11. Market value of Equity after distribution ofcash dividends =\cŽ ûü $2 ñìî $ ûv$d 0 c &+ $2 ñìîd o # ñ$2 öé*]

Ž ûü $2 ñìî $ ûv $

12. Post-repurchase share price =Žûü $2 ñìî $ ûv $ 0 c &+ $2 ñìî o < ûìò 2 ûü ÷2 ñìî ìîøðìí 2 ñ$î ]

c Ž ûü $2 ñìî $ ûv$/ Ž ûü $2 ñìî $ cíñê , î ìîøðìí 2ñ$îö , ó ñ # û

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 ofinventory + No of days of receivables – Noof days payables

3. Money Market Yield =Vñíî *ñùðî/ëðìí 2 ñ$î øìéíî

ëðìí 2ñ$î øìéíî 0

opf

/ û ûü öñó $ òû õñòðìéòó

4. Bond Equivalent Yield =Vñíî *ñùðî/ëðìí 2 ñ$î øìéíî

ëðìí 2ñ$î øìéíî0

opu


5. Discount-basis Yield =Vñíî *ñùðî/ëðìí 2 ñ$î øìéíî

Vñíî + ñùðî0

opf


6. Wght Avg collection period = wghts ! Avg no of days to collect accounts withineach aging category

Where, Weights = % of total receivables ineach category

7. Float Factor = 8*' ôñéùó Vùûñò

8*' ôñéùó ôîøû $éò =

8*' ôñéùó Vùûñòaw„… ƒaz‘w aR ’“c‚”f jcbafewcS

`a aR j„{f

Where, Float =Amount of money that is intransit b/w payments (by customers) andfunds (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

ghi‘

? + where n = days beyond discount period

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

- ûñê 8 õûðêò

11. Bankers Acceptance Cost = úêòîìî $ò/ îò øìûíîîö $

=úêòîìî $ò

- ûñê ñõûðêò/úêòîìî $ò




12. Commercial Paper Cost =úêòîìî $ò'ôîñùîì _$ íûõõé $$éûê' ^ ñí 1ðø íû $ò$

- ûñê ñõûðêò/úêòîìî $ò

13. Annualized cost = Cost ! 12

Reading 40: The Corporate Governance ofListed Companies

Reading 41: Portfolio Management: AnOverview

1. NAV of bond mutual fund =c*ñùðî ûü îñí 2 , ûêö éê ò 2 î øûìòüûùéûd

/ û ûü $2 ñìî $

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

/8+ ûì ! ûòñù *ñùðî ûü ñ & ðòðñù Vðêö

3. New NAV of the Fund = NAV or Totalvalue of a Mutual Fund + Amount to beinvested in the Fund

4. No of shares need to be retired =8 õûðêò òû , î < éò2öìñ < ê üìûõ ò 2 î Vðêö

/8+ ûì ! ûòñù *ñùðî ûü ñ & ðòðñù Vðêö

Reading 42: Risk Management: AnIntroduction

Reading 43: Portfolio Risk & Return: Part I

1. Total Return = Capital Gain (or Loss) +Dividend Yield

2. Capital Gain = ë w/ë w¡%

ë w¡%

3. Dividend Yield = ô

ë h? +

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

5. Arithmetic mean (AM) R = YM 8Nƒ%'N ƒ‰'¶'N ƒ• ¡% 'N ƒ

* 8

&*

YMG*G[&

6. Geometric R for n periods = MDM 8

+ , Y & + , Y k l + , Y L& L ? +

7. IRR = #V ñò ! éõî ò

&'ú )) w 8 j!ò[f

8. Annual 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 Asset1 ! R of Asset 1) + (Wght of Asset 2 ! Rof Asset 2)

10. Gross R = R – Trading exp – other expdirectly related to the generation of returns.

11. Net R = Gross R - All managerial andadministrative exp

12. After-tax nominal R = Total R - Anyallowance for taxes on realized gains

13. (1 + Nominal R) = (1 + Real Rf R) ! (1 +Inf) ! (1 + RP)

14. (1 + Real R) = (1 + Real Rf R) ! (1 + RP)

15. (1 + Real R) = c&' / ûõéêñù ) d

c&'úêüd

16. Var of a Single Asset = Š k 8 NZ/ˆ ‰

ƒ„%

*

17. Sample Variance = Jk 8 ) w/ ) ‰

e„%

! /&

18. Cov of R b/w two assets = Cov (Ri,Rj) =

- ij! %i ! % j

19. Portfolio Var = – ëk 8 —&

k –&k , —k

k –kk ,

¬—&—k T§H M&–Mk 8 —&k –&

k , —kk –k

k ,¬—&—k ˜ &k–&–k

20. Portfolio S.D. = 3§¨ ? ¦§ >4§ =N̈ 4NB56

21. Cov b/w asset 1 & asset 2 = Correlation ofReturn b/w two assets ! S.D. of asset 1 ! S.D. of asset 2

22. Correlation of Return b/w two assets =# û *ñìéñêíî ûü ) îòðìê , v< ò< û ñ $$îò $

÷•ô•ûü ñ $$îò & 0 ÷•ô•ûü ñ $$îò k

23. 1 + Expected Return = + , Q M 8+ , ¨ ìü 0 + , Q ™ 0 + , Q M3




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

ORRemaining 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 callwill take place (P):

úêéòéñù õñì ' éê ª 'cë/ úêéòéñù ÷òûí 1 ëìéíîd

ë8

ŸN4B?6BNB56 ŸN¨F4B M6«K4̈6A6B? cÞd

4. Total cost of placement to the issuing firmin IPO ($)

= Gross proceeds received by the issuingfirm – Net proceeds received by the issuing

firm

5. Total cost of placement to the issuing firm

in IPO (%) =cýìû $$ 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 = &ffÞ

Þ ûü 7Cðéòó

7. Max leverage ratio for position financed bymin margin requirement =

&

& éê õñì ' éê ìî Cðéìîõîêò

Reading 47: 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 of

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

iii

P

P P w

1 0

01

5. % è in value of Total return of Index

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 +!

Total Re turn wi

P1 i ! P

0 i + Inci

P0 i

"

#$

%

&'

i = 1

N

(

Over Multiple Time Periods:7. Value of Price Return index at time t =

VPRIT = V PRI0 (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 ò2 î éêöî 9

11. Weight of security i under market-cap

weighting =/ f ûü $2 ñìî $ ûv$ ûü ÷é 0 ÷ 2ñìî øìéíî ûü ÷é

/ û ûü $2 ñìî $ ûv$ ûü ÷é 0 ÷ 2 ñìî øìéíî ûü ÷é`e

Where Si = Security i

12. Weight of Si under Mkt Cap weighting =Vìñíòéûê ûü $2 ñìî $ ûv$ õ 1ò üùûñò 0 ûü $2 ñìî $ ÷é 0

÷2ñìî øìéíî ûü $îíðìéòó écVìñíòéûê ûü $2 ñìî $ ûv $ &1 ò üùûñò 0 ûü $2 ñìî $ ûv$ ûü ÷é 0

÷2 ñìî øìéíî ûü $îíðìéòó éd




13. Fundamental weight on security i =Vðêöñõîêòñù $épî õîñ $ðìî ûü íûõøñêó éÌ

cVðêöñõîêòñù $épî õîñ $ðìî ûü íûõøñêó éd`e

*Book value, cash flow, revenues, earnings,

dividends, & number of employees.

Reading 48: Market Efficiency

Reading 49: Overview of equity Securities

1. Equity security’s Total Return =÷ñùî ë ûü ñ $2 ñìî/ëðì 2 ñ$î ëûü ñ $2 ñìî'íñ $2 v$òûí 1 ôé *

ëðìí 2 ñ$î øìéíî ûü ñ $2 ñìî

2. ROE in yr t =/ ú cüûì . ìöéêñìó ÷ 2 ñìî 2 ûùöîì $d éê óì ò

8*' ! ûòñù ^+ ûü 7Cðéòó

OR

ROE = / ú cüûì . ìöéêñìó ÷ 2 ñìî 2ûùöîì $d éê óì ò

÷2 ñìî 2 ûùöîì $_î Cðéòó ñò , î ' ûü óì ò

3. MV of equity = Mkt price per share ! Shares O/s

4. BV of equity per share = ! ûòñù ÷n _î Cðéòó

÷2 ñìî $ ûv $

5. Price-to-book ratio = & ñì 1 îò øìéíî øîì $2 ñìî

^+ ûü î Cðéòó øîì $2 ñìî

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 î Cðéòó

Reading 50: Introduction to Industry &Company Analysis

Reading 51: Equity Valuation: Concepts &Basic Tools

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

c&'ìî Cðéìîö ).) ûê $òûí 1d¬òò[&

If an investor intends to buy and hold a sharefor 1 yr:

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

c&'ìî C ) û ) ûê $òûí 1d¬&

3. Value of a share of stock for n holding period or investment horizon =

79 øîíòîö ôé * éê óì ò

&'ìî C ) ûê $òûí 1 w ,LG[&

79 øîíòîö øìéíî éê ê øîìéûö $

&'ìî C ) ûê $òûí 1 ‘

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

5. FCFE = CFO – FCInv + Net Borrowing

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

stock = V#V7 éê óîñì ò

&'ìî C ) ûê $òûí 1 wò[&

7. Req RoR on share i = Current expected Rfrate + Beta i [MRP]

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

( ) ( )r

D

r

D

g r

g DV 000

00

011=

!+

=!

+=

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

convertible) with maturity at time n =Af 8

‡ f

c+ , 5d G ,L

G/&

Ô+ , 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 ratio)

Two-stage valuation model:12. Value of share today = V0 =

Af 8‡ f + , Ž 7

G

c + , 5 d G ,AL

c + , 5 d L

L

M[&

AL 8‡ L'&

5 ? Ž B

‡ L'& 8 ‡ f c + , Ž 7dL + , Ž B

13. Justified P/E = ëf

7 &8 ô %v7 %

ì/ ' 8 ø

ì/ '

14. EV = MV of stock + MV of debt – Cashand cash Equivalents

15. Asset-based value = Value of Equipmentand inventory – Value of Liabilities




Reading 52: Fixed Income Securities: DefiningElements

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 acapital-indexed bond= [Par value ! (1 + CPI)] ! coupon rate

Reading 53: Fixed Income Markets: Issuance,Trading & Funding

Reading 54: Introduction to Fixed IncomeValuation

1. Amount of discount below par value =Present value of deficiency

2. Present value of deficiency =# ûðøûê ìñòî/ & ñì 1 îò öé $íûðêò ìñòî 0ëñì *ñùðî

&' & ñì 1 îò öé $íûðêò ìñòî wêò[&

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 = ›r 8 G*

0@\]

8. Full price of a fixed-rate bond betweencoupon payments = PV Full

=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, givenmarket discount rates for 2 and 5 yrs) =

(Average yield for 2 year bonds) + o/k

u/k !

(average yield for 5 year bonds – averageyield 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 ò 2 î 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 =

PV = FV ! 1 " DaysYear

! DR#$% &'(

15. Market Discount Rate =

DR = Year Days( )! FV " PV

FV

#$%

&'(

16. Price of Money Market Instrument =

PV =FV

1 + DaysYr ! AOR"#$ %&'

17. Add-on rate =




AOR =

Yr Days

!

"#

$

%&' FV ( PV

PV

!"#

$%&

Relation b/w two spot rates and Implied

Forward Rate:

18. (1 + z A)A ! (1 + IFR A,B-A )B-A = (1 + z B)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 tomaturity of the bond - Linearlyinterpolated yield to the same maturity onan appropriate reference curve

Reading 55: Introduction to Asset BackedSecurities

1. Loan-to-value ratio (LTV) =ëìûøîìòó _$ øðìí 2 ñ$î øìéíî

8 õûðêò ûü & ûìò ' ñ ' î

2. Monthly CF for a MPS = Monthly CF ofunderlying pool of mortgages - Servicingfee - Other fees

3. Pass-through rate = Mortgage rate on theunderlying pool of mortgages – ServicingFee - Other fees

4. SMM = Pre-pmt for month ÷ (Begmortgage 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 formonth)

• Total principal re-pmt =Scheduled principal re-pmt +Prepayment

• Beg mortgage balance for thefollowing month = Beg mortgage

balance for the month – TotalPrincipal Pmt

• Projected CF for MPS = Net i- pmt + Total principal re-pmt

7. DSC ratio = ëìûøîìòó ®$ ñêêðñù /. ú

ôî , ò $îì *éíî

Reading 56: Understanding Fixed Income Risk& Return

1. Interest-on-interest gain fromcompounding = Future value of reinvestedcoupons - Total amount of coupon

paymentsWhere,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 ! Parvalue ! No of periods

RR = Re-invstmnt rate per periodCR = coupon rate

2. Realized RoR on Bond=

÷ðõ ûü ) îéê * î $òîö # ûðøûê $') îöîõøòéûê ûü ëìéêíéøñù ñò & ñòðìéòó

^ ûêö ëìéíî

%m

? +

3. Carrying value of bond (if bond purchased

below par) = Purchase price + Amortizedamount of Discount

4. Carrying value of a bond (if bond purchased above par) = Purchase price –Amortized amount of Premium

5. Amortized amount for 1 st year = BondPrice after 1-yr - Initial bond price




6. Capital g / (l) = Sale price of Bond after nyears – Carrying value of Bond after nyears

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 PV Full = - AnnModDur ! 1 Yield

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 =

Ÿ §I t §¦ q §BI + 0 &+ ûü ^ ûêö &

! ûòñù &+ ûü ëûìòü

+ Ÿ§I t §¦ q §BI ¬ 0 &+ ûü ^ ûêö k

! ûòñù &+ ûü ëûìòü +

…+ Ÿ§I t §¦ q§BI ¯ 0 &+ ûü ^ ûêö /! ûòñù &+ ûü ëûìòü

17. Money D = Annualized Mod D ! FullBond 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) = Moneyduration ! 0.0001 (1 bp)

21. Bloomberg’s Risk Statistic = PVBP ! 100

22. %* PV Full = (-AnnModDur ! * Yield) +&

k 0 == W= 4£>:° 0cèt>4³<d k

Or%* PV Full = (-AnnModDur ! * Yield) +

&

k 0 == W= 4£>:° 0cèt>4³<d k

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) + [ &

k !

MoneyCon ! (* Yield) 2]

26. Money Convexity of bond = AnnualConvexity ! Full Price

27. Effective Convexity =

PV !( )+ PV

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

' Curve( )2" PV

0 )( )

28. Duration Gap = Bond’s MacaulayDuration – Investment Horizon

Reading 57: Fundamentals of Credit Analysis

1. Expected Loss = Default Probability ! Loss Severity given Default

2. Operating Profit Margin = . øîìñòéê ' úêíûõî) î * îêðî

3. EBITDA = Operating Income + Dep +Amort




4. FCF = CFO – Cap exp– Div

5. Capital expenditures = Additions to P&E +Additions to product rights & intangibles –Proceeds of sale of P&E

6. Total debt = ST debt + Current portion ofLT debt + LT debt

7. Capital = Debt + Equity

8. Yield on Corp Bond = Rf rate + ExpectedInf rate + Maturity P + Liquidity P+ Creditspread

9.

Yield spread = Liquidity P + Credit spread

10. Return impact for smaller spread *# % * in price # -Modified Duration ! * Spread

11. Return impact for larger spread * # % * in price # - (Modified D ! * Spread) +&

kConvexity ! (* Spread) 2

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

7^ ú! ô 8

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

7^ ú! ô 8

14. Total Leverage = ! ûòñù öî , ò

7^ ú! ô 8

15. Net Leverage = ! ûòñù öî , ò/ # ñ$27^ ú! ô 8

Reading 58: Derivatives Markets andInstruments

1. Value of the contract to the ‘Long’ atexpiration = S T – F 0(T)

2. Value of the contract to the ‘Short’ atexpiration = F 0(T) – S T

3. Margin % in stock market =&+ ûü ÷òûí 1 / &+ ûü ôî , ò

&+ ûü ÷òûí 1

4. Margin Call:• Long position: Price ± that would

trigger a margin call = IM req – MM

req• Short position: Price ( that would

trigger a margin call = IM req – MMreq

5. TED spread = LIBOR – T-Bill rate

6. At expiration (for option Buyer):• Value of Call option =

CT = Max (0, S T - X)

• Profit from Call option =Max (0, S T - X) – C 0

• Value of Put option = P 0 =Max (0, X- S T)

• Profit from Put option =Max (0, X- S T) – P 0

7. At expiration (for option Seller):• Profit from Call option =

– Max (0, S T - X) + C 0 • Profit from Put option =

– Max (0, X- S T) + P 0

8. To eliminate arbitrage opportunity:Forward Price should be = Spot Price0 + , > 5;:4 Þ G

Reading 59: Basics of Derivative Pricing &Valuation

1. Pricing of risky assets = S 0 = 7 c÷! d

&'ì' ²

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

where, 2 = Convenience yield 0 Cost ofcarry

3. S0 = 7 c÷! d

&'ì' ² – 3 + 4

where, 3 (theta) = Present value of thecosts and 4 (gamma) = Present value of

benefits

4. Arbitrage and Derivatives = Underlyingasset + Opposite position in derivative =Underlying payoff – Derivative payoff =Rf return

5. Pricing and Valuation of ForwardContracts:• At Expiration F (0, T) = S 0 (1 + r) T or

S0 = F (0, T) / (1 + r) T • Value of forward (long) during

contract life (where t < T) = V t (0, T)= S t – F (0, T) / (1 + r) (T – t)




• Value of forward (short) duringcontract life (where t < T ) = V t (0, T) = F (0, T) / (1 + r) (T – t) - S t

• Value of forward (long) at expiration(where t = T) = V T (0, T) = S T - F (0,T)

• Value of forward (long) at initiation(where t = 0) = V t (0, T) = S 0 – F (0,T) / (1 + r) T = 0

• Forward price of an asset with benefitsand/or costs = (S 0 – 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 ofthe contract = S t – (4 - 3) (1 + r) T - F

(T) / (1 + r)(T – t)

6. FRAs: An example of 3 ! 9 FRA (read asthree 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 300-day Euro$ T.D and short position in a 30-day Euro$ T.D

•

For synthetic forward position in a 90-day zero-coupon that begins in 30 day(buy 120 day & sell 30 day (zerocoupon bonds)

7. Pricing and Valuation of Swap Contract (afixed for floating swap contract):

• Fixed Periodic rate =

RN

=1 - Z

N

Z1

+ Z2

+ .... + ZN

• Where Z n are n period zero coupon

bonds (i.e. $1 discount factors)

)360/(1 1

Z n days Ln !+

=

• Value of a fixed rate side (per $1 NP)

= V fixed rate = [Fixed payment ! (Z

1+ Z

2 + .... + Z

N )] + ($1 ! Z N)

• Value of a floating rate side (per $ 1 NP) = V floating rate = ($1 + 1 st floating pmt) ! Z1

Pricing and valuation of Options:

8. Payoff of Call options:

• At expiration call option = c T = Max(0, S T –X)

• Profit (call buyer) = Max (0, S T – X) –c0

• Profit (call seller) = -Max (0, S T – X)+ c0

9. Payoff of Put options:

• p T = Max (0, X- S T)• Profit (put buyer) = Max (0, X-S T) – p 0 • Profit (put seller) = - Max (0, X – S T) +

p0

10. Max Profit/Loss for Option writer/holder:

• Max profit of option seller/writer ! Option premium.

• Max loss of option seller/writer ! unlimited.

• Max loss of option holder ! Option premium

Put-Call Parity

11. Protective Put• Value PP = p 0 + S 0 • Payoff at expiration (put out-of-the-

money) = S T.• Payoff at expiration (put in-the-

money) = (X-S T) + S T = X.

12. Fiduciary Call

• Value FC = c 0 + X / (1+r) T • Payoff at expiration (when call out-of-

the-money) = X.• Payoff at expiration (call in-the-

money) = X + (S T – X) = S T.

13.

Put-Call Parity (to avoid arbitrage) = c 0 +X / (1+r) T = p 0 + S 0

• Synthetic long position in a call =

C = p 0+ S 0 ! X

(1 + r )T




• Synthetic long position in a put =

p 0= 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 ! c0

14. Put-Call-Forward Parity = F 0(T) / (1 + r) T + p 0 = c 0 + X/(1 + r) T

15. Valuing a callable bond using Binomial

Model:

• R u = R d ! e2% : • Value at time 0 = V 0 = hS 0 0 c0

• Value at time 1 will either V 1+ = hS 1

+ -c1

+ or V 1- = hS 1

- - c1-

• If the portfolio was hedged, then V + would equal V -.

• Value of the call =

• Value of the put =

Reading 60: Risk Management Applications ofOption Strategies

1. For Call Option Buyer• cT = max (0, S T –X)• When S T ( X " cT = 0• When S T > X " cT = S T – X• Value at expiration = c T • Profit = c T – c 0 • Maximum profit = 5 ! no upper limit• Maximum loss = c 0 • Breakeven = S T* = X + c 0

2. For Call Option Seller

• cT = max (0, S T –X)• When S T ( X " cT = 0• When S T > X " cT = S T –X• Value at expiration = -c T • Profit = –c T+ c 0 • Maximum profit = c 0

• Maximum loss = 5 ! no upper limit• Breakeven = S T* = X +c 0

3. For Put Option Buyer

• pT = max (0, X - S T)• When S T < X " pT = X - S T • When S T " X " pT = 0• Value at expiration = p T

• Profit = p T – p 0 • Maximum profit = X – p 0 • Maximum loss = p 0 • Breakeven = S T* = X –p 0

4. For Put Option Seller

• pT = max (0, X –S T)• When S T < X " pT = X – S T • When S T " X " pT = 0• Value at expiration = –p T • Profit = –p T + p 0 • Maximum profit = p 0 • Maximum loss = X - p 0 • Breakeven = S T* = X - p 0

5. Covered Call = Long stock position +Short call position

• Value at expiration = V T = S T – max(0, S T – X)

• When S T ( X " VT = S T • When S T > X " VT = S T - ST +X = X• Profit = V T – S 0 + c 0 • Maximum Profit = X – S 0 + c 0 • Maximum Loss = S 0 – c 0 • Breakeven =S T* = S 0 – c 0

6. Protective Put = Long stock position +Long Put position

• Value at expiration: V T = S T + max (0,X - S T)

• When S T ( X " VT = S T + X - S T = X• When S T > X " VT = S T




• Profit = V T – S 0 - p 0 • Maximum Profit = 5 • Maximum Loss = S 0 + p 0 – X• Breakeven =S T* = S 0 + p 0

Reading 61: Introduction to AlternativeInvestments

1. Total Return = Alpha R + Beta R

2. Asset Based Valuation = Co value = Co’sassets value – Co’s liabilities value

Real Estate Valuation3. Direct Cap Approach " Valuation of a

property = 1UgQHRMGHwM³ HGMOL NHGI where

NOI = Gross potential income –Estimatedvacancy losses – Estimated collectivelosses – Insurance – Property Taxes –Utilities – Repairs, maintenance exp.

4. Income Based Approach " FFO = NI +Dep exp on R.E + Def Tax charges – Gainsfrom 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) + Storagecosts – Convenience yield

8. Roll yield = Spot price of a commodity –Futures contract price orRoll yield = Futures contract price withexpiration date ‘X’– Futures contract price

with expiration date ‘Y.

9. Returns on a passive investment incommodity futures= Return on the collateral + RP orconvenience yield net of storage costs.

10. Sharpe ratio = (Investment return – Rfreturn) / S.D. of return

11.

Sortino Ratio = (Annualized RoR –Annualized Rfe rate)/Downside Deviation

cfa level 1, june, 2016 - formula sheet

Documents