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## CFA Level 1 Formula Sheet Updated 2016

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• r June 2016 CFA Level 1

## Description

### CFA® EXAM REVIEW

COVERS ALL TOPICS IN LEVEL I

# New Jersey

## No part of this publication may be reproduced,

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or transmitted in any form or by any means,

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Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book,

they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose

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The advice and strategies contained herein may not be suitable for your situation

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### If this book refers to media such as a CD or DVD that is not included in the version you purchased,

• visit www

Quantitative Methods

The Time Value of Money

### The Time Value of Money  The Future Value of a Single Cash Flow FVN = PV (1 + r) N

The Present Value of a Single Cash Flow PV =

## FV (1 + r) N

### PVAnnuity Due = PVOrdinary Annuity × (1 + r) FVAnnuity Due = FVOrdinary Annuity × (1 + r)

Present Value of a Perpetuity PV(perpetuity) =

PMT I/Y

### Any unauthorized copying or distribution will constitute an infringement of copyright

Discounted Cash Flow Applications

Discounted Cash Flow Applications Net Present Value N

# CFt t t=0 (1 + r )

## NPV = ∑

where: CFt = the expected net cash flow at time t N = the investment’s projected life r = the discount rate or appropriate cost of capital Bank Discount Yield rBD =

D 360 × F t

where: rBD = the annualized yield on a bank discount basis D'= the dollar discount (face value – purchase price) F = the face value of the bill t = number of days remaining until maturity Holding Period Yield HPY =

## P1 − P0 + D1 P1 + D1 = −1 P0 P0

where: P0 = initial price of the investment

### P1 = price received from the instrument at maturity/sale

D1 = interest or dividend received from the investment

#### Effective Annual Yield EAY = (1 + HPY)365/ t − 1

where: HPY = holding period yield t = numbers of days remaining till maturity HPY = (1 + EAY) t /365 − 1

#### Any unauthorized copying or distribution will constitute an infringement of copyright

Discounted Cash Flow Applications

### Money Market Yield R MM =

• 360 × rBD 360 − (t × rBD )

R MM = HPY × (360/t)

### Bond Equivalent Yield BEY = [(1 + EAY)0

• 5 − 1] × 2

Any unauthorized copying or distribution will constitute an infringement of copyright

Statistical Concepts

Statistical Concepts Population Mean N

• ∑ xi i =1

where: xi = is the ith observation

Sample Mean n

• ∑ xi i =1

## G = n X1X 2 X 3 … X n with X i > 0 for i = 1,

 T R G =  ∏ (1 + R t )  − 1  t =1 

Harmonic Mean Harmonic mean: X H =

### N with X i > 0 for i = 1,2,…,N

• 1 ∑x i =1 i N

#### Percentiles Ly =

• ( n + 1) y 100

where: y = percentage point at which we are dividing the distribution Ly = location (L) of the percentile (Py) in the data set sorted in ascending order Range Range = Maximum value − Minimum value

# Mean Absolute Deviation n

• ∑ Xi − X i =1

where: n = number of items in the data set X = the arithmetic mean of the sample Population Variance N

• ∑ (X i − µ)2 i =1

where: Xi = observation i μ = population mean N = size of the population Population Standard Deviation N

• ∑ (X i −

### Sample Variance n

Sample variance = s2 =

• ∑ (X i − i =1
• where: n = sample size

### Sample Standard Deviation n

• ∑ (X i − X)2 i =1

## Any unauthorized copying or distribution will constitute an infringement of copyright

Statistical Concepts

## Coefficient of Variation Coefficient of variation =

where: s'= sample standard deviation X = the sample mean

# Sharpe Ratio Sharpe ratio =

• rp − rf sp

where: rp = mean portfolio return rf = risk‐free return sp = standard deviation of portfolio returns Sample skewness,

also known as sample relative skewness,

• is calculated as: n

### (X i − X)3 ∑ 

 n i =1 SK =    ( n − 1)( n − 2 ) 

As n becomes large,

the expression reduces to the mean cubed deviation

1 SK ≈ n

• ∑ (X i − X)3 i =1

where: s'= sample standard deviation Sample Kurtosis uses standard deviations to the fourth power

Sample excess kurtosis is calculated as: n   (X i − X)4  ∑  n(n + 1) 3(n − 1)2 i =1 − KE =  4 s' (n − 1)(n − 2)(n − 3)  (n − 2)(n − 3)    

## As n becomes large the equation simplifies to: n

### (X i − X)4 ∑ 1 i=1

where: s'= sample standard deviation For a sample size greater than 100,

a sample excess kurtosis of greater than 1

• 0 would be considered unusually high

## Most equity return series have been found to be leptokurtic

Any unauthorized copying or distribution will constitute an infringement of copyright

### Probability Concepts

Probability Concepts Odds for an Event P (E) =

• (a + b)

### Where the odds for are given as “a to b”,

then: Odds for an Event P (E) =

• b (a + b)

# Where the odds against are given as “a to b”,

then: Conditional Probabilities P(A B) =

P(AB) given that P(B) ≠ 0 P(B)

## For Independant Events P(A B) = P(A),

• or equivalently,

### The Total Probability Rule P(A) = P(AS) + P(ASc ) P(A) = P(A S) × P(S) + P(A Sc ) × P(Sc )

The Total Probability Rule for n Possible Scenarios P(A) = P(A S1 ) × P(S1 ) + P(A S2 ) × P(S2 ) +  + P(A Sn ) × P(Sn ) where the set of events {S1 ,

## Any unauthorized copying or distribution will constitute an infringement of copyright

Probability Concepts

## Expected Value E(X) = P(X1 )X1 + P(X 2 )X 2 + … P(X n )X n n

### E(X) = ∑ P(X i )X i i =1

where: Xi = one of n possible outcomes

Variance and Standard Deviation σ 2 (X) = E{[X − E(X)]2} n

# E(X) = E(X | S1) × P(S1) + E(X | S2) × P(S2) +

+ E(X  | Sn) × P(Sn) where: E(X) = the unconditional expected value of X E(X | S1) = the expected value of X given Scenario 1 P(S1) = the probability of Scenario 1 occurring The set of events {S1,

S2,

•   ,

Sn} is mutually exclusive and exhaustive

Covariance Cov(XY) = E{[X − E(X)][Y − E(Y)]} Cov(R A ,R B ) = E{[R A − E(R A )][R B − E(R B )]}

# Probability Concepts

### Expected Return on a Portfolio N

#### E(R p ) = ∑ wi E(R i ) = w1E(R1 ) + w2 E(R 2 ) + + w N E(R N ) i =1

• where: Weight of asset i =

### Portfolio Variance N N

Var(R p ) = ∑ ∑ wi w jCov(R i ,R j ) i =1 j=1

Variance of a 2 Asset Portfolio Var(R p ) = w2A σ 2 (R A ) + w2B σ 2 (R B ) + 2w A w B Cov(R A ,R B ) Var(R p ) = w2A σ 2 (R A ) + w2B σ 2 (R B ) + 2w A w Bρ(R A ,R B )σ (R A )σ (R B )

Variance of a 3 Asset Portfolio Var(R p ) = w2A σ 2 (R A ) + w2B σ 2 (R B ) + w2C σ 2 (R C ) + 2w A w B Cov(R A ,R B ) + 2w B wC Cov(R B ,R C ) + 2wC w A Cov(R C ,R A )

Bayes’ Formula P(Event Information) =

P (Information Event) × P (Event) P (Information)

Counting Rules The number of different ways that the k tasks can be done equals n1 × n2 × n3 × … nk

### Combinations n Cr

! =  =  r  ( n − r )

Remember: The combination formula is used when the order in which the items are assigned the labels is NOT important

## Permutations n Pr

• ( n − r )

#### Any unauthorized copying or distribution will constitute an infringement of copyright

Common Probability Distributions

Common Probability Distributions Discrete Uniform Distribution F(x) = n × p(x) for the nth observation

Binomial Distribution P(X=x) = n Cx (p)x (1 − p)n-x

where: p = probability of success 1 − p = probability of failure nCx = number of possible combinations of having x successes in n trials

Stated differently,

it is the number of ways to choose x from n when the order does not matter

Variance of a Binomial Random Variable σ 2x = n × p × (1 − p)

## The Continuous Uniform Distribution P(X < a),

P (X > b) = 0 P (x1 ≤ X ≤ x 2 ) =

• x 2 − x1 b−a

Confidence Intervals For a random variable X that follows the normal distribution: The 90% confidence interval is x − 1

• 65s to x + 1
• 65s The 95% confidence interval is x − 1
• 96s to x + 1
• 96s The 99% confidence interval is x − 2
• 58s to x + 2
• 58s The following probability statements can be made about normal distributions
• • • • •

Approximately 50% of all observations lie in the interval  Approximately 68% of all observations lie in the interval  Approximately 95% of all observations lie in the interval  Approximately 99% of all observations lie in the interval

## μ ± (2/3)σ μ ± 1σ μ ± 2σ μ ± 3σ

#### Any unauthorized copying or distribution will constitute an infringement of copyright

Common Probability Distributions

z‐Score z = (observed value − population mean)/standard deviation = (x − µ)/σ

Roy’s Safety‐First Criterion Minimize P(RP< RT) where: RP = portfolio return RT = target return Shortfall Ratio Shortfall ratio (SF Ratio) or z-score =

# E (RP ) − RT σP

Continuously Compounded Returns EAR = e r − 1 cc

#### HPR t = e r

rcc = continuously compounded annual rate

Any unauthorized copying or distribution will constitute an infringement of copyright

Sampling and Estimation

Sampling and Estimation Sampling Error Sampling error of the mean = Sample mean − Population mean = x − µ

#### Standard Error of Sample Mean when Population Variance is known σx = σ

where: σ x = the standard error of the sample mean σ = the population standard deviation n = the sample size Standard Error of Sample Mean when Population Variance is not known sx =

where: s'x = standard error of sample mean s'= sample standard deviation

Confidence Intervals Point estimate ± (reliability factor × standard error)

where: Point estimate = value of the sample statistic that is used to estimate the population parameter Reliability factor = a number based on the assumed distribution of the point estimate and the level of confidence for the interval (1 − α)

Standard error = the standard error of the sample statistic (point estimate)

## Any unauthorized copying or distribution will constitute an infringement of copyright

Sampling and Estimation

• x ± z α /2

where: x = The sample mean (point estimate of population mean) zα/2 = The standard normal random variable for which the probability of an observation lying in either tail is σ / 2 (reliability factor)

σ = The standard error of the sample mean

• n x ± tα 2

where: x = sample mean (the point estimate of the population mean) tα = the t‐reliability factor 2 s'= standard error of the sample mean n s'= sample standard deviation

Any unauthorized copying or distribution will constitute an infringement of copyright

Hypothesis Testing

# Sample statistic − Hypothesized value Standard error of sample statistic

### Power of a Test Power of a test = 1 − P(Type II error)

Decision Rules for Hypothesis Tests Decision Do not reject H0

H0 is True Correct decision

Reject H0

Incorrect decision Type I error Significance level = P(Type I error)

H0 is False Incorrect decision Type II error Correct decision Power of the test = 1 − P(Type II error)

Confidence Interval  sample   critical   standard    population   sample   critical   standard    statistic −  value   error   ≤  parameter  ≤  statistic +  value   error       x (s n) x (s n) − (z α /2 ) ≤ µ0 ≤ + (z α /2 )

### Summary

H0 : μ ≤ μ0

Alternate hypothesis Ha : μ > μ0

H0 : μ ≥ μ0

## Ha : μ < μ0

### Test statistic < critical value

Test statistic ≥ critical value

Probability that lies below the computed test statistic

## Two‐tailed

H0 : μ = μ0

Ha : μ ≠ μ0

Test statistic < lower critical value Test statistic > upper critical value

Lower critical value ≤ test statistic ≤ upper critical value

Probability that lies above the positive value of the computed test statistic plus the probability that lies below the negative value of the computed test statistic

Null hypothesis

# Reject null if Test statistic > critical value

Test statistic ≤ critical value

## P‐value represents Probability that lies above the computed test statistic

Any unauthorized copying or distribution will constitute an infringement of copyright

Hypothesis Testing

• t‐Statistic t-stat =
• x − µ0 s'n

where: x = sample mean μ0 = hypothesized population mean s'= standard deviation of the sample n = sample size z‐Statistic z-stat =

• x − µ0 σ n

z-stat =

where: x = sample mean μ = hypothesized population mean σ = standard deviation of the population n = sample size

• x − µ0 s'n

where: x = sample mean μ = hypothesized population mean s'= standard deviation of the sample n = sample size

## Tests for Means when Population Variances are Assumed Equal t=

(x1 − x2 ) − (µ1 − µ 2 )  s2p s2p  n +n   1 2

• where: s2p =

(n1 − 1)s12 + (n 2 − 1)s22 n1 + n 2 − 2

• s12 = variance of the first sample s22 = variance of the second sample
• n1 = number of observations in first sample n2 = number of observations in second sample degrees of freedom = n1 + n2 −2

# Hypothesis Testing

## Tests for Means when Population Variances are Assumed Unequal t-stat =

(x1 − x2 ) − (µ1 − µ 2 )  s12 s22   n + n  1 2  s12 s22   n + n  1 2

• (s12 n1 )2 + (s22 n2 )2 n1

where: s12 = variance of the first sample s22 = variance of the second sample

• n1 = number of observations in first sample n2 = number of observations in second sample

## Paired Comparisons Test t=

• d − µ dz sd

where: d'= sample mean difference sd s'd'= standard error of the mean difference = n sd = sample standard deviation n = the number of paired observations Hypothesis Tests Concerning the Mean of Two Populations ‐ Appropriate Tests Population distribution Normal

# Relationship between samples Independent

## Independent

Unequal

t‐test with variance not pooled

Dependent

t‐test with paired comparisons

Type of test t‐test pooled variance

Any unauthorized copying or distribution will constitute an infringement of copyright

Hypothesis Testing

Chi Squared Test‐Statistic χ2 =

• ( n − 1) s2 σ 20

where: n = sample size s2 = sample variance σ 20 = hypothesized value for population variance Test‐Statistic for the F‐Test F=

s12 s22

where: s12 = Variance of sample drawn from Population 1 s22 = Variance of sample drawn from Population 2 Hypothesis tests concerning the variance

## Hypothesis Test Concerning Variance of a single,

normally distributed population

### Appropriate Test Statistic Chi‐square stat

#### Equality of variance of two independent,

normally distributed populations

F‐stat

Any unauthorized copying or distribution will constitute an infringement of copyright

# Technical Analysis

## Technical Analysis Setting Price Targets with Head and Shoulders Patterns Price target = Neckline

Setting Price Targets for Inverse Head and Shoulders Patterns Price target = Neckline + (Neckline − Head)

# Momentum or Rate of Change Oscillator M = (V − Vx ) × 100

where: M = momentum oscillator value V = last closing price Vx = closing price x days ago,

typically 10 days Relative Strength Index RSI = 100 −

100 1 + RS

• where: RS =

Σ (Up changes for the period under consideration) Σ(| Down changes for the period under consideration|)

Stochastic Oscillator C − L14  %K = 100   H14 − L14 

where: C = last closing price L14 = lowest price in last 14 days H14 = highest price in last 14 days %D (signal line) = Average of the last three %K values calculated daily

### Short Interest ratio Short interest ratio =

Short interest Average daily trading volume

Arms Index Arms index =

Number of advancing issues / Number of declining issues Volume of advancing issues / Volume of declining issues

Economics

## Demand and Supply Analysis: Introduction

Demand and Supply Analysis: Introduction The demand function captures the effect of all these factors on demand for a good

Demand function: QDx = f(Px,

…) … (Equation 1) Equation 1 is read as “the quantity demanded of Good X (QDX) depends on the price of Good X (PX),

consumers’ incomes (I) and the price of Good Y (PY),

” The supply function can be expressed as:

### Supply function: QSx = f(Px,W,

…) … (Equation 5) The own‐price elasticity of demand is calculated as: EDPx =

%∆QDx … (Equation 16) %∆Px

## Equation 16 can be expanded to the following form:

• %∆QDx = = %∆Px
• ∆QDx ∆Px

Slope of demand function

 ∆QDx   Px  = … (Equation 17)  ∆Px   QDx 

Coefficient on own‐price in market demand function

### Arc elasticity is calculated as: (Q 0

• - Q1 ) × 100 % change in quantity demanded % ∆ Q d'(Q 0 + Q1 )/2 = = EP = (P0
• - P1 ) % change in price %∆P × 100 (P0 + P1 )/2

Any unauthorized copying or distribution will constitute an infringement of copyright

### Demand and Supply Analysis: Introduction

Income Elasticity of Demand Income elasticity of demand measures the responsiveness of demand for a particular good to a change in income,

holding all other things constant

#### Same as coefficient on I in market demand function (Equation 11)

• %∆QDx ED I = = %∆I
• ∆QDx ∆I
• =  

∆QDx   I  … (Equation 18)  ∆I   QDx 

% change in quantity demanded % change in income

Cross‐Price Elasticity of Demand Cross elasticity of demand measures the responsiveness of demand for a particular good to a change in price of another good,

holding all other things constant

### Same as coefficient on PY in market demand function (Equation 11)

• %∆QDx = = %∆Py
• ∆QDx ∆Py

 ∆QDx   Py  =   … (Equation 19)  ∆Py   QDx 

% change in quantity demanded % change in price of substitute or complement

### Any unauthorized copying or distribution will constitute an infringement of copyright

Demand and Supply Analysis: Consumer Demand

Demand and Supply Analysis: Consumer Demand The Utility Function In general a utility function can be represented as:

U = f(Q x ,Q x ,

• … ,Q x ) 1

## Demand and Supply Analysis: The Firm

Demand and Supply Analysis: The Firm Accounting Profit Accounting profit (loss) = Total revenue − Total accounting costs

Economic Profit Economic profit (also known as abnormal profit or supernormal profit) is calculated as: Economic profit = Total revenue − Total economic costs Economic profit = Total revenue − (Explicit costs + Implicit costs) Economic profit = Accounting profit − Total implicit opportunity costs Normal Profit Normal profit = Accounting profit − Economic profit Total,

## Total revenue (TR)

Price times quantity (P × Q),

or the sum of individual units sold times their respective prices

• (TR / Q)

• (ΔTR / ΔQ)

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Demand and Supply Analysis: The Firm

# Average,

### Sum of all fixed expenses

here defined to include all opportunity costs

### Sum of all variable expenses,

or per unit variable cost times quantity

• (per unit VC × Q)

Total costs (TC)

#### Total fixed cost plus total variable cost

• (TFC + TVC)

Average fixed cost (AFC)

### Total fixed cost divided by quantity

• (TFC / Q)

Average variable cost (AVC)

• (TVC / Q)

## Average total cost (ATC)

### Total cost divided by quantity

• (TC / Q) or (AFC + AVC)

## Change in total cost divided by change in quantity

• (ΔTC / ΔQ)

Marginal revenue product (MRP) of labor is calculated as: MRP of labor = Change in total revenue / Change in quantity of labor For a firm in perfect competition,

## MRP of labor equals the MP of the last unit of labor times the price of the output unit

MRP = Marginal product * Product price A profit‐maximizing firm will hire more labor until: MRPLabor = PriceLabor Profits are maximized when: MRP1 MRPn =…= Price of input 1 Price of input n

2 Exhibit

Volume 2,

CFA Program Curriculum 2012

### The Firm And Market Structures

The Firm And Market Structures The relationship between MR and price elasticity can be expressed as: MR = P[1 − (1/E p )]

#### MC = MR so: P[1 − (1/E p )] = MC

N‐firm concentration ratio: Simply computes the aggregate market share of the N largest firms in the industry

### The ratio will equal 0 for perfect competition and 100 for a monopoly

Herfindahl‐Hirschman Index (HHI): Adds up the squares of the market shares of each of the largest N companies in the market

### The HHI equals 1 for a monopoly

If there are M firms in the industry with equal market shares,

• the HHI will equal 1/M

## Aggregate Output,

And Economic Growth

## Aggregate Output,

And Economic Growth Nominal GDP refers to the value of goods and services included in GDP measured at current prices

### Nominal GDP = Quantity produced in Year t × Prices in Year t

Real GDP refers to the value of goods and services included in GDP measured at base‐year prices

## Real GDP = Quantity produced in Year t × Base-year prices

### GDP Deflator GDP deflator =

Value of current year output at current year prices × 100 Value of current year output at base year prices

# GDP deflator =

## Nominal GDP × 100 Real GDP

### The Components of GDP Based on the expenditure approach,

GDP may be calculated as: GDP = C + I + G + (X − M)

C = Consumer spending on final goods and services I = Gross private domestic investment,

which includes business investment in capital goods (e

plant and equipment) and changes in inventory (inventory investment) G = Government spending on final goods and services X = Exports M = Imports Expenditure Approach Under the expenditure approach,

GDP at market prices may be calculated as: GDP = Consumer spending on goods and services + Business gross fixed investment + Change in inventories + Government spending on goods and services + Government gross fixed investment + Exports − Imports + Statistical discrepancy

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# GDP = C + I + G + (X − M)

### Aggregate Output,

And Economic Growth

Income Approach Under the income approach,

GDP at market prices may be calculated as: GDP = National income + Capital consumption allowance + Statistical discrepancy … (Equation 1)

National income equals the sum of incomes received by all factors of production used to generate final output

## It includes:

• Employee compensation • Corporate and government enterprise profits before taxes,

which includes: ○○ Dividends paid to households ○○ Corporate profits retained by businesses ○○ Corporate taxes paid to the government • Interest income • Rent and unincorporated business net income (proprietor’s income): Amounts earned by unincorporated proprietors and farm operators,

• who run their own businesses

• Indirect business taxes less subsidies: This amount reflects taxes and subsidies that are included in the final price of a good or service,

and therefore represents the portion of national income that is directly paid to the government

The capital consumption allowance (CCA) accounts for the wear and tear or depreciation that occurs in capital stock during the production process

It represents the amount that must be reinvested by the company in the business to maintain current productivity levels

You should think of profits + CCA as the amount earned by capital

Personal income = National income − Indirect business taxes − Corporate income taxes − Undistributed corporate profits + Transfer payments … (Equation 2)

Personal disposable income = Personal income − Personal taxes … (Equation 3) Personal disposable income = Household consumption + Household saving

• … (Equation 4)

### Aggregate Output,

And Economic Growth

Household saving = Personal disposable income − Consumption expenditures − Interest paid by consumers to businesses − Personal transfer payments to foreigners … (Equation 5) Business sector saving = Undistributed corporate profits + Capital consumption allowance … (Equation 6)

# GDP = Household consumption + Total private sector saving + Net taxes

The equality of expenditure and income S = I + (G − T) + ( X − M) … (Equation 7)

The IS Curve (Relationship between Income and the Real Interest Rate) Disposable income = GDP − Business saving − Net taxes S − I = (G − T) + ( X − M) … (Equation 7)

The LM Curve Quantity theory of money: MV = PY The quantity theory equation can also be written as: M/P and MD/P = kY where: k = I/V M = Nominal money supply MD = Nominal money demand MD/P is referred to as real money demand and M/P is real money supply

Equilibrium in the money market requires that money supply and money demand be equal

# Money market equilibrium: M/P = RMD Solow (neoclassical) growth model Y = AF(L,K)

where: Y = Aggregate output L'= Quantity of labor K = Quantity of capital A = Technological knowledge or total factor productivity (TFP)

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#### Aggregate Output,

And Economic Growth

# Growth accounting equation

Growth in potential GDP = Growth in technology + WL (Growth in labor) + WK (Growth in capital) Growth in per capital potential GDP = Growth in technology + WK (Growth in capital-labor ratio)

Measures of Sustainable Growth Labor productivity = Real GDP/Aggregate hours Potential GDP = Aggregate hours × Labor productivity This equation can be expressed in terms of growth rates as: Potential GDP growth rate = Long‐term growth rate of labor force + Long‐term labor productivity growth rate

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Understanding Business Cycles Unit labor cost (ULC) is calculated as: ULC = W/O

where: O = Output per hour per worker W = Total labor compensation per hour per worker

### Monetary And Fiscal Policy

Monetary And Fiscal Policy Required reserve ratio = Required reserves / Total deposits Money multiplier = 1/ (Reserve requirement) The Fischer effect states that the nominal interest rate (RN) reflects the real interest rate (RR) and the expected rate of inflation (IIe)

R N = R R + Πe

### The Fiscal Multiplier Ignoring taxes,

the multiplier can also be calculated as:

• 1 1 = = 10 (1 − MPC) (1 − 0

# Assuming taxes,

the multiplier can also be calculated as: 1 [1 − MPC(1 − t)]

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#### International Trade And Capital Flows

International Trade And Capital Flows Balance of Payment Components A country’s balance of payments is composed of three main accounts: • The current account balance largely reflects trade in goods and services

• The capital account balance mainly consists of capital transfers and net sales of non‐produced,

• non‐financial assets

• The financial account measures net capital flows based on sales and purchases of domestic and foreign financial assets

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Currency Exchange Rates

Currency Exchange Rates The real exchange rate may be calculated as: Real exchange rate DC/FC = SDC/FC × (PFC /PDC )

where: SDC/FC = Nominal spot exchange rate PFC = Foreign price level quoted in terms of the foreign currency PDC = Domestic price level quoted in terms of the domestic currency The forward rate may be calculated as:

This version of the formula is perhaps easiest to remember because it contains the DC term in numerator for all three components: FDC/FC,

## FDC/FC =

1 SFC/DC

• (1 + rDC ) (1 + rDC ) or FDC/FC = SDC/FC × (1 + rFC ) (1 + rFC )

Forward rates are sometimes interpreted as expected future spot rates

Ft = St +1 (St +1 ) (r − r ) − 1 = ∆%S(DC/FC)t +1 = DC FC S (1 + rFC )

Exchange Rates and the Trade Balance The Elasticities Approach Marshall-Lerner condition: ω x ε x + ω M (ε M − 1) > 0

where: ωx = Share of exports in total trade ωM = Share of imports in total trade εx = Price elasticity of demand for exports εM = Price elasticity of demand for imports

## Financial Reporting and Analysis

Financial Reporting Mechanics

# Financial Reporting Mechanics

2 Exhibit

CFA Program Curriculum 2012

## Any unauthorized copying or distribution will constitute an infringement of copyright

Understanding the Income Statement

Understanding the Income Statement Basic EPS Basic EPS =

Net income − Preferred dividends Weighted average number of shares outstanding

Diluted EPS

## Diluted EPS =

 Preferred   Net income − dividends  +   Weighted average + shares

### Shares from conversion of convertible preferred shares

 Convertible  Convertible preferred +  × (1 − t )  debt   dividends  interest  Shares from conversion of + convertible debt

Shares + issuable from stock options

### Comprehensive Income Net income + Other comprehensive income = Comprehensive income

Ending Shareholders’ Equity Ending shareholders’ equity = Beginning shareholders’ equity + Net income + Other comprehensive income − Dividends declared

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Understanding the Balance Sheet

# Items recognized on the income statement

Held‐to‐Maturity Securities Reported at cost or amortized cost

Interest income

## Realized gains and losses

Available‐for‐Sale Securities Reported at fair value

Trading Securities Reported at fair value

Unrealized gains or losses due to changes in market values are reported in other comprehensive income within owners’ equity

# Dividend income

## Understanding Cash Flow Statements

Understanding Cash Flow Statements Cash Flow Classification under U

## GAAP CFO Inflows Cash collected from customers

### Sale proceeds from long‐term investments

Outflows Cash paid to employees

Cash paid to suppliers

Cash paid for other expenses

# Outflows Repayment of LT debt

### Dividends payments

Cash Flow Statements under IFRS and U

# GAAP IFRS

Classification of Cash Flows Interest and dividends received Interest paid

# CFO or CFI CFO or CFF

## Dividend paid Dividends received Taxes paid

### CFO or CFF CFO or CFI CFO,

but part of the tax can be categorized as CFI or CFF if it is clear that the tax arose from investing or financing activities

# CFF CFO CFO

Bank overdraft

Included as a part of cash equivalents

## Direct or indirect method

The former is preferred

### Direct or indirect method

The former is preferred

However,

• if the direct method is used,

a reconciliation of net income and CFO must be included

## Taxes paid should be presented separately on the cash flow statement

### If taxes and interest paid are not explicitly stated on the cash flow statement,

details can be provided in footnotes

Presentation Format CFO (No difference in CFI and CFF presentation) Disclosures

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### Understanding Cash Flow Statements

Free Cash Flow to the Firm FCFF = NI + NCC + [Int * (1 − tax rate)] − FCInv − WCInv FCFF = CFO + [Int * (1 − tax rate)] − FCInv

Free Cash Flow to Equity FCFE = CFO − FCInv + Net borrowing

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Financial Analysis Techniques

### Financial Analysis Techniques Inventory Turnover Inventory turnover =

Cost of goods sold Average inventory

### Days of Inventory on Hand Days of inventory on hand (DOH) =

• 365 Inventory turnover

Receivables Turnover Receivables turnover =

## Days of Sales Outstanding Days of sales outstanding (DSO) =

• 365 Receivables turnover

Payables Turnover Payables turnover =

### Number of Days of Payables Number of days of payables =

• 365 Payables turnover

Working Capital Turnover Working capital turnover =

#### Revenue Average working capital

Fixed Asset Turnover Fixed asset turnover =

## Revenue Average fixed assets

### Total Asset Turnover Total asset turnover =

Revenue Average total assets

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## Financial Analysis Techniques

### Current Ratio Current ratio =

Current assets Current liabilities

#### Quick Ratio Quick ratio =

Cash + Short-term marketable investments + Receivables Current liabilities

# Cash + Short-term marketable investments Current liabilities

Defensive Interval Ratio Defensive interval ratio =

Cash + Short-term marketable investments + Receivables Daily cash expenditures

Cash Conversion Cycle Cash conversion cycle = DSO + DOH − Number of days of payables

### Debt‐to‐Assets Ratio Debt

• -to-assets ratio =

## Total debt Total assets

Debt‐to‐Capital Ratio Debt

• -to-capital ratio =

### Total debt Total debt + Shareholders’ equity

Debt‐to‐Equity Ratio Debt

• -to-equity ratio =

## Interest Coverage Ratio Interest coverage ratio =

EBIT Interest payments

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#### Financial Analysis Techniques

Fixed Charge Coverage Ratio Fixed charge coverage ratio =

EBIT + Lease payments Interest payments + Lease payments

#### Gross profit Revenue

Operating Profit Margin Operating profit margin =

Operating profit Revenue

Pretax Margin Pretax margin =

EBT (earnings before tax,

• but after interest) Revenue

# EBIT Short-term debt + Long-term debt + Equity

### Return on Equity Return on equity =

Net income Average total equity

# Financial Analysis Techniques

DuPont Decomposition of ROE Net income Average shareholders’ equity

• 2‐Way Dupont Decomposition Net income Average total assets × Average total assets Average shareholders’ equity

Leverage

• 3‐Way Dupont Decomposition Net income Average total assets Revenue × × Revenue Average total assets Average shareholders’ equity

Net profit margin

### Leverage

• 5‐Way Dupont Decomposition

### Asset turnover

Net income EBT Average total assets EBIT Revenue × × × × EBT EBIT Revenue Average total assets Avg

• shareholders’ equity ↓

Tax burden

EBIT margin

### Leverage

Price‐to‐Earnings Ratio P /E =

### Price per share Earnings per share

Price to Cash Flow P /CE =

## Price to Sales P /S =

Price per share Sales per share

### Price to Book Value P /BV =

Price per share Book value per share

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Financial Analysis Techniques

#### Per Share Ratios Cash flow from operations Average number of shares outstanding

Cash flow per share =

# EBITDA per share =

EBITDA Average number of shares outstanding

Dividends per share =

Common dividends declared Weighted average number of ordinary shares

### Dividend Payout Ratio Dividend payout ratio =

#### Retention Rate Retention Rate =

Net income attributable to common shares − Common share dividends Net income attributable to common shares

Growth Rate Sustainable growth rate = Retention rate × ROE

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## Inventories LIFO versus FIFO (with rising prices and stable inventory levels

) LIFO versus FIFO when Prices are Rising LIFO COGS Higher Income before taxes Lower Income taxes Lower Net income Lower Cash flow Higher EI Lower Working capital Lower

FIFO Lower Higher Higher Higher Lower Higher Higher

### Effect on Numerator Income is lower under LIFO because COGS is higher

Effect on Denominator Sales are the same under both

Current ratio

## Current liabilities are the same

#### Lower under LIFO

Quick ratio

Assets are higher as a result of lower taxes paid

Current liabilities are the same

Higher under LIFO

#### COGS is higher under LIFO

Average inventory is Higher under LIFO lower under LIFO

Total asset turnover

## Sales are the same

Lower total assets under LIFO

## Effect on Ratio Lower under LIFO

Higher under LIFO

### The LIFO Method and the LIFO Reserve: EI FIFO = EI LIFO + LR

where LR = LIFO Reserve COGSFIFO = COGSLIFO − (Change in LR during the year) Net income after tax under FIFO will be greater than LIFO net income after tax by: Change in LIFO Reserve × (1 − Tax rate)

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Inventories

When converting from LIFO to FIFO assuming rising prices: Equity (retained earnings) increase by: LIFO Reserve × (1 − Tax rate) Liabilities (deferred taxes) increase by: LIFO Reserve × (Tax rate) Current assets (inventory) increase by: LIFO Reserve

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### Initially when the cost is capitalized In future periods when the asset is depreciated or amortized

When the cost is expensed

Net income (first year) Net income (future years) Total assets Shareholders’ equity Cash flow from operations Cash flow from investing Income variability Debt-to-equity

#### Effect on Financial Statements • Noncurrent assets increase

• Cash flow from investing activities decreases

• • • • • •

Noncurrent assets decrease

# Equity decreases

Net income decreases by the entire after‐tax amount of the cost

• No related asset is recorded on the balance sheet and therefore,

no depreciation or amortization expense is charged in future periods

• Operating cash flow decreases

• Expensed costs have no financial statement impact in future years

# Straight Line Depreciation Depreciation expense =

Original cost − Salvage value Depreciable life

# Accelerated Depreciation DDB depreciation in Year X =

• 2 × Book value at the beginning of Year X Depreciable life

## Estimated Useful Life Estimated useful life =

Gross investment in fixed assets Annual depreciation expense

# Average Cost of Asset Average age of asset =

#### Accumulated depreciation Annual depreciation expense

Remaining Useful Life Remaining useful life =

## Net investment in fixed assets Annual depreciation expense

Gross investment in fixed assets Accumulated depreciation Net investment in fixed assets = + Annual depreciation expense Annual depreciation expense Annual depreciation expense

Estimated useful or depreciable life The historical cost of an asset divided by its useful life equals annual depreciation expense under the straight line method

#### Therefore,

the historical cost divided by annual depreciation expense equals the estimated useful life

## Remaining useful life

Annual depreciation expense times the number of years that the asset has been in use equals accumulated depreciation

### Therefore,

accumulated depreciation divided by annual depreciation equals the average age of the asset

The book value of the asset divided by annual depreciation expense equals the number of years the asset has remaining in its useful life

## Carrying Value versus Tax Base Carrying amount is greater

Tax base is greater

Carrying amount is greater

## Results in… DTL DTA DTA DTL

### Income Tax Accounting under IFRS versus U

GAAP IFRS ISSUE SPECIFIC TREATMENTS Revaluation of fixed assets Recognized in equity as and intangible assets

• deferred taxes

GAAP Revaluation is prohibited

Treatment of undistributed profit from investment in subsidiaries

Recognized as deferred taxes except when the parent company is able to control the distribution of profits and it is probable that temporary differences will not reverse in future

# No recognition of deferred taxes for domestic subsidiaries when amounts are tax‐free

#### Treatment of undistributed profit from investments in joint ventures

Recognized as deferred taxes except when the investor controls the sharing of profits and it is probable that there will be no reversal of temporary differences in future

No recognition of deferred taxes for foreign corporate joint ventures that fulfill indefinite reversal criteria

# Treatment of undistributed profit from investments in associates

Recognized as deferred Deferred taxes are taxes except when the recognized from temporary investor controls the sharing differences

of profits and it is probable that there will be no reversal of temporary differences in future

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Income Taxes

### Recognized if it is probable that sufficient taxable profit will be available in the future

GAAP Only enacted tax rates and tax laws are used

Deferred tax assets are recognized in full and then reduced by a valuation allowance if it is likely that they will not be realized

## DEFERRED TAX PRESENTATION Offsetting of deferred tax Offsetting allowed only if Same as in IFRS

• assets and liabilities

the entity has right to legally enforce it and the balance is related to a tax levied by the same authority

Balance sheet classification

### Classified on balance sheet as net noncurrent with supplementary disclosures

Classified as either current or noncurrent based on classification of underlying asset and liability

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### Non-Current (Long-Term) Liabilities

Non-Current (Long-Term) Liabilities Income Statement Effects of Lease Classification Income Statement Item Operating expenses Nonoperating expenses EBIT (operating income) Total expenses‐ early years Total expenses‐ later years Net income‐ early years Net income‐ later years

Finance Lease Lower Higher Higher Higher Lower Lower Higher

## Operating Lease Higher Lower Lower Lower Higher Higher Lower

Balance Sheet Effects of Lease Classification Balance Sheet Item Assets Current liabilities Long term liabilities Total cash

# Capital Lease Higher Higher Higher Same

Operating Lease Lower Lower Lower Same

# Capital Lease Higher Lower Same

## Operating Lease Lower Higher Same

Impact of Lease Classification on Financial Ratios

Ratio Asset turnover

Numerator under Finance Lease Sales‐ same

Denominator Ratio Better or under Finance Worse under Lease Effect on Ratio Finance Lease Assets‐ higher Lower Worse

# Assets‐ higher

Current ratio

Current assetssame

Current liabilitieshigher

## Leverage ratios (D/E and D/A)

Debt‐ higher

### Return on equity*

#### Net income lower in early years

Equity same

• * In early years of the lease agreement

#### Non-Current (Long-Term) Liabilities

Financial Statement Effects of Lease Classification from Lessor’s Perspective Total net income Net income (early years) Taxes (early years) Total CFO Total CFI Total cash flow

Financing Lease Same Higher Higher Lower Higher Same

# Operating Lease Same Lower Lower Higher Lower Same

Definitions of Commonly Used Solvency Ratios Solvency Ratios

# Numerator

Denominator

## Debt‐to‐assets ratio

Expresses the percentage of total assets financed by debt

#### Total debt

Total assets

Debt‐to‐capital ratio

Measures the percentage of a company’s total capital (debt + equity) financed by debt

## Debt‐to‐equity ratio

### Average total assets Average shareholders’ equity

Leverage Ratios

Coverage Ratios Interest coverage ratio

### Measures the number of times a EBIT company’s EBIT could cover its interest payments

Interest payments

# Fixed charge coverage ratio

Measures the number of times a company’s earnings (before interest,

taxes and lease payments) can cover the company’s interest and lease payments

# EBIT + Lease payments

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Financial Reporting Quality

Financial Reporting Quality Relationship between Financial Reporting Quality and Earnings Quality Financial Reporting Quality Low Earnings High (Results) Quality LOW financial reporting quality impedes assessment of earnings quality and Low impedes valuation

High HIGH financial reporting quality enables assessment

HIGH earnings quality increases company value

HIGH financial reporting quality enables assessment

LOW earnings quality decreases company value

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# Corporate Finance

## Capital Budgeting  Net Present Value (NPV) n

CFt − Outlay (1 + r) t t =1

NPV = ∑

where: CFt = after‐tax cash flow at time,

r = required rate of return for the investment

This is the firm’s cost of capital adjusted for the risk inherent in the project

### CFt ∑ (1 + IRR) t = Outlay t =1

t ∑ (1 + IRR) t − Outlay = 0 t =1

### Average Accounting Rate of Return (AAR) AAR =

#### Average net income Average book value

Profitability Index PI =

PV of future cash flows NPV = 1+ Initial investment Initial investment

### Cost of Capital

Cost of Capital Weighted Average Cost of Capital WACC = (wd )(rd )(1 − t) + (wp )(rp ) + (we )(re )

where: wd = Proportion of debt that the company uses when it raises new funds rd = Before‐tax marginal cost of debt t = Company’s marginal tax rate wp = Proportion of preferred stock that the company uses when it raises new funds rp = Marginal cost of preferred stock we = Proportion of equity that the company uses when it raises new funds re = Marginal cost of equity To Transform Debt‐to‐equity Ratio into a Component’s Weight D

# E = D'=w d'D 1+ E D'+ E wd + we = 1

Valuation of Bonds    n PMT  FV  P0 =  ∑ t + n  t =1  rd    rd  1 + 1 +   2    2

where: P0 = current market price of the bond

#### PMTt = interest payment in period t

rd = yield to maturity on BEY basis

n = number of periods remaining to maturity

FV = Par or maturity value of the bond

Valuation of Preferred Stock Vp =

where: Vp = current value (price) of preferred stock

#### Dp = preferred stock dividend per share

• rp = cost of preferred stock

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### Cost of Capital

Required Return on a Stock Capital Asset Pricing Model re = R F + β i [E(R M ) − R F ]

where: [E(RM) − Rf] = Equity risk premium

RM = Expected return on the market

βi = Beta of stock

# Beta measures the sensitivity of the stock’s returns to changes in market returns

## RF = Risk‐free rate

re = Expected return on stock (cost of equity)

Dividend Discount Model P0 =

## D1 re − g

where: P0 = current market value of the security

D1 = next year’s dividend

re = required rate of return on common equity

g = the firm’s expected constant growth rate of dividends

## Rearranging the above equation gives us a formula to calculate the required return on equity: re =

D1 +g P0

Sustainable Growth Rate D' g = 1 − × ( ROE )  EPS 