PDF -Cash Flows Part 1 - Updated - KnowledgEquity - CFA Level 1 Formula Sheet Updated 2016
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- r June 2016 CFA Level 1

COVERS ALL TOPICS IN LEVEL I

All rights reserved

Published by John Wiley & Sons,

Published simultaneously in Canada

- stored in a retrieval system,

or transmitted in any form or by any means,

- electronic,
- mechanical,
- photocopying,
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except as permitted under Section 107 or 108 of the 1976 United States Copyright Act,

without either the prior written permission of the Publisher,

or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center,

- 222 Rosewood Drive,

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- copyright

Requests to the Publisher for permission should be addressed to the Permissions Department,

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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

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

Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages,

including but not limited to special,

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please contact our Customer Care Department within the United States at (800) 762-2974,

outside the United States at (317) 572-3993 or fax (317) 572-4002

Wiley publishes in a variety of print and electronic formats and by print-on-demand

Some material included with standard print versions of this book may not be included in e-books or in print-on-demand

you may download this material at http://booksupport

- visit www

Quantitative Methods

The Time Value of Money

The Present Value of a Single Cash Flow PV =

Present Value of a Perpetuity PV(perpetuity) =

PMT I/Y

Discounted Cash Flow Applications

Discounted Cash Flow Applications Net Present Value N

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 =

where: P0 = initial price of the investment

D1 = interest or dividend received from the investment

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

Discounted Cash Flow Applications

- 360 × rBD 360 − (t × rBD )

R MM = HPY × (360/t)

- 5 − 1] × 2

© Wiley 2016 All Rights Reserved

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

T R G = ∏ (1 + R t ) − 1 t =1

Harmonic Mean Harmonic mean: X H =

- 1 ∑x i =1 i N

- ( 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

- ∑ 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 = s2 =

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

- ∑ (X i − X)2 i =1

Statistical Concepts

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

- 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

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)

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

Any unauthorized copying or distribution will constitute an infringement of copyright

Probability Concepts Odds for an Event P (E) =

- (a + b)

then: Odds for an Event P (E) =

- b (a + b)

then: Conditional Probabilities P(A B) =

P(AB) given that P(B) ≠ 0 P(B)

- or equivalently,

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 ,

Probability Concepts

where: Xi = one of n possible outcomes

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

+ 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 )]}

- where: Weight of asset i =

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

! = = r ( n − r )

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

- ( n − r )

© Wiley 2016 All Rights Reserved

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)

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

© Wiley 2016 All Rights Reserved

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 =

Continuously Compounded Returns EAR = e r − 1 cc

rcc = continuously compounded annual rate

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Sampling and Estimation

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

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)

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

© Wiley 2016 All Rights Reserved

Any unauthorized copying or distribution will constitute an infringement of copyright

Hypothesis Testing

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 )

H0 : μ ≤ μ0

Alternate hypothesis Ha : μ > μ0

H0 : μ ≥ μ0

Test statistic ≥ critical value

Probability that lies below the computed test statistic

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

Test statistic ≤ critical value

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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

(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

(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

- 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

Unequal

t‐test with variance not pooled

Dependent

t‐test with paired comparisons

Type of test t‐test pooled variance

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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

normally distributed population

normally distributed populations

F‐stat

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- - (Head − Neckline)

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

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 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 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:

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

%∆QDx … (Equation 16) %∆Px

- %∆QDx = = %∆Px
- ∆QDx ∆Px

Slope of demand function

∆QDx Px = … (Equation 17) ∆Px QDx

Coefficient on own‐price in market demand function

- - 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

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

- %∆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

- %∆QDx = = %∆Py
- ∆QDx ∆Py

∆QDx Py = … (Equation 19) ∆Py QDx

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

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 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,

Price times quantity (P × Q),

or the sum of individual units sold times their respective prices

- (TR / Q)

- (ΔTR / ΔQ)

Demand and Supply Analysis: The Firm

here defined to include all opportunity costs

or per unit variable cost times quantity

- (per unit VC × Q)

Total costs (TC)

- (TFC + TVC)

Average fixed cost (AFC)

- (TFC / Q)

Average variable cost (AVC)

- (TVC / Q)

- (TC / Q) or (AFC + AVC)

- (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 = 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 relationship between MR and price elasticity can be expressed as: MR = P[1 − (1/E p )]

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

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

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

- the HHI will equal 1/M

© Wiley 2016 All Rights Reserved

And Economic Growth

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

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

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

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

Any unauthorized copying or distribution will constitute an infringement of copyright

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

• 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)

© Wiley 2016 All Rights Reserved

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)

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

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

Any unauthorized copying or distribution will constitute an infringement of copyright

And Economic Growth

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

© Wiley 2016 All Rights Reserved

Any unauthorized copying or distribution will constitute an infringement of copyright

Understanding Business Cycles

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 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 multiplier can also be calculated as:

- 1 1 = = 10 (1 − MPC) (1 − 0

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

© Wiley 2016 All Rights Reserved

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

© Wiley 2016 All Rights Reserved

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,

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 Mechanics

2 Exhibit

CFA Program Curriculum 2012

Understanding the Income Statement

Understanding the Income Statement Basic EPS Basic EPS =

Net income − Preferred dividends Weighted average number of shares outstanding

Diluted EPS

Preferred Net income − dividends + Weighted average + shares

Convertible Convertible preferred + × (1 − t ) debt dividends interest Shares from conversion of + convertible debt

Shares + issuable from stock options

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

Understanding the Balance Sheet

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

Interest income

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

© Wiley 2016 All Rights Reserved

Understanding Cash Flow Statements Cash Flow Classification under U

Interest and dividends received

Outflows Cash paid to employees

Cash paid to suppliers

Cash paid for other expenses

Cash Flow Statements under IFRS and U

Classification of Cash Flows Interest and dividends received Interest paid

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

Bank overdraft

Included as a part of cash equivalents

The former is preferred

The former is preferred

However,

- if the direct method is used,

a reconciliation of net income and CFO must be included

details can be provided in footnotes

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

Any unauthorized copying or distribution will constitute an infringement of copyright

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

Financial Analysis Techniques

Cost of goods sold Average inventory

- 365 Inventory turnover

Receivables Turnover Receivables turnover =

- 365 Receivables turnover

Payables Turnover Payables turnover =

Purchases Average trade payables

- 365 Payables turnover

Working Capital Turnover Working capital turnover =

Fixed Asset Turnover Fixed asset turnover =

Revenue Average total assets

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Current assets Current liabilities

Cash + Short-term marketable investments + Receivables 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

- -to-assets ratio =

Debt‐to‐Capital Ratio Debt

- -to-capital ratio =

Debt‐to‐Equity Ratio Debt

- -to-equity ratio =

EBIT Interest payments

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Fixed Charge Coverage Ratio Fixed charge coverage ratio =

EBIT + Lease payments Interest payments + Lease payments

Operating Profit Margin Operating profit margin =

Operating profit Revenue

Pretax Margin Pretax margin =

EBT (earnings before tax,

- but after interest) Revenue

Adjusted ROA =

Net income Average total equity

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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

- 5‐Way Dupont Decomposition

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

- shareholders’ equity ↓

Tax burden

EBIT margin

Price‐to‐Earnings Ratio P /E =

Price to Cash Flow P /CE =

Price per share Sales per share

Price per share Book value per share

Financial Analysis Techniques

Cash flow per share =

EBITDA Average number of shares outstanding

Dividends per share =

Common dividends declared Weighted average number of ordinary shares

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

Growth Rate Sustainable growth rate = Retention rate × ROE

) 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 Denominator Sales are the same under both

Current ratio

Quick ratio

Assets are higher as a result of lower taxes paid

Current liabilities are the same

Higher under LIFO

Average inventory is Higher under LIFO lower under LIFO

Total asset turnover

Lower total assets under LIFO

Higher under LIFO

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)

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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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

• Cash flow from investing activities decreases

- • • • • •

Noncurrent assets decrease

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

Original cost − Salvage value Depreciable life

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

Gross investment in fixed assets Annual depreciation expense

Remaining Useful Life Remaining useful life =

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

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

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

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

Tax base is greater

Carrying amount is greater

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

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

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

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

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

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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

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

Operating Lease Lower Lower Lower 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

Current ratio

Current assetssame

Current liabilitieshigher

Debt‐ higher

Equity same

- * In early years of the lease agreement

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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

Definitions of Commonly Used Solvency Ratios Solvency Ratios

Denominator

Expresses the percentage of total assets financed by debt

Total assets

Debt‐to‐capital ratio

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

Leverage Ratios

Coverage Ratios Interest coverage ratio

Interest payments

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

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

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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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

t ∑ (1 + IRR) t − Outlay = 0 t =1

Profitability Index PI =

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

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

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

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

- rp = cost of preferred stock

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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

re = Expected return on stock (cost of equity)

Dividend Discount Model P0 =

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

D1 +g P0

Sustainable Growth Rate D' g = 1 − × ( ROE ) EPS