CFA Level 1 Formula Sheet Updated 2016

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CFA

®

_{EXAM REVIEW}

FORMULA SHEETS

COVERS

ALL TOPICS

IN LEVEL I

CFA

®

LEVEL I

2016

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The Time Value of money

The Time Value of Money

The Future Value of a Single Cash Flow

FV_N =PV (1 r)+ N

The Present Value of a Single Cash Flow

PV FV (1 r)N = + = × + = × + PV PV (1 r)

FVAnnuity Due_{Annuity Due} FVOrdinary Annuity_{Ordinary Annuity} (1 r)

Present Value of a Perpetuity

PV(perpetuity) PMT

I/Y =

Continuous Compounding and Future Values

FV_N =PVer Ns⋅ Effective Annual Rates

= + −

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DiscounTeD cash floW applicaTions

4

Discounted Cash Flow Applications

Net Present Value

∑

₍

₎

= + NPV CF 1 r t t t=0 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

= × r D F 360 t BD 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 P P D P P D P 1 1 0 1 0 1 1 0 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

= + −

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DiscounTeD cash floW applicaTions

Money Market Yield

= × − × R 360 r 360 (t r ) MM BD BD = × R_MM HPY (360/t)

Bond Equivalent Yield

= + − ×

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sTaTisTical concepTs

6

Statistical Concepts

Population Mean

∑

µ = = x N i i 1 N where:

x_i = is the ith observation.

Sample Mean

∑

= = X x n i i 1 n Geometric Mean 1 R (1 R ) (1 R ) (1 R ) OR G X X X X with X 0 for i 1, 2, , n. R (1 R ) 1 G T 1 2 T n 1 2 3 n i G t t 1 T _T1

∏

+ = + × + ×…× + = … > = … = +      − = Harmonic Mean

∑

= > = … = Harmonic mean: X N 1 x with X 0 for i 1,2, ,N. H i i 1 N i Percentiles

(

)

= + L n 1 y 100 y where:

y = percentage point at which we are dividing the distribution

L_y = location (L) of the percentile (P_y) in the data set sorted in ascending order

Range

= −

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Mean Absolute Deviation

∑

= − = MAD X X n i i 1 n where:

n = number of items in the data set

X = the arithmetic mean of the sample

Population Variance (X ) N 2 i 2 i 1 N

∑

σ = − µ = where: X_i = observation i μ = population mean N = size of the population

Population Standard Deviation

∑

σ = − µ = (X ) N i 2 i 1 N Sample Variance

∑

= = − − = Sample variance s (X X) n 1 2 i 2 i 1 n where: n = sample size.

Sample Standard Deviation

∑

= − − = s (X X) n 1 i 2 i 1 n

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8 Coefficient of Variation Coefficient of variation s X = where:

s = sample standard deviation

X = the sample mean.

Sharpe Ratio Sharpe ratio r r s p f p = − where:

r_p = mean portfolio return rf = risk‐free return

s_p = standard deviation of portfolio returns

Sample skewness, also known as sample relative skewness, is calculated as:

∑

(

)(

)

= − −    _ − = S n n 1 n 2 (X X) s K i 3 i 1 n 3

As n becomes large, the expression reduces to the mean cubed deviation.

∑

≈ − = S 1 n (X X) s K i 3 i 1 n 3 where:

Sample Kurtosis uses standard deviations to the fourth power. Sample excess kurtosis is calculated as:

∑

= + − − − −             − − − − = K n(n 1) (n 1)(n 2)(n 3) (X X) s 3(n 1) (n 2)(n 3) E i 4 i 1 n 4 2

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As n becomes large the equation simplifies to:

∑

≈ − − K 1 n (X X) s 3 E i 4 i=1 n 4 where:

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.

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pRobabiliTy concepTs

10

Probability Concepts

Odds for an Event

P E a

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)

P(B) given that P(B) 0

= ≠

Multiplication Rule for Probabilities

P(AB) P(A B) P(B)= ×

Addition Rule for Probabilities

P(A or B) P(A) P(B) P(AB)= + −

For Independant Events

= =

= + −

= ×

P(A B) P(A), or equivalently, P(B A) P(B) P(A or B) P(A) P(B) P(AB)

P(A and B) P(A) P(B)

The Total Probability Rule

P(A) P(AS) P(AS )

P(A) P(A S) P(S) P(A S ) P(S )

c

c c

= +

= × + ×

The Total Probability Rule for n Possible Scenarios

P(A) P(A S ) P(S ) P(A S ) P(S ) P(A S ) P(S )

where the set of events {S , S , , S } is mutually exclusive and exhaustive.

1 1 2 2 n n

1 2 n

= × + × + + ×

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pRobabiliTy concepTs Expected Value = + + … E(X) P(X )X₁ ₁ P(X )X₂ ₂ P(X )X_n _n E(X) P(X )X_i _i i 1 n

∑

= = where:

Xi = one of n possible outcomes.

Variance and Standard Deviation

σ2(X) E{[X E(X)] }= − 2

∑

σ = − = (X) P(X ) [X E(X)] 2 i i 2 i 1 n

The Total Probability Rule for Expected Value

1. E(X) = E(X | S)P(S) + E(X | Sc_)P(Sc₎

2. 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, . . . , S_n} is mutually exclusive and exhaustive.

Covariance

= − −

Cov(XY) E{[X E(X)][Y E(Y)]}

Cov(R ,R ) E{[R_A _B _A E(R )][R_A _B E(R )]}_B

Correlation Coefficient = ρ = σ σ Corr(R ,R ) (R ,R ) Cov(R ,R ) ( )( ) A B A B A B A B

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pRobabiliTy concepTs

12

Expected Return on a Portfolio

E(R )_p w E(R ) w E(R ) w E(R )_i _i ₁ ₁ ₂ ₂ w E(R )_N _N

i 1 N

∑

= = + + + = where:

Weight of asset i Market value of investment i Market value of portfolio = Portfolio Variance

∑

= = = Var(R )_p w w Cov(R ,R )_i _j _i _j j 1 N i 1 N

Variance of a 2 Asset Portfolio

Var(R ) w_p = 2_Aσ2(R ) w_A + _B2σ2(R ) 2w w Cov(R ,R )_B + _A _B _A _B

Var(R ) w_p = 2_Aσ2(R ) w_A + _B2σ2(R ) 2w w (R ,R ) (R ) (R )_B + _A _Bρ _A _B σ _A σ _B

Variance of a 3 Asset Portfolio

= σ + σ + σ

+ + +

Var(R ) w (R ) w (R ) w (R )

2w w Cov(R ,R ) 2w w Cov(R ,R ) 2w w Cov(R ,R )

p 2A 2 A B2 2 B C2 2 C

A B A B B C B C C A C 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 n_k.

Combinations C n r n! n r ! r! n r =  _{ =}₍ ₋ ₎

_{( )}

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

Permutations

P n!

n r !

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common pRobabiliTy DisTRibuTions

Common Probability Distributions

Discrete Uniform Distribution

F(x) n p(x) for the th observation.= × n

Binomial Distribution = − P(X=x) _{n x}C (p) (1 p)x 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 = × × −_x2 n p (1 p)

Tracking Error

Tracking error Gross return on portfolio Total return on benchmark index= −

The Continuous Uniform Distribution

P(X a), P (X b) 0< > = ≤ ≤ = − − P (x X x ) x x b a 1 2 2 1 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 μ ± (2/3)σ

• Approximately 68% of all observations lie in the interval μ ± 1σ

• Approximately 95% of all observations lie in the interval μ ± 2σ

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common pRobabiliTy DisTRibuTions

14

z‐Score

= − = − µ σ

z (observed value population mean)/standard deviation (x )/

Roy’s Safety‐First Criterion

Minimize P(RP< RT) where: RP = portfolio return R_T = target return Shortfall Ratio

( )

= − σ Shortfall ratio (SF Ratio) or z-score E RP RT

P Continuously Compounded Returns

EAR e= rcc −1 r_cc=continuously compounded annual rate

= × −

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sampling anD esTimaTion

Sampling and Estimation

Sampling Error

= − = − µ

Sampling error of the mean Sample mean Population mean x

Standard Error of Sample Mean when Population Variance is known

σ = σx _n

where:

σx = 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

=

s s

n

x

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).

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sampling anD esTimaTion

16 ± _α σ x z n /2 where:

x = The sample mean (point estimate of population mean)

z_α/2 = The standard normal random variable for which the probability of an observation lying in either tail is σ / 2 (reliability factor).

σ

n = The standard error of the sample mean.

± α

x t s

n

2

where:

x = sample mean (the point estimate of the population mean)

α

t

2 = the t‐reliability factor

s

n = standard error of the sample mean

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hypoThesis TesTing

Hypothesis Testing

Test Statistic

= −

Test statistic 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 H0 is True H0 is False

Do not reject H₀ Correct decision Incorrect decision

Type II error

Reject H₀ Incorrect decision

Type I error

Significance level = P(Type I error)

Correct decision Power of the test = 1 − P(Type II error) Confidence Interval    −      ≤    ≤_  +  _ − _α ≤ µ ≤ + _α sample statistic critical value standard error population parameter sample statistic critical value standard error x (z _/2) (s n) ₀ x (z _/2) (s n) Summary Type of test Null hypothesis Alternate

hypothesis Reject null if

Fail to reject

null if P‐value represents

One tailed (upper tail) test

H0 : μ ≤ μ0 Ha : μ > μ0 Test statistic >

critical value Test statistic ≤ critical value

Probability that lies above the computed test statistic.

One tailed (lower tail) test

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 H_a : 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.

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hypoThesis TesTing

18 t‐Statistic = − µ t-stat x s n 0 where: x = sample mean

μ₀ = hypothesized population mean s = standard deviation of the sample n = sample size z‐Statistic = − µ σ z-stat x n 0 _z-stat₌x− µ s n 0 where: where:

x = sample mean x = sample mean

μ = hypothesized population mean μ = hypothesized population mean σ = standard deviation of the population s = standard deviation of the sample n = sample size n = sample size

Tests for Means when Population Variances are Assumed Equal

= − − µ − µ +       t (x x ) ( ) s n s n 1 2 1 2 p 2 1 p 2 2 1/2 where: = − + − + − s (n 1)s (n 1)s n n 2 p 2 1 12 2 22 1 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

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hypoThesis TesTing

Tests for Means when Population Variances are Assumed Unequal

= − − µ − µ +     t-stat (x x ) ( ) s n s n 1 2 1 2 12 1 2 2 2 1/2 df s n s n s n n s n n 12 1 2 2 2 2 12 1 2 1 2 2 2 2 2

(

) (

)

= +     + 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

= − µ t d s dz d where:

d = sample mean difference

s_d = standard error of the mean difference = s

n

d

s_d = sample standard deviation n = the number of paired observations

Hypothesis Tests Concerning the Mean of Two Populations ‐ Appropriate Tests

Population distribution Relationship between samples Assumption regarding

variance Type of test

Normal Independent Equal t‐test pooled variance Normal Independent Unequal t‐test with

variance not pooled Normal Dependent N/A t‐test with

paired comparisons

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hypoThesis TesTing

20

Chi Squared Test‐Statistic

(

)

χ = − σ n 1 s 2 2 0 2 where: n = sample size s2_{= sample variance} 0 2

σ = hypothesized value for population variance

Test‐Statistic for the F‐Test

F s s 12 2 2 = 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 Appropriate Test Statistic

Variance of a single, normally distributed population

Chi‐square stat

Equality of variance of two independent, normally distributed populations

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Technical analysis

Technical Analysis

Setting Price Targets with Head and Shoulders Patterns

= −

Price target Neckline - (Head Neckline)

Setting Price Targets for Inverse Head and Shoulders Patterns

= + −

Price target Neckline (Neckline Head)

Momentum or Rate of Change Oscillator

= − ×

M (V V ) 100x

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 (Up changes for the period under consideration)

(| Down changes for the period under consideration|) = Σ Σ Stochastic Oscillator %K 100 C L14 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 =

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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: QD_x f(P , I, P , )_x _y … (Equation 1)

Equation 1 is read as “the quantity demanded of Good X (QD_X) depends on the price of Good X (PX), consumers’ incomes (I) and the price of Good Y (PY), etc.”

The supply function can be expressed as:

= …

Supply function: QSx f(P ,W, )x … (Equation 5)

The own‐price elasticity of demand is calculated as:

ED % QD % P Px x x = ∆ ∆ … (Equation 16)

If we express the percentage change in X as the change in X divided by the value of X, Equation 16 can be expanded to the following form:

ED % QD % P QD QD P P QD P P QD Px x x x x x x x x x x = ∆ ∆ = ∆ ∆ = ∆_ _∆ __ _ … (Equation 17)

Arc elasticity is calculated as:

= = ∆

∆ =

+ ×

E % change in quantity demanded

% change in price % Q % P (Q - Q ) (Q Q )/2 100 (P - P ) (P P )/2 100 P d 0 1 0 1 0 1 0 1 Slope of demand function. Coefficient on own‐price in market demand function

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DemanD anD Supply analySiS: introDuction

26

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.

ED % QD % I QD QD I I QD I I QD I x x x x x = ∆ ∆ = ∆ ∆ = ∆ _∆ _ _ … (Equation 18) =

% change in income

I

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.

ED % QD % P QD QD P P QD P P QD Py x y x x y y x y y x = ∆ ∆ = ∆ ∆ = ∆_∆    __ _ … (Equation 19)

% change in price of substitute or complement

C= Same as coefficient on I in market demand function (Equation 11) Same as coefficient on PY in market demand function (Equation 11)

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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 ,Q ,_x _x ,Q )_x

1 2 n

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DemanD anD Supply analySiS: the Firm

28

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

Normal profit = Accounting profit − Economic profit

Economic profit = Accounting profit − Total implicit opportunity costs Economic profit = Total revenue − (Explicit costs + Implicit costs)

Normal Profit

Total, Average and Marginal Revenue

Table: Summary of Revenue Terms2

Revenue Calculation

Total revenue (TR) Price times quantity (P × Q), or the sum of individual units sold times their respective prices; Σ(Pi × Qi) Average revenue (AR) Total revenue divided by quantity; (TR / Q)

Marginal revenue (MR) Change in total revenue divided by change in quantity; (ΔTR / ΔQ)

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DemanD anD Supply analySiS: the Firm

MRP_Labor = Price_Labor

2 _{Exhibit 3, Volume 2, CFA Program Curriculum 2012}

Total, Average, Marginal, Fixed and Variable Costs

Table: Summary of Cost Terms3

Costs Calculation

Total fixed cost (TFC) Sum of all fixed expenses; here defined to include all opportunity costs

Total variable cost (TVC) 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) Total variable cost divided by quantity; (TVC / Q) Average total cost (ATC) Total cost divided by quantity; (TC / Q) or (AFC + AVC) Marginal cost (MC) 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

MRP = Marginal product * Product price

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.

A profit‐maximizing firm will hire more labor until:

Profits are maximized when:

MRP Price of input 1

MRP Price of input n

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the Firm anD market StructureS

30

The Firm And Market Structures

The relationship between MR and price elasticity can be expressed as:

= −

MR P[1 (1/E )]_p

In a monopoly, MC = MR so:

− =

P[1 (1/E )] MC_p

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.

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aggregate output, price, anD economic groWth

Aggregate Output, Price, 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 Value of current year output at base year prices 100

= ×

GDP deflator Nominal GDP

Real GDP 100

= ×

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.g. 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

This equation is just a breakdown of the expression for GDP we stated in the previous LOS, i.e. GDP = C + I + G + (X − M).

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32

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)

(35)

= − − −

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 M_D/P = kY

where: k = I/V

M = Nominal money supply MD = Nominal money demand

M_D/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 = RM_D

Solow (neoclassical) growth model

Y AF(L,K)=

where:

Y = Aggregate output L = Quantity of labor K = Quantity of capital

(36)

34

Growth accounting equation

= +

+

Growth in potential GDP Growth in technology W (Growth in labor) W (Growth in capital)_K L

= +

Growth in per capital potential GDP Growth in technology

W (Growth in capital-labor ratio)K Measures of Sustainable Growth

Potential GDP = Aggregate hours × Labor productivity Labor productivity = Real GDP/Aggregate hours

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

(37)

unDerStanDing BuSineSS cycleS

Understanding Business Cycles

Unit labor cost (ULC) is calculated as:

ULC W/O=

where:

O = Output per hour per worker

(38)

monetary anD FiScal policy

36

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 (R_N) 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 MPC)}₋1 =_{(1 0.9)}₋1 =10

Assuming taxes, the multiplier can also be calculated as:

− −

1 [1 MPC(1 t)]

(39)

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.

(40)

currency exchange rateS

38

Currency Exchange Rates

The real exchange rate may be calculated as:

Real exchange rate_DC/FC=S_DC/FC×(P /P )_FC _DC

where:

SDC/FC = Nominal spot exchange rate

P_FC = 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:

F 1 S (1 r ) (1 r ) or F S (1 r ) (1 r ) DC/FC FC/DC DC FC DC/FC DC/FC DC FC = × + + = × + +

Forward rates are sometimes interpreted as expected future spot rates.

F_t =S_{t 1}₊ (S ) S 1 %S(DC/FC) (r r ) (1 r ) t 1 t 1 DC FC FC − = ∆ = − + + +

Exchange Rates and the Trade Balance The Elasticities Approach

Marshall-Lerner condition:ω ε + ω ε − >_{x x} _M( _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 This version of the

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

(41)

(42)

(43)

Financial RepoRting Mechanics

Financial Reporting Mechanics

(44)

UndeRstanding the incoMe stateMent

42

Understanding the Income Statement

Basic EPS

= −

Basic EPS Net income Preferred dividends

Weighted average number of shares outstanding

Diluted EPS

Diluted EPS

Net income Preferred

dividends Convertible preferred dividends Convertible debt interest 1 t Weighted average shares Shares from conversion of convertible preferred shares 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

= + +

(45)

UndeRstanding the Balance sheet

Understanding the Balance Sheet

Gains and Losses on Marketable Securities Held‐to‐Maturity

Securities Available‐for‐Sale Securities Trading Securities

Balance Sheet Reported at cost or amortized cost.

Reported at fair value. Reported at fair value.

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

Items recognized on the income statement

Interest income. Realized gains and losses.

Dividend income. Interest income.

Realized gains and losses.

Dividend income. Interest income.

Realized gains and losses. Unrealized gains and losses due to changes in market values.

(46)

UndeRstanding cash FloW stateMents

44

Understanding Cash Flow Statements

Cash Flow Classification under U.S. GAAP

IFRS U.S. GAAP

Classification of Cash Flows

Interest and dividends received Interest paid CFO or CFI CFO or CFF CFO CFO 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. Not considered a part of cash equivalents and included in CFF.

Presentation Format

CFO

(No difference in CFI and CFF presentation)

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.

Disclosures

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.

CFO

Inflows Outflows

Cash collected from customers. Interest and dividends received.

Proceeds from sale of securities held for trading.

Cash paid to employees. Cash paid to suppliers. Cash paid for other expenses. Cash used to purchase trading securities.

Interest paid. Taxes paid.

CFI

Sale proceeds from fixed assets.

Sale proceeds from long‐term investments.

Purchase of fixed assets.

Cash used to acquire LT investment securities.

CFF

Proceeds from debt issuance.

Proceeds from issuance of equity instruments.

Repayment of LT debt.

Payments made to repurchase stock. Dividends payments.

(47)

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

= − +

(48)

Financial analysis techniqUes

46

Financial Analysis Techniques

Inventory Turnover

Cost of goods sold Average inventory

Inventory turnover=

Days of Inventory on Hand

= 365

Inventory turnover

Days of inventory on hand (DOH)

Receivables Turnover

= Revenue

Average receivables

Receivables turnover

Days of Sales Outstanding

=

( ) 365

Receivables turnover

Days of sales outstanding DSO

Payables Turnover

= Purchases

Average trade payables

Payables turnover

Number of Days of Payables

= 365

Payables turnover

Number of days of payables

Working Capital Turnover

= Revenue

Average working capital

Working capital turnover

Fixed Asset Turnover

= Revenue

Average fixed assets

Fixed asset turnover

Total Asset Turnover

Revenue Average total assets

(49)

Financial analysis techniqUes Current Ratio = Current assets Current liabilities Current ratio Quick Ratio

=Cash Short-term marketable investments Receivables+ + Current liabilities

Quick ratio

Cash Ratio

=Cash Short-term marketable investments+ Current liabilities

Cash ratio

Defensive Interval Ratio

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

Defensive interval ratio

Cash Conversion Cycle

=DSO DOH Number of days of payables+ −

Cash conversion cycle

Debt‐to‐Assets Ratio

=

- - Total debt

Total assets

Debt to assets ratio

Debt‐to‐Capital Ratio

- - Total debt

Total debt Shareholders’ equity

Debt to capital ratio=

+

Debt‐to‐Equity Ratio

- - Total debt

Shareholders’ equity

Debt to equity ratio=

Financial Leverage Ratio

= Average total assets Average total equity

Financial leverage ratio

Interest Coverage Ratio

= EBIT

Interest payments

(50)

48

Fixed Charge Coverage Ratio

= +

+

EBIT Lease payments Interest payments Lease payments

Fixed charge coverage ratio

Gross Profit Margin

= Gross profit Revenue

Gross profit margin

Operating Profit Margin

= Operating profit Revenue

Operating profit margin

Pretax Margin

=EBT (earnings before tax, but after interest) Revenue

Pretax margin

Net Profit Margin

= Net profit Revenue

Net profit margin

Return on Assets

= Net income

Average total assets

ROA

= Net income Interest expense (1 Tax rate)+ − Average total assets

Adjusted ROA

Operating income or EBIT Average total assets

Operating ROA=

Return on Total Capital

=

+ +

EBIT

Short-term debt Long-term debt Equity

Return on total capital

Return on Equity

= Net income

Average total equity

Return on equity

Return on Common Equity

= Net income Preferred dividends− Average common equity

(51)

DuPont Decomposition of ROE

Net income

Average shareholders’ equity

ROE=

2‐Way Dupont Decomposition

Net income Average total assets

Average total assets Average shareholders’ equity

ROA Leverage

ROE= ×

↓ ↓

Net income Revenue

Revenue Average total assets

Net profit margin Asset turnover Leverage

ROE= × ×

↓ ↓ ↓

Interest burden Asset turnover

Net income EBT EBT EBIT EBIT Revenue Revenue Average total assets

Average total assets Avg. shareholders’ equity

Tax burden EBIT margin Leverage

↓ ↓ = × × × × ↓ ↓ ↓ ROE Price‐to‐Earnings Ratio =

/ Price per share

Earnings per share

P E

Price to Cash Flow

=

/ Price per share

Cash flow per share

P CE

Price to Sales

/ Price per share

Sales per share

P S=

Price to Book Value

/ Price per share

Book value per share

(52)

50

Per Share Ratios

Cash flow from operations Average number of shares outstanding

Cash flow per share=

EBITDA

Average number of shares outstanding

EBITDA per share=

= Common dividends declared

Weighted average number of ordinary shares

Dividends per share

Dividend Payout Ratio

= Common share dividends

Net income attributable to common shares

Dividend payout ratio

Retention Rate

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

Retention Rate= −

Growth Rate

=Retention rate ROE×

(53)

inventoRies

Inventories

LIFO versus FIFO (with rising prices and stable inventory levels.) LIFO versus FIFO when Prices are Rising

LIFO FIFO

COGS Higher Lower

Income before taxes Lower Higher Income taxes Lower Higher

Net income Lower Higher

Cash flow Higher Lower

EI Lower Higher

Working capital Lower Higher

Type of Ratio Effect on Numerator Effect on Denominator Effect on Ratio

Profitability ratios NP and GP margins

Income is lower under LIFO because COGS is higher

Sales are the same under both

Lower under LIFO

Debt-to-equity Same debt levels Lower equity under LIFO

Higher under LIFO

Current ratio Current assets are lower under LIFO because EI is lower

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

Inventory turnover COGS is higher under LIFO

Average inventory is lower under LIFO

Higher under LIFO

Total asset turnover Sales are the same Lower total assets 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:

× −

(54)

inventoRies

52

When converting from LIFO to FIFO assuming rising prices:

Equity (retained earnings) increase by: LIFO Reserve × (1 − Tax rate)

LIFO Reserve × (Tax rate)

LIFO Reserve

Liabilities (deferred taxes) increase by:

(55)

long-lived assets

Long-Lived Assets

Financial Statement Effects of Capitalizing versus Expensing

Effect on Financial Statements

Initially when the cost is capitalized

• Noncurrent assets increase.

• Cash flow from investing activities decreases. In future periods when the asset is

depreciated or amortized

• Noncurrent assets decrease.

• Net income decreases.

• Retained earnings decrease.

• Equity decreases.

When the cost is expensed • 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.

Capitalizing Expensing

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

(56)

long-lived assets

54

Straight Line Depreciation

= −

Depreciation expense Original cost Salvage value

Depreciable life

Accelerated Depreciation

DDB depreciation in Year X 2

Depreciable life Book value at the beginning of Year X

= ×

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.

Average age of asset

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.

Remaining useful life

The book value of the asset divided by annual depreciation expense equals the number of years the asset

(57)

incoMe taxes

Income Taxes

Effective Tax rate

=

Effective tax rate Income tax expense Pretax income

Income Tax Expense

= + −

Income tax expense Taxes Payable Change in DTL Change in DTA

Treatment of Temporary Differences

Balance Sheet Item Carrying Value versus Tax Base Results in…

Asset Carrying amount is greater. DTL Asset Tax base is greater. DTA Liability Carrying amount is greater. DTA Liability Tax base is greater. DTL

Income Tax Accounting under IFRS versus U.S. GAAP

ISSUE SPECIFIC TREATMENTS

Revaluation of fixed assets and intangible assets.

Recognized in equity as deferred taxes.

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 foreign subsidiaries that fulfill indefinite reversal criteria. 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 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.

Deferred taxes are

recognized from temporary differences.

(58)

incoMe taxes

56

DEFERRED TAX MEASUREMENT

Tax rates. Tax rates and tax laws enacted or substantively enacted.

Only enacted tax rates and tax laws are used.

Deferred tax asset recognition.

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

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 assets and liabilities.

Offsetting allowed only if the entity has right to legally enforce it and the balance is related to a tax levied by the same authority.

Same as in IFRS.

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.

(59)

non-cURRent (long-teRM) liaBilities

Non-Current (Long-Term) Liabilities

Income Statement Effects of Lease Classification

Income Statement Item Finance Lease Operating Lease

Operating expenses Lower Higher Nonoperating expenses Higher Lower EBIT (operating income) Higher Lower Total expenses‐ early years Higher Lower Total expenses‐ later years Lower Higher Net income‐ early years Lower Higher Net income‐ later years Higher Lower

Balance Sheet Effects of Lease Classification

Balance Sheet Item Capital Lease Operating Lease

Assets Higher Lower

Current liabilities Higher Lower Long term liabilities Higher Lower

Total cash Same Same

Cash Flow Effects of Lease Classification

CF Item Capital Lease Operating Lease

CFO Higher Lower

CFF Lower Higher

Total cash flow Same Same

Impact of Lease Classification on Financial Ratios

Ratio Numerator under Finance Lease Denominator under Finance

Lease Effect on Ratio

Ratio Better or Worse under Finance Lease

Asset turnover Sales‐ same Assets‐ higher Lower Worse Return on

assets*

Net income lower in early

years

Assets‐ higher Lower Worse

Current ratio Current assets-same Current liabilities-higher Lower Worse Leverage ratios (D/E and D/A)

Debt‐ higher Equity same Assets higher Higher Worse Return on equity* Net income lower in early years

Equity same Lower Worse

(60)

non-cURRent (long-teRM) liaBilities

58

Financial Statement Effects of Lease Classification from Lessor’s Perspective Financing Lease Operating Lease

Total net income Same Same Net income (early years) Higher Lower Taxes (early years) Higher Lower

Total CFO Lower Higher

Total CFI Higher Lower

Total cash flow Same Same

Definitions of Commonly Used Solvency Ratios

Solvency Ratios Description Numerator Denominator

Leverage Ratios

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.

Total debt Total debt + Total shareholders’ equity

Debt‐to‐equity ratio Measures the amount of debt financing relative to equity financing

Total debt Total shareholders’ equity

Financial leverage ratio Measures the amount of total assets supported by one money unit of equity

Coverage Ratios

Interest coverage ratio Measures the number of times a company’s EBIT could cover its interest payments.

EBIT 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

Interest payments + Lease payments

(61)

Financial RepoRting qUality

Financial Reporting Quality

Relationship between Financial Reporting Quality and Earnings Quality Financial Reporting Quality

Low High

Earnings (Results) Quality

High

LOW financial reporting quality impedes assessment of earnings quality and impedes valuation.

HIGH financial reporting quality enables assessment.

HIGH earnings quality increases company value.

Low HIGH financial reporting quality enables assessment.

LOW earnings quality decreases company value.

(62)

(63)

(64)

(65)

Capital Budgeting

Net Present Value (NPV)

NPV CF (1 r) Outlay t t t 1 n

∑

= + − = where:

CFt = after‐tax cash flow at time, t.

r = required rate of return for the investment. This is the firm’s cost of capital adjusted for the risk inherent in the project.

Outlay = investment cash outflow at t = 0.

Internal Rate of Return (IRR)

CF (1 IRR) Outlay CF (1 IRR) Outlay 0 t t t 1 n t t t 1 n

∑

₊ =

∑

+ − = = =

Average Accounting Rate of Return (AAR)

AAR Average net income

Average book value =

Profitability Index

PI PV of future cash flows

Initial investment 1

NPV Initial investment

(66)

Cost of Capital

64

Cost of Capital

Weighted Average Cost of Capital

WACC (w )(r )(1 t) (w )(r ) (w )(r )= _d _d − + _p _p + _e _e

where:

w_d = 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

r_p = Marginal cost of preferred stock

we = Proportion of equity that the company uses when it raises new funds

r_e = Marginal cost of equity

To Transform Debt‐to‐equity Ratio into a Component’s Weight

D E 1 D E D D E w w w 1 d d e + = + = + = Valuation of Bonds P PMT 1 r 2 FV 1 r 2 0 d t t 1 n d n

∑

= +                + +    = where:

P0 = current market price of the bond.

PMT_t = 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

V_p Dp_r p

=

where:

Vp = current value (price) of preferred stock.

D_p = preferred stock dividend per share. rp = cost of preferred stock.

(67)

Cost of Capital

Required Return on a Stock

Capital Asset Pricing Model

= + β −

r_e R_F _i[E(R ) R ]_M _F

where:

[E(RM) − Rf] = Equity risk premium.

R_M = 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.

r_e = Expected return on stock (cost of equity).

Dividend Discount Model

P D r g 0 1 e = − 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: r D P g e 1 0 = +

Sustainable Growth Rate

g 1 D

EPS

(

ROE

)

= −_ _{ ×}

Where (1 − (D/EPS)) = Earnings retention rate

Bond Yield plus Risk Premium Approach

(68)

Cost of Capital

66

To Unlever the beta

1 1 1 t D E ASSET EQUITY

(

)

β = β +_ − _            

To Lever the beta

1 1 t D E PROJECT ASSET

(

)

β = β  +_ − _   

Country Risk Premium

r_e =R_F+ β[E(R ) R_M − _F+CRP]

Country risk premium

Sovereign yield spread

Annualized standard deviation of equity index Annualized standard deviation of sovereign bond market in terms of the developed market

currency

= ×

Break point Amount of capital at which a component’s cost of capital changes Proportion of new capital raised from the component =

(69)

MeasuRes of leveRage

Measures of Leverage

Degree of Operating Leverage

DOL Percentage change in operating income

Percentage change in units sold = DOL Q P V Q P V F ( ) ( ) = × − × − − where:

Q = Number of units sold P = Price per unit

V = Variable operating cost per unit F = Fixed operating cost

Q × (P − V) = Contribution margin (the amount that units sold contribute to covering fixed costs)

(P − V) = Contribution margin per unit

Degree of Financial Leverage

DFL Percentage change in net income

Percentage change in operating income = DFL [Q(P V) F](1 t) [Q(P V) F C](1 t) [Q(P V) F] [Q(P V) F C] = − − − − − − − = − − − − − where:

Q = Number of units sold P = Price per unit

C = Fixed financial cost t = Tax rate

(70)

MeasuRes of leveRage

68

Degree of Total Leverage

DTL Percentage change in net income

Percentage change in the number of units sold = DTL DOL DFL= × DTL Q (P V) [Q(P V) F C] = × − − − − where:

Q = Number of units produced and sold P = Price per unit

C = Fixed financial cost

Break point

PQ VQ F C= + +

where:

P = Price per unit

Q = Number of units produced and sold V = Variable cost per unit

F = Fixed operating costs C = Fixed financial cost

The breakeven number of units can be calculated as:

Q F C

P C

BE = +₋

Operating breakeven point

PQ_OBE =VQ_OBE+F

Q F

P V

(71)

WoRking Capital ManageMent

Working Capital Management

Current Ratio Current assets

Current liabilities =

Quick Ratio Cash Short term marketable investments Receivables

Current liabilities

= + +

Accounts receivable turnover Credit sales

Average receivables =

Number of days of receivables Accounts receivable

Average days sales on credit Accounts receivable

Sales on credit / 365 =

=

Inventory turnover Cost of goods sold Average inventory =

Number of days of inventory Inventory

Average day’s cost of goods sold Inventory

Cost of goods sold / 365 =

=

Payables turnover Purchases

Average trade payables =

Number of days of payables Accounts payables

Average day’s purchases Accounts payables

Purchases / 365 =

=

Operating cycle = Number of days of inventory + Number of days of receivables

Net operating cycle = Number of days of inventory + Number of days of receivables − Number of days of payables

(72)

WoRking Capital ManageMent

70

Money market yield Face value price

Price

360

Days Holding period yield

360 Days =_ − _{ ×}   = ×    

Bond equivalent yield Face value price

Price

365

Days Holding period yield

365 Days =_ − _{ ×}   = ×    

Discount basis yield Face value price

Face value 360 Days % discount 360 Days =_ − _{ ×}    = ×    

% Discount Face value Price

Price

= −

Inventory turnover Cost of goods sold Average inventory =

Number of days of inventory Inventory

Average days cost of goods sold Inventory

Cost of goods sold / 365 365

Inventory turnover =

= =

Implicit rate Cost of trade credit 1 Discount

1 Discount 1

365

Number of days beyond discount period

= = + −    −    

Number of days of payables Accounts payable

Average day’s purchases Accounts payable Purchases / 365 365 Payables turnover = =

Line of credit cost Interest Commitment fee

Loan amount

= +

Banker’s acceptance cost Interest

Net proceeds

Interest

Loan amount Interest

= =

− Interest Dealer’s commission Backup costs

Loan amount Interest

+ +

(73)

(74)