elan guides formula sheet cfa 2013 level 2

7/18/2019 Elan Guides Formula Sheet CFA 2013 Level 2

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Sample covariance = Cov (X,Y) = n

i = 1

(Xi X)(Yi Y)/(n 1)

where:n = sample size

Xi = ith observation of Variable XX = mean observation of Variable XYi = ith observation of Variable YY = mean observation of Variable Y

Sample correlation coefficient = r =

Cov (X,Y)

sXsY

Sample variance = s X

2=

n

i = 1

(Xi X)2/(n 1)

Sample standard deviation = s X = s X

2

Test-stat = t =r n 2

1 r 2

Where:

n = Number of observationsr = Sample correlation

Test statistic

Regression model equation = Y i = b0 + b1 X i + i, i = 1,...., n

b1 and b0 are the regression coefficients. b1 is the slope coefficient. b0 is the intercept term.

is the error term that represents the variation in the dependent variable that

is not explained by the independent variable.

Linear Regression with One Independent Variable

CORRELATION AND R EGRESSION

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QUANTITATIVE METHODS



Regression line equation = Y i = b0 + b1 X i , i = 1,...., nˆ ˆ ˆ

n

i = 1

[Y i (b0 b1 X i)]2ˆˆ

Regression Residuals

where:Y i = Actual value of the dependent variableb0 + b1 X i = Predicted value of dependent variableˆ ˆ

SEE =

1/2

( )n 2

n

i = 1

(Y i b0 b1 X i)2ˆ ˆ 1/2

( )n

i = 1

(i)2ˆ

n 2= = ( )SSE

n 2

1/2

The Standard Error of Estimate

Hypothesis Tests on Regression Coefficients

CAPM: R ABC = R F + ABC(R M – R F)

R ABC – R F = + ABC(R M – R F) +

The intercept term for the regression, b0, is . The slope coefficient for the regression, b1, is ABC

The Coefficient of Determination

R 2 = =Explained variation

Total variation

Total variation Unexplained variation

Total variation

= 1 Total variation

Unexplained variation

Total variation = Unexplained variation + Explained variation

n

i = 1

(Y i Y )2^RSS = Explained variation

The regression sum of squares (RSS)

n

i = 1

(Y i Y i )2^

SSE = Unexplained variation

The sum of squared errors or residuals (SSE)

© 2013 ELAN GUIDES




s f 2

s2

= 1 1

n

(X X)2

(n 1) s x2[ ]

Y t c s f ^

Prediction Intervals

Source of Variation

Regression (explained)

Error (unexplained)

Total

Degrees of Freedom

k

n k + 1)

n 1

Sum of Squares

RSS

SSE

SST

Mean Sum of Squares

MSR = RSS

k

RSS

1= RSS=

MSE =SSE

n 2

k = the number of slope coefficients in the regression.

ANOVA Table

© 2013 ELAN GUIDES




Multiple regression equation = Y i = b0 + b1 X 1i + b2 X 2i + . . .+ bk X ki + i, i = 1,2, . . . , n

Y i X jib0

b1, . . . , bk

i

n

= the ith observation of the dependent variable Y

= the ith observation of the independent variable X j , j = 1,2, . . . , k = the intercept of the equation

= the slope coefficients for each of the independent variables= the error term for the ith observation= the number of observations

Multiple regression equation

i = Y i Y i = Y i (b0 + b1 X 1i + b2 X 2i + . . .+ bk X k i)ˆ ˆ ˆ ˆ ˆ ˆ

Residual Term

MULTIPLE R EGRESSION AND ISSUES IN R EGRESSION ANALYSIS

b j ± (t c sb j)ˆ

ˆ

estimated regression coefficient ± (critical t -value)(coefficient standard error)

Confidence Intervals

F-stat =RSS/k

SSE/[n k + 1)]

MSR

MSE=

F -statistic

(1 R2)

n 1

n k 1( )Adjusted R2 = R2 = 1

R 2 =Total variation Unexplained variation

Total variation

SST SSE

SST=

RSS

SST=

R 2 and Adjusted R 2

2 = nR 2 with k degrees of freedom

n = Number of observationsR 2 = Coefficient of determination of the second regression (the regression when the squared

residuals of the original regression are regressed on the independent variables).

k = Number of independent variables

Testing for Heteroskedasticity- The Breusch-Pagan (BP) Test

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MULTIPLE REGRESSION AND ISSUES IN REGRESSION



Y i = b0 + b1lnX 1i + b2 X 2i +

Model Specification Errors

yt = b0 + b1t + t , t = 1, 2, . . . , T

where: yt = the value of the time series at time t (value of the dependent variable)b0 = the y-intercept term

b1 = the slope coefficient/ trend coefficient

t = time, the independent or explanatory variablet = a random-error term

Linear Trend Models

Testing for Serial Correlation- The Durban-Watson (DW) Test

DW 2(1 – r ); where r is the sample correlation between squared residuals from one period andthose from the previous period.

Value of Durbin-Watson Statistic

Inconclusive

d l

d u

(H0: No serial correlation)

Reject H0,

conclude

Positive Serial

Correlation Inconclusive

Do not Reject

H0

Reject H0,

conclude

Negative Serial

Correlation

0 4 d l

44 d u

Problems in Linear Regression and Solutions

Problem

Heteroskedasticity

Serial correlation

Multicollinearity

Effect

Incorrect standard errors

Incorrect standard errors (additional

problems if a lagged value of the

dependent variable is used as anindependent variable)

High R 2 and low t-statistics

Solution

Use robust standard errors

(corrected for conditionalheteroskedasticity)

Use robust standard errors

(corrected for serial correlation)

Remove one or more independentvariables; often no solution based

in theory

© 2013 ELAN GUIDES

MULTIPLE REGRESSION AND ISSUES IN REGRESSION



yt = eb0 + b1t

ln yt = b0 + b1t + t , t = 1,2, . . . , T

where: yt = the value of the time series at time t (value of the dependent variable)b0 = the y-intercept termb1 = the slope coefficientt = time = 1, 2, 3 ... T

We take the natural logarithm of both sides of the equation to arrive at the equation for the log-linear model:

Log-Linear Trend Models

xt = b0 + b1 xt 1 + t

xt

= b0

+ b1

xt 1

+ b2

xt 2

+ . . . + b p

xt p

+ t

AUTOREGRESSIVE (AR) TIME-SERIES MODELS

Detecting Serially Correlated Errors in an AR Model

t-stat =Residual autocorrelation for lag

Standard error of residual autocorrelation

TIME-SERIES ANALYSIS

Linear Trend Models

yt = b0 + b1t + t , t = 1, 2, . . . , T

where: yt = the value of the time series at time t (value of the dependent variable)b0 = the y-intercept termb1 = the slope coefficient/ trend coefficient

t = time, the independent or explanatory variable

t = a random-error term

A series that grows exponentially can be described using the following equation:

A pth order autoregressive model is represented as:

where:Standard error of residual autocorrelation = 1/ T

T = Number of observations in the time series

© 2013 ELAN GUIDES

TIME SERIES ANALYSIS



xt =b0

1 b1

Mean Reversion

xt+1 = b0 + b1 xt ^ ^^

Multiperiod Forecasts and the Chain Rule of Forecasting

xt = xt 1 + t , E(t ) = 0, E(t 2) = 2, E(t s) = 0 if t s

yt = xt xt 1 = xt 1 + t xt 1= t , E(t ) = 0, E(t

2) = 2, E(t s) = 0 for t s

Random Walks

The first difference of the random walk equation is given as:

xt = b0 + b1 xt 1 + t

b1 = 1, b0 0, or

xt = b0 + xt 1 + t , E(t ) = 0

yt = xt xt 1 , yt = b0 + t , b0 0

Random Walk with a Drift

The first-difference of the random walk with a drift equation is given as:

The Unit Root Test of Nonstationarity

xt b0 + b1 xt 1 + t

xt xt 1 b0 + b1 xt 1 xt 1 + t

xt xt 1 b0 + (b1 1) xt 1 + t

xt xt 1 b0 + g 1 xt 1 + t

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t

2 = a0 + a1t

2

1 + ut ^ ^

t + 1 = a0 + a1t 2^ ^2 ^^

Autoregressive Conditional Heteroskedasticity Models (ARCH Models)

xt = b0 + b1 xt 1 + . . . + b p xt p + t + 1t 1 +. . . + qt q

E(t ) = 0, E(t 2

) = 2

, E(t s) = 0 for t s

Autoregressive Moving Average (ARMA) Models

The error in period t +1 can then be predicted using the following formula:

© 2013 ELAN GUIDES




CURRENCY EXCHANGE R ATES: DETERMINATION AND FORECASTING

For example, given the USD/EUR and JPY/USD exchange rates, we can calculate the cross rate

between the JPY and the EUR, JPY/EUR as follows:

=USD

EUR

JPY

EUR USD

JPY

Currency Cross Rates

Cross Rate Calculations with Bid-Ask Spreads

USD/EUR bid = 1.3802

Represents the price of EUR (base

currency). An investor can sell EUR for USD

at this price (as it is the bid pricequoted by the dealer).

USD/EUR ask = 1.3806

Represents the price of EUR

An investor can buy EUR withUSD at this price.

Determining the EUR/USD bid cross rate:

EUR/USD bid = 1/(USD/EUR ask )

Determining the EUR/USDask cross rate:

EUR/USDask = 1 / (USD/EUR bid)

Forward exchange rates (F) - One year Horizom

FFC/DC = SFC/DC (1 + iFC)

(1 + iDC)FPC/BC = SPC/BC

(1 + iPC)

(1 + iBC)

FPC/BC SPC/BC=1 + (iBC Actual 360)

1 + (iPC Actual 360)

FFC/DC SFC/DC= 1 + (iDC Actual 360)

1 + (iFC Actual 360)

Forward exchange rates (F) - Any Investment Horizom

Currencies Trading at a Forward Premium/Discount

FFC/DC SFC/DC = SFC/DC(iFC iDC) Actual 360

1 + (iDC Actual 360)( )

( )FPC/BC SPC/BC = SPC/BC(iPC iBC) Actual 360

1 + (iBC Actual 360)

© 2013 ELAN GUIDES

CURRENCY EXCHANGE RATES: DETERMINATION AND FORECASTING



The expected percentage change in the spot exchange rate can becalculated as:

Covered Interest Rate Parity

FPC/BC 1 + (i

BC

Actual 360

)

1 + (iPC Actual 360)SPC/BC=

Forward premium (discount) as a % =FPC/BC SPC/BC

SPC/BC

Forward premium (discount) as a % FPC/BC SPC/BC iPC iBC

Uncovered Interest Rate Parity

Expected future spot exchange rate:

(1 + iFC)

(1 + iDC)Se

FC/DC = SFC/DC

Expected % change in spot exchange rate =SePC/BC =

The expected percentage change in the spot exchange rate can beestimated as:

Expected % change in spot exchange rate SePC/BC iPC iBC

SPC/BC

SePC/BC – SPC/BC

The forward premium (discount) on the base currency can be expressed as a percentage as:

The forward premium (discount) on the base currency can be estimated as:

Purchasing Power Parity (PPP)

Law of one price: PXFC = PX

DC SFC/DC

Law of one price: PXPC = PX

BC SPC/BC

Absolute Purchasing Power Parity (Absolute PPP)

SFC/DC = GPLFC / GPLDC

SPC/BC = GPLPC / GPLBC

Relative Purchasing Power Parity (Relative PPP)

Relative PPP: E(STFC/DC) = S0

FC/DC

1 FC

1 + DC( )

T

Ex Ante Version of PPP

Ex ante PPP: %SeFC/DC e

FC eDC

Ex ante PPP: %SePC/BC e

PC eBC

© 2013 ELAN GUIDES




Real Exchange Rates

The real exchange rate (qFC/DC) equals the ratio of the domestic price level expressed in the foreign

currency to the foreign price level.

qFC/DC SFC/DCPFC

PDC in terms of FC PDC SFC/DC

PFC

= ==PDC

PFC( )

The Fisher Effect

Fischer Effect: i = r + e

International Fisher effect: (iFC – iDC) = (eFC – e

DC)

Figure 1: Spot Exchange Rates, Forward Exchange Rates, and Interest Rates

Ex Ante PPP

Forward Rate as

an Unbiased

Predictor

International Fisher

Effect

Covered

Interest Rate

Parity

Uncovered Interest

Rate Parity

Expected change

in

Spot Exchange Rate%Se

FC/DC

Foreign-DomesticExpected Inflation

Differentiale

FC eDC

Foreign-Domestic

Interest rate

DifferentialiFC iDC

Forward Discount

FFC/DC SFC/DC

SFC/DC

Balance of Payment

Current account + Capital account + Financial account = 0

Real Interest Rate Differentials, Capital Flows and the Exchange Rate

qL/H – qL/H = (iH – iL) – (eH – e

L) – (H – L)

© 2013 ELAN GUIDES




The Taylor rule

i = r n + + y y*)

wherei = the Taylor rule prescribed central bank policy rater n = the neutral real policy rate = the current inflation rate* = the central bank’s target inflation rate

y = the log of the current level of outputy* = the log of the economy’s potential/sustainable level of output

© 2013 ELAN GUIDES


qPC/BC = qPC/BC + ( r nBC

r nPC) + BC BC PC PC

yBC y*BC) yPC y*PC)] BC PC)



ECONOMIC GROWTH AND THE INVESTMENT DECISION

P = GDP

E

GDP( )P

E( )P = Aggregate price or value of earnings.E = Aggregate earnings

This equation can also be expressed in terms of growth rates:

P = (GDP) + (E/GDP) + (P/E)

Production Function

Y = AK L1-

Y = Level of aggregate output in the economyL = Quantity of labor

K = Quantity of capital

A = Total factor productivity. Total factor productivity (TFP) reflects the general levelof productivity or technology in the economy. TFP is a scale factor i.e., an increasein TFP implies a proportionate increase in output for any combination of inputs.

= Share of GDP paid out to capital

1 = Share of GDP paid out to labor

y = Y/L = A(K/L)(L/L)1- = Ak

y = Y/L = Output per worker or labor productivity.k = K/L = Capital per worker or capital-labor ratio

Cobb-Douglas production function

Y/Y =A/A + K/K + (1 )L/L

Growth rate in potential GDP = Long-term growth rate of labor force

+ Long-term growth rate in labor productivity

Labor Supply

Total number of hours available for work = Labor force Average hours worked per worker

Relationship between economic growth and stock prices

Potential GDP

© 2013 ELAN GUIDES




Neoclassical Model (Solow’s Model)

= + + nY

K

1

s( )

(1-)( )[ ]s = Fraction of income that is saved = Growth rate of TFP

= Elasticity of output with respect to capitaly = Y/L or income per worker

k = K/L or capital-labor ratio = Constant rate of depreciation on physical stock n = Labor supply growth rate.

= + + n

(1 )( )[ ]sy k

Savings/Investment Equation:

Growth rates of Output Per Capita and the Capital-Labor Ratio

ye = f(k e) = ck e

=y

y

(1)

Y

K + s

=k k

(1)( ) Y

K ( )+ s

Production Function in the Endogenous Growth Model

© 2013 ELAN GUIDES




INVENTORIES: IMPLICATIONS FOR FINANCIAL STATEMENTS AND R ATIOS

Ending Inventory = Opening Inventory + Purchases - Cost of goods sold

LIFO and FIFO Comparison with Rising Prices and Stable Inventory Levels

COGS

Income before taxes

Income taxes

Net income

Total cash flow

EI

Working capital

LIFO

Higher

Lower

Lower

Lower

Higher

Lower

Lower

FIFO

Lower

Higher

Higher

Higher

Lower

Higher

Higher

LIFO versus FIFO with Rising Prices and Stable Inventory Levels

Income is lower under LIFO becauseCOGS is higher

Same debt levels

Profitability ratios

NP and GP margins

Solvency ratios

Debt-to-equity and

debt ratio

Sales are the sameunder both

Lower equity and

assets under LIFO

Lower under LIFO

Higher under LIFO

Type of Ratio

Effect on

Numerator

Effect on

Denominator Effect on Ratio

Liquidity ratios

Current ratio

Quick ratio

Activity ratios

Inventory turnover

Total asset turnover

Current assets are

lower under LIFO because EI is lower

Quick assets arehigher under LIFO asa result of lower taxes

paid

COGS is higher under LIFO

Sales are the same

Current liabilities are

the same.

Current liabilities arethe same

Average inventory islower under LIFO

Lower total assetsunder LIFO

Lower under LIFO

Higher under LIFO

Higher under LIFO

Higher under LIFO

© 2013 ELAN GUIDES

INVENTORIES: IMPLICATIONS FOR FINANCIAL STATEMENT AND RATIOS



LIFO reserve (LR)

EIFIFO = EILIFO + LR

COGSFIFO = COGSLIFO (Change in LR during the year)

Change in LIFO Reserve (1 Tax rate)

When converting from LIFO to FIFO assuming rising prices:

Equity (retained earnings) increases by:

Liabilities (deferred taxes) increase by:

LIFO Reserve (Tax rate)

LIFO Reserve (1 Tax rate)

Current assets (inventory) increase by:

LIFO Reserve

where LR = LIFO Reserve

Net Income after tax under FIFO will be greater than LIFO net income after tax by:

COGSFIFO is lower than COGSLIFO during periods of rising prices:

© 2013 ELAN GUIDES




Impact of an Inventory Write-Down on Various Financial Ratios

COGS increases so profits fall

Debt levels remain

the same

Current assetsdecrease (due tolower inventory)

COGS increases

Sales remain thesame

Profitability ratios NP and GP margins

Solvency ratios

Debt-to-equity and

debt ratio

Liquidity ratiosCurrent ratio

Activity ratios

Inventory turnover

Total asset turnover

Sales remain thesame

Equity decreases

(due to lower profits)and current assetsdecrease (due tolower inventory)

Current liabilitiesremain the same.

Average inventorydecreases

Total assets decrease

Lower (worsens)

Higher (worsens)

Lower (worsens)

Higher (improves)

Higher (improves)

Type of Ratio

Effect on

Numerator

Effect on

Denominator Effect on Ratio

© 2013 ELAN GUIDES




LONG-LIVED ASSETS: IMPLICATIONS FOR FINANCIAL STATEMENTS AND

R ATIOS

Straight Line Depreciation

Depreciation expense =Depreciable life

Original cost Salvage value

Accelerated Depreciation

DDB depreciation in Year X =2

Depreciable lifeBook value at the beginning of Year X×

Effects of Expensing

When the item is expensed

Effects on Financial Statements

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.

Initially when the cost is capitalized

In future periods when the asset is

depreciated or amortized

Effects on Financial Statements

Noncurrent assets increase. Cash flow from investing activities decreases.

Noncurrent assets decrease.

Net income decreases.

Retained earnings decrease.

Equity decreases.

Effects of Capitalization

Financial Statement Effects of Capitalizing versus Expensing

Net income (first year)

Net income (future years)

Total assets

Shareholders’ equity

Cash flow from operations activities

Cash flow from investing activities

Income variability

Debt to equity ratio

Capitalizing

Higher

Lower

Higher

Higher

Higher

Lower

Lower

Lower

Expensing

Lower

Higher

Lower

Lower

Lower

Higher

Higher

Higher

© 2013 ELAN GUIDES

LONG-LIVED ASSETS: IMPLICATIONS FOR FINANCIAL STATEMENTS AND RATIOS



Remaining useful life

The book value of the asset divided

by annual depreciation expense

equals the number of years the asset

has remaining in its useful life.

= +Gross investment in fixed assets

Annual depreciation expense

Accumulated depreciation


Net investment in fixed assets


Average age of asset


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.

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.

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 (Depreciation)

Higher (Interest expense)

Higher

Higher

Lower

Lower Higher

Operating Lease

Higher (Lease payment)

Lower (None)

Lower

Lower

Higher

Higher Lower

Income Statement Effects of Lease Classification

CF Item

CFO

CFF

Total cash flow

Finance Lease

Higher

Lower

Same

Operating Lease

Lower

Higher

Same

Cash Flow Effects of Lease Classification

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Effect on Ratio

Lower

Lower

Lower

Higher

Lower

Denominator

under Finance

Lease

Assets- higher

Assets- higher

Currentliabilities-

higher

Equity- same

Assets- higher

Equity- same

Numerator under

Finance Lease

Sales- same

Net income- lower

Current assets-same

Debt- higher

Net income- lower

Ratio Better or

Worse under

Finance Lease

Worse

Worse

Worse

Worse

Worse

Ratio

Asset turnover

Return on assets*

Current ratio

Leverage ratios

(D/E and D/A**)

Return on equity*

Table 9: Impact of Lease Classification on Financial Ratios

**Notice that both the numerator and the denominator for the D/A ratio are higher when classifying

the lease as a finance lease. Beware of such exam questions. When the numerator and the denominator

of any ratio are heading in the same direction (either increasing or decreasing), determine which of the

two is changing more in percentage terms. If the percentage change in the numerator is greater than the

percentage change in the denominator, the numerator effect will dominate.

Firms usually have lower levels of total debt compared to total assets. The increase in both debt and

assets by classifying the lease as a finance lease will lead to an increase in the debt to asset ratio because

the percentage increase in the numerator is greater.

Operating Lease

Same

Lower

Lower

Higher

Lower

Same

Financing Lease

Same

Higher

Higher

Lower

Higher

Same

Total net income

Net income (early years)

Taxes (early years)

Total CFO

Total CFI

Total cash flow

Financial Statement Effects of Lease Classification from Lessor’s Perspective

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Summary of Accounting Treatment for Investments

Influence

Typical percentageinterest

AccountingTreatment

In Financial Assets

Not significant

Usually < 20%

Classified into one of four categories based on

management intent andtype of security.

Debt only: Held-to-maturity

(amortized cost,

changes in value

ignored unlessdeemed as impaired)

Debt and Equity:

Held for trading(fair value, changesin value recognizedin profit or loss)

Available-for-sale

(fair value, changesin value recognized

in equity) Designated at fair

value (fair value,changes in value

recognized in profitor loss)

In Associates

Significant

Usually 20% 50%

Equity method

BusinessCombinations

Controlling

Usually > 50%

Consolidation

In Joint Ventures

Shared Control

Varies

IFRS: Equity methodor proportionate

consolidation

U.S. GAAP: Equitymethod(except for unincorporated

ventures in

specialized industries)

INTERCORPORATE INVESTMENTS

Combination

Merger

Acquisition

Consolidation

Description

Company A + Company B = Company A

Company A + Company B = (Company A + Company B)

Company A + Company B = Company C

© 2013 ELAN GUIDES




CFO

CFF

Total cash flow

Current assets

Current liabilities

Current ratio

Adjusted Values Upon Reclassification of Sale of Receivables:

Lower

Higher

Same

Higher

Higher

Lower (Assuming it was greater than 1)

Difference between QSPE and SPE

Securitized Transaction: Qualified Special

Purpose Entity

Originator of receivables sells financial

assets to an SPE. The originator does not own or hold

or expect to receive beneficial interest.

SFAS 140 (before 2008 revision)

allowed seller to derecognize the sold

assets if transferred assets have been

isolated from the transferor and are

beyond the reach of bankruptcy, and are

financial assets.

Securitized Transaction: Special

Purpose Entity

Originator of receivables sells financial

assets to an SPE. Seller is primary beneficiary; absorbs

risks and rewards.

Seller maintains some level of control.

Seller is required to consolidate.

Seller’s balance sheet would still

show receivables as an asset.

Debt of SPE would appear on seller’s

balance sheet.

Impact of Different Accounting Methods on Financial Ratios

Leverage

Net Profit

Margin

ROE

ROA

Better (lower) as liabilities are

lower and equity is the same

Better (higher) as sales are lower

and net income is the same

Better (higher) as equity is lower and net income is the same

Better (higher) as net income isthe same and assets are lower

Equity Method

In-between

In-between

Same as under theequity method

In-between

Proportionate

Consolidation

Worse (higher) as liabilities are

higher and equity is the same

Worse (lower) as sales are higher

and net income is the same

Worse (lower) as equity is higher and net income is the same

Worse (lower) as net income isthe same and assets are higher

Acquisition Method

© 2013 ELAN GUIDES




EMPLOYEE COMPENSATION: POST-EMPLOYMENT AND SHARE-BASED

Types of Post-Employment Benefits

Type of Benefit

Defined contribution pension plan

Defined benefit

pension plan

Other post-employment benefits

(e.g., retirees’ healthcare)

Amount of Post-

Employment Benefit to

Employee

Amount of future benefit isnot defined. Actual future

benefit will depend oninvestment performance of plan assets.Investment risk is borne byemployee.

Amount of future benefit is

defined, based on the plan’sformula (often a function of length of service and finalyear’s compensation).

Investment risk is borne bycompany.

Amount of future benefitdepends on plan

specifications and type of benefit.

Obligation of Sponsoring

Company

Amount of the company’sobligation (contribution)

is defined in each period.The contribution, if any, istypically made on a periodic basis with no additionalfuture obligation.

Amount of the future

obligation, based on the plan’s formula, must beestimated in the current period.

Eventual benefits arespecified. The amount of the

future obligation must beestimated in the current period.

Sponsoring Company’s

Pre-funding of Its Future

Obligation

Not applicable.

Companies typically pre-

fund the DB plans bycontributing funds to a pension trust. Regulatoryrequirements to pre-fund

vary by country.

Companies typically do not pre-fund other post-

employment benefitobligations.

Estimated annual payment = (Estimated final salary × Benefit formula) × Years of service

Final year’s salary = Current salary × [(1 + Annual compensation increase)years until retirement]

Annual unit credit = Value at retirement / Years of service

A company’s pension obligation will increase as a result of:

Current service costs.

Interest costs. Past service costs. Actuarial losses.

A company’s pension obligation will decrease as a result of:

Actuarial gains. Benefits paid.

© 2013 ELAN GUIDES




Priodic pension cost = Ending funded status Beginning funded status + Employer contributions

Periodic pension cost = Current service costs + Interest costs + Past service costs + Actuarial losses Actuarial gains Actual return on plan assets

Reconciliation of the Pension Obligation:

Pension obligation at the beginning of the period

+ Current service costs

+ Interest costs + Past service costs

+ Actuarial losses – Actuarial gains – Benefits paidPension obligation at the end of the period

The fair value of assets held in the pension trust (plan) will increase as a result of: A positive actual dollar return earned on plan assets; and Contributions made by the employer to the plan.

The fair value of plan assets will decrease as a result of: Benefits paid to employees.

Reconciliation of the Fair Value of Plan Assets:

Fair value of plan assets at the beginning of the period

+ Actual return on plan assets + Contributions made by the employer to the plan Benefits paid to employeesFair value of plan assets at the end of the period

Funded status = Pension obligation Fair value of plan assets

If Pension obligation > Fair value of plan assets:

Plan is underfunded Positive funded status Net pension liability. If Pension obligation < Fair value of plan assets:

Plan is overfunded Negative funded status Net pension asset.

Balance Sheet Presentation of Defined Benefit Pension Plans

Calculating Periodic Pension Cost

Under the corridor method, if the net cumulative amount of unrecognized actuarial gains and losses at the

beginning of the reporting period exceeds 10% of the greater of (1) the defined benefit obligation or (2) thefair value of plan assets, then the excess is amortized over the expected average remaining working lives of

the employees participating in the plan and included as a component of periodic pension expense on the P&L.

© 2013 ELAN GUIDES




Components of a Company’s Defined Benefit Pension Periodic Costs

IFRS Component

Service costs

Net interest

income/ expense

Remeasurements:

Net return on plan

assets and actuarial

gains and losses

IFRS Recognition

Recognized in P&L.

Recognized in P&L as

the following amount:

Net pension liability or

asset × interest rate(a)

Recognized in OCI and

not subsequently

amortized to P&L.

Net return on plan

assets = Actual return

(Plan assets ×Interest rate).

Actuarial gains and

losses = Changes in a

company’s pension

obligation arising from

changes in actuarial

assumptions.

U.S. GAAP Component

Current service costsPast service costs

Interest expense on

pension obligation

Expected return on

plan assets

Actuarial gains and losses

including differences

between the actual and

expected returns on plan

assets

U.S. GAAP Recognition

Recognized in P&L.Recognized in OCI and

subsequently amortized to

P&L over the service life of

employees.

Recognized in P&L.

Recognized in P&L as the

following amount: Plan assets

× expected return.

Recognized immediately in

P&L or, more commonly,

recognized in OCI and

subsequently amortized to

P&L using the corridor or

faster recognition method.(b)

Difference between

expected and actual return

on assets = Actual return (Plan assets × Expected

return).

Actuarial gains and losses

= Changes in a company’s

pension obligation arising

from changes in actuarial

assumptions.

(a) The interest rate used is equal to the discount rate used to measure the pension liability (the yield on high-quality corporate bonds.)

(b) If the cumulative amount of unrecognized actuarial gains and losses exceeds 10 percent of the greater of thevalue of the plan assets or of the present value of the DB obligation (under U.S. GAAP, the projected benefitobligation), the difference must be amortized over the service lives of the employees.

© 2013 ELAN GUIDES




Impact of Key Assumptions on Net Pension Liability and Periodic Pension Cost

Assumption

Higher discountrate

Higher rate of

compensationincrease

Higher expectedreturn on plan

assets

Impact of Assumption on Net

Pension Liability (Asset)

Lower obligation

Higher obligation

No effect, because fair valueof plan assets are used on

balance sheet

Impact of Assumption on Periodic

Pension Cost and Pension Expense

Pension cost and pension expense will both typically be lower because of lower opening obligation and lower servicecosts

Higher service and interest costs willincrease periodic pension cost and

pension expense.

Not applicable for IFRS No effect on periodic pension cost under

U.S. GAAPLower periodic pension expense under U.S. GAAP

© 2013 ELAN GUIDES




MULTINATIONAL OPERATIONS

The presentation currency (PC) is the currency in which the parent company reports

its financial statements. It is typically the currency of the country where the parent is

located. For example, U.S. companies are required to present their financial results inUSD, German companies in EUR, Japanese companies in JPY, and so on.

The functional currency (FC) is the currency of the primary business environment in

which an entity operates. It is usually the currency in which the entity primarily generatesand expends cash.

The local currency (LC) is the currency of the country where the subsidiary operates.

Table 1

Export sale

Import purchase

Loss

Gain

Asset (account receivable)

Liability (account payable)

Foreign Currency

Gain

Loss

Transaction Type of Exposure Strengthens Weakens

Methods for Translating Foreign Currency Financial Statements of Subsidiaries

FunctionalCurrency

LocalCurrency

LocalCurrency

PresentationCurrency


TemporalMethod

Current Rate

Method

Current Rate/

Temporal Method

FunctionalCurrency

FunctionalCurrency


LocalCurrency

T

T

CR

CR

=

=

The current rate is the exchange rate that exists on the balance sheet date. The average rate is the average exchange rate over the reporting period. The historical rate is the actual exchange rate that existed on the original transaction date.

© 2013 ELAN GUIDES




Income Statement Component

Sales

Cost of goods sold

Selling expenses

Depreciation expense

Amortization expense

Interest expense

Income tax

Net income before translation

gain (loss)Translation gain (loss)

Net income

Less: Dividends

Change in retained earnings

Current Rate Method

FC = LC

Temporal Method

FC = PC

Exchange Rate Used

Average rate

Average rate

Average rate

Average rate

Average rate

Average rate

Average rate

N/A

Computed as Rev – Exp

Historical rate

Computed as NI – Dividends

Used as input for translated

B/S

Average rate

Historical rate

Average rate

Historical rate

Historical rate

Average rate

Average rate

Computed as Rev – Exp

Plug in Number

Computed as RE +

Dividends

Historical rate

From B/S

Rules for Foreign Currency Translation

Balance Sheet Component Exchange Rate Used

Cash

Accounts receivableMonetary assets

Inventory

Nonmonetary assets measured at

current value

Property, plant and equipment

Less: Accumulated depreciation

Nonmonetary assets measured at

historical cost

Accounts payableLong-term notes payable

Monetary liabilities

Nonmonetary liabilities:

Measured at current value

Measured at historical cost

Capital stock

Retained earnings

Cumulative translation adjustment

Current rate

Current rate Current rate

Current rate

Current rate

Current rate

Current rate

Current rate


Current rate

Current rate

Current rate

Historical rate

From I/S

Plug in Number

Current rate


Historical rate

Current rate

Historical rate

Historical rate

Historical rate


Current rate

Current rate

Historical rate

Historical rate

To balance Used as input for

translated I/S

N/A

© 2013 ELAN GUIDES




Balance Sheet Exposure

Net asset Net liability

Balance Sheet Exposure

Foreign Currency (FC)

Strengthens

Positive translation adjustment Negative translation adjustment

Weakens

Negative translation adjustmentPositive translation adjustment

Effects of Exchange Rate Movements on Financial Statements

Foreign currency

strengthens

relative to

parent’s

presentation

currency

Foreign currency

weakens relative

to parent’s

presentation

currency

Temporal Method,

Net Monetary

Liability Exposure

Revenues

Assets

Liabilities

Net income


Translation loss

Revenues

Assets

Liabilities

Net income


Translation gain

Temporal Method,

Net Monetary Asset

Exposure

Revenues

Assets

Liabilities

Net income


Translation gain

Revenues

Assets

Liabilities

Net income


Translation loss

Current Rate Method

Revenues

Assets

Liabilities

Net income


Positive translation

adjustment

Revenues

Assets

Liabilities

Net income


Negative translation

adjustment

Measuring Earnings Quality

Aggregate accruals = Accrual-basis earnings – Cash earnings

Balance Sheet Approach

Net Operating Assets (NOA)

NOAt = [(Total assetst Casht) (Total liabilitiest Total debtt)]

Aggregate Accruals

Aggregate accrualst b/s = NOAt NOAt1

Aggregate Ratio

Accruals ratiot

b/s

= (NOAt + NOAt1)/2

(NOAt NOAt1)

© 2013 ELAN GUIDES




A Financial Statement Analysis Framework :

Phase Sources of Information Examples of Output

Define the purposeand context of theanalysis.

Collect input data.

Process input data,as required, intoanalytically usefuldata.

Analyze/interpretthe data.

The nature of the analyst’sfunction, such as evaluating anequity or debt investment or issuing a credit rating.Communication with client or supervisor on needs and

concerns.

Institutional guidelines relatedto developing specific work product.

Financial statements, other financial data, questionnaires,

and industry/economic data.Discussions with management,suppliers, customers, and

competitors.Company site visits (e.g., to production facilities or retail

stores)

Data from the previous phase.

Input data and processed data

Statement of the purpose or objective of analysis.A list (written or unwritten) of specific questions to beanswered by the analysis. Nature and content of report

to be provided.

Timetable and budgetedresources for completion.

Organized financial statements.Financial data tables.

Completed questionnaires, if applicable.

Adjusted financial statements.Common-size statements.Forecasts.

Analytical results

1.

2.

3.

4.

ROE = Tax Burden × Interest burden × EBIT margin × Total asset turnover × Financial leverage

ROE = NI

EBT EBIT

EBT

Revenue

EBIT

Average Asset

Revenue

Average Equity

Average Asset××××

DuPont Analysis

Develop andcommunicateconclusions and

recommendations

(e.g., with an

analysis report).

Follow-up.

5.

6.

Analytical results and previousreportsInstitutional guidelines for

published reports

Information gathered by

periodically repeating abovesteps as necessary to determine

whether changes to holdingsor recommendations arenecessary

Analytical report answeringquestions posed in Phase 1Recommendations regarding

the purpose of the analysis,

such as whether to make an

investment or grant credit.

Update reports and

recommendations

INTEGRATION OF FINANCIAL STATEMENT ANALYSIS TECHNIQUES

© 2013 ELAN GUIDES

INTEGRATION OF FINANCIAL STATEMENT ANALYSIS TECHNIQUES



CAPITAL BUDGETING

Expansion Project

Initial investment outlay for a new investment = FCInv + NWCInv

NWCInv = Non-cash current assets – Non-debt current liabilities

Annual after-tax operating cash flows (CF)

CF = (S – C – D) (1 – t) + D or CF = (S – C) (1 – t) + tD

Terminal year after-tax non-operating cash flow (TNOCF):

TNOCF = SalT + NWCInv – t(SalT – BVT)

Replacement Project

Investment outlays:

Initial investment for a replacement project = FCInv + NWCInv – Sal0 + t(Sal0 – BV0)

Annual after-tax operating cash flow:

CF = (S – C) (1 – t) + tD

Terminal year after-tax non-operating cash flow:

TNOCF = SalT + NWCInv – t(SalT – BT)

Mutually Exclusive Projects with Unequal Lives

Least Common Multiple of Lives Approach

In this approach, both projects are repeated until their ‘chains’ extend over the same time

horizon. Given equal time horizons, the NPVs of the two project chains are comparedand the project with the higher chain NPV is chosen.

Equivalent Annual Annuity Approach (EAA)

This approach calculates the annuity payment (equal annual payment) over the project’s

life that is equivalent in present value (PV) to the project’s NPV. The project with thehigher EAA is chosen.

SML

R i = R F + ßi[E(R M) – R F]

R i = Required return for project or asset i

R F = Risk-free rate of returnßi = Beta of project or asset i[E(R M) – R F] = Market risk premium

© 2013 ELAN GUIDES

CAPITAL BUDGETING



Economic Income

Economic income = After-tax operating cash flow + Increase in market valueEconomic income = After-tax operating cash flow + (Ending market value – Beginning market value)

Economic income = After-tax operating cash flow – (Beginning market value – Ending market value)

Economic income = After-tax cash flows – Economic depreciation

Economic Profit

Economic profit = [EBIT (1 – Tax rate)] – $WACC

Economic profit = NOPAT – $WACC

NOPAT = Net operating profit after tax$WACC = Dollar cost of capital = Cost of capital (%) × Invested capital

Under this approach, a project’s NPV is calculated as the sum of the present values of economic profit earnedover its life discounted at the cost of capital.

(1 + WACC)t

EPt NPV = MVA =

Residual Income

Residual income = Net income for the period – Equity charge for the period

Equity charge for the period = Required return on equity × Beginning-of-period book value of equity

The RI approach calculates value from the perspective of equity holders only. Therefore, future residual incomeis discounted at the required rate of return on equity to calculate NPV.

NPV =

(1 + r E)t

RIt

Claims Valuation

First, we separate the cash flows available to debt and equity holders Then we discount them at their respective required rates of return.

o Cash flows available to debt holders are discounted at the cost of debt,

o Cash flows available to equity holders are discounted at the cost of equity. The present values of the two cash flow streams are added to calculate the total value of the company/asset.

© 2013 ELAN GUIDES

CAPITAL BUDGETING



CAPITAL STRUCTURE

r WACC = r D(1 t) + r E

The Capital Structure Decision

r WACC = r D + r E r 0=( ) ( )

MM Proposition II without Taxes: Higher Financial Leverage Raises the Cost of Equity

Independent variableIntercept

Dependent variable Slope

r E = +r 0 (r 0 r D)

The systematic risk (ß) of the company’s assets can be expressed as the weighted average of the systematicrisk of the company’s debt and equity.

=A +( ) ( )

This formula can also be expressed as:

=E + (A D)

( )

r D = Marginal cost of debtr E = Marginal cost of equity

t = Marginal tax rateD = Market value of the company’s outstanding debtE = Market value of shareholders’ equityV = D + E = Value of the company

Company’s cost of equity (r E) under MM Proposition II without taxs is calculated as:

The total value of the company is calculated as:

V = +r E

EBIT Interest

r D

Interest

© 2013 ELAN GUIDES

CAPITAL STRUCTURE



= +tD

Relaxing the Assumption of no Taxes

r WACC = r D(1 t) + r E

The WACC is then calculated as:

r E = +r 0 (r 0 r D) (1 t)

And the cost of equity is calculated as:

Modigilani and Miller Propositions

Without Taxes With Taxes

=

r E = +r 0 (r 0 r D)

+ tD=

r E = +r 0 (r 0 r D) (1 t)

Proposition I

Proposition II

The Optimal Capital Structure: The Static Trade-Off Theory

VL = VU + tD – PV(Costs of financial distress)

© 2013 ELAN GUIDES

CAPITAL STRUCTURE



DIVIDENDS AND SHARE R EPURCHASE

Pw = Share price with the right to receive the dividend

PX = Share price without the right to receive the dividendD = Amount of dividendTD = Tax rate on dividends

TCG = Tax rate on capital gains

Double Taxation System

ETR = CTR + [(1 – CTR) × MTR D]

ETR = Effective tax rateCTR = Corporate tax rateMTR D = Investor’s marginal tax rate on dividends

Split-Rate Tax System

ETR = CTR D + [(1 – CTR D) × MTR D]

CTR D = Corporate tax rate on earnings distributed as dividends.

Stable Dividend Policy

The expected increase in dividends is calculated as:

Expected dividend increase = Increase in earnings × Target payout ratio × Adjustment factor

Adjustment factor = 1/N

N = Number of years over which the adjustment is expected to occur

Analysis of Dividend Safety

Dividend payout ratio = (dividends / net income)

Dividend coverage ratio = (net income / dividends)

FCFE coverage ratio = FCFE / [Dividends + Share repurchases]

PW PX = D

The expected decrease in share price when it goes ex-dividend can be calculated using the following equation:

© 2013 ELAN GUIDES

DIVIDENDS AND SHARE REPURCHASE



Industry Life

Cycle Stage

Pioneering

development

Rapid

acceleratinggrowth

Mature

growth

Stabilization

and market

maturity

Deceleration

of growth

and decline

Industry

Description

Low but slowly

increasing salesgrowth.Substantialdevelopment costs.

High profit

margins.Low competition.

Decrease in theentry of newcompetitors.Growth potential

remains.

Increasing capacityconstraintsIncreasing

competition.

Overcapacity.Eroding profitmargins.

Types of

Merger

Conglomerate

Horizontal

Conglomerate

Horizontal

HorizontalVertical

Horizontal

HorizontalVerticalConglomerate

Motives for Merger

Younger, smaller companies may sell

themselves to larger firms in matureor declining industries to enter into anew growth industry.Young companies may merge with

firms that allow them to pool

management and capital resources.

To meet substantial capital

requirements for expansion.

To achieve economies of scale,savings, and operational efficiencies.

To achieve economies of scale inresearch, production, and marketingto match low costs and prices of

competitors.Large companies may buy smaller companies to improve management

and provide a broader financial base.

Horizontal mergers to ensure survival.Vertical mergers to increase efficiencyand profit margins.Conglomerate mergers to exploit

synergy.

Companies in the industry may

acquire companies in youngindustries.

Source: Adapted from J. Fred Weston, Kwang S. Chung, and Susan E. Hoag, Mergers, Restructuring, and

Corporate Control (New York: Prentice Hall, 1990, p.102) and Bruno Solnik and Dennis McLeavy, International

Investments, 5th edition (Boston: Addison Wesley, 2004, p. 264 – 265).

Mergers and the Industry Life Cycle

MERGERS AND ACQUISITION

© 2013 ELAN GUIDES




Major Differences of Stock versus Asset Purchases

Payment

Approval

Tax: Corporate

Tax: Shareholder

Liabilities

Stock Purchase

Target shareholders receive

compensation in exchange for their shares.

Shareholder approval required.

No corporate-level taxes.

Target company’s shareholders

are taxed on their capital gain.

Acquirer assumes the target’s

liabilities.

Asset Purchase

Payment is made to the selling

company rather than directly toshareholders.

Shareholder approval might not berequired.

Target company pays taxes on anycapital gains.

No direct tax consequence for target

company’s shareholders.

Acquirer generally avoids the

assumption of liabilities.

n

i ( Sales or output of firm i

Total sales or output of market100)

2

Herfindahl-Hirschman Index (HHI)

Post-Merger HHI

Less than 1,000

Between 1,000 and 1,800More than 1,800

Concentration

Not concentrated

Moderately concentratedHighly concentrated

Change in HHI

Any amount

100 or more50 or more

Government Action

No action

Possible challengeChallenge

HHI Concentration Levels and Possible Government Response

FCFF is estimated by:

Net income+ Net interest after tax

= Unlevered income

+ Changes in deferred taxes

= NOPLAT (net operating profit less adjusted taxes)+ Net noncash charges

– Change in net working capital

– Capital expenditures (capex)

Free cash flow to the firm (FCFF)

Net interest after tax = (Interest expense – Interest income) (1 – tax rate)Working capital = Current assets (excl. cash and equivalents) – Current liabilities (excl. short-term debt)

© 2013 ELAN GUIDES




Comparable Company Analysis

TP = Takeover premium

DP = Deal price per shareSP = Target’s stock price per share

TP =SP

(DP SP)

Bid Evaluation

Target shareholders’ gain = Takeover premium = PT – VT

Acquirer’s gain = Synergies – Premium= S – (PT – VT)

S = Synergies created by the merger transaction

The post-merger value of the combined company is composed of the pre-merger value of theacquirer, the pre-merger value of the target, and the synergies created by the merger. These

sources of value are adjusted for the cash paid to target shareholders to determine the value of the combined post-merger company.

VA* = VA + VT + S – C

VA* = Value of combined companyC = Cash paid to target shareholders

© 2013 ELAN GUIDES




Perceived mispricing:

Perceived mispricing = True mispricing + Error in the estimate of intrinsic value.

VE – P = (V – P) + (VE – V)

VE = Estimate of intrinsic valueP = Market price

V = True (unobservable) intrinsic value

EQUITY VALUATION: APPLICATIONS AND PROCESSES

© 2013 ELAN GUIDES

EQUITY VALUATION: APPLICATIONS AND PROCESSES



R ETURN CONCEPTS

Holding period return = PH – P0 + DH

P0

Intrinsic Value = Next year’s expected dividend

Required return – Expected dividend growth rate

V0 =D1

k e – g

k e (IRR) = g+D1

P0

If the asset is assumed to be efficiently-priced (i.e. the market price equals its intrinsic value), the IRR wouldequal the required return on equity. Therefore, the IRR can be estimated as:

Required return (IRR) = + Expected dividend growth rateMarket price

Next year’s dividend

Holding Period Return

PH = Price at the end of the holding periodP0 = Price at the beginning of the periodDH = Dividend

Required Return

The difference between an asset’s expected return and its required return is known asexpected alpha, ex ante alpha or expected abnormal return. o Expected alpha = Expected return – Required return

The difference between the actual (realized) return on an asset and its required returnis known as realized alpha or ex post alpha. o Realized alpha = Actual HPR – Required return for the period

When the investor’s estimate of intrinsic value (V0) is different from the current market price(P0), the investor’s expected return has two components:

1. The required return (r T) earned on the asset’s current market price; and

2. The return from convergence of price to value [(V0 – P0)/P0].

Internal Rate of Return

© 2013 ELAN GUIDES

RETURN CONCEPTS



BIRR model

r i = T-bill rate + (Sensitivity to confidence risk × Confidence risk) + (Sensitivity to time horizon risk × Time horizon risk)

+ (Sensitivity to inflation risk × Inflation risk) + (Sensitivity to business cycle risk × Business cycle risk)

+ (Sensitivity to market timing risk × Market timing risk)

Build-up method

r i = Risk-free rate + Equity risk premium + Size premium + Specific-company premium

For companies with publicly-traded debt, the bond-yield plus risk premium approach can beused to calculate the cost of equity:

BYPRP cost of equity = YTM on the company’s long-term debt + Risk premium

Adjusting Beta for Beta Drift

Adjusted beta = (2/3) (Unadjusted beta) + (1/3) (1.0)

Estimating the Asset Beta for the Comparable Publicly Traded Firm:

where:

D/E = debt-to-equity ratio of the comparable company.

t = marginal tax rate of the comparable company.

To adjust the asset beta of the comparable for the capital structure (financial risk) of the projector company being evaluated, we use the following formula:

where:D/E = debt-to-equity ratio of the subject company.t = marginal tax rate of the subject company.

BASSET reflects only

business risk of the

comparable

company. Thereforeit is used as a proxy

for business risk of

the project being

studied.

BEQUITY

reflects

business and

financial risk of

comparable

company.

ßASSET = ßEQUITY

)1

(1 + (1 - t)D

E

BPROJECT

reflects

business and

financial risk of the

project.

BASSET

reflects

business risk of

project. ßPROJECT = ßASSET 1 + (1 - t)

D

E

Country Spread Model

ERP estimate = ERP for a developed market + Country premium

© 2013 ELAN GUIDES

RETURN CONCEPTS



Weighted Average Cost of Capital (WACC)

WACC = + r MVCE

MVD + MVCE

r d (1 – Tax rate )MVD

MVD + MVCE

MVD = Market value of the company’s debtr d = Required rate of return on debtMVCE = Market value of the company’s common equity

r = Required rate of return on equity

© 2013 ELAN GUIDES

RETURN CONCEPTS



Justified leading P/E ratio =P0

E1

D1/E1

r g= =

(1 b)

r g

Justified trailing P/E = P0

E0

D1/E0

r g= = (1 b)(1 g)

r g

D0 (1 g) / E0

r g=

P/E ratio

Present value of Growth Opportunities

V0 = + PVGOE1

r

V0 = The value of the stock today (t = 0)P1 = Expected price of the stock after one year (t = 1)

D1 = Expected dividend for Year 1, assuming it will be paid at the end of Year 1 (t = 1)r = Required return on the stock

One-Period DDM

Multiple-Period DDM

DISCOUNTED DIVIDEND VALUATION

V0 += = D1

(1 + r)1

P1

(1 + r)1

D1 P1

(1 + r)1

+

V0 += D1

(1 + r)1

Pn

(1 + r)n

Dn

(1 + r)n+ +...

V0 += Dt

(1 + r)t

Pn

(1 + r)nn

t = 1

Expression for calculating Value of a share of stock

V0 = Dt

(1 + r)

t

t = 1

V0 = D0 (1 + g)

(r – g), or V0 =

D1

(r – g)

Gordon Growth Model

© 2013 ELAN GUIDES




gS = Short term supernormal growth rate

gL = Long-term sustainable growth rate

r = required returnn = Length of the supernormal growth period

Two-Stage Dividend Discount Model

gS = Short term high growth rategL = Long-term sustainable growth rater = required return

H = Half-life = 0.5 times the length of the high growth period

The H-model equation can be rearranged to calculate the required rate of return as follows:

The H-Model

r = [(1 + gL) + H(gs – gL)] + gL

D0

P0

)(

The Gordon growth formula can be rearranged to calculate the required rate of return given the other variables.

r = + gD1

P0

V0 =D

r

Value of Fixed-Rate Perpetual Preferred Stock

V0 = n

t = 1

D0 (1 + gS)t

(1 + r)t + D0 (1 + gS)

n(1 + gL)

(1 + r)n(r – gL)

V0 = D0 (1 + gL)

r – gL

+ D0H (gs – gL)

r – gL

Sustainable growth rate (SGR)

b = Earnings retention rate, calculated as 1 – Dividend payout ratio

g = b × ROE

© 2013 ELAN GUIDES




ROE can be calculated as:

ROE = × × Net income

Sales Total assets

Sales Total assets


g = × × Net income

Sales Total assets

Sales Total assets


Net income - Dividends

Net income×

PRAT model

g = Profit margin × Retention rate × Asset turnover × Financial leverage

© 2013 ELAN GUIDES




FCFF = NI + NCC + Int(1 Tax Rate) FCInv WCInv

Computing FCFF from Net Income

FCInv = Capital expenditures Proceeds from sale of long-term assets

Investment in fixed capital (FCInv)

WCInv = Change in working capital over the year

Working capital = Current assets (exc. cash) Current liabilities (exc. short-term debt)

Investment in working capital (WCInv)

WACC =MV(Debt)

MV(Debt) + MV(Equity)r d(1 Tax Rate)

MV(Equity)

MV(Debt) + MV(Equity)r +

=Firm Value

t =1

FCFFt

(1+WACC)t

Equity Value Firm Value Market value of debt=

Equity Value =

t =1

FCFEt

(1 + r )t

FCFF/FCFE

FREE CASH FLOW VALUATION

Table: Noncash Items and FCFF

Noncash Item

Depreciation

Amortization and impairment of intangibles

Restructuring charges (expense)

Restructuring charges (income resulting from reversal)

Losses

Gains

Amortization of long-term bond discounts

Amortization of long-term bond premiums

Deferred taxes

Adjustment to NI to

Arrive at FCFF

Added back

Added back

Added back

Subtracted

Added back

Subtracted

Added back

Subtracted

Added back but requiresspecial attention

© 2013 ELAN GUIDES




FCFE = EBIT(1 – Tax rate) – Int(1 – Tax rate) + Dep – FCInv – WCInv + Net borrowing

Computing FCFE from EBIT

FCFE = EBITDA(1 – Tax rate) – Int(1 – Tax rate) + Dep(Tax rate) – FCInv – WCInv + Net

borrowing

Computing FCFE from EBITDA

FCFF = CFO + Int(1 Tax rate) FCInv

Computing FCFF from CFO

FCFF = EBIT(1 – Tax rate) + Dep – FCInv – WCInv

Computing FCFF from EBIT

FCFF = EBITDA(1 – Tax rate) + Dep(Tax rate) – FCInv – WCInv

Computing FCFF from EBITDA

FCFE = FCFF – Int(1– Tax rate) + Net borrowing

Computing FCFE from FCFF

FCFE = NI + NCC – FCInv – WCInv + Net Borrowing

Computing FCFE from Net Income

FCFE = CFO + FCInv – Net borrowing

Computing FCFE from CFO

Table: IFRS versus U.S. GAAP Treatment of Interest and Dividends

Interest received

Interest paid

Dividend received

Dividends paid

IFRS

CFO or CFI

CFO or CFF

CFO or CFI

CFO or CFF

U.S. GAAP

CFO

CFO

CFO

CFF

© 2013 ELAN GUIDES




Value of the firm = FCFF1

WACC - gFCFF0 (1 + g)

WACC - g=

WACC = Weighted average cost of capitalg = Long-term constant growth rate in FCFF

Constant Growth FCFF Valuation Model

Value of equity =FCFE1

r - g

FCFE0 (1 + g)

r - g=

r = Required rate of return on equityg = Long-term constant growth rate in FCFE

Constant Growth FCFE Valuation Model

Increases in cash balances

Plus: Net payments to providers of debt capital

+ Interest expense (1 – tax rate) + Repayment of principal

New borrowings

Plus: Net payments to providers of equity capital

+ Cash dividends

+ Share repurchases

New equity issues

= Uses of FCFF

Increases in cash balances

Plus: Net payments to providers of equity capital

+ Cash dividends

+ Share repurchases

New equity issues

= Uses of FCFE

Uses of FCFF

Uses of FCFE

An International Application of the Single-Stage Model

Value of equity =r real greal

FCFE0 (1 + greal)

© 2013 ELAN GUIDES




General expression for the two-stage FCFF model:

n

t = 1

Firm value =

(1 + WACC)

n

1FCFFt

(1 + WACC)

t

FCFFn+1

(WACC g)

+

Firm value = PV of FCFF in Stage 1 + Terminal value × Discount Factor

General expression for the two-stage FCFE model:

Equity value = n

t = 1

FCFEt

(1 + r)t

FCFFn+1

r g (1 + r)n

1+

Equity value = PV of FCFE in Stage 1 + Terminal value × Discount Factor

Terminal value in year n = Justified Trailing P/E × Forecasted Earnings in Year n

Terminal value in year n = Justified Leading P/E × Forecasted Earnings in Year n + 1

Determining Terminal Value

Non-operating Assets and Firm Value

Value of the firm = Value of operating assets + Value of non-operating assets

© 2013 ELAN GUIDES




MARKET-BASED VALUATION: PRICE AND ENTERPRISE VALUE

MULTIPLES

Trailing P/E ratio = Current Stock PriceLast year’s EPS

Forward P/E ratio =Current Stock Price

Expected EPS

P/B ratio =Market price per share

Book value per share

P/B ratio =Market value of common shareholders’ equity

Book value of common shareholders’ equity

Book value of equity = Common shareholders’ equity= Shareholders’ equity – Total value of equity claims that are senior to common stock

Book value of equity = Total assets – Total liabilities – Preferred stock

P/S ratio =Market price per share

Sales per share

P/E × Net profit margin = (P / E) × (E / S) = P/S

P/CF ratio =Market price per share

Free cash flow per share

Leading dividend yield = Next year’s dividend / Current price per share

Trailing dividend yield = Last year’s dividend / Current price per share

Price to Book Ratio

Price to Sales Ratio

Relationship between the P/E ratio and the P/S ratio

Justified leading dividend yield

Justified trailing dividend yield

Price to Cash Ratio

Price to Earnings Ratio

Dividend Yield

© 2013 ELAN GUIDES

MARKET-BASED VALUATION: PRICE AND ENTERPRISE VALUE MULTIPLES



V0 =D1

(r g)

Justified P/E Multiple Based on Fundamentals

Justified leading P/E multiple

Justified leading P/E =P0

E1

D1/E1

r g= =

(1 b)

r g

(1 – b) is the payout ratio.

Justified trailing P/E multiple

Justified trailing P/E =P0

E0

D1/E0

r g= =

(1 b)(1 g)

r g

D0 (1 g) / E0

r g=

Justified P/B Multiple Based on Fundamentals

=P0

B0

ROE g

r g

ROE = Return on equityr = required return on equityg = Sustainable growth rate

Justified P/CF Multiple Based on Fundamentals

V0 =FCFE0 (1 g)

(r g)

P0

S0

=(E0/S0)(1 b)(1 g)

r g

Justified P/S Multiple Based on Fundamentals

E0/S0 = Net profit margin

1 – b = Payout ratio

Justified Dividend Yield

D0

P0

r g

1 g=

© 2013 ELAN GUIDES




P/E-to-growth (PEG) ratio

TVn = Justified leading P/E Forecasted earningsn +1

TVn = Justified trailing P/E Forecasted earningsn

TVn = Benchmark leading P/E Forecasted earningsn +1

TVn = Benchmark trailing P/E Forecasted earningsn

Terminal price based on fundamentals

Terminal price based on comparables

Enterprise value = Market value of common equity + Market value of preferred stock

+ Market value of debt – Value of cash and short-term investments

EBITDA = Net income + Interest + Taxes + Depreciation and amortization

Alternative Denominators in Enterprise Value Multiples

Free CashFlow to theFirm =

EBITDA=

EBITA =

EBIT =

NetIncome

Net

Income

NetIncome

Net

Income

plusInterestExpense

plus

InterestExpense

plusInterestExpense

plus

InterestExpense

minusTax Savingson Interest

plus

Taxes

plusTaxes

plus

Taxes

plusDepreciation

plus

Depreciation

plusAmortization

plus

Amortization

plusAmortization

lessInvestment inWorking Capital

lessInvestment inFixed Capital

Justified forward P/E after accounting for Inflation

1

(1 ) I

P0

E1

=

= The percentage of inflation in costs that the company can pass through to revenue. = Real rate of returnI = Rate of inflation

PEG =P/E

Growth (%)

EV/EBITDA Multiple

© 2013 ELAN GUIDES




Unexpected earnings (UE)

UEt = EPSt – E (EPSt)

SUEt =EPSt E (EPSt )

[EPSt E (EPSt )]

EPSt = Actual EPS for time t

E (EPSt ) = Expected EPS for time t

[EPSt E (EPSt )] = Standard deviation of [EPSt E (EPSt )]

Standardized unexpected earnings (SUE)

© 2013 ELAN GUIDES




R ESIDUAL INCOME VALUATION

The Residual Income

V0 = Intrinsic value of the stock today

B0 = Current book value per share of equityBt = Expected book value per share of equity at any time tr = Required rate of return on equity

Et = Expected EPS for period tRIt = Expected residual income per share

E t rBt-1

(1 + r )t V 0 = B0 +

i = 1

RIt

(1 + r )t

i = 1

= B0 +

Intrinsic value of a stock:

Residual income = Net income – Equity charge

Equity charge = Cost of equity capital × Equity capital

RIt = Et – (r × Bt-1)

The Residual Income Model

RIt = Residual income at time tEt = Earnings at time tr = Required rate of return on equity

Bt-1 = Book value at time t-1

Capital charge = Equity charge + Debt charge

Debt charge = Cost of debt × (1 – Tax rate) × Debt capital

Residual income = After-tax operating profit Capital charge

NOPAT = Net operating profit after tax = EBIT (1 – Tax rate)C% = Cost of capital (WACC)TC = Total capital

Economic Value Added

EVA = NOPAT – (C% × TC)

Market value of company = Market value of debt + Market value of equity.

MVA = Market value of the company – Accounting book value of total capital

Market Value Added

© 2013 ELAN GUIDES

RESIDUAL INCOME VALUATION



RIt = EPSt - (R × Bt-1)

RIt = (ROE - r)Bt-1

V0 = B0 +

t = 1

(ROEt r )Bt-1

(1 + r )t

Residual Income Model (Alternative Approach)

Tobin’s q =Market value of debt and equity

Replacement cost of total assets

Tobin’s q

ROE r

r gB0 + B0V0 =

V0 = B0 +T - 1

t = 1

(Et rBt 1)

(1 + r)t+

ET rBT-1

(1 + r )(1 + r)T1

= Persistence factor.

When residual income fades over time as ROE declines towards the required return on equity, the intrinsic

value of a stock is calculated using the following formula:

V0 = B0 +(Et rBt 1)

(1 + r)t

+PT BT

(1 + r)T

T

t = 1

Multi-Stage Residual Income Valuation

g = r (ROE r) × B0

V0 B0[ ]

Implied Growth Rate

© 2013 ELAN GUIDES

RESIDUAL INCOME VALUATION



PRIVATE COMPANY VALUATION

DLOC = 1 -1

1 + Control Premium

V = Value of the equityFCFE1 = Free cash flow to the equity for next twelve months

r = Required return on equity

g = Sustainable growth rate of free cash flow to the equity

V = FCFE1

r g

Vf =FCFF1

WACC gf

Vf = Value of the firm

FCFF1 = Free cash flow to the firm for next twelve monthsWACC = Weighted average cost of capitalgf = Sustainable growth rate of free cash flow to the firm

The Capitalized Cash Flow Method

Discount for Lack of Control (DLOC)

Methods Used to Estimate the Required Rate of Return for a Private Company

Capital Asset Pricing Model

Required return on equity = Risk-free rate + (Beta × Market risk premium)

Expanded CAPM

Required return on equity = Risk-free rate + (Beta × Market risk premium) + Small stock premium + Company-specific risk premium

Build-Up Approach

Required return on equity = Risk-free rate + Equity risk premium + Small stock premium + Company-specific risk premium + Industry risk premium

© 2013 ELAN GUIDES

PRIVATE COMPANY VALUATION



PRIVATE R EAL ESTATE INVESTMENTS

Net Operating Income

Rental income at full occupancy+ Other income (such as parking)

= Potential gross income (PGI) Vacancy and collection loss

= Effective gross income (EGI) Operating expenses (OE)= Net operating income (NOI)

The Direct Capitalization Method

Cap rate = Discount rate – Growth rate

The cap rate can be defined as the current yield on an investment:

Capitalization rate = NOI1

Value

Rearranging the above equation, we can estimate the value of a property by dividing its first-

year NOI by the cap rate.

Value = NOI

1Cap rate

An estimate of the appropriate cap rate for a property can be obtained from the selling price of similar or comparable properties.

Cap rate = Sale price of comparable property

NOI

The cap rate derived by dividing rent by recent sales prices of comparables is known as theall

risks yield (ARY). The value of a property is then calculated as:

Market value =Rent1

ARY

Gross income multiplier =Selling price

Gross income

Value of subject property = Gross income multiplier Gross income of subject property

Other Forms of the Income Approach

© 2013 ELAN GUIDES

PRIVATE REAL ESTATE INVESTMENTS



Value = NOI1

(r – g)

The Discounted Cash Flow Method (DCF)

Terminal value = NOI for the first year of ownership for the next investor

Terminal cap rate

The Terminal Capitalization Rate

Appraisal-Based Indices

Return = NOI Capital expenditures + (Ending market value Beginning market value)

Beginning market value

LTV ratio =Loan amount

Appraised value

Debt Service Coverage ratio

DSCR =Debt service

NOI

Loan to Value ratio

Equity dividend rate/Cash-on-cash return

Equity dividend rate =First year cash flow

Equity investment

© 2013 ELAN GUIDES

PRIVATE REAL ESTATE INVESTMENTS



PUBLICLY TRADED R EAL ESTATE SECURITIES

Capitalization rate = NOI of a comparable property

Total value of comparable property

NAVPS = Net Asset Value

Shares outstanding

Net Asset Value per Share

Capitalization rate

VALUATION: RELATIVE VALUATION (PRICE MULTIPLE) APPROACH

Funds from operations (FFO)

Accounting net earningsAdd: Depreciation charges on real estate

Add: Deferred tax chargesAdd (Less): Losses (gains) from sales of property and debt restructuringFunds from operations

Adjusted funds from operations (AFFO)

Funds from operations

Less: Non-cash rentLess: Maintenance-type capital expenditures and leasing costsAdjusted funds from operations

AFFO is preferred over FFO as it takes into account the capital expenditures necessary to maintain

the economic income of a property portfolio.

VALUATION: NET ASSET VALUE APPROACH

© 2013 ELAN GUIDES

PUBLICLY TRADED REAL ESTATE SECURITIES



Post-money value =Exit value

(1 + Required rate of return ) Number of years to exists

Required wealth = Investment (1 + IRR) Number of years to exit

Proportionate ownership of the VC investor

= I / POST

Post-money value

Required wealth

Quantitative Measures of Return

PIC (paid in capital): Ratio of paid in capital to date to committed capital.

DPI (distributed to paid-in) or cash-on-cash return: Value of cumulative distributions paid to LPs as a proportion of cumulative invested capital. o (DPI = Cumulative distributions / PIC)

RVPI (residual value to paid-in): Value of LPs’ shareholdings held with the fund as a proportion of cumulative invested capital.

o RVPI = NAV after distributions / PIC

TVPI (total value to paid-in): Value of portfolio companies’ distributed (realized) andundistributed (unrealized) value as a proportion of cumulative invested capital.

o TVPI = DPI + RVPI

NAV before distributions = Prior year’s NAV after distributions + Capital calleddown – Management Fees + Operating results

NAV after distributions = NAV before distributions – Carried interest – Distributions

Total Exit Value

Exit value = Initial cost + Earnings growth + Multiple expansion + Debt reduction

Post-money valuation (POST)

POST = PRE + I

PRIVATE EQUITY VALUATION

Ownership proportion = Required wealth / Exit value

Ownership propotion

© 2013 ELAN GUIDES




Shares to be issued =

Proportion of venture capitalist investment Shares held bycompany founders

Proportion of investment of company founders

Price per share =Amount of venture capital investment

Number of shares issued to venture capital investment

Adjusted discount rate = – 11 + r 1 – q

r = Discount rate unadjusted for probability of failure.q = Probability of failure.

Adjusted discount rate

Shares to be issued

Price per share

© 2013 ELAN GUIDES




FUNDAMENTALS OF CREDIT ANALYSIS

Expected loss = Default probability Loss severity given default

Expected Loss

Yield on a corporate bond:

Yield on a corporate bond = Real risk-free interest rate + Expected inflation rate + Maturity premium + Liquidity premium + Credit spread

Yield spread = Liquidity premium + Credit spread

For small, instantaneous changes in the yield spread, the return impact (i.e. the percentage changein price, including accrued interest) can be estimated using the following formula:

Spread – Modified duration ×Return impact

For larger changes in the yield spread, we must also incorporate the (positive) impact of convexity

into our estimate of the return impact:

Return impact – (MDur × Spread) + (1/2 × Convexity × Spread2)

Yield Spread:

© 2013 ELAN GUIDES

FUNDAMENTALS OF CREDIT ANALYSIS



TERM STRUCTURE AND VOLATILITY OF INTEREST R ATES

X t = 100 ln yt

yt1( )where

yt = yield on day t

Measuring Historical Yield Volatility

Annualizing the Standard Deviation

Annualized standard deviation = Daily standard deviation of days in a year

Variance =T

t = 1

X t 2

T 1

Variance =T

t = 1

W t X t 2

T 1

where:W t = the weight assigned to each daily yield change observation such that the sum of the weights

equals 1.

Calculating Variance of Daily Yield Changes

... assigns an equal weight to all observations

... attaches a greater weight to more recent information

© 2013 ELAN GUIDES

TERM STRUCTURE AND VOLATILITY OF INTEREST RATES



Specific Bond Sector with a Given Credit Rating Benchmark

Treasury Market Benchmark

Nominal

Zero-volatility

Option-adjusted

Treasury yield curve

Treasury spot rate curve

Treasury spot rate curve

Credit risk, liquidity risk and option risk


Credit risk and liquidity risk

Spread Measure Benchmark Reflects Compensation For

Nominal

Zero-volatility

Option-adjusted

Sector yield curve

Sector spot rate curve

Sector spot rate curve



Credit risk and liquidity risk


Issuer-Specific Benchmark

Nominal

Zero-volatility

Option-adjusted

Issuer yield curve

Issuer spot rate curve

Issuer spot rate curve

Liquidity risk and option risk

Liquidity risk and option risk

Liquidity risk


Summary of Relationships between Benchmark, OAS and Relative Value

Benchmark

Treasury market

Bond sector with a

given credit rating

(assumes credit rating

higher than security

being analyzed )

Negative OAS

Overpriced (rich) security


(assumes credit rating higher

than security being analyzed )

Zero OAS

Overpriced (rich)

security

Overpriced (rich)

security


higher than security

being analyzed )

Positive OAS

Comparison must be made

between security OAS and OAS

of comparable securities

(required OAS):

If security OAS > required OAS,

security is cheap

If security OAS < required OAS,

security is rich

If security OAS = required OAS,

security is fairly priced




(required OAS):


security is cheap


security is rich



VALUING BONDS WITH EMBEDDED OPTIONS

© 2013 ELAN GUIDES




Determining Bond Value at a Node Applying Backward Induction

1-year rate at the

node at which we

are calculating the

bond's value, VHHL

Bond's value in higher-rate

state 1-year forward

NHHL

r 3,HHL

VHHL

VHHHL

C

r 4,HHHL

NHHHL

NHHLL

r 4,HHLL

VHHLL C

Cash flow in higher

rate state

Cash flow in lower

rate state

Bond's value in lower-rate

state 1-year forward

Summary of Relationships between Benchmark, OAS and Relative Value (Contd.)

Underpriced (cheap) security

(assumes credit rating lower than

security being analyzed )

Under priced (cheap) security

Underpriced (cheap)

security


lower than security

being analyzed )

Fairly valued




(required OAS):


security is cheap


security is rich




Bond sector with a

given credit rating


lower than security

being analyzed )

Issuer’s own securities

Positive OASZero OASNegative OASBenchmark

The present values of the these two cash flows discounted at the 1-year rate (r 3,HHL) at Node NHHL

are:

VHHHL + C

1 + r 3,HHL( ) 1. Present value in the higher one-year rate scenario

VHHLL + C

1 + r 3,HHL( ) 2. Present value in the lower one-year rate scenario

© 2013 ELAN GUIDES




VHHHL + C

1 + r 3,HHL

( )

VHHLL + C

1 + r 3,HHL

( )+

1

2

Finally, the expected value of the bond, VHHL at Node NHHLis calculated as:

Effective Duration and Effective Convexity

V V+ 2V0

2V0 ( y)2Convexity =

V V+

2V0 ( y)Duration =

Conversion value = Market price of common stock Conversion ratio

Market conversion price =Market price of convertible security

Conversion ratio

Market conversion premium per share = Market conversion price Current market price

Market conversion premium ratio =

Market conversion premium per share

Market price of common stock

Premium payback period =Market conversion premium per share

Favorable income differential per share

Favorable income differential per share =Coupon interest (Conversion ratio Common stock dividend per share)

Conversion ratio

Determining Call Option Value

Value of call option = Value of option-free bond – Value of callable bond.

Determining Put Option Value

Value of put option = Value of putable bond Value of option-free bond

Traditional Analysis of a Convertible Security

Premium over straight value =Market price of convertible bond

Straight value

© 2013 ELAN GUIDES




An Option-Based Valuation Approach

Covertible security value = Straight value Value of the call option on the stock

Covertible callable bond value = Straight value Value of the call option on the

stock Value of the call option on the bond

Covertible callable and putable bond value = Straight value Value of the call option on the stock

Value of the call option on the bond

Value of the put option on the bond

© 2013 ELAN GUIDES




Single Monthly Mortality Rate (SMM)

SMMt = Prepayment in month t Beginning mortgage balance for month t Scheduled principal payment in month t

Prepayment in month t = SMM × (Beginning mortgage balance for month t

Scheduled principal payment in month t )

Conditional Prepayment Rate (CPR)

CPR = 1 (1 SMM)12

SMM = 1 (1 CPR )1/12

Given the CPR, the SMM can be computed as:

Average life = t = 1

T t Projected principal recieved at time t

12 Total principal

t = Number of months

Average Life

Prepayment Risk in Different PAC Tranches

TranchePAC I - Senior

PAC I - Junior

PAC II

Support

Prepayment Risk LOW

HIGH

Distribution of Prepayment Risk in a Sequential-Pay CMO

Tranche

A (sequential pay)

B (sequential pay)

C (sequential pay)

Z (accrual pay)

Contraction Risk

HIGH

LOW

Extension Risk

LOW

HIGH

MORTGAGE-BACKED SECTOR OF THE BOND MARKET

© 2013 ELAN GUIDES

MORTGAGE-BACKED SECTOR OF THE BOND MARKET



ASSET-BACKED SECTOR OF THE BOND MARKET

Parties to the Securitization

Party

Seller

Issuer/Trust

Servicer

Description

Originates the loans andsells loans to the SPV

The SPV that buys theloans from the seller

and issues the asset- backed securities

Services the loans

Party in Illustration

ABC Company

SPV

Servicer

SMM =1 – [ABS × (M – 1)]

ABS

ABS =1 + [SMM × (M – 1)]

SMM

Manufactured Housing-Backed Securities

Cash Flow Yield

ABS and MBS typically have monthly cash flows, so the cash flow yield on these securities is compared tothe yield on Treasury coupon securities based on their bond equivalent yields. The bond equivalent yield for MBS/ABS is calculated as:

Bond equivalent yield = 2 [(1 + monthly cash flow yield)6 – 1]

Option cost = Zero-volatility spread – Option-adjusted spread

Option Cost

Duration =V V+

2V0 ( y)

Duration

VALUING MORTGAGE-BACKED AND ASSET-BACKED SECURITIES

© 2013 ELAN GUIDES

ASSET-BACKED SECTOR OF THE BOND MARKET



DERIVATIVES

Value of a Forward Contract

St F(0,T)

(1 + r)T-t

Time

St

F(0,T)

(1 + r)T-t

ST F(0,T)

Long Position Value

Zero, as the contract is priced to prevent arbitrage

F(0,T) ST

Short Position Value

Zero, as the contract is priced to prevent arbitrage

At expiration

At initiation

During life of the

contract

Price of an Equity Forward with Discrete Dividends

PV(D,0,T) = n

i = 1

Di

(1 + r)ti

F(0,T) = [S0 – PV(D,0,T)] (1 + r)T

FV(D,0,T) =

n

i = 1

Di(1 + r)Tti

F(0,T) = S0 (1 + r)T – FV(D,0,T)

... Approach I

... Approach II

F(0,T) = (S0ecT)er cT

F(0,T) = S0 e(r cc)T

c = Continuously compounded dividend yield

r c = Continuously compounded risk-free rate

Price of an Equity Forward with Continuous Dividends

Value of an Equity Forward

Vt(0,T) = [St – PV(D,t,T)] – [F(0,T) / (1 + r)T – t

]

PV(D,t,T) = PV of dividends expected to be received over the remainder of the contract term (between t and T).

Assuming continuous compounding, the value of a forward contract on a stock index or portfoliocan be calculated as:

Vt(0,T) = Ste – c(T – t) – F(0,T)e –rc(T – t)

Vt(0,T) = –

St

ec(T – t)

F(0,T)

erc(T – t)

FORWARD MARKETS AND CONTRACTS

© 2013 ELAN GUIDES

DERIVATES



Calculating the No-Arbitrage Forward Price for a Forward Contract on a Coupon Bond

F(0,T) = [B0C(T+Y) – PV(CI,0,T)] × (1 + r)T

Or

F(0,T) = [B0C(T+Y)] (1 + r)T – FV(CI,0,T)

BC = Price of coupon bondT = Time of forward contract expiration

Y = Remaining maturity of bond upon forward contract expiration

T+Y = Time to maturity of the bond at forward contract initiation.PV(CI,0,T) = Present value of coupon interest expected to be received between time 0

(contract initiation) and time T (contract expiration).FV(CI,0,T) = Future value of coupon interest expected to be received between time 0

(contract initiation) and time T (contract expiration).

Valuing a Forward Contract on a Coupon Bond

The value of the long position in a forward contract on a fixed income security prior to expirationcan be calculated as:

Vt(0,T) = BtC(T+Y) – PV(CI,t,T) – F(0,T) / (1 + r)T – t

PV(CI,t,T) = Present value of coupon payments that are expected to be received between timet and time T.

BtC

(T+Y) = Current value of coupon bond with time T+Y remaining until maturity

FRA(0,h,m) =360m( ) 1

1 + L0(h + m)360

h + m( )1 + L0( h )

h

360( )FRA(0,h,m) = The annualized rate on an FRA initiated at Day 0, expiring on Day h, and based

on m-day LIBOR.

h = Number of days until FRA expiration

m = Number of days in underlying hypothetical loan

h+m = Number of days from FRA initiation until end of term of underlying hypothetical loan.

L0 = (Unannualized) LIBOR rate today

Pricing a Forward Rate Agreement

© 2013 ELAN GUIDES

DERIVATES



Valuing FRA prior to expiration

FRA payoff =1 + [Market LIBOR × (No. of days in the loan term / 360)]

NP × [(Market LIBOR – FRA rate) × No. of days in the loan term / 360]

FRA Payoff

g = Number of days since FRA initiation.

Vg (0,h,m) =1

1 + Lg (h g) )( h g360

1 + Lg(h + m g)360

h + m g )(

1 + FRA(0,h,m)360

m )(

NP × [(Current forward rate – FRA rate) × No. of days in the loan term / 360]

1 + {Current LIBOR × [(No. of days in loan term + No. of days till contract expiration) / 360]}

Pricing a Currency Forward Contracts

(1 + R DC)T

(1 + R FC)TF(0,T) = S0 ×

F and S are quoted in terms of DC per unit of FC

R DC = Domestic risk-free rateR FC = Foreign risk-free rateT = Length of the contract in years. Remember to use a 365-day basis to calculate T ifthe term is given in days.

Valuing a Currency Forward Contract

The value of the long position in a currency forward contract at any time prior to maturity can be calculated as follows:

Vt (0,T) =(1 + R FC)(Tt)

St (1 + R DC)(Tt)

F (0,T)

Assuming continuous compounding, the price and value of a currency forward contract can be

calculated by applying the formulas below:

Vt(0,T) = [St / er cFC × (T – t)] – [F(0,T) / er cDC × (T – t)]

r c here represents a

continuouslycompounded risk-free rate in theseformulas.

or F(0,T) = S0 × e(r cDC – r cFC) × TF(0,T) = (S0e – r cFC × T) × er cDC × T

Or:

© 2013 ELAN GUIDES

DERIVATES



FUTURES MARKETS AND CONTRACTS

If we ignore the effects of the mark-to-market adjustment on futures contracts, we can make thesimplifying assumption that the futures price and forward price are the same.

f 0(T) = F(0,T) = S0 × (1 + r)T

f 0(T) = Futures price today of a futures contract that expires at time T.F(0,T) = Forward price of a forward contract that expires at time T.

S0 = Spot price of underlying asset todayr = Annual risk-free rate

The Effect of Storage or Carrying Costs on the Futures Price

f 0(T) = S0 (1 + r)T + FV(SC,0,T)

The Effect of Monetary Benefits on the Futures Price

f 0(T) = S0 (1 + r)T FV(CF,0,T)

FV(CB,0,T) = Costs of storage – Nonmonetary benefits (Convenience yield)

If costs exceed benefits, FV(CB,0,T) is a positive number and is known ascost of carry. In thiscase, the general futures pricing formula is given as:

f 0(T) = S0 (1 + r)T

+ FV(CB,0,T)

The Effect of Non-Monetary Benefits on the Futures Price

Pricing Treasury Bond Futures

f 0(T) = B0C(T+Y) [(1 + r 0(T)]T – FV(CI,0,T)

BC = Price of coupon bondT = Time of futures contract expiration

Y = Remaining maturity of bond upon futures contract expiration

T+Y = Time to maturity of the bond at futures contract initiation.r 0(T) = Interest rate at time 0 for period until time T.

FV(CI,0,T) = Future value of coupon interest expected to be received between time0 (contract initiation) and time T (contract expiration).

The adjusted futures price of a t-bond futures contract is calculated as:

f 0(T) =B0

C (T + Y) [1 + r 0 (T)]T FV (CI,0,T)

CF(T)

CF(T) = Conversion factor on CTD bond

© 2013 ELAN GUIDES




Pricing Stock Index Futures

f 0(T) = S0 (1 + r)T – FV(D,0,T)

f 0(T) = S0 e(r

c

– c

)T

Pricing Currency Futures

f 0(T) = S0 (1 + r DC)T

(1 + r FC)T

F and S are quoted in terms of DC/FCr DC = Domestic currency interest rater FC = Foreign currency interest rate

T = Length of the contract in years. Remember to use a 365-day year if maturity is given in days.

If interest rates are assumed to be continuously compounded, then the no-arbitrage futures priceis calculated as:

f 0(T) = S0 × e(r cDC – r cFC)×T

r c represents the continuously compounded risk-free rate.

© 2013 ELAN GUIDES




Put-Call Parity

C0 + = P0 + S0

X

(1 + R F)T

Synthetic Securities

Value

C0 +X

(1 + R F)T

C0

P0

S0

X(1 + R F)

T

X

(1 + R F)TC0 S0 +

P0 + S0

X

(1 + R F)T

P0 + S0

P0 + S0 C0

C0 +X

(1 + R F)T P0

ValueStrategy

fiduciary call

long call

long put

long

underlying

asset

long bond

long call +

long bond

long call

long put

long

underlying

asset

long bond

Consisting of

=

=

=

=

=

Equals

Protective

put

Synthetic call

Synthetic put

Synthetic

underlying

asset

Synthetic

bond

Strategy

long put + long

underlying asset

long put + long

underlying asset

+ short bond

long call + short

underlying asset

+ long bond

long call + long

bond + short put

long put + long

underlying asset

+ short call

Consisting of

OPTION MARKETS AND CONTRACTS

© 2013 ELAN GUIDES




One-Period Binomial Model

Computing the two possible values of the stock:

S+

= SuS- = Sd

Binomia Call Option Pricing

Call payoff = Max(0, S+ – X)

=(1 + r d

(u d)

c = c+ + (1 – ) c-

1 + r

Calculating the value of the call option:

n =c+ c-

S+ S-

Hedge Ratio

Binomial Put Option Pricing

Put payoff = Max (0, X – ST)

Compute the risk-neutral probabilities:

p = p+ + (1 – ) p-

1 + r

Calculating the value of the put option:

Intrinsic value of caplet at expiration:

Caplet value =Max {0, [(One-year rate – Cap rate) Notional principal]}

1 + One-year rate

Floorlet value =max {0, [(Floor rate – One-year rate) Notional principal]}

1 + One-year rate

Intrinsic value of floorlet at expiration:

© 2013 ELAN GUIDES




Put-Call Parity for Forward Contracts

Call and Bond Buy call

Buy bond

Total

Put and Forward

Buy put

Buy forward contract

Total

Transaction

c0

[X – F(0,T)]/(1 + r)T

c0 + [X – F(0,T)]/(1 + r)T

p0

0

p0

Current Value

Value at Expiration

ST – X

X – F(0,T)

ST – F(0,T)

0

ST – F(0,T)

ST – F(0,T)

ST > X

0

X – F(0,T)

X – F(0,T)

X – ST

ST – F(0,T)

X – F(0,T)

ST X

Delta =Change in option price

Change in underlying price

Change in option price = Delta Change in underlying price

An approximate measure for option delta can be obtained from the BSM model: N(d1) from the BSM model approximately equals call option delta.

N(d1) – 1 approximately equals put option delta.

Therefore:

N(d1) – 1] p S

N(d1) Sc

The Black-Scholes-Merton Formula

c = S0 N(d1) Xer cT N(d2)

p = Xe

-r cT

[1 N(d2)] S0[1 N(d1)]Where:

d1 =

ln(S0 X) + [r c + (

d2 = d1

= the annualized standard deviation of the continuously compounded return on the stock

r c = the continuously compounded risk-free rate of return

N(d1) = Cumulative normal probability of d1.

© 2013 ELAN GUIDES


Delta



c0 + = p0

X – F(0,T)

(1 + r)T

Forward Contract and Synthetic Forward Contract

Forward Contract

Long forward contract

Synthetic Forward Contract

Buy call

Sell putBuy (or sell) bond

Total

Transaction

0

c0

– p0

[X – F(0,T)]/(1 + r)T

c0 – p0 + [X – F(0,T)]/(1 + r)T

Current Value

Value at Expiration

ST – F(0,T)

0

– ( X – ST)X – F(0,T)

ST – F(0,T)

ST X

ST – F(0,T)

ST – X

0X – F(0,T)

ST – F(0,T)

ST > X

Put-call-forward parity

The Black Model

The Black model is used to price European options on futures.

Where:

d1 =

ln(f 0(T) X) + (

d2 = d1

c = e

r cT

[f 0(T)N(d1) XN(d2)]

p = er cT (X[1 N(d2)] f 0(T)[1 N(d1)])

f 0(T) = the futures price

Notice that the Black model is similar to the BSM model except that er cT f(T) is substituted for

S0. In fact, the price of a European option on a forward or futures would be the same as the priceof a European option on the underlying asset if the options and the forward/futures contractexpire at the same point in time.

© 2013 ELAN GUIDES




SWAP MARKETS AND CONTRACTS

Swap fixed rate = 1 B0(N)B0(1) + B0(2) + B0(3) + ... + B0(N) )( 100

The Swap Fixed Rate

Present value of floating-rate payments Present value of fixed-rate payments

Value of pay-floating side of plain-vanilla interest rate swap:

Present value of fixed-rate payments Present value of floating-rate payments

[(1 + Return on equity) Notional principal] PV of the remaining fixed-rate payments

[(1 + Return on equity) Notional principal] PV (Next coupon payment + Par value)

[(1 + Return on Index 2) NP] – [(1 + Return on Index 1) NP]

Valuing Equity Swaps

‘Pay a fixed rate and receive the return on equity’ swap

‘Pay a floating rate and receive the return on equity’ swap

The value of a ‘pay the return on one equity instrument and receive the return on another equity

instrument’ swap is calculated as the difference between the values of the two (hypothetical)equity portfolios:

Payer swaption

Notional principal(Market fixed-rate – Exercise rate) No. of days in the payment period

360

Receiver swaption

Notional principal(Exercise rate – Market fixed-rate) No. of days in the payment period

360

Valuing a Swap

Value of pay-fixed side of plain-vanilla interest rate swap:

© 2013 ELAN GUIDES

SWAP MARKETS AND CONTRACTS



Table: Caps, Floors, Interest Rate Options, Bond Options and Interest Rates

Security

Long cap (floor)Long call (put) option on interest rates

Long call (put) option on a fixed income instrument

Benefits when…

Interest rates rise (fall)Interest rates rise (fall)

Interest rates fall (rise)

Payoff to the buyer of an interest rate cap

Payoff to the buyer of an interest rate floor

Payoff = Max [0,(Market interest-rate – Cap rate) Notional principal] No. of days

360

INTEREST R ATE DERIVATIVE INSTRUMENTS

Notional principal] No. of days

360Payoff = Max [0,(Floor rate – Market interest-rate)

© 2013 ELAN GUIDES

INTEREST RATE DERIVATIVE INSTRUMENTS



Expected return on Two-Asset Portfolio

E(R P) = w1E(R 1) + w2E(R 2)

E(R 1) = expected return on Asset 1

E(R 2) = expected return on Asset 2w1 = weight of Asset 1 in the portfolio

w2 = weight of Asset 2 in the portfolio

Variance of 2-asset portfolio:

1 1P 222 = w22 + w22 + 2w1w2 12

1= the standard deviation of return on Asset 12= the standard deviation of return on Asset 2 = the correlation between the two assets’ returns


Cov1,2 = 12

1 1P 222 = w22 + w22

+ 2w1w2Cov1,2

Expected Return and Standard Deviation for a Three-Asset Portfolio

Expected return on 3-asset portfolio:


1 1P 22 332 = w22 + w22 + w22 + 2w1w2 12 + 2w1w3 13 + 2w2w3 23


E(R P) = w1E(R 1) + w2E(R 2) + w3E(R 3)

1 1P 22 332 = w22 + w22 + w22 + 2w1w2Cov + 2w1w3Cov + 2w2w3Cov

PORTFOLIO CONCEPTS

© 2013 ELAN GUIDES

PORTFOLIO CONCEPTS



2

P2 =

1

n+( )

P2

=1

n 2

+n 1

n Cov

Variance of an Equally-weighted Portfolio

E(R P) =n

j=1

w jE(R j)

The variance of the portfolio is calculated as:

P2 =

n

j=1

n

i=1

wiw jCov(R i ,R j)

For a portfolio of n assets, the expected return on the portfolio is calculated as:

Standard Deviation of a Portfolio Containing a Risky Asset and the Risk-Free Asset

E(R P) = RFR + P

[E(R i) RFR]

i

P = wii

Expected Return for a Portfolio Containing a Risky Asset and the Risk-Free Asset

Expected Return and Variance of the Portfolio

© 2013 ELAN GUIDES

PORTFOLIO CONCEPTS



Equation of CML:

E(R P) = R f + P

E(R m) R f m

E(R P) = w1R f + (1 w1)E(R m)

Variance of portfolios that lie on CML:

2 = w22 + (1 w1)22 + 2w1(1 w1)Cov(R f , R m)1 f m

Expected return on portfolios that lie on CML:

CML

The Decision to Add an Investment to an Existing Portfolio

i Cov(R i,R m)

2 2

i,mi,m

i,mi

m m m

Calculation and Interpretation of Beta

E(R i) R f + i[E(R m) – R f ]

The Capital Asset Pricing Model

E(R new) R F

new

E(R p) R F p

Corr(R new,R p)

Market Model Estimates

R i = i + i R M + i

R i = Return on asset i

R M = Return on the market portfolioi = Average return on asset i unrelated to the market returni = Sensitivity of the return on asset i to the return on the market portfolio

i = An error term

i is the slope in the market model. It represents the increase in the return on asset i if

the market return increases by one percentage point. i is the intercept term. It represents the predicted return on asset i if the return on the

market equals 0.

E(R i) = i + iE(R M)

Expected return on asset i

© 2013 ELAN GUIDES

PORTFOLIO CONCEPTS



Cov(R i,R j) = i j2

M

Covariance of the returns on asset i and asset j

Correlation of returns between assets i and j

Corr(R i,R j) =i j

2

M

j M(22 + 2 )1/2

jMi(22 + 2 )1/2

i

R i = ai + bi1FDY + bi2FPE + i

R i = the return to stock iai = intercept

FDY = return associated with the dividend yield factor FPE = return associated with the P-E factor bi1 = the sensitivity of the return on stock i to the dividend yield factor.bi2 = the sensitivity of the return on stock i to the P-E factor.

i = an error term

bij =Assets i’s attribute value Average attribute value

Attribute values)

Fundamental Factor Models

Standardized sensitivities are computed as follows:

Var(R i) = 22 + 2i M i

Variance of the return on asset i

R i = ai + bi1FINT + bi2

FGDP + i

Market Model Estimates: Adjusted Beta

Adjusted beta = 0.333 + 0.667 (Historical beta)

Macroeconomic Factor Models

R i = the return to stock i

ai = the expected return to stock i

FINT = the surprise in interest ratesFGDP = the surprise in GDP growthbi1 = the sensitivity of the return on stock i to surprises in interest rates.

bi2 = the sensitivity of the return on stock i to surprises in GDP growth.i = an error term with a zero mean that represents the portion of the return to stock i

that is not explained by the factor model.

© 2013 ELAN GUIDES

PORTFOLIO CONCEPTS



Active specific risk =n

i=1i i

wa

Where:wa= The ith asset’s active weight in the portfolio (i.e., the difference between the asset’s weight

in the portfolio and its weight in the benchmark). = The residual risk of the ith asset (i.e., the variance of the ith asset’s returns that is not explained by the factors).

i

i

Active factor risk = Active risk squared – Active specific risk.

Active return = R p – R B

Active return = Return from fctor tilts + Return from asset selection

Active return =K

j=1

[(Portfolio sensitivity) j (Benchmark sensitivity) j] (Factor return) j + Asset selection

Active Return

E(R P ) = R F + 1 p, p,

Arbitrage Pricing Theory and the Factor Model

E(R p) = Expected return on the portfolio p

R F = Risk-free rate j = Risk premium for factor j p,j = Sensitivity of the portfolio to factor j

K = Number of factors

Active Risk

TE = s(R p R B)

Active risk squared = s

2

(R p R B)

Active risk squared = Active factor risk + Active specific risk

© 2013 ELAN GUIDES

PORTFOLIO CONCEPTS



FMCAR j =

K

i=1b

a j b

ai Cov(F j,Fi)

Active risk squared

FMCAR j = Active risk squared

Active factor risk

K

i=1b

a j b

ai Cov(F j,Fi) = The active factor risk for factor j

where:

ba = The portfolio’s active exposure to factor j j

Factor’s Marginal Contribution to Active Risk Squared (FMCAR)

IR =R p R B

s(R p R B)

The Information Ratio

© 2013 ELAN GUIDES

PORTFOLIO CONCEPTS



THE THEORY OF ACTIVE PORTFOLIO MANAGEMENT

The expression for the optimal weight, w*, of the active portfolio (Portfolio A) in the optimalrisky portfolio (Portfolio P) is given as:

w* = A

A(1 A) + R M

2(e A)

2 M

Assuming (for simplicity) that the beta of Portfolio A equals 1, the optimal weight, w0, of Portfolio

A in Portfolio P is calculated as:

w0 =

A

R M

2(e A)

2

M

A /2(e A)

R M /2 M

=

If the beta of Portfolio A does not equal 1, we can use the following equation to determine theoptimal weight, w*, of Portfolio A in Portfolio P.

Information Ratio

w* =w0

(1 A)w0

Evaluation of Performance

Sharpe Ratio

The Sharpe ratio of the optimal risky portfolio (Portfolio P) can be separated into contributions

from the market and active portfolio as follows:

S P =2

S M

2+

2(e A)

2 A

=R M

M +

(e A)

A 22

Weight of security k in the active portfolio (Portfolio A)

wk =

ni=1

i / ei

k / ek

© 2013 ELAN GUIDES


(e A)

A 2

(ei)

i 2

n

i=1=



Imperfect Forecasts of Alpha Values

Actual (realized) alpha: R R M

R

f

+

f

+

To measure the forecasting accuracy of the analyst, we can regress alpha forecasts ( f

) on realizedalpha ().

We can evaluate the quality of the analyst’s forecasts by calculating the coefficient of determination

of the regression described above.

© 2013 ELAN GUIDES


f a a

For simplicity, we assume that a and a equal 0 and 1 respectively. Given that forecast errors () are uncorrelated

with true alpha () i.e., Cov, equals 0, the variance of the forecast is given as:

This estimate of R 2 is used as a shrinking factor to adjust the analyst’s forecasts of alpha.



Risk Tolerance

Willingness to Take Risk

Below Average

Above Average

Below AverageBelow-average risk tolerance

Resolution needed

Above AverageResolution needed

Above-average risk tolerance

Ability to Take Risk

Return Requirements and Risk Tolerances of Various Investors

Individual

Pension Plans (Defined

Benefit)

Pension Plans (Defined

Contribution)

Depends on stage of life,

circumstances, and obligations

The return that will adequately

fund liabilities on an inflation-

adjusted basis

Depends on stage of life of

individual participants

Varies

Depends on plan and

sponsor characteristics,

plan features, funding status,

and workforce characteristics

Varies with the risk

tolerance of individual

participants

Return RequirementType of Investor Risk Tolerance

Foundations and

Endowments

Life Insurance

Companies

Non-Life- Insurance

Companies

B k

The return that will cover

annual spending, investment

expenses, and expected inflation

Determined by rates used to

determine policyholder reserves

Determined by the need to price

policies competitively and by

financial needs

D t i d b t f f d

Determined by amount of

assets relative to needs, but

generally above- average

or average

Below average due to factors

such as regulatory constraints

Below average due to factors

such as regulatory constraints

V i

THE PORTFOLIO MANAGEMENT PROCESS AND THE INVESTMENT POLICY

STATEMENT

THE PORTFOLIO MANAGEMENT PROCESS AND THE INVESTMENT POLICY STATEMENT

elan guides formula sheet cfa 2013 level 2

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