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# CFA 2018 Level 2 Equity

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2017 Instructor: Jie

Reading 28: Return Concepts • Reading 30:Discounted Dividend Valuation • Reading 31: Free Cash Flow Valuation • Reading 32: Market-Based Valuation:Orice and EnterpriseReading 27: Equity Valuation:Applications and Process • Reading 28: Return Concepts Ø>Reading 33: Residual Income Valuation Reading 34:Private Company Valuation • Reading 29: Industry And Company Analysis • Reading 27: Equity Valuation:Applications and ProcessFree cash flow vs. dividends for controlling inteEndogenous factors (poorly performing companies tend to

expand by making acquisitions in unrelated businesses)

Research measurement errors

Summary Ø ☆

Importance: Definitions of Return and

Ø Content:

Equity Risk Premium (ERP)

valuation processTasks:

issues in industry and competitive analysis

Ø Distinguish among realized holding period return, expected

valuation models

holding period return, required return, return from

sum-of-the-part and conglomerate discount

convergence of price to intrinsic value, discount rate, and

selection of valuation approach

internal rate of return

Ø Exam tips:

Ø Calculate and interpret an equity risk premium using

了解估值过程，行业与竞争分析中需要考虑的问题，估值

模型，分类加总法和跨业大企业估值折价，以及估值方法 historical and forward-looking estimation approaches 选择要考虑的因素

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Return Concepts Return Concepts

Holding Period Return (HPR)Required Return

Ø Ø

The return earned from investing in an asset over s specified The minimum level of expected return that an investor requires time period over a specified time period, given the asset's riskiness.

P P D t t Ø

It represents the opportunity cost for investment in the asset

r price return dividend yield P

Ø

It is therefore the issuer's marginal cost of capital (cost of equity)Expected alpha = Expected return - Required return Realized Return

Ø

When expected alpha is higher than zero, the asset is

Ø

Historical return based on observed prices and cash flow

Ø

undervalued

V P

Equal to HPR

E(R t ) r t PExpected Return

E(R ) r

= Expected holding-period return; = required return t t

Ø

Return based on forecasts of future prices and cash flows

V P

= return from convergence

P Equity Risk Premium Return Concepts

Discount RateEquity Risk Premium (ERP)

Ø Ø

The rate used in finding the present value of a future cash flow The incremental return that investors require for holding

It reflects the compensation required by investors for delaying

Ø equities rather than a risk-free asset.

Ø

The risk free rate should be consistent with the investor's consumption and for the risk of the cash flow investment horizon

Ø

It depends on the characteristics of the investment rather than

T-Bills for short horizons

on the characteristics of the investor

Internal Rate of Return (IRR)

T-Bonds for longer holding periods Ø

The discount rate that equates the present value of the asset's

Ø The ERP can be used to determine the required return

expected future cash flows to the asset's price

R R ( R R ) i f i M f

Ø

An IRR coumputed under the assumption of market efficiency equals the required return on equity

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Approaches to Estimating ERP Approaches to Estimating ERPHistorical Estimates

Ø

The mean value of the differences between broad-based equity

Ø

Estimating the ERP based on current market conditions and market index returns and government debt returns over the expectations concerning economic and financial variables sample period

Strength—less subject to nonstationarity and data biases

Strength—objective and simple •

Weaknesses: Weaknesses:

ü ü

Requires frequent updates Assumes stationary of mean and variance of returns over time

ü

Makes lots of assumptions

ü Upwardly biased due to survivorship bias

ü Geometric mean(lower) vs. arithmetic mean(higher)

ü

Which risk-free rate to use (T-bond yield or T-bill yield?)

Approaches to Estimating ERP Approaches to Estimating ERPForward-Looking Estimates - Gordon Growth Model Forward-Looking Estimates - Macroeconomic Model

D 1 ERP g R f

Ø

Estimating the ERP from expected macroeconomic and financial P

D 1 variables such as inflation, earning growth, P/E growth, etc.

Ø

=dividend yield on broad-based equity index based on year-

P

ahead aggregate forecasted dividends and aggregate market Strength—use of proven models and current information

value

Weakness—only appropriate for developed counties where Ø g

= Consensus long-term earnings growth rate public equities represent a relatively large share of the

Ø R

= long-term government bond yield f economyMultiple Growth Stages Model

Ø

Equity index price =PVFastGrowthStage(r)+PVTransition(r)+PVMatureStage(r)

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Approaches to Estimating ERP ØExample of Macroeconomic Model - Ibbotson and Chen Model ERP = EDY+[(1+EINFL)(1+EGREPS)(1+EGPE)-1]-E( )

Strength—easy to obtain Weakness—wide disparity among experts Ø

estimate the required return on an quity investment

Ø Describe strengths and weaknesses of methods used to

public companies and nonpublic companies

Ø Explain beta estimation for public companies, thinly traded

the capital asset pricing model, the Fama-French model, the Pastor-Stambaugh model, macro-economic multifactor models

Ø Estimate the required return on an equity investment using

Summary Estimation of Required Return (1)

Exam tips:

Ø Content:

Importance: ☆☆

Asking a sample of experts about their expectations for ERP

R

f

=expected risk-free return f R

Ø

EGPE=expected growth rate in the P/E ratio (the baseline value is zero)

Ø

EGREPS=expected growth rate in real earnings per share (approximately track the real GDP growth rate)

Ø

EINFL=expected inflation (yield spread between T-bond and TIPS)

Ø

EDY=expected dividend yield

Ø

Approaches to Estimating ERPTasks:

return concepts ERP estimation Ø了解不同回报率概念重点掌握权益风险溢价(ERP)评估方法的优缺点和计算。

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Models of Required Return Models of Required Return

Ø

The Capital Asset Pricing Model

Ø

The Multifactor Models (APT)

R R ( R R ) i f i M f

Ø

The Build-up Methods

Ø

Investors evaluate the risk of an asset in terms of the asset's contribution to the systematic risk of their portfolio

Ø

The beta measures the asset's systematic risk

Ø

It assumes that equity prices are largely determined by local investors

Ø

The assumption that all investors worldwide participate equally in setting prices results in the international CAPM in which risk premium is relative to a world market portfolio

Beta Estimation Beta EstimationBeta for Thinly Traded stocks or Nonpublic Companies Beta for a Public Company

Ø Ø Four-step procedure

Resulting from regressing the company's returns on the returns

1. Identify a publicly traded firm with similar industry

of the market index (raw beta, or unadjusted beta) characteristics

Ø Beta Drift : the beta value in future tends to be closer to the

2. Estimate the beta of the publicly traded firm using

mean value of 1 regression -> B

E Ø

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

3. Unlever the beta:

B = [1/(1+(D/E ))]B

unlevered peer firm E

4. Relever beta:

B = [1+(D/E )]B

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Models of Required Return Models of Required ReturnMultifactor Models

Ø

Use multiple factors to explain returns

Ø

The Fama-French Model

Ø

CAPM is a single factor model

Ø

The Pastor-Stambaugh Model

Ø Arbitrage pricing theory (APT) models are based on a

Ø

Macroeconomic Multifactor Model(The BIRR Model) multifactor representation of the drivers of return

r R ( Factor risk premium) ( Factor risk premium) f 1 1 2 2 ... ( Factor risk premium) n n

β = factor sensitivity/factor beta=the asset's sensitivity to a

particular factor (holding all other factors constant)

Factor risk premium=the expected return of a particular factor

in excess of the risk-free rate

Models of Required Return Models of Required Return

The Fama-French Model (FFM) mkt size valueThe Pastor-Stambaugh Model (PSM)

r R RMRF SMB HML i f i i i

Ø

The PSM model adds to the Fama-French model a liquidity factor

Ø

RMRF = the return on a market value-weighted equity index in mkt size value liq r R RMRF SMB HML LIQ i f i i i i excess of the one-month T-bill rate

Ø Ø

SMB (small minus big), a size factor = small-cap return premium LIQ, a liquidity factor = liquidity return premium = the mean = the mean return to shorting large-cap shares and investing the return to shorting high-liquidity shares and investing the proceeds in small-cap shares proceeds in low-liquidity shares

Ø Ø

HML(high minus low), a value factor = value return premium = An average-liquidity equity have a liquidity beta of 0 the mean return from shorting low book-to-market(high P/B) shares and investing the proceeds in high book-to-market shares

咨询电话：Macroeconomic Multifactor Model

Confidence risk: the unanticipated change in the returnTime horizon risk: the unanticipated change in the returnInflation risk: the unexpected change in inflation rate Business cycle risk: the unexpected change in the level of

Market timing risk: the portion of the total return that

Ø Estimate the required return on an equity investment using

Content:

models)

Ø Exam tips:

特征

Summary Estimation of Required Return (2)

Ø Describe strengths and weaknesses of methods used to

the buiild-up method

estimate the required return on an quity investment

Ø Explain international considerations in required return

estimation

Ø Explain and calculate the weighted average cost of capital

for a company

☆☆☆ Ø

Ø Importance:

remains unexplained by the first four risk factors

real business activity

difference between T-bonds and T-bill

difference between risky corporate bonds and T-bonds

A specific example is the five-factor BIRR model (Burmeister, Roll, Ross)

Ø

Models of Required Return

flows of the stocks or issuers and the discount rate appropriate to determining their present value

macroeconomic factors that affect the expected future cash

The macroeconomic factor models are based on multiple

factors that reflect attributes of the stocks or issuers themselves Ø

The FFM and PSM models are based on multiple fundamental

Models of Required Return ØTasks:

capital asset pricing model beta estimation multifactor models(Fama-French, Pastor Stambaugh, BIRR重要考点，掌握权益要求回报的各种评估方法的计算及其

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Models of Required Return Models of Required ReturnBuild-Up Method for Private Business Valuation

r R Equity risk premium Size premium i f i

Ø

Estimating the required return as the sum of the risk-free rate

Specific company premium - i and a set of risk premiums

Ø R = required return on average- Equity risk premium f

Ø

It is useful when beta estimates are “ unobtainable ” systematic-risk large-cap public stocks

Ø

Widely used for closely held companies

Ø

The size premium is inversely related to the company size r R Equity risk premium one or more premium(di scounts) i f

Ø

Unsystematic risk related to a privately-held company is less

easily diversified away Models of Required Return

Strengths and Weaknesses of Required Return ApproachesBond Yield Plus Risk Premium

Ø

simple, easy to compute, single factor model but

CAPM— Ø

Appropriate for companies with publicly traded debt

simplicity comes with potential loss of explanatory power Ø

Required return (cost of equity) = YTM on the company's long Ø

Multi-factor models— higher explanatory power but more term debt + risk premium complex and expensive

Ø

The YTM on the company's long term debt include:

Ø Build up— simple and applied to closely held firms but use

a real interest rate and a premium for expected inflation

historical values

a default risk premium which captures factors such as profitability, the sensitivity of profitability to the business cycle, and leverage(operating, financial)

Ø

The risk premium compensates for the additional risk of the equity holders compared with the debt holders

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Summary

MVE MVD MVD WACC d

Exam tips:

Ø Content:

Importance: ☆☆

Important: you must align the discount rate with the cash flows ! Ø

cash flows

Ø Nominal (real) discount rate must be used with nominal (real)

Equity value = firm value – MV of debt

E

Ø Equity value = FCFE/Dividend, discount at R

Ø Firm value = FCFF, discount at WACC

Discount rate Selection in Relation to Cash Flow

MVE MVD MVE Tax rate)r 1 (

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Use the target capital structure e r

Ø

(1-tax rate) adjusts the pretax cost of debt downward to reflect the tax duductibility of interest payments

Weighted Average Cost of Capital Ø

developed market

Equity risk premium for an emerging market = Equity risk premium for a developed market + Country premium

and add an emerging market premium

Ø Country Spread Model—use a developed market benchmark

currency and adjust it by the forecast for the change in the exchange rate

Exchange rates—compute the required return in the home

International Considerations in Required Return Estimation Ø

Country premium= YTM of emerging market – YTM ofthe build-up method the international consideration WACC discount selection ØUse FCFE when capital structure are not volatile Use FCFF with high debt levels, negative FCFE Ø重点掌握权益要求回报的叠加法 理解不同权益要求回报评估方法的优缺点，以及国际考虑掌握WACC计算，在给定现金流时能选择匹配贴现率

Ø Hybrid analysis: incorporate elements of both top-down and bottom-up analysis.

Economies of Scale in an industry Ø

Ø

Economies of Scale are observed when larger companies:

The relationship between GDP and company sales could be modeled as “ GDP growth plus x% ”, or “ GDP growth rate times (1+x%)

Ø

Top-Down Approaches to Modeling Revenue

macroeconomic variable (e.g. GDP)

Ø Top-down analysis: begins with expectations about a

start with analysis of an individual company or its business segments

Bottom-up analysis:

Approach for developing inputs to equity valuation models ØTasks:

Ø Forecast COGS, SG&A, Financing costs and income taxes

industry by analyzing operating margins and sales levels

Ø Evaluate whether economies of scale are present in an

growth and market share” approaches to forecasting revenue

Ø Compare “growth relative to GDP growth” and “market

developing inputs to equity valuation models

Ø Compare top-down, bottom-up, and hybrid approaches for

Industry and Company Analysis (1)Growth Relative to GDP Growth

Sales volume and margins tend to be positively correlatedhave larger margin have lower COGS as a proportion of salesMarket Growth and Market Share

Revenue = market share ×market sales

Ø

Forecasting growth of industry sales, and how the company's market share is likely to change over time

Ø

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Forecasting COGS, SG&A, Financing Costs, Income Taxes Forecasting COGS, SG&A, Financing Costs, Income Taxes Ø

Ø

COGS has a direct link with sales SG&A overall are less closely linked to revenue than COGS

Ø

Forecasted GOGS = (historical COGS/revenue)*(estimate of Selling and distribution expenses are more variable than future revenue) or others and can be estimated as a percentage of sales

Ø

Forecasted COGS = (1 – gross margin)*(estimate of future Other general and administrative expenses (overhead costs, revenue) R&D expenses, etc) are more fixed in nature

Ø

Be aware of the impact of the company's hedging strategy on gross margin

Ø

Competitors' gross margins can provide a useful cross check

Forecasting COGS, SG&A, Financing Costs, Income Taxes Forecasting COGS, SG&A, Financing Costs, Income Taxes Financing CostsIncome Taxes

Ø Ø

Gross interest expense depends on the level of debt and

Statutory tax rate: the tax rate applying to what is considered

market interest rates to be a company's domestic tax base

Ø Effective tax rate: calculated as the reported tax amount on Net debt = gross debt – cash/cash equivalents – short term

the income statement divided by pre-tax income securities

Ø Cash tax rate: the tax actually paid divided by pre-tax income Net interest expense = gross interest expense – interest income

Ø

Differences between the statutory tax rate and the effective on cash and short term debt securities tax rate can arise from tax credits, withholding tax, etc.

咨询电话： Summary Industry and Company Analysis (2)

Content:

☆☆ Ø

Ø Importance: Tasks:

Approaches for developing inputs Modeling revenues Economies of scale Forecasting COGS, SG&A, financing costs and income taxes Ø>重点掌握预期revenue, COGS, SG&A, financing costs和 income taxes的能判断行业和公司是否实现规模经济

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Ø

capital invested LAT) taxes(NOP adjusted less profit operating net ROIC

Invested capital = operating assets - operating liabilities

Ø

the capital invested by the company's shareholders and debt holders

Return on invested capital (ROIC) measures the profitability of

Return on Invested Capital and Compatitive Advantage Ø

365 sales forecasted g outstandin sales days receivable account projected

ratio turnover inventory COGS annual forecasted value inventory

current business

Capital expenditures include:

PP&E: determined by depreciation and capital expenditures

Exam tips:

Ø

Balance Sheet Modeling Ø

costs when they are subject to price inflation and deflation

Ø Explain how to forecast industry and company sales and

Porter’s five forces analysis

Ø Judge the competitive position of a company based on a

Ø Explain how competitive factors affect prices and costs

and competitive advantage

Ø Describe the relationship between return on invested capital

Ø Describe approaches to balance sheet modeling

Many balance sheet items flow directly from, or very closely linked to income statement.

ROIC is not affected by financial leverage High ROIC is a sign of a competitive advantageMaintenance capital expenditure necessary to sustain theGrowth capital expenditure needed to expand the business

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Competitive position based on Porter’s model Competitive position based on Porter’s model

Ø Threat of substitute

Ø Bargaining power of customers

Pricing power and profitability are limited when numerous • Pricing power and profitability are limited when industries • substitutes exist and switching costs are low. have a concentrated customer base, standardized product,

Ø Rivalry among incumbent companies

low switching costs for customers

Pricing power and profitability are limited when industries Ø

Threat of new entrants are fragmented, have limited growth, high exit barriers, high Pricing power and profitability are limited when barriers to • fixed costs, identical products entry are low

Ø Bargaining power of suppliers

Profitability is limited when suppliers have greater ability to • increase prices, limit the quality and quantity of inputs

Industry/Company sales - inflation and deflation Industry/Company costs - inflation and deflation

Ø Ø

Companies that can pass on inflation through higher prices are The impact of volatility in input costs can be mitigated by:

likely to have higher and more stable profits and cash flow

long-term price-fixed forward contracts and hedges

Industry structure is an important factor •

access to alternative inputsmakes accurate revenue projections vertically integrPrice-volume trade-off

Ø

difficult Monitor production costs by product category and geographic

ü

higher price have a negative impact on volume location, with a focus on significant factors affecting input prices

ü

the decline in volume depend on price elasticity of (e.g. weather, regulation, taxation, etc,) demand, the reaction of competitors, and availability of substitutes

咨询电话： Summary Industry and Company Analysis (3)

Content:

☆☆ Ø

Ø Importance: Tasks:

Balance sheet modeling return on invested capital Porter’s model Impact of inflation and deflation on sales and costs Ø>掌握资产负债表相关科目的预期方法，计算ROIC，利用波 特模型分析行业理解通胀和紧缩对销售额和成本的影响

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Ø

activity are considered temporary

Use normalized earnings : expected mid-cycle earnings in the absence of any unusual or temporary factors

Ø

The horizon for highly cyclical companies should be long enough to include the middle of a business cycle.

Ø

Forecast horizon = expected holding period

Forecast Horizon

the existing product that will be taken by the new substitute

Result in improved substitutes or wholly new products

Technological developments can decrease costs of production, increase profit margins and industry supply and sales

Exam tips:

Effects of technological developments on demand, price, costs and margin Ø

Ø Demonstrate the development of a sales-based pro forma

beyond the short-term forecast horizon

Ø Explain an analyst’s choices in developing projections

horizon

Ø Explain considerations in the choice of an explicit forecast

demand, selling prices, costs, and margins

Ø Evaluate the effects of technological developments on

company model

Cannibalization factor : the percentage of the market forImpactful events such as merger/acquisition, restructuring Overall economic environment Business cycle stage Government regulations technology

Summary

3. Estimate SG&A

Exam tips:

Content:

☆ Ø

Ø Importance:

9. Construct a pro forma cash flow statement with the completed pro forma income statement and balance sheet

8. Estimate capital expenditure and net PP&E

7. Model the balance sheet based on items from income statement

6. Estimate cash taxes, taking into account changes in deferred tax items

5. Estimate income tax expenses and cash taxes

4. Estimate financing costs

2. Estimate COGS

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1. Estimate revenue growth and future expected revenue

Steps in developing a sales-based pro forma model:

Sales-based pro forma model

The terminal value is can be estimated using either a relative valuation (price multiple) or discounted cash flow approach (DDM)

Ø

Use the earnings/some measure of cash flow over a forecast period, plus the terminal value

Ø

Assume that a trend growth rate of revenue over the previous cycle will continue.

Methods for projections beyond short term Ø

The difficult part is recognizing inflection points : instances when the future will not be like the past, due to changes in such as:

Forecast Horizon Ø

Effects of technological developments Forecast horizon Sales-based pro forma model Ø>评估技术发展对需求，价格，成本，和利了解影响预期长度的因素 了解长期预期方法 了解基于销售额的预期模型

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Discounted Cash Flow Valuation Ø

An asset’s intrinsic value is the present value of its expected future cash flows

Overview of Discounted Cash Flow Models

CF t

V t

Tasks:

t 1 (1 r )

Ø Ø

Compare dividends, free cash flow, and residual income as Measures of “cash flow”

inputs to discounted cash flow models

Dividends

= cash paid to shareholders, used in DDM

Ø Identify investment situations for which each measure is suitable

Free cash flow = cash “available” to pay shareholders

Ø Calculate and interpret the value of a common stock using the

Residual income = economic profit

dividend discount model for single and multiple holding periods

Key point: Valuation metric (e.g., divs or FCF) must be

measurable and related to earnings power Dividends

Dividends Ø

ØAdvantages

Disadvantages

Dividends less volatile than other cash flow measures, more

Firm may not pay dividends due to lack of profitability or • stable and predictable little cash available for distributionDCF model is less sensitive to short term fluctuationHistorically many firms are paying less dividends for tax

underlying value

reasons

Theoretically justified – dividends are what you receive when

Dividends may not reflect the control perspective desired by • you buy a stock the investor

DCF models reflect long term intrinsic value Accounts for reinvested earnings to provide a basis for increased future dividends

咨询电话： period

Company has history of paying dividends Board of directors has a dividend policy that has anMinority shareholder takes a non-control perspective Mature firms , profitable but not fast growthUsed with any firm that has different dividend andNo dividend payment history Dividends not related to earnings or dividends and FCF differFCF can be viewed as what a firm could pay in dividends Popular with many analystsFCF consistent with profitability within a reasonable timeNegative free cash flow , resulting from large capitalControlling shareholder perspectiveMay require long forecast periods for CF to turn positive, introducing greater model uncertainty

Advantages

Situations when appropriate

Free Cash Flow (FCF) Ø

expenditure demands

Disadvantages

Ø

financing/leverage policies

Free Cash Flow (FCF) Ø

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Free cash flow to equity ( FCFE ) is cash flow from operations minus net capital expenditures minus net payments to debt holders (interest and principal), represents returns to equity ownership

Ø

Free cash flow to the firm ( FCFF ) is cash flow from operations (CFO) minus net capital expenditures, represents firm ownership

Free Cash Flow (FCF) Definitions Ø

understandable and consistent relationship to profitability

Situations when appropriate

Dividends Suitability Ø

significantly

Wide applicability , even if FCF < 0 Used for dividend and non-div paying firms Incorporates opportunity cost of capital for both debt andBrings recognition value closer to the present by focusing onRestated dividend discount modelApplication of the RI model requires a detailed knowledgeThe quality of accounting disclosure can make the use ofUsed with firms that have no dividend historyUsed with negative FCFLess horizon dependence

Disadvantages

V 1 r

D

t t t 1

Ø Problem: Requires estimation of infinite stream of CFs

discounted at required return

The Rule: Value is present value of all future dividends

Dividend Discount Models Ø

Ø Situations when appropriate

RI valuation less robust and more error prone

of accrual accounting

Residual Income (RI) Ø

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current book value plus forecasted residual income

equity holders

Advantages

Residual Income (RI) Ø

Intrinsic value equals the book value per share plus the present value of expected future residual earnings, similar to DDM and EVA

Ø

RI focuses on profitability in relation to all opportunity costs faced by the firm

Ø

required return on the beginning-of-period investment (common stockholders' equity)

Residual income is the earnings in excess of the investors’

Residual Income (RI) Definition Ø

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Single Period DDM Multiple-Period DDM

Ø Ø

Single-period DDM is the present value of the future For n-period model, the value of a stock is the present dividend and sales price value of the expected dividends for the n periods plus the present value of the expected price in n periods

D P D P

1

1

1

1 D D P 1 n n V ...

V 1 n n

1

1

1 1 r 1 r 1 r

(1 r ) (1 r ) (1 r ) n

D P t n V t 1 t n 1 r 1 r

Ø

Notice that there are two cash flows in the final period!

Ø

the expected price in n periods depends on the expected dividends after the n periods.

Multiple-Period DDM Multiple-Period DDM Example: Fragrance Ltd. Expects dividends of €1, €1.5, and €2.0 To use the DDM, the forecasting problem must be simplified.

Two broad approaches exist: over the next three years. Expected stock price at the end of year 3 is €80. If the cost of equity is 18%, compute the value of

1. Future dividends can be forecast by assuming one of several

stylized growth patterns Fragrance shares today.

D 1 D 2 D 3 P 3

V 1 2 3

constant growth forever (Gordon growth model)

(1 r ) 1 r 1 r

two distinct stages of growth

1.0 1.5 2.0 80 EUR51.83 1 2

3

three distinct stages of growth

1.18

1.18

1.18

2. A finite number of dividends can be forecast individually up

If the current market price of Fragrance Ltd is 45.00 euros, then to a terminal point, then the terminal value is estimated the security is undervalued using some method

咨询电话： Summary Gordon Growth Model

Content:

☆ Ø

Ø Importance: ☆Tasks:

DDM FCFE/FCFF models Residual income models Ø了解DDM，FCF，和residual income模型的优缺点，能判断能运用单期和多期DDM对权益证券进行估值

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Situations in which model is useful:

2. Growth rate less than required return (r > g)

1. Dividends grow at constant rate (g) forever

Gordon Growth Model Assumptions:

= Dividend expected in one year g = sustainable growth rate r = required return on equity

1

where D

V (r g) (r g)

Gordon Growth Model

Exam tips:

using Gordon growth model

Ø Calculate and interpret the justified leading and trailing P/E

Ø Calculate and interpret the present value of growth

using the Gordon growth model and current stock price

Ø Calculate and interpret the implied growth rate of dividends

model and explain the model’s underlying assumptions

Ø Calculate the value of a common stock using the Gordon growth

每个模型适合的情景

opportunities and the component of the leading price-to- earnings ratio related to PVGOMature (late in life cycle) firms Broad-based equity index Terminal value in more complex models Estimate g, r and PVGO Can be used to calculate P/E ratio Minority perspective

Firm just paid $1.20 dividend per share Required return is 13% Market price is $15.75 Ø

40 9%) 1.6(1 r

9

% 36 . 13 %

1 D r = + g P

is $40 with expected growth of 9% the required return is:

Ø Example: If dividends today are $1.60 and the current price

Solving GGM for r:

Ø

Point: DDM can be used to find implied r

Ø

0.13 g g 0.05 5.0% Gordon Growth Model - Required Return - r

$1.20 1 g $15.75

Implied dividend growth rate is:

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Assume:

Gordon Growth Model - Implied Growth Rate Ø

Correct answer V = ($1.50 × 1.05) / (0.10 – 0.05) = $31.50

Ø

dividends are expected to grow at a long term constant rate of 5%. The required return is 10%. Calculate the intrinsic value

Example: A firm paid a dividend yesterday of $1.50 and

Gordon Growth Model Ø

Sensitivity analysis may be required to obtain a range of values rather than a specific point estimate of value

Ø

The model’s intrinsic values V are very sensitive to the input variables for r and g

Ø

expectations – GDP growth, industry life cycle stages and the impact of the five force model

Gordon Growth Model Ø

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Present Value of Growth Opportunities (PVGO) Present Value of Growth Opportunities (PVGO)

Ø Ø

Increase in shareholder wealth comes when reinvested Stock value is the sum of earnings are directed toward investments which earn greater

Value of no growth (E /r)

1 returns than the opportunity cost of the fund s needed to

Present value of future growth opportunities (PVGO) • undertake the project (ROE > r or ROIC > WACC)

V = E /r + PVGO

1 Ø

Companies without positive NPV projects should distribute all

Ø

Component of leading P/E related to PVGO earnings in dividends because earnings cannot be reinvested

P /E = 1/r + PVGO/E

1

1

profitably and earnings will be flat in perpetuity, assuming a 1/r is the P/E ratio for a no growth company •

1

constant ROE

PVGO/E is the P/E component related to growth

1

1 Present Value of Growth Opportunities (PVGO) Gordon Growth Model - Justified P/E

Ø Ø

Example: ABV Inc. shares sell for $80 on future earnings per The Gordon model can also be used to calculate a share of $4.00. If the required return is 20%, compute the “justified (or fundamental)” price multiple

Justified leading P/E 1 ,

Ø PVGO.

$4.00

$80 PVGO

assuming constant dividend payout ratio

0.20

define b as the retention rate PVGO = $80-$20 = $60

D 1 P =

Market assigns 75% of the price ($60/$80) to future growth

r - g D 1 1- b

P E 1 justified leading = = E r - g r - g 1

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Ø Importance:

assuming constant dividend payout ratio define b as the retention rateGordon growth modelImplied growth rate, required return>

g r E /) D 1 ( E PJustified P/E Ø必须掌握戈登增长模型计算和适用前提，能利用戈登增长

Use the Gordon Growth Model to value preferred stock

Summary Multi-Stage Models (1)

模型计算增长率和要求回报率

Exam tips:

Content:

☆ Ø

1 )( 1 (

Valuation of Non-Callable, Fixed Rate, Perpetual, Preferred Stock Ø

)

g r g b g

Justified trailing P/E

Gordon Growth Model - Justified P/E Ø

必须掌握PVGO和justified P/E计算

Ø

The discount or capitalization rate r is often at a positive spread over the firms junior ranking debt yieldTasks:

Ø Describe terminal value and explain alternative approaches

to determining the terminal value in a DDM

Ø Calculate and interpret the value of common shares using

the two-stage DDM, the H-model, and three-stage DDM

Ø Estimate a required return based on any DDM

stage DDM, the H-model, the three-stage DDM

Ø Calculate the value of a preferred stockAnnual Dividend = $12 r = 10% Value = $12/0.10 = $120

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Ø

Fixed rate level dividends are ranked senior to equity and extend indefinitely into the future

P = Annual fixed Dividend / Capitalization rate Ø

Example:

Ø Explain the assumptions and justify the selection of the two-

Growth phase ü

= $1.00(1.09)

the terminal value is then discounted back and added to the present value of prior stage dividends

Multi-Stage DDM Models Terminal value - Example:

Postini Ltd had the following data

S

= 9.0% for four years and r = 10%

Answer: Forecasted EPS for year 4 is

4

4

fundamental such as P/E, P/B

/ 0.40 = $3.52

t

in year t

Ø

Terminal value in year 4 = 15 × $3.52 = $52.93

Two-Stage DDM Models Ø

First version of the two-stage DDM assumes:

abnormal growth

2. Gordon Growth Model Ø

1. Apply a price multiple to a projected terminal value of a

Two estimation methods:

Transition phase (transition to maturity) ü

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Multi-Stage DDM Models Ø

Growth can fall into three distinct stages:

Rapid EPS growth, negative FCF

ü

ROE > r, no or low dividend payout

Sales and EPS growth slow, dividend payout increases

ü

ROE approaching r, positive FCF

Growth at economy-wide rate, positive FCF

ü

ROE = r, high competition, saturation

Multi-Stage DDM Models Ø

mature growth phase

Ø

Mature phase ü

the whole of stage 1 represents a period of fixed andD = $1.00, payout ratio of 40%, ggrowth rate is expected to drop suddenly to a matureTrailing P/E for t = 4 is 15.0EApply trailing multiple (P/E) × forecasted EPS

-SS 08 -L2 12- S76 Dividend Growth (g) 15% 3% Stage 1 Stage 2 4 years Time the growth rate declines linearly from an abnormal rate to

growth rate at stage 2

Summary Multi-Stage Models (2)

Two-Stage DDM Models Example: BTeam, Inc., currently pays a dividend of $1.30. The

Dividend Growth (g) 15% 3%

Stage 1 Stage 2 4 years Time 7- L2 -M P2 -S S1 2- S9 45 Two-Stage DDM Models

Ø H-model:

company if it were to grow at forever

s g

L g

L S L L L D 1 g D H g g

V r g r g s g

growth rate is 25% and is expected to decline over the next 5 year horizon to a stable rate of 5% thereafter. The required return is 14%. Calculate the intrinsic value of BTeam stock using the H-Model.

Second version of the two-stage DDM assumes - H-model

[ (1 )] [ ( ]

5 [$1.30 (1.05)] [$1.30 (0.25 0.05]

2 0.14 0.05

$22.39 L S L L

D g D H g g

V r g

the mature growth rate during the course of stage 1

Two-Stage DDM Models Ø

= the extraordinary growth rate at the first stage = the mature growth rate at the second stage

L g

Two-Stage DDM Models Ø

First version of the two-stage DDM assumes:

s g

constant growth at the mature growth rate in stage 2

L L n s g r g g

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) 1 ( D 1 (

)

n t L n L n s t t s

g r r g g r g 1

) ( ) 1 ( )

V n

) 1 ( )

D 1 (

V

) 1 ( D 1 (

= the extraordinary growth rate at the first stage = the mature growth rate at the second stage H = half-life in years of the high-growth period the first term on the right-hand side is the present value of thethe second term is an approximation of the extra value accruing to the stock due to its supernormal growth for year 1 to 2H.

☆ Ø

L L L g g g )] H(g )

Content:

H-Models - Required Return - r

For H-model, the required rate of return can be derived as:

Ø Importance:

1 [( P D r s

Valuation of preferred stockEstimation of terminal valueTwo-stage DDM (H-model)掌握优先股估值计算 理解多阶段股利增长模型的假设 掌握终值的计算方法 必须掌握H-model计算，包括利用H-model推算要求回报

growth rate is 25% and is expected to decline over the next 5 year horizon to a stable rate of 5% thereafter. Calculate the implied expected return for BTeam if the market price is $30.

% 7 . 11 % 5 %)]

5 2.5(25% %)

5 1 [(

30

1.3 r

Example: BTeam, Inc., currently pays a dividend of $1.30. The

1. Three distinct phases, simply add an additional growth stage

Three-Stage DDM Models Two version of 3-stage model

Ø Exam tips: Tasks:

Ø Calculate and interpret the value of common shares using

Growth, transition, and matureHigh growth followed by linearly declining followed by

Ø Explain the use of spreadsheet modeling to forecast

dividends and to value common shares

Ø Calculate and interpret the sustainable growth rate of a

company and demonstrate the use of DuPont analysis to estimate a company’s sustainable growth rate

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to the two stage model

1. High-growth phase + H-model pattern

perpetual growth

the two-stage DDM, the H-model, and three-stage DDM

Steps:

2 $15.06

2

= $0.469 $0.30 × 1.25

3

= $0.586

7 $0.586 0.25 0.03

$0.586 1.03

0.10 0.03 0.10 0.03

1

Multi-Stage DDM Models Ø Strengths

Weaknesses

Spreadsheet Modeling Ø

Can handle any range of growth assumptions over varying periods

Ø

The most flexible method

= $0.375 $0.30 × 1.25

1.1 $0.30 × 1.25

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2

Three-Stage DDM Models Example: Netweb Inc.’s current annual growth rate of 25% is

expected to last three years and then fall linearly to a sustainable 3% over the following seven years. The most recent dividend was $0.30 and the required return on equity is 10%. Calculate the value of Netweb’s shares today.

Three-Stage DDM Models

1

2

3 D

1

= D

= D

1.1

3

= P

3

=

$12.48 $0.375 $0.469 $15.646 $0.586 + $15.06

2 3 $0.375 $0.469 $15.646

P $12.48

1.1

Ability to model many growth patterns Solve for V, g, and r ØRequire high-quality inputs (GIGO) Model must be fully understood Value estimates sensitive to g and r Model suitability very importantEstablish base level cash flows>Forecast deviations for near future (e.g., supernormal growth for first four ye>Project normal growth beyond near future Discount all cash flows to PV

Growth from internally generated sources Capital structure remains unchanged No new equity issued

the lower the earnings retention ratio, the lower the growth

Exam tips:

Ø Content:

☆ ☆

Ø Importance:

ROE m argin turnover m ultiplier

net incom e sales assets ROE sales assets equity net profit asset equity

exam (unless told otherwise) g = retention ratio*net profit margin*asset turnover*leverage

3-Part DuPont ROE Decomposition :

SGR: The Sustainable Growth Rate Ø

SGR = Retention rate× ROE SGR = (1 – 0.25) × 10% = 7.5%

Compute SGR.

SGR: The Sustainable Growth Rate Example: Green, Inc. pays out 25% of it’s $1.00 of earnings as dividends, BVPS is $10.00 therefore Green earns an ROE of 10%.

rate ( dividend displacement of earnings )

g = retention rate×ROE

SGR (g) = sustainable growth rate in earnings and dividends if we assume:

SGR: The Sustainable Growth Rate Ø

Three-stage DDM>Spreadsheet modeSustainable growth rate ØNote: Always use beginning of year balance sheet numbers on重点掌握三阶段估值模型 理解持续增长率的假设，能利用杜邦系统评估持续增长率

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Summary

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Introduction to Free Cash Flows Ø

Dividends are the cash flows actually paid to stockholders

Ø

Free cash flows are the cash flows available for distribution

Introduction to FCFF and FCFE

after fulfilling all obligations (operating expenses and taxes)Tasks:

and without impacting on the future growth plans of the

Ø Compare the free cash flow to the firm and free cash flow to

company (working capital and fixed capital) equity approaches to valuation

Ø Explain the ownership perspective implicit in the FCFE

approach

Introduction to Free Cash Flows Introduction to Free Cash Flows

Ø Strengths

Ø FCFF (Free Cash Flow to the Firm)

Used with firms that have no dividends

Cash available to shareholders and bondholders after taxes,

Functional model for assessing alternative financing

capital investment, and WC investment, pre-levered cash flow policies

FCFE (Free Cash Flow to Equity)

Ø

Rich framework provides additional detailed insights into company Cash available to equity holders after payments to and

Other measures such as EBIT, EBITDA, and CFO either • inflows from bondholders, post-leverage cash flow double count or omit important cash flows

Not equal to dividends actually paid

Ø Limitations

If FCF < 0 due to large capital demands •

Requires detailed understanding of accounting and FSAInformation not readily available or published

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Ability to change dividend policyStrengths and limitations of FCF modelsUsed in control perspectiveOwnership perspectives of FCF

FCF Formula References Ø

Ø NCC = net non-cash charges

Ownership Perspective Ø

FCFE = control perspective

Ø DDM = minority owner

Ø Importance:

☆ Ø

Content:

Ø Exam tips:

Summary Calculation of FCFF and FCFE (1)

理解自由现金流模型的优缺点 理解自由现金流的所有权角度No control Used in valuing minority position in publicly traded shares

dividends but before common dividends

NI = Net income to common shareholders, after preferredTasks:

Calculate FCFF and FCFE

Explain the appropriate adjustments to net income to calculate FCFF and FCFE

Ø

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Ø Int(1-t) = after tax interest expense

Ø FCInv = net fixed capital investment (capital expenditure less

proceeds from sales)

Ø WCInv = working capital investment excluding cash and short-

term debt (notes payable and current portion of long-term debt)

Ø Net borrowings = new debt – repayments

Ø

A decrease in an asset account is a source (addition/plus) of cash

Net investment in working capital for the purpose of calculating FCF excludes

Ø

An increase in an asset account is a use (negative/subtraction) of cash

Ø

There is an inverse relationship between changes in assets and changes in cash flow

Investment in Working Capital Ø

The exclusions are considered financing activities not operating items and therefore not included in WCInv

Investment in Working Capital Ø

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Noncash Adjustment Noncash Item adjustment to NI depreciation added back amortization and impairment of intangibles added back restructuring expenses added back restructuring charges (income from reversal) subtracted losses added back gains subtracted amortization of long-term bond discounts added back amortization of long-term premiums subtracted

Ø FCFE = NI + NCC – WCInv – FCInv + Net borrowing

Ø FCFE = FCFF – Int(1 – t) + Net borrowing

Subtracting after-tax interest and adding back net borrowing from the FCFF equations gives us the FCFE from NI

FCFF = NI + NCC + Int(1– t) – WCInv – FCInv Ø

FCFF and FCFE Beginning with Net Income Ø

changes in cash/cash equivalents notes payable current portion of L.T. debt ØInvestment in Working Capital

5 20 (15) Use/Subtract WCInv = –15

10 Use/Subtract WCInv = –10

Accounting receivable 25 30 (5) Source/Add

WCInv = +5 Accounting payable

30

10

20 Source/Add WCInv = +20

Accrued Expenses

Net FCInv Adjustments Ø

50

Investments in fixed capital (FCInv) represent a cash out flow necessary to support the company's current and future operations

Ø

Viewed as a capital expenditure (Cap Ex) that reduces both FCFE and FCFF

Ø

Expenditures can include acquisition of intangible items such as trademarks

Ø

Care should be used with non-recurring large acquisitions in forecasts

40

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Investment in Working Capital Ø

Decrease ↓FCF

There is a direct relationship between changes in liabilities and changes in cash flow

Ø

An increase in a liability account is a source (addition/plus) of cash

Ø

A decrease in a liability is a use (negative/subtraction) of cash

Investment in Working Capital

Increase in WCInv

Decrease in WCInv

Accrued Taxes & Expenses ↑ Accrued Taxes & Expenses

Increase ↑ FCF

Increase in Assets or Decrease in Liabilities

Decrease in Assets or Increase in Liabilities

↑ Inventory

↓ Inventory

↑ Accounts Receivable ↓ Accounts Receivable ↓

Accounts Payable ↑

Accounts Payable ↓

Account 2009 2008 Change Source/Use Inventory

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Net FCInv Adjustments Net FCInv Adjustments

Ø Ø

If given gross PP&E on the balance sheet, identify the the analyst must deduct this cash in arriving at the net • additions (cap ex) by taking the year over year change in investment in PP&E (FCInv)

Ø

gross PP&E, only if there were no disposals during the period, Gain/Loss on asset sale = Proceeds from sale – book value of to identify the capital expenditures for the period asset

Ø

If given net PP&E, use the equation: Subtract gains on sales from NI

Ø

Ending net PP&E = Beginning net PP&E – Depreciation + Add losses on sales to NI

Ø Assets purchased – Book value of assets sold

Deduct the proceeds from sale in arriving at the net FCInv

Net Borrowing Adjustments Net Borrowing Adjustments

Ø Ø

&em