Chapter 11 AN INTRODUCTION TO VALUATION. Chapter 11 Questions When valuing an asset, what are the required inputs?When valuing an asset, what are the

Chapter 11Chapter 11

AN INTRODUCTION TO AN INTRODUCTION TO VALUATIONVALUATION

Chapter 11 QuestionsChapter 11 Questions

• When valuing an asset, what are the When valuing an asset, what are the required inputs?required inputs?

• After we have valued an asset, what is After we have valued an asset, what is the investment decision process?the investment decision process?

• What are the tow major approaches to What are the tow major approaches to the investment decision process?the investment decision process?

• What are the specifics and logic of the What are the specifics and logic of the top-down, three-step approach?top-down, three-step approach?


• How do we determine the value of bonds?How do we determine the value of bonds?• What causes a change in the value of a What causes a change in the value of a

bond?bond?• How do we determine the value of preferred How do we determine the value of preferred

stock?stock?• What are the two primary approaches to the What are the two primary approaches to the

valuation of common stock?valuation of common stock?• Under what conditions is it best to use the Under what conditions is it best to use the

present value of cash flow approach for present value of cash flow approach for valuing a company’s equity?valuing a company’s equity?


• What conditions make it appropriate to use What conditions make it appropriate to use the relative valuation techniques for valuing a the relative valuation techniques for valuing a company’s equity?company’s equity?

• What are the major discounted cash flow What are the major discounted cash flow valuation techniques?valuation techniques?

• What is the dividend discount model (DDM), What is the dividend discount model (DDM), and what is its logic?and what is its logic?

• What is the effect of the assumptions of the What is the effect of the assumptions of the DDM when valuing a growth company?DDM when valuing a growth company?


• How do we apply the DDM to the valuation of How do we apply the DDM to the valuation of a firm that is expected to experience a firm that is expected to experience temporary supernormal growth?temporary supernormal growth?

• How do we apply the present value of How do we apply the present value of operating cash flow technique?operating cash flow technique?

• How do we apply the present value of free How do we apply the present value of free cash flow to equity technique?cash flow to equity technique?

• How do we apply the relative valuation How do we apply the relative valuation approach?approach?

• What are the major relative valuation ratios?What are the major relative valuation ratios?


• What does the DDM imply are the factors that What does the DDM imply are the factors that determine a stock’s P/E ratio?determine a stock’s P/E ratio?

• What two general variables need to be What two general variables need to be estimated in any valuation approach?estimated in any valuation approach?

• How do we estimate the major inputs to the How do we estimate the major inputs to the stock valuation models: (1) the required rate stock valuation models: (1) the required rate of return and (2) the expected growth rate of of return and (2) the expected growth rate of earnings, cash flows, and dividends?earnings, cash flows, and dividends?

What determines the What determines the value of an asset?value of an asset?

• The value of a financial asset is the The value of a financial asset is the present value of expected future cash present value of expected future cash flows received from the assetflows received from the asset

• Required inputs:Required inputs:– A discount rate used to calculate the A discount rate used to calculate the

present value of the cash flowspresent value of the cash flows– The stream of expected future cash flowsThe stream of expected future cash flows

Discount RateDiscount Rate

Determined by:Determined by:1.1. The real risk-free rate of return (to The real risk-free rate of return (to

compensate for the time for which funds compensate for the time for which funds are invested), plusare invested), plus

2.2. The expected rate of inflation, plusThe expected rate of inflation, plus3.3. A risk premium to compensate for the A risk premium to compensate for the

uncertainty of returnsuncertainty of returns• Sources of uncertainty, and therefore risk Sources of uncertainty, and therefore risk

premiums, vary by the type of investmentpremiums, vary by the type of investment

Stream of Expected Cash Stream of Expected Cash FlowsFlows

Types of cash flowsTypes of cash flows• Depending on the investment, cash flows can Depending on the investment, cash flows can

be in the form of:be in the form of:– DividendsDividends– Interest paymentsInterest payments– Capital gainsCapital gains

• Cash flows are sometimes easy to estimate Cash flows are sometimes easy to estimate (E.g. Government bonds) but can also be (E.g. Government bonds) but can also be very difficult to estimate (E.g. Growth stocks)very difficult to estimate (E.g. Growth stocks)

Investment Decision Investment Decision ProcessProcess

• Once expected (intrinsic) value is Once expected (intrinsic) value is calculated, the investment decision is calculated, the investment decision is rather straightforward and intuitive:rather straightforward and intuitive:– If Estimated Value > Market Price, buyIf Estimated Value > Market Price, buy– If Estimated Value < Market Price, do not If Estimated Value < Market Price, do not

buybuy

• The particulars of the valuation process The particulars of the valuation process vary by type of investmentvary by type of investment

The Valuation ProcessThe Valuation Process

• Two basic approaches:Two basic approaches:– Top-down, three-step approachTop-down, three-step approach– Bottom-up, stock-picking approachBottom-up, stock-picking approach

General Approaches to General Approaches to Security AnalysisSecurity Analysis

• Top-Down Approach (Our focus)Top-Down Approach (Our focus)1.1. Review the macro-economyReview the macro-economy2.2. Analyze different industries and sectorsAnalyze different industries and sectors3.3. Determine buy/sell candidatesDetermine buy/sell candidates

• Bottom-up ApproachBottom-up Approach– Focus primarily on the firm-specific Focus primarily on the firm-specific

factors that will lead to finding factors that will lead to finding undervalued companies, regardless of undervalued companies, regardless of industry or macroeconomic factorsindustry or macroeconomic factors

A Three-Step ProcessA Three-Step Process

• Within the three-step process of the Within the three-step process of the top-down approach, all steps are crucialtop-down approach, all steps are crucial

• General economic influencesGeneral economic influences– Government policies strongly influence the Government policies strongly influence the

economic environment, leading to economic environment, leading to profound effects on industriesprofound effects on industries

– We can see the influence of changes in We can see the influence of changes in the overall economy on various classes of the overall economy on various classes of investmentsinvestments


• Industry InfluencesIndustry Influences– We seek to determine which industries will likely We seek to determine which industries will likely

do better than others in the expected economic do better than others in the expected economic environmentenvironment

– Also, changing demographic factors have different Also, changing demographic factors have different effects across industrieseffects across industries

• Company AnalysisCompany Analysis– Individual investments will either make or break Individual investments will either make or break

portfolio performanceportfolio performance– Once well-positioned industries are determined, Once well-positioned industries are determined,

find well-positioned firms within those industriesfind well-positioned firms within those industries


• There is academic support for this top-down There is academic support for this top-down approachapproach– Most changes in individual companies’ earnings Most changes in individual companies’ earnings

related to changes in aggregate earnings and related to changes in aggregate earnings and changes in a firm’s industrychanges in a firm’s industry

– There is a relationship between stock and bond There is a relationship between stock and bond prices and macroeconomic variablesprices and macroeconomic variables

– Rates of return for individual stocks can be Rates of return for individual stocks can be explained by the aggregate stock market and the explained by the aggregate stock market and the firm’s industryfirm’s industry


Three cheers for the Three cheers for the three-step process!three-step process!

Review of Valuation Review of Valuation ComponentsComponents

• The value of a financial asset is the The value of a financial asset is the present value of its expected future present value of its expected future cash flowscash flows

• Two components:Two components:– The required rate of return on the The required rate of return on the

investmentinvestment– The stream of expected future returns, or The stream of expected future returns, or

cash flowscash flows

Required Rate of ReturnRequired Rate of Return

• Determined by the risk of an investment Determined by the risk of an investment and available returns in the marketand available returns in the market

• Determined by:Determined by:1.1. The real risk-free rate of return, plusThe real risk-free rate of return, plus

2.2. The expected rate of inflation, plusThe expected rate of inflation, plus

3.3. A risk premium to compensate for the A risk premium to compensate for the uncertainty of returnsuncertainty of returns

• Sources of uncertainty, and therefore risk premiums, Sources of uncertainty, and therefore risk premiums, vary by the type of investmentvary by the type of investment

Stream of Expected Stream of Expected Returns (Cash Flows)Returns (Cash Flows)

From of returnsFrom of returns• Depending on the investment, returns can be Depending on the investment, returns can be

in the form of:in the form of:– EarningsEarnings– DividendsDividends– Interest paymentsInterest payments– Return of principalReturn of principal

Time period and growth rate of returnsTime period and growth rate of returns• When will the cash flows be received from When will the cash flows be received from

the investment?the investment?

Valuation of Alternative Valuation of Alternative InvestmentsInvestments

We will consider the valuation of three We will consider the valuation of three important types of investments:important types of investments:

• The valuation of bondsThe valuation of bonds

• The valuation of preferred stockThe valuation of preferred stock

• The valuation of common stockThe valuation of common stock

Valuation of BondsValuation of Bonds

What are the cash flows?What are the cash flows?• Bond cash flows (typically fixed)Bond cash flows (typically fixed)

– Interest payments every six months equal to one-Interest payments every six months equal to one-half of: (Coupon rate x Face value)half of: (Coupon rate x Face value)

– The payment of principal (Face or par value) at The payment of principal (Face or par value) at maturitymaturity

• Discount at the required rate of return to find Discount at the required rate of return to find the bond’s valuethe bond’s value

• Process made relatively easy with a financial Process made relatively easy with a financial calculator or spreadsheet softwarecalculator or spreadsheet software

Bond Valuation PrinciplesBond Valuation Principles

• The value of a bond moves in the The value of a bond moves in the opposite direction of the discount rateopposite direction of the discount rate

• For a given change in the discount rate, For a given change in the discount rate, the change in value will differ the change in value will differ depending on the characteristics of the depending on the characteristics of the bondbond– More on this in Chapter 12More on this in Chapter 12

Valuation of Preferred Valuation of Preferred StockStock

• What are the cash flows?What are the cash flows?– Preferred stock cash flowsPreferred stock cash flows

• Stated, usually fixed, dividends for an infinite Stated, usually fixed, dividends for an infinite periodperiod

• Since there is no maturity, the payments Since there is no maturity, the payments represent a perpetuityrepresent a perpetuity


• The discount rate on preferred stockThe discount rate on preferred stock– Payment by the firm does not carry the same legal Payment by the firm does not carry the same legal

obligation as with bond cash flows, so preferred is obligation as with bond cash flows, so preferred is more risk indicating the discount rate should be more risk indicating the discount rate should be higher than the bonds of the same corporationhigher than the bonds of the same corporation

– Preferred dividends have a tax advantage over Preferred dividends have a tax advantage over interest income from bonds for some investors, interest income from bonds for some investors, indicating a lower required rate of returnindicating a lower required rate of return

• The yield on preferred is generally lower than The yield on preferred is generally lower than the yield on high quality bondsthe yield on high quality bonds


• Present value of a perpetuity:Present value of a perpetuity:

V = PMT/Discount rateV = PMT/Discount rate

• Value of Preferred Stock:Value of Preferred Stock:

V = Dividend/kV = Dividend/kPP

• kkPP = Required Return on Preferred = Required Return on Preferred

• Yield on Preferred Stock:Yield on Preferred Stock:

kkPP = Dividend/Price = Dividend/Price

Approaches to Common Approaches to Common Stock ValuationStock Valuation

• Discounted Cash Flow TechniquesDiscounted Cash Flow Techniques– Present value of Dividends (DDM)Present value of Dividends (DDM)– Present value of Operating Cash FlowPresent value of Operating Cash Flow– Present value of Free Cash FlowPresent value of Free Cash Flow

• Relative valuation techniquesRelative valuation techniques– Price-earnings ratio (P/E)Price-earnings ratio (P/E)– Price-cash flow ratios (P/CF)Price-cash flow ratios (P/CF)– Price-book value ratios (P/BV)Price-book value ratios (P/BV)– Price-sales ratio (P/S)Price-sales ratio (P/S)

When to Use Discounted When to Use Discounted Cash Flow ValuationCash Flow Valuation

• What is the measure of cash flow?What is the measure of cash flow?– DividendsDividends

• These cash flows that go straight to the These cash flows that go straight to the investor, and would be discounted at the investor, and would be discounted at the required return on the stockrequired return on the stock

• Difficult to apply to firms that pay low or no Difficult to apply to firms that pay low or no dividends because of growth opportunitiesdividends because of growth opportunities

• Most applicable to stable, mature firms where Most applicable to stable, mature firms where the assumption of relatively constant growth for the assumption of relatively constant growth for the long term is appropriatethe long term is appropriate


• What is the measure of cash flow?What is the measure of cash flow?– Free cash flow to equityFree cash flow to equity

• Measure of cash flows available to equity Measure of cash flows available to equity holders, including those retained by the firm, holders, including those retained by the firm, would be discounted at the firm’s cost of equitywould be discounted at the firm’s cost of equity

– Operating free cash flowOperating free cash flow• Measure of cash flows available to all suppliers Measure of cash flows available to all suppliers

of capital to a firm, would be discounted the of capital to a firm, would be discounted the firm’s weighted average cost of capitalfirm’s weighted average cost of capital


• Potential difficulty is that estimates of value Potential difficulty is that estimates of value are highly dependent on two important are highly dependent on two important inputs:inputs:– The growth rates of cash flowsThe growth rates of cash flows– The estimate of the appropriate discount rateThe estimate of the appropriate discount rate

• Small changes can be drastic differencesSmall changes can be drastic differences• GIGOGIGO

When to Use Relative When to Use Relative ValuationValuation

• Relative valuation focuses on how the Relative valuation focuses on how the market is currently valuing financial market is currently valuing financial assetsassets– This does not necessarily imply that This does not necessarily imply that

current valuations are appropriatecurrent valuations are appropriate– The overall market or a particular industry The overall market or a particular industry

can become seriously overvalued or can become seriously overvalued or undervalued for a period of timeundervalued for a period of time

When to Use Relative When to Use Relative ValuationValuation

• Appropriate to use under two Appropriate to use under two conditions:conditions:– You have a good set of comparable You have a good set of comparable

entities entities • Similar size, risk, etc.Similar size, risk, etc.

– The aggregate market or the relevant The aggregate market or the relevant industry is not at a valuation extremeindustry is not at a valuation extreme• It is fairly valuedIt is fairly valued

Which approach to use?Which approach to use?

• No need to choose!No need to choose!

• The best approach is to use both The best approach is to use both approaches to come up with the best approaches to come up with the best valuation estimate possible.valuation estimate possible.

Discounted Cash Flow Discounted Cash Flow TechniquesTechniques

• Based on the basic valuation model: the Based on the basic valuation model: the value of a financial asset is the present value of a financial asset is the present value of its expected future cash flowsvalue of its expected future cash flows

VVjj = = CFCFtt/(1+k)/(1+k)tt

• The different discounted cash flow The different discounted cash flow techniques consider different cash flows techniques consider different cash flows and also different appropriate discount and also different appropriate discount ratesrates

Dividend Discount ModelsDividend Discount Models

Simplifying assumptions help in estimating Simplifying assumptions help in estimating present value of future dividendspresent value of future dividends

VVjj = = DDtt/(1+k)/(1+k)tt

• Can also assume various dividends for a Can also assume various dividends for a finite period of time with a reselling price, and finite period of time with a reselling price, and simply calculate the combined present value simply calculate the combined present value of the dividendsof the dividends


Infinite Period DDMInfinite Period DDM• Constant Growth Model:Constant Growth Model:

– Assumes dividends started at DAssumes dividends started at D00 (last year’s (last year’s

dividend) and will grow at a constant growth rate dividend) and will grow at a constant growth rate – Growth will continue for an infinite period of timeGrowth will continue for an infinite period of time– The required return (k) is greater than the The required return (k) is greater than the

constant rate of growth (g)constant rate of growth (g)

V = DV = D11/(k-g)/(k-g)

where Dwhere D11= D= D00(1+g)(1+g)


• Constant Growth ModelConstant Growth Model– Growth rate Growth rate

• Can be estimated from past growth in earnings Can be estimated from past growth in earnings and dividendsand dividends

• Can be estimated using the sustainable growth Can be estimated using the sustainable growth modelmodel

– Discount rateDiscount rate• The required rate of return on the stockThe required rate of return on the stock


• Valuation with Temporary Supernormal Valuation with Temporary Supernormal GrowthGrowth

– If you expect a company to experience rapid If you expect a company to experience rapid growth for some period of timegrowth for some period of time

1.1. Find the present value of each dividend during the Find the present value of each dividend during the supernormal growth period separatelysupernormal growth period separately

2.2. Find the present value of the remaining dividends Find the present value of the remaining dividends as of the beginning of the period when constant as of the beginning of the period when constant growth starts.growth starts.

3.3. Find the present value of the remaining dividends Find the present value of the remaining dividends by finding the present value of the estimate by finding the present value of the estimate obtained in step 2.obtained in step 2.

Present Value of Operating Present Value of Operating Cash FlowsCash Flows

• Another discounted cash flow approach Another discounted cash flow approach is to discount operating cash flows is to discount operating cash flows – Operating cash flows are pre-interest cash Operating cash flows are pre-interest cash

flows, so the required rate of return would flows, so the required rate of return would be adjusted to incorporate the required be adjusted to incorporate the required returns of all investors (use the WACC)returns of all investors (use the WACC)

VVFjFj = = OCFOCFtt/(1+WACC/(1+WACCjj))tt

Present Value of Operating Present Value of Operating Cash FlowsCash Flows

• If we further assume a growth rate of If we further assume a growth rate of ggOCFOCF for operating cash flows, we can for operating cash flows, we can

value the firm as:value the firm as:

VVFjFj = OCF = OCFtt/(WACC/(WACCjj – g – gOCFOCF))

Present Value of Free Cash Present Value of Free Cash Flow to EquityFlow to Equity

• A third discounted cash flow technique A third discounted cash flow technique is to consider the free cash flows of a is to consider the free cash flows of a firm available to equity as the cash flow firm available to equity as the cash flow stream to be discounted.stream to be discounted.

• Since this is an equity stream, the Since this is an equity stream, the appropriate discount rate is the required appropriate discount rate is the required return on equityreturn on equity

VVSjSj = = FCFFCFtt/(1+k/(1+kjj))tt

Present Value of Free Cash Present Value of Free Cash Flow to EquityFlow to Equity

• Once again, if we constant growth in Once again, if we constant growth in free cash flows, this expression free cash flows, this expression reduces to the followingreduces to the following

VVSjSj = FCF = FCFtt/(k/(kjj – g – gFCFFCF))

Relative Valuation Relative Valuation TechniquesTechniques

These techniques assume that prices These techniques assume that prices should have stable and consistent should have stable and consistent relationships to various firm variables relationships to various firm variables across groups of firmsacross groups of firms

• Price-Earnings RatioPrice-Earnings Ratio• Price-Cash Flow RatioPrice-Cash Flow Ratio• Price-Book Value RatioPrice-Book Value Ratio• Price-Sales RatioPrice-Sales Ratio

Relative Valuation Relative Valuation TechniquesTechniques

• Price Earnings RatioPrice Earnings Ratio– Earnings Multiplier ModelEarnings Multiplier Model– Affected by two variables:Affected by two variables:

1. Required rate of return on its equity (k)1. Required rate of return on its equity (k)

2. Expected growth rate of dividends (g)2. Expected growth rate of dividends (g)

gk

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Price-Earnings RatioPrice-Earnings Ratio

• Look at the relationship between the Look at the relationship between the current market price and expected current market price and expected earnings per share over the next yearearnings per share over the next year– The ratio is the earnings multiplier, and is a The ratio is the earnings multiplier, and is a

measure of the prevailing attitude of measure of the prevailing attitude of investors regarding a stock’s valueinvestors regarding a stock’s value

• P/E factorsP/E factors– Expected growth in dividends and earningsExpected growth in dividends and earnings– Required rate of return on the stockRequired rate of return on the stock

Price-Earnings RatioPrice-Earnings Ratio

• Using the P/E approach to valuation:Using the P/E approach to valuation:1.1. Estimate earnings for next yearEstimate earnings for next year2.2. Estimate the P/E ratio (Earnings Estimate the P/E ratio (Earnings

Multiplier)Multiplier)3.3. Multiply expected earnings by the Multiply expected earnings by the

expected P/E ratio to get expected expected P/E ratio to get expected priceprice

V =EV =E11x(P/E)x(P/E)

Price-Cash Flow RatioPrice-Cash Flow Ratio

• Cash flows can also be used in this Cash flows can also be used in this approach, and are often considered approach, and are often considered less susceptible to manipulation by less susceptible to manipulation by management.management.

• The steps are similar to using the P/E The steps are similar to using the P/E ratioratio

V =CFV =CF11x(P/CF)x(P/CF)

Price-Book Value RatioPrice-Book Value Ratio

• Book values can also be used as a Book values can also be used as a measure of relative valuemeasure of relative value

• The steps to obtaining valuation The steps to obtaining valuation estimates are again similar to using the estimates are again similar to using the P/E ratioP/E ratio

V =BVV =BV11x(P/BV)x(P/BV)

Price-Sales RatioPrice-Sales Ratio

• Finally, sales can be used in relation to stock Finally, sales can be used in relation to stock price. price. – Some drawbacks, in that sales do not necessarily Some drawbacks, in that sales do not necessarily

produce profit and positive cash flowsproduce profit and positive cash flows– Advantage is that sales are also less susceptible Advantage is that sales are also less susceptible

to manipulationto manipulation

• The steps are similar to using the P/E ratioThe steps are similar to using the P/E ratio

V =SV =S11x(P/S)x(P/S)

Implementing the Relative Implementing the Relative Valuation TechniqueValuation Technique

1.1. Compare the valuation ratio for the Compare the valuation ratio for the company to the comparable ratio for company to the comparable ratio for the market, industry, and other firmsthe market, industry, and other firms

2.2. Explain the relationshipExplain the relationship• Why is the ratio similar or different?Why is the ratio similar or different?• Do fundamental factors justify a Do fundamental factors justify a

difference in relative valuation?difference in relative valuation?

Estimating the InputsEstimating the Inputs

• Two critical inputs common on most Two critical inputs common on most valuation models:valuation models:– The Required Rate of ReturnThe Required Rate of Return– Expected Growth RatesExpected Growth Rates

The Required Rate of The Required Rate of ReturnReturn

• Three influences:Three influences:– The economy’s real risk-free rate (RRFR)The economy’s real risk-free rate (RRFR)– The expected rate of inflation E(I)The expected rate of inflation E(I)– A risk premiumA risk premium

• The first two influences collectively determine The first two influences collectively determine the nominal risk-free rate (NRFR):the nominal risk-free rate (NRFR):

NRFR = [1 + RRFR] [1 + E(I)] – 1NRFR = [1 + RRFR] [1 + E(I)] – 1

The Required Rate of The Required Rate of ReturnReturn

• The risk premium varies between different The risk premium varies between different securities, due to differences in:securities, due to differences in:– Business risk, financial risk, liquidity riskBusiness risk, financial risk, liquidity risk– Additionally, exchange rate risk, political risk for Additionally, exchange rate risk, political risk for

international investmentsinternational investments

• Risk premiums change over time as investors Risk premiums change over time as investors attitudes toward risk and expectations of the attitudes toward risk and expectations of the future changefuture change

Expected Growth RatesExpected Growth Rates

• Often need growth rates to estimate Often need growth rates to estimate future values for cash flowsfuture values for cash flows

• Estimating growth from fundamentalsEstimating growth from fundamentalsg = (Retention Rate) x (Return on Equity)g = (Retention Rate) x (Return on Equity)

• Growth is a function of earnings Growth is a function of earnings retention, profitability, asset turnover, retention, profitability, asset turnover, the use of leverage (Modified DuPont)the use of leverage (Modified DuPont)

ROE = NPM x TAT x FLMROE = NPM x TAT x FLM

Estimating Growth RatesEstimating Growth Rates

• Estimating growth based on historyEstimating growth based on history– Can look at historic averages in growthCan look at historic averages in growth

• Geometric or arithmetic meansGeometric or arithmetic means

– Can use various modelsCan use various models• Linear regression:Linear regression:

EPSEPStt = a + b = a + btt

• Log-linear regression:Log-linear regression:

ln (EPSln (EPStt) = a + b) = a + btt

Documents

Chapter 11 AN INTRODUCTION TO VALUATION. Chapter 11 Questions When valuing an asset, what are the required inputs?When valuing an asset, what are the