1 Chapter 7 Brief History of Risk and Return Ayşe Yüce – Ryerson University Copyright © 2012...

1

Chapter 7Brief History of Risk and Return

Ayşe Yüce – Ryerson UniversityAyşe Yüce – Ryerson University Copyright © 2012 McGraw-Hill RyersonCopyright © 2012 McGraw-Hill Ryerson

222Ayşe Yüce – Ryerson UniversityAyşe Yüce – Ryerson University Copyright © 2012 McGraw-Hill RyersonCopyright © 2012 McGraw-Hill Ryerson

Learning ObjectivesLearning Objectives

Separate yourself from the commoners by having a good

understanding of these security valuation methods:

1. The basic dividend discount model.2. The two-stage dividend growth model.3. The residual income model and free

cash flow model.

4. Price ratio analysis.

333

Common Stock ValuationCommon Stock Valuation


Our goal in this chapter is to examine the methods commonly used by financial analysts to assess the economic value of common stocks.

These methods are grouped into four categories:Dividend discount modelsResidual Income modelFree Cash Flow modelPrice ratio models


Security Analysis: Be Careful Out Security Analysis: Be Careful Out ThereThere

Fundamental analysis is a term for studying a company’s accounting statements and other financial and economic information to estimate the economic value of a company’s stock.

The basic idea is to identify “undervalued” stocks to buy and “overvalued” stocks to sell.

In practice however, such stocks may in fact be correctly priced for reasons not immediately apparent to the analyst.


The Dividend Discount ModelThe Dividend Discount Model

The Dividend Discount Model (DDM) is a method to estimate the value of a share of stock by discounting all expected future dividend payments. The basic DDM equation is:

In the DDM equation:P0 = the present value of all future dividendsDt = the dividend to be paid t years from now k = the appropriate risk-adjusted discount

rate

TT

33

221

0k1

D

k1

D

k1

D

k1

DP


Example: The Dividend Discount Example: The Dividend Discount ModelModel

Suppose that a stock will pay three annual dividends of $200 per year, and the appropriate risk-adjusted discount rate, k, is 8%.

In this case, what is the value of the stock today?

$515.42

0.081

$200

0.081

$200

0.081

$200P

k1

D

k1

D

k1

DP

320

33

221

0

777

The Dividend Discount Model: The Dividend Discount Model:

The Constant Growth Rate ModelThe Constant Growth Rate Model


Assume that the dividends will grow at a constant growth rate g. The dividend in the next period, (t + 1), is:

For constant dividend growth for “T” years, the DDM formula becomes:

g)(1g)(1D g)(1 D D So,

g1DD

012

t1t

g k if D T P

g k if k1

g11

gk

g)(1DP

00

T

10


Example: The Constant Growth Rate Example: The Constant Growth Rate ModelModel

Suppose the current dividend is $10, the dividend growth rate is 10%, there will be 20 yearly dividends, and the appropriate discount rate is 8%.

What is the value of the stock, based on the constant growth rate model?

$243.86

1.08

1.101

.10.08

1.10$10P

k1

g11

gk

g)(1DP

20

0

T

00


The Dividend Discount Model: The Dividend Discount Model: The Constant Perpetual Growth ModelThe Constant Perpetual Growth Model

Assuming that the dividends will grow forever at a constant growth rate g.

For constant perpetual dividend growth, the DDM formula becomes:

k)g :(Important

gk

D

gk

g1DP 10

0


Example: Constant Perpetual Growth Example: Constant Perpetual Growth ModelModel

Think about the electric utility industry. In 2009, the dividend paid by the utility company, DTE

Energy Co. (DTE), was $2.12. Using D0 =$2.12, k = 5.75%, and g = 2%, calculate an

estimated value for DTE.

Note: the actual mid-2009 stock price of DTE was $40.29.

What are the possible explanations for the difference?

$57.66

.02.05751.02$2.12

P0


The Dividend Discount Model:The Dividend Discount Model:Estimating the Growth RateEstimating the Growth RateThe growth rate in dividends (g) can be

estimated in a number of ways:

Using the company’s historical average growth rate.

Using an industry median or average growth rate.

Using the sustainable growth rate.


The Historical Average Growth Rate The Historical Average Growth Rate

Suppose the Broadway Joe Company paid the following dividends:

2005: $1.50 2008: $1.80 2006: $1.70 2009: $2.00 2007: $1.75 2010: $2.20

The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages.

Year: Dividend: Pct. Chg:2010 $2.20 10.00%2009 $2.00 11.11%2008 $1.80 2.86% Grown at2007 $1.75 2.94% Year: 7.96%:2006 $1.70 13.33% 2005 $1.502005 $1.50 2006 $1.62

2007 $1.758.05% 2008 $1.89

2009 $2.047.96% 2010 $2.20

Arithmetic Average:

Geometric Average:


The Sustainable Growth RateThe Sustainable Growth Rate

Ratio) Payout - (1 ROE

Ratio Retention ROE Rate Growth eSustainabl

Return on Equity (ROE) = Net Income / Equity

Payout Ratio = Proportion of earnings paid out as dividends

Retention Ratio = Proportion of earnings retained for investment


Example: Calculating and Using the Example: Calculating and Using the Sustainable Growth RateSustainable Growth Rate

In 2009, American Electric Power (AEP) had an ROE of 10%, projected earnings per share of $2.90, and a per-share dividend of $1.64. What was AEP’s:Retention rate?Sustainable growth rate?

Payout ratio = $1.64 / $2.90 = .566 or 56.6%

So, retention ratio = 1 – .566 = .434 or 43.4%

Therefore, AEP’s sustainable growth rate = .10 .434 = .0434, or 4.34%


Example: Calculating and Using the Example: Calculating and Using the Sustainable Growth RateSustainable Growth Rate What is the value of AEP stock using the perpetual growth

model and a discount rate of 5.75%?

The actual late-2009 stock price of AEP was $31.83.

In this case, using the sustainable growth rate to value the stock gives a reasonably poor estimate.

What can we say about g and k in this example?

$121.36

.0434.05751.0434$1.64

P

0


Analyzing ROEAnalyzing ROE To estimate a sustainable growth rate, you need the

(relatively stable) dividend payout ratio and ROE. Changes in sustainable growth rate likely stem from

changes in ROE. The DuPont formula separates ROE into three parts (profit

margin, asset turnover, equity multiplier)

Managers can increase the sustainable growth rate by:Decreasing the dividend payout ratioIncreasing profitability (Net Income / Sales)Increasing asset efficiency (Sales / Assets)Increasing debt (Assets / Equity)

EquityAssets

AssetsSales

SalesIncome Net

ROEEquity

Income Net


The Two-Stage Dividend Growth The Two-Stage Dividend Growth ModelModelThe two-stage dividend growth model

assumes that a firm will initially grow at a rate g1 for T years, and thereafter, it will

grow at a rate g2 < k during a perpetual second stage of growth.

The Two-Stage Dividend Growth Model formula is:

2

20

T

1

T

1

1

10

gk

)g(1D

k1

g1

k1

g11

gk

)g(1DP

0


Using the Two-Stage Dividend Growth Using the Two-Stage Dividend Growth

ModelModel Although the formula looks complicated, think

of it as two parts:Part 1 is the present value of the first T

dividends (it is the same formula we used for the constant growth model).

Part 2 is the present value of all subsequent dividends.

So, suppose MissMolly.com has a current dividend of D0 = $5, which is expected to shrink at the rate, g1 = 10%, for 5 years but grow at the rate, g2 = 4%, forever.

With a discount rate of k = 10%, what is the present value of the stock?

http://www.missmolly.com/


Using the Two-Stage Dividend Growth Using the Two-Stage Dividend Growth ModelModel

$46.03.

$31.78 $14.25

0.040.10

0.04)$5.00(1

0.101

0.90

0.101

0.901

0.10)(0.10

)$5.00(0.90P

gk

)g(1D

k1

g1

k1

g11

gk

)g(1DP

55

2

20

T

1

T

1

1

10

0

0

The total value of $46.03 is the sum of a $14.25 present value of the first five dividends, plus a $31.78 present value of all subsequent dividends.


Example: Using the DDM to Value a Firm Example: Using the DDM to Value a Firm Experiencing “Supernormal” GrowthExperiencing “Supernormal” Growth

Chain Reaction, Inc., has been growing at a phenomenal rate of 30% per year.

You believe that this rate will last for only three more years.

Then, you think the rate will drop to 10% per year.

Total dividends just paid were $5 million.

The required rate of return is 20%.

What is the total value of Chain Reaction, Inc.?


Example: Using the DDM to Value a Example: Using the DDM to Value a Firm Experiencing “Supernormal” Firm Experiencing “Supernormal” GrowthGrowth First, calculate the total dividends over the “supernormal”

growth period:

Using the long run growth rate, g, the value of all the shares at Time 3 can be calculated as:

P3 = [D3 x (1 + g)] / (k – g)

P3 = [$10.985 x 1.10] / (0.20 – 0.10) = $120.835

Year Total Dividend: (in $millions)

1 $5.00 x 1.30 = $6.50

2 $6.50 x 1.30 = $8.45

3 $8.45 x 1.30 = $10.985


Example: Using the DDM to Value a Example: Using the DDM to Value a Firm Experiencing “Supernormal” Firm Experiencing “Supernormal” GrowthGrowth To determine the present value of the firm today, we need the present value of $120.835 and the present value of the dividends paid in the first 3 years:

million. $87.58

$69.93$6.36$5.87$5.42

0.201

$120.835

0.201

$10.985

0.201

$8.45

0.201

$6.50P

k1

P

k1

D

k1

D

k1

DP

332

33

33

221

0

0

If there are 20 million shares outstanding, the price per share is $4.38.


The H-ModelThe H-Model

For Chain Reaction, Inc., we assumed a supernormal growth rate of 30 percent per year for three years, and then growth at a perpetual 10 percent.

The growth rate is more likely to start at a high level and then fall over time until reaching its perpetual level.

Many possible ways to assume how the growth rate declines

A popular way is the H-model: which assumes a linear growth rate decline


The H-ModelThe H-Model Let’s revisit Chain Reaction, Inc.

Suppose the growth rate begins at 30% and reaches 10% in year 4 and beyond.

Using the H-model, we would assume that the company’s growth rate would decline by 20% from the end of year 1 to the beginning of year 4.

If we assume a linear decline: the growth rate falls by 6.67% per year (20%/3 years). Growth estimates would be: 30%, 23.33%, 16.66%, and 10%

Using these growth estimates, you will find that the firm value is $75.93 million, or $3.80 per share.

The value is lower than before because of the lower growth rates in years 2 and 3.


Discount Rates for Dividend Discount Discount Rates for Dividend Discount ModelsModels The discount rate for a stock can be estimated using the capital asset pricing model (CAPM ).

We will discuss the CAPM in a later chapter. However, we can estimate the discount rate

for a stock using this formula:Discount rate = time value of money + risk premium = U.S. T-bill Rate + (Stock Beta x Stock Market Risk Premium)

T-bill Rate: return on 90-day U.S. T-bills

Stock Beta: risk relative to an average stock

Stock Market Risk Premium:

risk premium for an average stock


Observations on Dividend Discount Observations on Dividend Discount

ModelModel Constant Perpetual Growth Model:

Simple to compute Not usable for firms that do not pay dividends Not usable when g > k Is sensitive to the choice of g and k k and g may be difficult to estimate accurately. Constant perpetual growth is often an unrealistic

assumption.

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Observations on Dividend Discount Observations on Dividend Discount ModelsModels


Two-Stage Dividend Growth Model:

More realistic in that it accounts for two stages of growth Usable when g > k in the first stage Not usable for firms that do not pay dividends Is sensitive to the choice of g and k k and g may be difficult to estimate accurately.

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Residual Income Model Residual Income Model (RIM)(RIM)


We have valued only companies that pay dividends.

But, there are many companies that do not pay dividends.

What about them? It turns out that there is an elegant way to value

these companies, too.

The model is called the Residual Income Model (RIM).

Major Assumption (known as the Clean Surplus Relationship, or CSR): The change in book value per share is equal to earnings per share minus dividends.

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Residual Income Model (RIM)Residual Income Model (RIM)


Inputs needed:Earnings per share at time 0, EPS0Book value per share at time 0, B0Earnings growth rate, gDiscount rate, k

There are two equivalent formulas for the Residual Income Model:

gk

gBEPSP

or

gk

kBg)(1EPSBP

010

0000

BTW, it turns out that the RIM is mathematically the same as the constant perpetual growth model.

3030

Using the Residual Income Using the Residual Income ModelModel


Duckwall—Alco Stores, Inc. (DUCK) It is July 1, 2010—shares are selling in the market for

$10.94. Using the RIM:

EPS0 = $1.20DIV = 0B0 = $5.886g = 0.09k = .13

What can we sayabout the marketprice of DUCK?

$19.46..04

$.7652$1.308$5.886P

.09.13

.13$5.886.09)(1$1.20$5.886P

gk

kBg)(1EPSBP

0

0

0000

3131

The Growth of DUCKThe Growth of DUCK


Using the information from the previous slide, what growth rate results in a DUCK price of $10.94?

3.55%. or .0355g

6.254g.2222

.43481.20g5.054g$.6570

.76521.20g1.20g)(.13$5.054

g.13

.13$5.886g)(1$1.20$5.886$10.94

gk

kBg)(1EPSBP 00

00

3232

Free Cash FlowFree Cash Flow


We can value companies that do not pay dividends using the residual income model.

Note: We assume positive earnings when we use the residual income model.

But, there are companies that do not pay dividends and have negative earnings.

Negative earnings = little value?We calculate earnings based on accounting rules

and tax codes. It is possible that a company has:

negative earnings positive cash flows a positive value.

3333

Free Cash FlowFree Cash Flow


Depreciation—the key to understand how a company can have negative earnings and positive cash flows

Depreciation reduces earnings because it is counted as an expense (more expenses = lower taxes paid).

Most stock analysts, however, use a relatively simple formula to calculate Free Cash Flow, FCF:

FCF = Net Income + Depreciation – Capital Spending

We can see that it is possible for: Net Income < 0 and FCF > 0

Depreciation and Capital Spending matter in FCF.

3434

DDMs Versus FCFDDMs Versus FCF


The DDMs calculate a value of the equity only.DDMs use dividends, a cash flow only to equity

holdersDDMs use the CAPM to estimate required returnDDMs use an equity beta to account for risk

Using the FCF model, we calculate a value for the firm.Free cash flow can be paid to debt holders and to

stockholders.We can still calculate the value of equity using FCF

Calculate the value of the entire firmSubtract out the value of debt

We need a beta for assets, not the equity, to account for risk

3535

Asset BetasAsset Betas


Asset betas measure the risk of the company’s industry. Firms in an industry should have about the

same asset betas.Their equity betas, however, could be quite

different.Investors can increase portfolio risk by using

margin (i.e., borrowing money to buy stock). A business can increase risk by using debt.

So, to value the company, we must “convert” reported equity betas into asset betas by adjusting for leverage.

The following conversion formula is widely used:

What happens when a firm has no debt?

)](1EquityDebt

[1AssetEquity tBB

tax rate.

3636

The FCF Approach, ExampleThe FCF Approach, Example


InputsAn estimate of FCF:

Net IncomeDepreciationCapital Expenditures

The growth rate of FCFThe proper discount rateTax rateDebt/Equity ratioEquity beta

Calculate value using a “DDM” formula

“DDM” because we are using FCF, not dividends.

3737

Valuing Landon Air: A New Valuing Landon Air: A New AirlineAirline


An estimate of FCF:Net Income: $25 millionDepreciation: $10 millionCapital Expenditures: $3 millionGrowth rate of FCF: 3%Tax rate: 35%Debt/Equity ratio: .40Equity beta: 1.2

Asset Beta: 1.2 = BAsset x [1+.4 x (1-.35)]

1.2 = BAsset x 1.26

BAsset = 0.95

The proper discount rate: k = 4.00 + (7.00 × 0.95) = 10.65%

Assume: No dividends Risk-free rate = 4% Market risk premium = 7%

shares.of number /million $330.85 share per Value

million. $330.85 isequity theof value thedebt, in $100 has AirLandonIf

million $430.85.03-.1065

(1.03)3)-10(25 Value AirLandon

:DDM Basic Using

3838

Price Ratio AnalysisPrice Ratio Analysis


Price-earnings ratio (P/E ratio)Current stock price divided by annual earnings

per share (EPS)

Earnings yieldInverse of the P/E ratio: earnings divided by

price (E/P)

High-P/E stocks are often referred to as growth stocks, while low-P/E stocks are often referred to as value stocks.

3939



Price-cash flow ratio (P/CF ratio)Current stock price divided by current cash

flow per shareIn this context, cash flow is usually taken to be

net income plus depreciation.

Most analysts agree that in examining a company’s financial performance, cash flow can be more informative than net income.

Earnings and cash flows that are far from each other may be a signal of poor quality earnings.

4040



Price-sales ratio (P/S ratio)Current stock price divided by annual sales per

shareA high P/S ratio suggests high sales growth,

while a low P/S ratio suggests sluggish sales growth.

Price-book ratio (P/B ratio)Market value of a company’s common stock

divided by its book (accounting) value of equityA ratio bigger than 1.0 indicates that the firm is

creating value for its stockholders.

4141

Price/Earnings Analysis, Intel Price/Earnings Analysis, Intel Corp.Corp.


Intel Corp (INTC) - Earnings (P/E) Analysis

5-year average P/E ratio 20.96Current EPS $.92EPS growth rate 8.5%

Expected stock price = historical P/E ratio projected EPS

$20.92 = 20.96 ($.92 1.085)

Late-2009 stock price = $19.40

4242

Price/Cash Flow Analysis, Intel Price/Cash Flow Analysis, Intel Corp.Corp.


Intel Corp (INTC) - Cash Flow (P/CF) Analysis

5-year average P/CF ratio 10.85Current CFPS $1.74CFPS growth rate 7.5%

Expected stock price = historical P/CF ratio projected CFPS

$20.29 = 10.85 ($1.74 1.075)


4343

Price/Sales Analysis, Intel Corp.Price/Sales Analysis, Intel Corp.


Intel Corp (INTC) - Sales (P/S) Analysis

5-year average P/S ratio 3.14Current SPS $6.76SPS growth rate 7%

Expected stock price = historical P/S ratio projected SPS

$22.71 = 3.14 ($6.76 1.07)


4444

An Analysis of the McGraw-Hill An Analysis of the McGraw-Hill CompanyCompany


The next few slides contain a financial analysis of the McGraw-Hill Company, using data from the Value Line Investment Survey.

4545

The McGraw-Hill Company AnalysisThe McGraw-Hill Company Analysis


4646

The McGraw-Hill Company The McGraw-Hill Company AnalysisAnalysis


47

The McGraw-Hill Company The McGraw-Hill Company Analysis, IIIAnalysis, IIIBased on the CAPM, k = 4.0% + (1.2 7%) =

12.4%

Retention ratio = 1 – $.90/$2.55 = .65

Sustainable g = .65 36.5% = 23.73%

(Value Line reports a projected ROE of 36.5%)

Because g > k, the constant growth rate model cannot be used. (We would get a value of -$9.83 per share)


48

The McGraw-Hill Company AnalysisThe McGraw-Hill Company Analysis(Using the Residual Income Model)(Using the Residual Income Model)

Let’s assume that “today” is January 1, 2010, g = 8.5%, and k = 12.4%.

Using the Value Line Investment Survey (VL), we can fill in column two (VL) of the table below.

We use column one and our growth assumption for column three (CSR) of the table below.End of 2009 2010 (VL) 2010 (CSR)

Beginning BV per share NA $5.95 $5.95

EPS $2.30 $2.55 $2.4955

DIV $.90 $.90 $1.9897

Ending BV per share $5.95 $7.05 $6.4558

1.0852.30 1.0855.95

5.95)- (6.4558-2.4955 Plug"" Ayşe Yüce – Ryerson UniversityAyşe Yüce – Ryerson University

Copyright © 2012 McGraw-Hill RyersonCopyright © 2012 McGraw-Hill Ryerson

49

The McGraw-Hill Company The McGraw-Hill Company AnalysisAnalysis(Using the Residual Income (Using the Residual Income Model)Model)

$51.02.P

.085.124.124$5.95.085)(1$2.30

$5.95P

gkkBg)(1EPS

BP

0

0

0000


Using the CSR assumption:

Using Value Line numbers for EPS1=$2.55, B1=$7.05B0=$5.95; and using the actual change in book value instead of an estimate of the new book value, (i.e., B1-B0 is = B0 x k)

Stock price at the time = $28.73.

What can we say?

$43.13P

.085.1245.95)-($7.05$2.55

$5.95P

gkkBg)(1EPS

BP

0

0

0000

50

The McGraw-Hill Company The McGraw-Hill Company AnalysisAnalysis


5151

Useful Internet SitesUseful Internet Sites


www.nyssa.org (The New York Society of Security Analysts)

www.aaii.com (The American Association of Individual Investors)

www.valueline.com (the home of the Value Line Investment Survey)

Websites for some companies analyzed in this chapter:• www.aep.com • www.intel.com • www.mcgraw-hill.com

http://www.nyssa.org/

http://www.aaii.com/

http://www.valueline.com/

http://www.aep.com/

http://www.intel.com/

http://www.mcgraw-hill.com/


Chapter Review Chapter Review

Security Analysis: Be Careful Out There

The Dividend Discount Model Constant Dividend Growth Rate Model Constant Perpetual Growth Applications of the Constant Perpetual Growth Model The Sustainable Growth Rate

The Two-Stage Dividend Growth Model Discount Rates for Dividend Discount Models Observations on Dividend Discount Models


Chapter Review Chapter Review

Residual Income Model (RIM)

Free Cash Flow Model

Price Ratio AnalysisPrice-Earnings RatiosPrice-Cash Flow RatiosPrice-Sales RatiosPrice-Book RatiosApplications of Price Ratio Analysis

An Analysis of the McGraw-Hill Company

1 Chapter 7 Brief History of Risk and Return Ayşe Yüce – Ryerson University Copyright © 2012...

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