Bob LeClair's Finance and Markets NewsletterChange Change

1/1/13 9/21/13 9/28/13 (Week) (Yr-to-Date)Dow Jones Ind. Avg. 13,104 15,451 15,258 (193) 2,154

(% Change) -1.25% 16.44%S & P 500 Index 1,426 1,710 1,692 (18) 266

(% Change) -1.07% 18.62%NASDAQ Composite 3,020 3,775 3,782 7 762

(% Change) 0.17% 25.24%

S & P 500 P/E Ratio 16.8 18.6 18.3 -0.3 1.5S & P 500 Div. Yield 2.25% 2.05% 2.08% 0.03% -0.17%T-bill - S&P 500 Yield -2.21% -2.04% -2.06% -0.02% 0.15%

30-Year T-Bond Yield 2.95% 3.76% 3.69% -0.07% 0.74%10-Year T-Bond Yield 1.76% 2.73% 2.62% -0.11% 0.86%91-Day T-Bill Yield 0.04% 0.01% 0.02% 0.01% -0.02%Yield Spread 2.91% 3.75% 3.67% -0.08% 0.76%

30-Year Mortgage 3.35% 4.50% 4.32% -0.18% 0.97%15-Year Mortgage 2.65% 3.54% 3.37% -0.17% 0.72%1-Year Adjustable Rate 2.56% 2.65% 2.63% -0.02% 0.07%30-Yr. - 1-Yr. ARM Rate 0.79% 1.85% 1.69% -0.16% 0.90%

$ Value of Euro (€) $1.3221 $1.3524 $1.3522 -$0.0002 $0.0301Japanese Yen (¥/$) 86.74 99.36 98.24 -1.12 11.50Crude Oil, Spot Price $91.82 $104.67 $103.03 -$1.64 $11.21Gasoline, Reg. ($/Gal.) $3.30 $3.49 $3.42 -$0.07 $0.12

For the Week Ending:

Chapter

Common Stock Valuation

McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

6

6-4

Common 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 models– Residual Income model– Free Cash Flow model– Price ratio models

6-5

Security Analysis: Be Careful Out There

• 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.

Are Dividends a Good Basisfor Valuing Your Stock?

• Does the stock pay a dividend?

• What is the stock’s dividend yield? [DPS ÷ Share Price (P0)]

• Are dividends increased regularly?

• What is the growth rate of EPS and DPS?

Are Dividends a Good Basisfor Valuing Your Stock?

• Compare dividend yield with:–Industry average

–The market (i.e., S & P 500)• 2.08% as of 9-27-13

–Competitors

• Examine payout ratio (DPS ÷ EPS)

6-9

The 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 dividends

– Dt = 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

6-10

Example: The Dividend Discount Model

• 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

6-11

The Dividend Discount Model: the 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 k if D T P

g k if k1

g11

gk

g)(1DP

00

T

10

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

g1DD

012

t1t

6-12

Example: The Constant Growth Rate Model

• 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

6-13

The Dividend Discount Model:the 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

6-14

Example: Constant Perpetual Growth Model

• 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

6-15

The Dividend Discount Model:Estimating the Growth Rate

• The 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.

6-16

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:

6-17

The Sustainable Growth Rate

• Return on Equity (ROE) = Net Income / Equity

• Payout Ratio = Proportion of earnings paid out as dividends

• Retention Ratio = Proportion of earnings retained for investment

Ratio) Payout - (1 ROE

Ratio Retention ROE Rate Growth eSustainabl

6-18

Example: Calculating and Using the Sustainable 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%

6-19

Example: Calculating and Using the Sustainable Growth Rate, Cont.

• 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

6-20

Analyzing 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 ratio– Increasing profitability (Net Income / Sales)– Increasing asset efficiency (Sales / Assets)– Increasing debt (Assets / Equity)

EquityAssets

AssetsSales

SalesIncome Net

ROEEquity

Income Net

6-21

The Two-Stage Dividend Growth Model

• The 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

6-22

Using the Two-Stage Dividend Growth Model, I.

• 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?

6-23

Using the Two-Stage Dividend Growth Model, II.

• 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.

$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

6-24

Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, I.

• 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.?

6-25

Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, II.

• 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

6-26

Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, III.

• 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.

6-29

Discount Rates for Dividend Discount Models

• 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

Capital Asset Pricing Model (CAPM)[Required Rate of Return]

500 P& S i.e., market, theon return

market the toiprelationsh sstock'

Treasuriesyear -3or bills,-T

(k) Return Required

)(

m

f

fmf

R

R

RR

RRRRR

Observations on Dividend Discount Models, I.

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.

Observations on Dividend Discount Models, II.

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.

What if a company pays no dividends?

• Residual Income Model

• P/E X EPS Model (Price Ratio Analysis)

6-34

Residual Income Model (RIM), I.

• 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.

6-35

Residual Income Model (RIM), II.

• Inputs needed:

– Earnings per share at time 0, EPS0

– Book value per share at time 0, B0

– Earnings growth rate, g– Discount 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.

6-38

Free Cash Flow, I.• 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.

6-39

Free Cash Flow, II.

• 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.

What is the “quality of earnings” for your company?

• Compare earnings per share with free cash flow per share.

• If earnings and cash flow per share are comparable, then quality of earnings is high.

• If earnings and cash flow per share are quite different, then quality of earnings may be low.

Price Ratio Analysis

• Future Cash Flows:DIV1 + DIV2 + DIV3 + PRICE3

PRICE3 = P/E3 X EPS3

• Estimating P/E3

• Estimating EPS3

6-46

Price Ratio Analysis, I.

• Price-earnings ratio (P/E ratio)

– Current stock price divided by annual earnings per share (EPS)

• Earnings yield

– Inverse 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.

6-47

Price Ratio Analysis, II.

• Price-cash flow ratio (P/CF ratio)

– Current stock price divided by current cash flow per share

– In 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.

6-48

Price Ratio Analysis, III.• Price-sales ratio (P/S ratio)

– Current stock price divided by annual sales per share– A 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 equity– A ratio bigger than 1.0 indicates that the firm is

creating value for its stockholders.

6-49

Price/Earnings Analysis, Intel 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

6-50

Price/Cash Flow Analysis, Intel 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)

Late-2009 stock price = $19.40

6-51

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)

Late-2009 stock price = $19.40

6-52

An Analysis of theMcGraw-Hill Company

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

6-53

The McGraw-Hill Company Analysis, I.

6-54

The McGraw-Hill Company Analysis, II.

6-55

The McGraw-Hill Company Analysis, III.• Based 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)

6-59

Useful 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