1 6 common stock valuation. 6-2 common stock valuation fundamental analysis: studying a company’s...

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6

Common Stock Valuation

6-2

Common Stock Valuation• Fundamental analysis:

Studying a company’s accounting statements and other financial and economic information to estimate the economic value of a company’s stock

• Basic Idea:• Find undervalued (“cheap”) stocks to buy• Find overvalued (“rich”) stocks to sell or short

• Three categories of methods:1. Dividend Discount Models2. Residual Income Models3. Price Ratio Models

6-3

The Dividend Discount Model• Dividend Discount Model (DDM):

• Estimates the value of a share of stock by discounting all expected future dividend payments.

• The basic DDM equation:

• 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

6-4

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%.

• 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

6-5

The Constant Growth Rate Model• Assume that the dividends will grow at a constant

growth rate g. The dividend next period (t + 1) is:

• For constant dividend growth, the DDM formula becomes:

g)(1g)(1D D

g)(1 D D

g1DD

02

12

t1t

g k if D T P

g k if k1

g11

gk

g)(1DP

00

T

10

6-6

The Constant Growth Rate Model• Current dividend = $10 = D(0)• Dividend growth rate = 10% = g• There will be 20 yearly dividends = T• Appropriate discount rate = 8%. = k• 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

6-7

k)g :(Important

gk

D

gk

g1DP 10

0

The Constant Perpetual Growth Model: “The Gordon Growth Model”

• Assume dividends will grow forever at a constant growth rate g.

• For constant perpetual dividend growth, the DDM formula becomes:

6-8

Example: Constant Perpetual Growth Model• In 2007, the dividend paid by DTE Energy, Inc.

(DTE) was $2.12.• Using D0=$2.12, k = 6.7%, and g = 2%, calculate an

estimated value for DTE:

Note: the actual mid-2007 stock price of DTE was $47.81.

$46.01

.02.067

1.02$2.12P0

6-9

The Dividend Discount Model:Estimating the Growth Rate

• Three possible sources for g:

• The company’s historical average growth rate

• An industry median or average growth rate• The sustainable growth rate

6-10

The Historical Average Growth Rate• Suppose the Broadway Joe Company paid the following

dividends:• 2002: $1.50 2005: $1.80• 2003: $1.70 2006: $2.00• 2004: $1.75 2007: $2.20

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

Year: Dividend: Pct. Chg:2007 $2.20 10.00%2006 $2.00 11.11%2005 $1.80 2.86% Grown at2004 $1.75 2.94% Year: 7.96%:2003 $1.70 13.33% 2002 $1.502002 $1.50 2003 $1.62

2004 $1.758.05% 2005 $1.89

2006 $2.047.96% 2007 $2.20

Arithmetic Average:

Geometric Average:

6-11

Historical Growth RatesExample

Year EOY Dividend

2002 $1.50

2003 $1.70

2004 $1.75

2005 $1.80

2006 $2.00

2007 $2.20

6-12

Geometric Average Dividend Growth Rate

Year EOY Dividend

2002 $1.50

2003 $1.70

2004 $1.75

2005 $1.80

2006 $2.00

2007 $2.20

0796.0150.1$

20.2$

)1(50.1$20.2$

1

5/1

5

/1

0

g

g

D

Dg

g

N

Geometric Average Dividend Growth Rate = 7.96%

6-13

Arithmetic Average Dividend Growth Rate

Year EOY Dividend

Yearly Growth Rate

2002 $1.50

2003 $1.70 ($1.70-$1.50)/$1.50 = 13.33%

2004 $1.75 ($1.75-$1.70)/$1.70 = 2.94%

2005 $1.80 ($1.80-$1.75)/$1.75 = 2.86%

2006 $2.00 ($2.00-$1.80)/$1.80 = 11.11%

2007 $2.20 ($2.20-$2.00)/$2.00 = 10%

Sum 40.24

Arithmetic Average Dividend Growth Rate = 40.24/5 = 8.048%

6-14

The Sustainable Growth Rate

• Return on Equity (ROE) = Net Income / Equity• Payout Ratio = % of earnings paid out as dividends• Retention Ratio = % of earnings retained for

investment

Ratio) Payout - (1 ROE

Ratio Retention ROE Rate Growth eSustainabl

6-15

Calculating and Using the Sustainable Growth Rate

• American Electric Power (AEP) in 2007:• ROE =10.17%• Projected earnings per share = $2.25• Dividend per-share = $1.56

• What was AEP’s:• Retention rate?• Sustainable growth rate?

• Payout ratio = $1.56 / $2.25 = .693 or 69.3%• Retention ratio = 1 – .693 = .307 or 30.7%• AEP’s sustainable growth rate = 0.1017 0.307 =

0.03122 = 3.122%

6-16

Calculating and Using the Sustainable Growth Rate• What is the value of AEP stock, using the perpetual

growth model, and a discount rate of 6.7%?

• The actual mid-2007 stock price of AEP was $45.41.

• Using the sustainable growth rate to value the stock gives a reasonably accurate estimate.

$44.96

.03122.067

1.03122$1.56P

0

6-17

The Two-Stage Dividend Growth Model

• Assumes a firm will:• Grow at a rate g1 for T years (g1 may be > k)

• Then will grow at a rate g2 < k during a perpetual

second stage of growth

• The Two-Stage Dividend Growth Model formula:

2

20

T

1

T

1

1

10

gk

)g(1D

k1

g1

k1

g11

gk

)g(1DP

0

6-18

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 Model

• First Component = Present value of the first T dividends

• Second Component =Present value of all subsequent dividends

First Component Second Component

6-19

Using the Two-Stage Dividend Growth Model• MissMolly.com:

• Current dividend, D0 = $5,

• Dividend expected to “shrink” at the rate g1 = -10% for 5 years (T)

• But grow at the rate g2 = 4% forever

• Discount rate, k = 10%

• What is the present value of the stock?

6-20

$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

Using the Two-Stage Dividend Growth Model

• $46.03 =$14.25 present value of the first five dividends plus $31.78 present value of all subsequent dividends

6-21

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

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

6-22


• First, calculate the total dividends over the “supernormal” growth period:

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

6-23


• 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

6-24


• The value of the firm today = the present value of $120.835 plus 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

3320

33

33

221

0

6-25

Nonconstant growth followed by constant growth

0

5.42

5.87

6.36

69.93

1 2 3 4k=20%

87.58 = P0

g1 = 30% g1 = 30% g1 = 30% g2 = 10%

D0 = 5.00 6.50 8.45 10.985 12.0835

P3 = $12.0835

0.20 – 0.10= $120.835

6-26

Discount Rates for Dividend Discount Models

• Estimate discount rate using the Capital Asset Pricing Model (CAPM )

• Discount rate = time value of money + risk premiumTime value of money = U.S. T-bill rate

Risk Premium = (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

6-27

Observations on Dividend Discount Models

Constant Perpetual Growth Model:

+ Simple to compute- Not usable for firms that do not pay dividends- Not usable when g > k- 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

6-28

Observations on Dividend Discount ModelsTwo-Stage Dividend Growth Model:

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

6-29

Residual Income Model (RIM)• Value firms that do NOT pay dividends

• Major Assumption:• The Clean Surplus Relationship, or CSR

The change in book value per share is equal to earnings per share minus dividends

• Mathematically equivalent to the Constant Perpetual Growth Model

6-30

Residual Income Model (RIM)• Inputs needed:

• Earnings per share at time 0, EPS0

• Book value per share at time 0, B0

• Earnings growth rate, g• Discount rate, k

• Two equivalent RIM formula:

(6.19) gk

gBEPSP

or

(6.18) gk

kBg)(1EPSBP

010

0000

6-31

The Residual Income Model

(6.19) gk

gBEPSPRIM 01

0

:

Where:

EPS1 = Earnings per share at t=0 times (1+g)

B0 = Book value per share at t=0

g = assumed perpetual growth rate

k = required return

6-32

$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

Using the Residual Income Model

• Superior Offshore International, Inc. (DEEP)• July 1, 2007—shares selling for $10.94• Using the RIM:

EPS0=$1.20

DIV = 0

B0=$5.886

g = 0.09

k = .13

6-33

The Growth of DEEP• Using the information from the previous slide, what

growth rate results in a DEEP 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

6-34

Price Ratio Analysis

• Price-earnings ratio (P/E ratio)

• Price-cash flow ratio (P/CF ratio)

• Price-sales ratio (P/S ratio)

• Price-book ratio (P/B ratio)

6-35

Price-Earnings Ratio (P/E)

• Most popular price ratio• Inverse = Earnings Yield (E/P)• High P/E Ratio stocks = “Growth Stocks”

• Expensive relative to earnings

• Low P/E Ratio stocks = “Value Stocks”• Cheap relative to earnings

EPS

PE/P

Where:

P = Current stock price

EPS = Annual earnings per share

6-36

Price-Cash Flow Ratio (P/CF)

CFPS

PCF/P

Where:


CFPS = Current cash flow per share

CF = NI + Depreciation

• P/CF can be more informative than P/E

•If EPS >> CFPS Poor quality earnings

6-37

Price-Sales Ratio (P/S)

• Focuses on firm’s ability to generate sales growth

• Cannot be compared in isolation• Industry specific comparisons

SPS

PS/P

Where:


SPS = Annual sales per share

6-38

Price-Book Ratio (P/B)• Also “Market to Book”• P/B Historical cost vs. Current Market

Value> 1.0 = firm has created value

< 1.0 = firm worth less than it cost

BVPS

PB/P

Where:


BVPS = Current book value per share

6-39

Price/Earnings Analysis: Intel Corp.

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

5-year average P/E ratio 27.30Current EPS $0.86EPS growth rate 8.5%

Expected stock price: = Historical P/E ratio projected EPS

$25.47 = 27.30 ($0.86 1.085)

Mid-2007 stock price = $24.27

6-40

Price/Cash Flow Analysis: Intel Corp.

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

5-year average P/CF ratio 14.04Current CFPS $1.68CFPS growth rate 7.5%

Expected stock price: = Historical P/CF ratio projected CFPS

$25.36 = 14.04 ($1.68 1.075)


6-41

Price/Sales Analysis, Intel Corp.Intel Corp (INTC) - Sales (P/S) Analysis

5-year average P/S ratio 4.51Current SPS $6.14SPS growth rate 7%

Expected stock price: = Historical P/S ratio x projected SPS

$29.63 = 4.51 ($6.14 1.07)


6-42

Intel Corp: Recap

Description5-year average Price Ratio 27.30 P/E 14.04 P/CF 4.051 P/S

Current Value per share $0.86 EPS $1.68 CFPS $6.14 SPSGrowth rate 8.50% 7.50% 7.00%

Expected stock priceActual Stock Price $24.27

Earnings Cash Flow Sales

$25.47 $25.36 $29.63

6-43

The McGraw-Hill Company Analysis

6-44


6-45


• Based on the CAPM:

k = 3.1% + (.80 9%) = 10.3%

• Retention ratio = 1 – $.66/$2.65 = .751• Sustainable g = .751 23% = 17.27%

• Because g > k, the constant growth rate model cannot be used. (We would get a value of -$11.10 per share)

6-46

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

• Assume “today” is January 1, 2008, g = 7.5%, and k = 12.6%.• 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.

= 3.05 x 1.075

= 6.50 x 1.075

“Plug” = 3.2788 – (6.9875 – 6.50)

End of 2007

2008 (VL)

2008 (CSR)

Beginning BVPS NA $6.50 $6.50

EPS $3.05 $3.45 $3.28 DIV $0.82 $0.82 $2.79 Ending BVPS $6.50 $9.25 $6.99

6-47

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

• Using the CSR assumption:

• Using Value Line numbers:• EPS1=$3.45• B1=$9.25• B0=$6.50; • And using the actual

change in book value instead of an estimate of the new book value

$54.73.P.075.126

.126$6.50.075)(1$3.05$6.50P

gk

kBg)(1EPSBP

0

0

0000

$20.23P.075.126

6.50)-($9.25$3.45$6.50P

gk

kBg)(1EPSBP

0

0

0000

Stock price at the time = $57.27.What can we say?

6-48

The McGraw-Hill Company Analysis, IV

6-49

Useful Internet Sites• www.nyssa.org (the New York Society of Security Analysts)• www.aaii.com (American Association of Individual Investors)• www.eva.com (Economic Value Added)• www.valueline.com (the home of the Value Line Investment

Survey)

• Websites for some companies analyzed in this chapter:• www.aep.com • www.americanexpress.com • www.pepsico.com • www.intel.com • www.corporate.disney.go.com • www.mcgraw-hill.com

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6

Common Stock Valuation

1 6 common stock valuation. 6-2 common stock valuation fundamental analysis: studying a company’s...

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constant dividend growth

d0 dividend growth rate

sustainable growth rate

sustainable growth rate

gordon growth model

dividend discount models

t appropriate discount

common stock valuation