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Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

6

Common Stock Valuation

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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 two categories:– Dividend discount models– Price ratio models

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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.

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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 DDM equation is:

• In the DDM equation:– V(0) = the present value of all future dividends– D(t) = the dividend to be paid t years from now– k = the appropriate risk-adjusted discount rate

T32 k1

D(T)

k1

D(3)

k1

D(2)

k1

D(1)V(0)

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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

$200V(0)

k1

D(3)

k1

D(2)

k1

D(1)V(0)

32

32

6-7

The Dividend Discount Model: the Constant Growth Rate Model

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

• Then, the dividend next period (t + 1) is:

• In this case, the DDM formula becomes:

g k if D(0) T V(0)

g k if k1

g11

gk

g)D(0)(1V(0)

T

g1tD1tD

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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$100V

g k if k1

g11

gk

g)D(0)(1V(0)

20

T

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The Dividend Discount Model:the Constant Perpetual Growth Model.

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

• In this case, the DDM formula becomes:

kg

gk

1D

gk

g10D0V

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Example: Constant Perpetual Growth Model

• Think about the electric utility industry. • In mid-2003, the dividend paid by the utility company, American

Electric Power (AEP), was $1.40.• Using D(0)=$1.40, k = 6.5%, and g = 1.5%, calculate an estimated

value for AEP.

• Note: the actual mid-2003 stock price of AEP was $25.88.

$28.42

.015.065

1.015$1.400V

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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.

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The Historical Average Growth Rate

• Suppose the Kiwi Company paid the following dividends:

– 1998: $1.50 2001: $1.80– 1999: $1.70 2002: $2.00– 2000: $1.75 2003: $2.20

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

Year: Dividend: Pct. Chg:2003 $2.20 10.00%2002 $2.00 11.11%2001 $1.80 2.86% Grown at2000 $1.75 2.94% Year: 7.96%:1999 $1.70 13.33% 1998 $1.501998 $1.50 1999 $1.62

2000 $1.758.05% 2001 $1.89

2002 $2.047.96% 2003 $2.20

Arithmetic Average:

Geometric Average:

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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

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Example: Calculating and Using the Sustainable Growth Rate

• In 2003, AEP had an ROE of 10%, projected earnings per share of $2.20, and a per-share dividend of $1.40. What was AEP’s– Retention rate?– Sustainable growth rate?

• Payout ratio = $1.40 / $2.20 = .636

• So, retention ratio = 1 – .636 = .364 or 36.4%

• Therefore, AEP’s sustainable growth rate = 10% .364 = 3.64%

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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 6.5%?

• Recall the actual mid-2003 stock price of AEP was $25.88.

• As discussed in Example 6.8, there was considerable uncertainty regarding AEP at the time of this analysis.

• It is important to note that dividend growth models do not capture severe uncertainty well.

$25.88 $50.73

.0364.065

1.0364$1.400V

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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 grow at a rate g2 < k during a perpetual

second stage of growth.

• The Two-Stage Dividend Growth Model formula is:

2

2

T

1

T

1

1

1

gk

)g1)(0(D

k1

g1

k1

g11

gk

)g1)(0(D)0(V

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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 D(0) = $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?

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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(0.90V(0)

gk

)gD(0)(1

k1

g1

k1

g11

gk

)gD(0)(1V(0)

55

2

2

T

1

T

1

1

1

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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.?

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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:

V(3) = [D(3) x (1 + g)] / (k – g)

V(3) = [$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

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

• Therefore, 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

$6.50V(0)

k1

V(3)

k1

D(3)

k1

D(2)

k1

D(1)V(0)

332

332

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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

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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.

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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.

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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.

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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.

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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.

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Price/Earnings Analysis, Intel Corp.

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

Current EPS $0.485-year average P/E ratio 38.72EPS growth rate 5.50%

Expected stock price = historical P/E ratio projected EPS

$19.61 = 38.72 ($0.48 1.055)

Early-2003 stock price = $15.05

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Price/Cash Flow Analysis, Intel Corp.

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

Current CFPS $1.205-year average P/CF ratio 21.55CFPS growth rate 6.50%

Expected stock price = historical P/CF ratio projected CFPS

$27.54 = 21.55 ($1.20 1.0650)

Early-2003 stock price = $15.05

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Price/Sales Analysis, Intel Corp.

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

Current SPS $4.005-year average P/S ratio 7.50SPS growth rate 5.50%

Expected stock price = historical P/S ratio projected SPS

$31.63 = 7.50 ($4.00 1.055)

Early-2003 stock price = $15.05

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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.

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The McGraw-Hill Company Analysis, I.

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The McGraw-Hill Company Analysis, II.

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The McGraw-Hill Company Analysis, III.

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The McGraw-Hill Company Analysis, IV.

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The McGraw-Hill Company Analysis, V.

• Based on the CAPM, k = 1% + (.80 9%) = 8.20%

• Retention ratio = 1 – $1.08/$3.20 = 66.25%

• Sustainable g = .6625 26% = 17.23%

• Because g > k, the constant growth rate model cannot be used. (We would get a value of -$13.24 per share)– However, using a growth rate of 17.23% is not realistic.– Using the actual dividend growth rate of 5.5% (over the last 10

years), yields a stock price of $39.86.– Recent price in Value Line: $54.49

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The McGraw-Hill Company Analysis, VI.

Quick calculations used: P/CF = P/E EPS/CFPS

P/S = P/E EPS/SPS

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The McGraw-Hill Company Analysis, VII.

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Useful Internet Sites

• www.nyssa.org (the New York Society of Security Analysts)• www.aaii.com (the American Association of Individual Investors)• www.aimr.com (the Association for Investment Management and

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

• Websites for the companies analyzed in this chapter:• www.aep.com • www.dteendergy.com • www.americanexpress.com • www.pepsico.com • www.starbucks.com • www.sears.com • www.intel.com • www.disney.go.com • www.mcgraw-hill.com

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Chapter Review, I.

• 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

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Chapter Review, II.

• The Two-Stage Dividend Growth Model– Discount Rates for Dividend Discount Models

– Observations on Dividend Discount Models

• Price Ratio Analysis– Price-Earnings Ratios

– Price-Cash Flow Ratios

– Price-Sales Ratios

– Price-Book Ratios

– Applications of Price Ratio Analysis

• An Analysis of the McGraw-Hill Company