6 6 c h a p t e r common stock valuation second edition fundamentals of investments valuation &...

66C h a p t e r

Common Stock ValuationCommon Stock Valuation

second edition

Fundamentals

of InvestmentsValuation & Management

Charles J. Corrado Bradford D. Jordan

McGraw Hill / Irwin Slides by Yee-Tien (Ted) Fu

2002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin

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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.

Goal

These methods are grouped into two categories: dividend discount models price ratio models


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Security Analysis: Be Careful Out There

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.

Numbers such as a company’s earnings per share, cash flow, book equity value, and sales are often called fundamentals because they describe, on a basic level, a specific firm’s operations and profits (or lack of profits).

Information, regarding such things as management quality, products, and product markets is often examined as well.

Fundamental analysisExamination of a firm’s accounting statements and other financial and economic information to assess the economic value of a company’s stock.


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The Dividend Discount Model A fundamental principle of finance holds that the economic

value of a security is properly measured by the sum of its future cash flows, where the cash flows are adjusted for risk and the time value of money.

For example, suppose a risky security will pay either $100 or $200 with equal

probability one year from today. The expected future payoff is $150 = ($100 + $200) / 2, and the security's value today is the $150 expected future value discounted for a one-year waiting period.

If the appropriate discount rate for this security is, say, 5 percent, then the present value of the expected future cash flow is $150 / 1.05 = $142.86. If instead the appropriate discount rate is 15 percent, then the present value is $150 / 1.15 = $130.43.

As this example illustrates, the choice of a discount rate can have a substantial impact on an assessment of security value.


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The Dividend Discount Model

where V(0) = the present value of the future dividend streamD(t) = the dividend to be paid t years from nowk = the appropriate risk-adjusted discount rate

Dividend discount model (DDM)Method of estimating the value of a share of stock as the present value of all expected future dividend payments.

Tk

TD

k

D

k

D

k

DV

1

)(

1

)3(

1

)2(

1

)1()0( 32


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Example 6.1 Using the DDM. Suppose again that a stock pays three annual dividends of $100 per year and the discount rate is k = 15 percent. In this case, what is the present value V(0) of the stock?

With a 15 percent discount rate, we have V(0) = $228.32.


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Example 6.2 More DDM. Suppose instead that the stock pays three annual dividends of $10, $20,and $30 in years 1, 2, and 3, respectively, and the discount rate is k = 10 percent. What is the present value V(0) of the stock?

Check that the answer is V(0) = $48.16.


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Constant Dividend Growth Rate Model

For many applications, the dividend discount model is simplified substantially by assuming that dividends will grow at a constant growth rate. This is called a constant growth rate model. Letting a constant growth rate be denoted by g, then successive annual dividends are stated as D(t+1) = D(t)(1+g).

constant growth rate model A version of the dividend discount model that assumes a constant dividend growth rate.


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

kgDTV

kgk

g

gk

gDV

T

00

1

11

100

gtDtD 11 Then

This is the constant growth rate model.


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Actually, when the growth rate is equal to the discount rate, that is, k = g, the effects of growth and discounting cancel exactly, and the present value V(0) is simply the number of payments T times the current dividend D(0):


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Example: Constant Growth Rate Model Suppose the dividend growth rate is 10%, the

discount rate is 8%, there are 20 years of dividends to be paid, and the current dividend is $10. What is the value of the stock based on the constant growth rate model?

86.243$

08.1

10.11

10.08.

10.110$0

20

V

Thus the price of the stock should be $243.86.


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Constant Perpetual Growth

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

kg

gk

D

gk

gDV

110

0

This is the constant perpetual growth model which is :A version of the dividend discount model in which dividends grow forever at a constant rate, and the growth rate is strictly less than the discount rate


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The reason is that a perpetual dividend growth rate greater than a discount rate implies an infinite value because the present value of the dividends keeps getting bigger and bigger. Since no security can have infinite value, the requirement that g < k simply makes good economic sense.


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Example: Constant Perpetual Growth Model Consider the electric utility industry. In late 2000, the

utility company Detroit Edison (DTE) paid a $2.06 dividend. Using D(0)=$2.06, k =8%, and g=2%, calculate a present value estimate for DTE. Compare this with the late-2000 DTE stock price of $36.13.

02.35$

02.08.

02.106.2$0

V

Our estimated price is a little lower than the $36.13 stock price.


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Applications of the Constant Perpetual Growth Model

A standard example of an industry for which the constant perpetual growth model can often be usefully applied is the electric utility industry. Consider the first company in the Dow Jones Utilities, American Electric Power, which is traded on the New York Stock Exchange under the ticker symbol AEP. At midyear 1997, AEP's annual dividend was $1.40; thus we set D(0) = $1.40, k= 6.5% , g=1.5 % ,

42.28$

015.065.

015.140.1$0

V


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Sustainable 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, Which

involves using a company’s earnings to estimate g. sustainable growth rate A dividend growth rate

that can be sustained by a company's earnings.)


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Sustainable Growth Rate As we have discussed, a limitation of the constant

perpetual growth model is that it should be applied only to companies with stable dividend and earnings growth. Essentially, a company's earnings can be paid out as dividends to its stockholders or kept as retained earnings within the firm to finance future growth.

(retained earnings Earnings retained within the firm to finance growth.)

(payout ratio Proportion of earnings paid out as dividends.) (retention ratio Proportion of earnings retained for

reinvestment.)


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Sustainable = ROE Retention ratio growth rate

Return on equity (ROE) = Net income / Equity

Retention ratio = 1 – Payout ratio

Payout ratio = dividends \net income


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Example: The Sustainable Growth Rate DTE has a ROE of 12.5%, earnings per share (EPS)

of $3.34, and a per share dividend (D(0)) of $2.06. Assuming k = 8%, what is the value of DTE’s stock?

Payout ratio = $2.06/$3.34 = .617So, retention ratio = 1 – .617 = .383 or 38.3%

Sustainable growth rate = 12.5% .383 = 4.79%

13.36$25.67$

0479.08.

0479.106.2$0

V

DTE’s stock is perhaps undervalued, or more likely, its growth rate has been overestimated.


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The Two-Stage Dividend Growth Model

In the previous section, we examined dividend discount models based on a single growth rate. You may have already thought that a single growth rate is often unrealistic, since companies often experience temporary periods of unusually high or low growth, with growth eventually converging to an industry average or an economy-wide average.

In such cases as these, financial analysts frequently use a two-stage dividend growth model.

(two-stage dividend growth model Dividend model that assumes a firm will temporarily grow at a rate different from its long-term growth rate.)


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The Two-Stage Dividend Growth Model

A 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.

2

211

1

1 10

1

1

1

11

100

gk

gD

k

g

k

g

gk

gDV

TT

The first term on the right-hand side measures the present value of the first T dividends and is the same expression we used earlier for the constant growth model. The second term then measures the present value of all subsequent dividends.


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The Two-Stage Dividend Growth Model Example 6.9 Using the Two-Stage Model Suppose a firm has a current

dividend of D(0) = $5, which is expected to “shrink” at the rate g1 = -10 percent for T = 5 years, and thereafter grow at the rate g2 = 4 percent. With a discount rate of k = 10 percent, what is the value of the stock?

Using the two-stage model, present value, V(0), is calculated as:

The total present 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.


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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 ).

Discount = time value + risk rate of money premium

= T-bill + ( stock stock market ) rate beta risk premium

T-bill rate = return on 90-day U.S. T-billsstock beta = risk relative to an average stockstock market = risk premium for an average stockrisk premium


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A stock’s beta is a measure of a single stock’s risk relative to an average stock, and we discuss beta at length in a later chapter. For now, it suffices to know that the market average beta is 1.0.

A beta of 1.5 indicates that a stock has 50 percent more risk than average, so its risk premium is 50 percent higher.

A beta of .50 indicates that a stock is 50 percent less sensitive than average to market volatility, and has a smaller risk premium

(beta Measure of a stock’s risk relative to the stock market average.)


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Example 6.13 Stride-Rite’s Beta Look back at Example 6.12. What beta did we use to determine the appropriate discount rate for Stride-Rite? How do you interpret this beta?

Again assuming a T-bill rate of 5 percent and stock market risk premium of 8.6 percent, we have

13.9% = 5% + Stock beta × 8.6% Thus Stock beta = (13.9% - 5%) / 8.6% = 1.035 Since Stride-Rite’s beta is greater than 1.0, it had

greater risk than an average stock — specifically, 3.5 percent more.


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Observations on Dividend Discount Models

Constant Perpetual Growth ModelSimple 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

Two-Stage Dividend Growth ModelMore realistic in that it accounts for two stages

of growth. ( it accounts for low, high, or zero growth in the first stage, followed by constant long-term)

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 Price-earnings ratio (P/E ratio)

The most popular price ratio used to assess the value of common stock

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

Earnings yield Inverse of the P/E ratio: earnings divided by price (E/P). annual earnings per share can be calculated either as the

most recent quarterly earnings per share times four or the sum of the last four quarterly earnings per share figures.

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

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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Most analysts agree that cash flow can be more informative than net income in examining a company's financial performance. To see why, consider the hypothetical example ?


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Twiddle-Dee Co. chooses straight-line depreciation and Twiddle-Dum Co. chooses accelerated depreciation. These two depreciation schedules are tabulated below:


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Now, let's look at the resulting annual cash flows and net income figures for the two companies, recalling that in each year, Cash flow = Net income + Depreciation:


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Price Ratio Analysis 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. A ratio smaller than 1.0 indicates that the company is

actually worth less than it cost. because of varied and changing accounting standards, book

values are difficult to interpret


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

Current EPS $1.355-year average P/E ratio 30.4EPS growth rate 16.5%

expected = historical projected EPS stock price P/E ratio

= 30.4 ($1.351.165)= $47.81

* Late-2000 stock price = $89.88


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

Current CFPS $1.975-year average P/CF ratio 21.6CFPS growth rate 15.3%

expected = historical projected CFPS stock price P/CF ratio

= 21.6 ($1.971.153)= $49.06



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

Current SPS $4.565-year average P/S ratio 6.7SPS growth rate 13.3%

expected = historical projected SPS stock price P/S ratio

= 6.7 ($4.561.133)= $34.62



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An Analysis of theMcGraw-Hill Company

An Analysis of the McGraw-Hill Company


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Based on the CAPM, k = 6% + (.85 9%) = 13.65%

Retention ratio = 1 – $1.02/$2.75 = 62.9%

sustainable g = .629 25.5% = 16.04% Since g > k, the constant growth rate model

cannot be used.


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Quick calculations used: P/CF = P/E EPS/CFPSP/S = P/E EPS/SPS


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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


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Chapter Review

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


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Chapter Review


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