January 2, 2020

Chapter 6

Common Stock Valuation

Slides

6-1. Chapter 6

6-2. The Stock Market

6-3. Learning Objectives

6-4. Common Stock Valuation

6-5. Security Analysis: Be Careful Out There

6-6. The Dividend Discount Model

6-7. Example: The Dividend Discount Model

6-8. The Dividend Discount Model: the Constant Growth Rate Model

6-9. Example: The Constant Growth Rate Model

6-10. The Dividend Discount Model: the Constant Perpetual Growth Model

6-11. Example: Constant Perpetual Growth Model

6-12. The Dividend Discount Model: Estimating the Growth Rate

6-13. The Historical Average Growth Rate

6-14. The Sustainable Growth Rate

6-15. Example: Calculating and Using the Sustainable Growth Rate

6-16. Example: Calculating and Using the Sustainable Growth Rate, Cont.

6-17. Analyzing ROE

6-18. The Two-Stage Dividend Growth Model

6-19. Using the Two-Stage Dividend Growth Model, I.

6-20. Using the Two-Stage Dividend Growth Model, II.

6-21. Example: Using the DDM to Value a Firm Experiencing “Supernormal”

Growth, I.

6-22. Example: Using the DDM to Value a Firm Experiencing “Supernormal”

Growth, II.

6-23. Example: Using the DDM to Value a Firm Experiencing “Supernormal”

Growth, III.

6-24. The H-Model, I.

6-25. The H-Model, II.

6-26. Discount Rates for Dividend Discount Models

6-27. Observations on Dividend Discount Models, I.

6-28. Observations on Dividend Discount Models, II.

6-29. Residual Income Model (RIM), I.

6-30. Residual Income Model (RIM), II.

6-31. Using the Residual Income Model

6-32. The Growth of DUCK

6-33. Free Cash Flow, I.

6-34. Free Cash Flow, II.

6-35. DDMs Versus FCF

6-36. Asset Betas

6-37. The FCF Approach, Example

6-38. Valuing Landon Air: A New Airline

6-39. Price Ratio Analysis, I.

6-40. Price Ratio Analysis, II.

6-41. Price Ratio Analysis, III.

6-42. Price/Earnings Analysis, Intel Corp.

6-43. Price/Cash Flow Analysis, Intel Corp.

6-44. Price/Sales Analysis, Intel Corp.

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Common Stock Valuation 6-2

6-45. Enterprise Value Ratios, Overview

6-46. Enterprise Value Ratios, Example

6-47. Using Enterprise Value Ratio to Estimate Stock Price

6-48. An Analysis of the E.I. du Pont Company

6-49. Using the Dividend Discount Model for to Value the E.I. du Pont Company

6-50. Next Task: Calculate a Sustainable Growth Rate

6-51. Dividend Discount Model: E.I. du Pont Company

6-52. The E.I. du Pont Company, Estimated Stock Price and Method

6-53. Final Thoughts: E.I. du Pont Company

6-54. Useful Internet Sites

6-55. Chapter Review, I.

6-56. Chapter Review, II.

Chapter Organization

6.1 Security Analysis: Be Careful Out There

6.2 The Dividend Discount Model

A. Constant Perpetual Growth

B. Historical Growth Rates

C. The Sustainable Growth Rate

D. Analyzing ROE

6.3 The Two-Stage Dividend Growth Model

A. Nonconstant Growth in the First Stage

B. The H-Model

C. Discount Rates for Dividend Discount Models

D. Observations on Dividend Discount Models

6.4 The Residual Income Model

A. Residual Income

B. The RIM versus the Constant Growth DDM

6.5 The Free Cash Flow Model

A. Free Cash Flow

B. The FCF Model versus the Constant Growth DDM

6.6 Price Ratio Analysis

A. Price-Earnings Ratios

B. Price-Cash Flow Ratios

C. Price-Sales Ratios

D. Price-Book Ratios

E. Applications of Price Ratio Analysis

F. Enterprise Value Ratios

6.7 An Analysis of the E. I. du Pont Company

A. Using the Dividend Discount Model

B. Using the Residual Income Model

C. Using the Free Cash Flow Model

D. Using Price Ratio Analysis

6.8 Summary and Conclusions

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Common Stock Valuation 6-3

Selected Web Sites

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

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

www.cfainstitute.org (the CFA Institute)

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

www.aep.com (American Electric Power)

www.dteenergy.com(Detroit Edison)

www.americanexpress.com

www.pepsico.com

www.starbucks.com

www.gm.com

www.intel.com

www.disney.go.com

www.dupont.com

www.cat.com

finance.yahoo.com (for general financial information)

For information on valuing companies:

www.dailystocks.com (Stock Sheet)

www.hoovers.com (Hoovers Online)

www.zacks.com (Zacks)

www.fool.com (Motley Fool)

Annotated Chapter Outline

6.1 Security Analysis: Be Careful Out There

Fundamental analysis: Examination of a firm's accounting statements

and other financial and economic information to assess the economic

value of a company's stock.

The basic premise of investing is to identify undervalued stocks to purchase and

overvalued stocks to sell. On the surface many stocks that appear cheap may be

correctly priced, due to reasons not immediately apparent. An analyst must be

willing to investigate deeper. This chapter discusses fundamental analysis; using

the firm's financial and economic information to assess the value of a company's

stock.

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Common Stock Valuation 6-4

6.2 The Dividend Discount Model

Dividend discount model (DDM): Method of estimating the value of a

share of stock as the present value of all expected future dividend

payments.

A basic principle of finance holds that the economic value of an investment is

measured by the sum of the present value of all expected future cash flows.

These cash flows must also be adjusted for risk. The dividend discount model

does this by taking the sum of the present value of all expected future dividends.

This model is general in that it allows the annual dividend to differ from year-to-

year. The DDM model is written as the sum of the following discounted cash flow

flows:

Lecture Tip: One way of explaining this model is to assume that dividends go on

forever (which they do, in theory), so an analyst must take the sum of the present

value of all expected future dividends, which continue on to perpetuity. The

problem is that dividends are assumed to change over time. Students recognize

that this becomes difficult to calculate. An acceptable assumption is that an

investor will sell the stock after "T" years. This simplifies the model such that one

can calculate the sum of the present value of expected future dividends for "T"

years, and then add the present value of the expected stock price in year "T."

This estimated future stock price in year "T" contains the value of all expected

future dividends and allows an easily calculated solution.

A. Constant Perpetual Growth

Constant perpetual growth model: a version of the dividend discount

model in which dividends grow forever at a constant growth rate. Here, the

growth rate is strictly less than the discount rate.

The constant growth rate model simplifies dramatically when we assume

perpetual dividends. Note that an important assumption of this model is that g<k.

The model is as follows:

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Education.

V0=D1

(

1+k

)

+D2

(

1+k

)

2+D3

(

1+k

)

3+ ⋯ DT

(

1+k

)

T

V0=D0(1+g)

(k−g)

V0=D1

(k−g)

Common Stock Valuation 6-5

Lecture Tip: It is important to point out to students what happens when g is

greater than k. In fact, an example with g > k helps start this discussion. Students

will have some very interesting explanations of the negative stock price that

results. When it is noted that a high growth rate may be an indication of a risky

firm, this then reflects on the estimate of the required return. How can a firm have

both a high growth rate and a low required return? We can then assume that our

estimate of growth or required return may not be correct.

The simplicity of the constant perpetual growth model makes it very attractive.

However, one must remember that given its assumptions, it should only be

applied to firms with stable earnings and whose dividend growth is expected to

continue into the future. The analyst should also be aware that changing the

assumed value of g or k can dramatically change the estimated stock price.

B. Historical Growth Rates

Geometric Average Dividend Growth Rate: A dividend growth rate

based on a geometric average of historical returns.

Arithmetic Average Dividend Growth Rate: A dividend growth rate

based on an arithmetic average of historical returns.

The arithmetic average is simply the average of the individual yearly

growth rates, while the geometric average is a compounded average. As

we discussed in Chapter 1, the geometric average will be less than the

arithmetic in the presence of volatility.

We can also use analyst estimates for forecasted growth rates.

C. The Sustainable Growth Rate

Sustainable growth rate: A dividend growth rate that can be sustained by

a company's earnings.

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.

Another way to estimate the firm's growth rate is to use the sustainable growth

rate, which involves using the company's earnings to estimate g. Since earnings

not paid out to investors as dividends are available for reinvestment, these funds

can be used to finance future growth. The dividend payout is called the payout

ratio and (1 - payout ratio) is the retention ratio, the proportion of funds retained

for reinvestment. The sustainable growth rate is calculated as follows:

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Common Stock Valuation 6-6

Sustainable growth rate = ROE x Retention ratio

= ROE x (1 - Payout ratio)

D. Analyzing ROE

Return on equity (ROE) = Net income / Equity

Keep in mind that because earnings fluctuate from year-to-year, security analysts

must adjust sustainable growth rates to smooth out these earnings fluctuations.

ROE can be decomposed using the DuPont formula:

ROE = net margin x TA turnover x equity multiplier

This illustrates that understanding the business’ strategy will help the analyst

determine the impact on growth and valuation.

6.3 The 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.

Since there are many instances of companies that do not have a constant growth

rate over the long term, the two-stage dividend growth model was developed to

allow two growth rates to be incorporated in the stock price estimate. This model

assumes an initial growth rate of g1 for T years, followed by a new growth rate,

g2, which continues forever. The model is as follows:

This model requires that g2 < K, but g1 can be greater than K. This allows for the

case where the growth rate in early years is large, and then settles down to a

lower long-term growth rate.

Lecture Tip: When students are first introduced to the two-stage growth model it

is normal for them to consider it complicated. It is much easier to grasp this

model after explaining that it is simply the combination of the constant growth

model calculated twice (first and last parts of the equation), with the additional

factors [(1 + g) / (1 + k)] just used to start and stop the two growth rates. It is also

important to point out that g1 is the only growth rate used in the "time factors,"

[(1 + g) / (1 + k)]. It is a common error for students to use g1 in the first factor, and

g2 in the second factor.

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V0=D0(1+g1)

k−g1

[

1−

(

1+g1

1+k

)

T

]

+

(

1+g1

1+k

)

TD0(1+g2)

k−g2

Common Stock Valuation 6-7

Lecture Tip: For those who are interested, a derivation of the above equation

follows:

We already know that the value of the stock at time T:

The present value of VT:

which is the second term in the equation.

The first term represents the value of the dividends through time T, which is the

total value calculated at a given growth rate less the value at time T assuming the

same growth rate:

with some rearranging, we get the term on the left side of the equation:

So, the total value is the sum of these two components.

A. Nonconstant Growth in the First Stage

The main advantage of the constant perpetual growth model is its simplicity;

however, there are several disadvantages:

To be used, the firm must pay dividends.

The growth rate must be less than the discount rate.

It is sensitive to the choice of the growth and discount rates.

It may be difficult to estimate the growth and discount rates.

Constant perpetual growth may not be a realistic assumption.

The two-stage growth model is more difficult to compute, but it has

improvements:

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VT=D0(1+g1)T(1+g2)

k−g2

VT=( 1

(1+k)T)D0(1+g1)T(1+g2)

k−g2

=

(

1+g1

1+k

)

TD0(1+g2)

k−g2

V0 through T=D0(1+g1)

k−g1

−

(

1

(1+k)T

)

D0(1+g1)(T+1)

k−g1

V0=D0(1+g1)

k−g1

[

1−

(

1+g1

1+k

)

T

]

Common Stock Valuation 6-8

It is more realistic because it allows for two growth rates.

It allows the first-stage growth rate to be greater than the discount rate.

This model is also sensitive to the choice of the growth and discount rates, and it

requires that the firm pay dividends to be used.

B. The H-Model

In most two-stage models, the assumption is two distinct growth rates. In reality,

though, there may be beginning and ending growth rates, with growth between

these times changing to approach the more constant ending growth rate. If we

assume a linear change over time, this is the H-Model.

C. Discount Rates for Dividend Discount Models

Beta: measure of a stock's risk relative to the stock market average.

Beta and the Capital Asset Pricing Model (CAPM) are introduced in this section.

It is a brief introduction, with the full development left for chapter 18. This model

is introduced to allow the calculation of the required return or discount rate for the

dividend discount models, as follows:

Discount rate = U.S. T-bill rate + (Stock beta x Stock market risk premium)

Remember that the risk-free rate (T-bill rate) is the "wait" component (or time-

value-of-money), and the beta times the market risk premium is the "worry"

component (or risk premium).

Lecture Tip: To help show the sensitivity of these models to the choice of growth

and discount rates it is useful to do a few examples. The constant perpetual

growth model is simple enough that one can vary the growth and discount rates

several times, and do the calculations in a few minutes. For example, start with

D1=$1.00, k=10%, and g=5%, which gives a stock value of $20. Now increase g

to 6% and decrease k to 9% and the stock value is $33.33. Now decrease g to

4% and increase k to 11% and the stock value is $14.29. This gives a range of

stock values from $14 to $33, which is not much help in determining if this stock

is overvalued or undervalued. This dramatically shows students how sensitive

the stock price is to the estimate of the growth and discount rates.

D. Observations on Dividend Discount Models

Financial analysts readily acknowledge the limitations of dividend discount

models. Consequently, they also turn to other valuation methods to expand their

analyses.

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00

00 g

)

(

k

k Bg

)

(

1

EPS

BP

Common Stock Valuation 6-9

6.4 The Residual Income Model

How do we value the many companies that don’t pay dividends? As it turns out,

the residual income model (RIM) is an elegant and simple model that can be

used just for this purpose. It turns out that that the RIM is closely related to the

constant perpetual growth dividend model.

A. Residual Income

Let Bt–1stand for the book equity per share at the beginning of a period that ends

at time t. Over the period, the stockholders have a required return on that

investment of k. Thus, the required return in dollars, or required earnings per

share (EPS), during the period that ends at time t, or REPSt, is just:

REPSt = Bt−1 × k.

The difference between actual earnings, EPSt, and required earnings, REPSt, in

the period is called the residual income, RI, and is given by:

RIt = EPSt − REPSt = EPSt − Bt−1 × k

Residual income is sometimes called Economic Value Added, or EVA for short. It

is also called “abnormal” earnings.

Next, we can write the value of a share of stock as the sum of two parts. The first

part is the current book value of the firm (i.e., what is currently invested). The

second part is the present value of all future residual earnings. That is,

⋯

3

23

2

12

1

01

00 k)(1

k BEPS

k)(1

k BEPS

k)(1

k BEPS

BP

When we developed the constant perpetual growth model for dividend-paying

stocks, we made the simplifying assumption that dividends grow at a constant

rate of g. Here we make the similar assumption that earnings grow at a constant

rate of g. With this assumption, we can simplify the equation above to:

The equation above is known as the residual income model, or RIM. If we write

both terms in the RIM equation with a common denominator, we get the alternate

form of the RIM:

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01

0g

)

(

k

gBEPS

P

Common Stock Valuation 6-10

B. The RIM versus the Constant Growth DDM

The RIM is closely related to the constant perpetual growth dividend model. To

see the connection, assume that the change in book value per share on a stock

is equal to earnings per share minus dividends. This is known as the clean

surplus relationship (CSR), written as:

EPS1 − D1 = B1 − B0 or D1 = EPS1 + B0 − B1

Note that in practice the CSR does not exactly hold because various “dirty”

surplus changes to book equity are allowed. But it is usually a good

approximation, particularly over the long run.

Assuming that earnings and dividends per share grow at rate g, the CSR shows

that book value per share must also grow at rate g, so we can write:

D1 = EPS1 + B0 − B1 = EPS1 + B0 − B0(1 + g) = EPS1 − B0 × g

Plugging the expression for D1 into the alternate form of the RIM, we see right

away that the residual income model is mathematically the same as the constant

perpetual growth model:

gk

D

gk

gBEPS

P1

01

0

So these two approaches are really the same, but the RIM is more flexible

because we can apply it to any stock, not just dividend payers.

6.5 The Free Cash Flow Model

How do we value a firm that has negative earnings and no dividends? Well, the

FCF model gives us an alternative. Because earnings are impacted by noncash

expenses (depreciation in particular), cash flow can be positive even if earnings

are negative.

A. Free Cash Flow

FCF is given as:

FCF = EBIT (1- tax rate) + Depreciation – Capital Expenditures – change in NWC

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Common Stock Valuation 6-11

B. The FCF Model Versus the Constant Growth DDM

Free cash flow could be used to pay down debt, reinvest in the firm, or pay

dividends. Thus, it is cash flow at the total firm level. So, when we use FCF to

value, we are valuing the firm, not simply equity. This has implications.

First, we need to use an asset beta, not an equity beta. This will adjust for the

amount of leverage used by the firm.

BEquity =BAssets×[1+Debt

Equity (1−t)]

Once we have the firm value (using similar formulas to the DDM), we need to

subtract out the debt value to get to the value of the firm’s equity.

6.6 Price Ratio Analysis

Price ratios are frequently used by financial analysts, and the ratios are used

more often than dividend discount models.

A. Price-Earnings Ratios

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

earnings per share (EPS).

Earnings yield: Inverse of the P/E ratio: earnings divided by price (E/P).

Growth stocks: A term often used to describe high P/E stocks.

Value stocks: A term often used to describe low P/E stocks.

The P/E ratio is one of the most popular ratios used to assess stock value. It is

calculated as the current stock price divided by the most recent annual earnings

per share. EPS can be computed using either the sum of the last four quarters'

earnings, or the most recent quarter's earnings times four. Stocks that have high

P/Es are considered growth stocks, while those with low P/Es are considered

value stocks. The growth stocks have higher expected earnings growth, while the

value stocks are considered "cheap" relative to current earnings. We only know

historically if growth and value stocks are truly good investments.

B. Price-Cash Flow Ratios

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

flow per share.

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Common Stock Valuation 6-12

The price-cash flow ratio is calculated as the current stock price divided by

annual cash flow per share. Like earnings, cash flow can be computed as the

sum of the most recent four quarters cash flow, or four times the most recent

quarter's cash flow. There are many definitions of cash, but the most common

and easiest to use is net income plus depreciation. It is easy to show that a firm

with higher depreciation will have a lower net income, but higher cash flow, since

depreciation is a non-cash charge. A firm is considered to have good-quality

earnings when its earnings per share is not significantly larger than its cash flow

per share.

C. Price-Sales Ratios

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

share.

Price-sales ratio is calculated as the current stock price divided by annual sales

revenue per share. This rate addresses the firm's ability to generate sales

growth. A high P/S ratio suggests high sales growth, while a low P/S ratio

indicates slow sales growth.

D. Price-Book Ratios

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

divided by its book (or accounting) value of equity.

The price-book ratio is also called the market-book ratio and is calculated as the

market value of the firm's outstanding stock divided by its book value of equity.

Book values represent historical cost. Thus, P/B indicates what the firm's equity

is worth relative to its cost. Due to changing accounting standards this ratio may

be more difficult to interpret.

E. Applications of Price Ratio Analysis

Three expected stock prices for Intel and Disney are estimated using the

price/earnings ratio, the price/cash flow ratio, and the price/sales ratio.

Expected Price = Historical P/E ratio x Current EPS x (1 + Projected EPS Growth

Rate)

Expected Price = Historical P/CF ratio x Current CFPS x (1 + Projected CFPS

Growth Rate)

Expected Price = Historical P/S ratio x Current SPS x (1 + Projected Sales

Growth Rate)

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Common Stock Valuation 6-13

F. Enterprise Value Ratios

The price ratios look exclusively at equity value. The enterprise value (EV) to

EBITDA ratio captures the value of both debt and equity.

EV = market value of firm’s equity + market value of debt – cash

The impact of leverage on this ratio is less pronounced since it captures the

value of debt.

6.7 An Analysis of the E. I. du Pont Company

A complete example of valuation for E. I. du Pont is provided in the text. This

example is extremely helpful in showing how these formulas can be

implemented. Students will be a bit “bleary-eyed” by all the formulas, and this

example really helps them grasp the application of these analyst tools. To save

time, students can be broken-out into their study groups to perform several of the

calculations, which they can then present to the class.

In this complete example, students are shown how to use actual information

available from free online sources information and four approaches:

A. Using the Dividend Discount Model

We also examine a multiperiod growth model in this section.

B. Using the Residual Income Model

C. Using the Free Cash Flow Model

D. Using Price Ratio Analysis

6.8 Summary and Conclusions

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