Type
Solution Manual
Book Title
Fundamentals of Investments: Valuation and Management 8th Edition
ISBN 13
978-1259720697

978-1259720697 Chapter 6 Lecture Note

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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Education.
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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McGraw-Hill
Education.
V0=D1
(
1+k
)
+D2
(
1+k
)
2+D3
(
1+k
)
3+ DT
(
1+k
)
T
V0=D0(1+g)
(kg)
V0=D1
(kg)
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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McGraw-Hill
Education.
V0=D0(1+g1)
kg1
[
1
(
1+g1
1+k
)
T
]
+
(
1+g1
1+k
)
TD0(1+g2)
kg2
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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McGraw-Hill
Education.
VT=D0(1+g1)T(1+g2)
kg2
V0 through T=D0(1+g1)
kg1
(
1
(1+k)T
)
D0(1+g1)(T+1)
kg1
V0=D0(1+g1)
kg1
[
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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McGraw-Hill
Education.
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 (1t)]
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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McGraw-Hill
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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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