CHAPTER 9
THE VALUATION OF COMMON STOCK
Teaching Guides for Questions and Problems in the Text
QUESTIONS
9-1. The sources of return from an investment in stock are dividend income, an increase in
the value of the stock, or a combination of both. An investment is made with the
anticipation of earning a return (i.e., the expected return). The required return is used to
value a stock. If the required return is less than the expected return, the stock is considered
9-2. This is the same question as 9-1 but expressed in monetary units instead of
percentages. The value is what the investor believes the stock is worth. If this value
9-3. According to the dividend-growth model, the determinants of a stock’s value are
current dividends, the rate of growth in dividends, and investors’ required rate of return.
9-4. Interest rates and risk enter the valuation process by affecting an investment’s required
9-5. Possible anomalies (exceptions) to efficient markets include the January effect and the
small firm effect. (Efficient market exceptions are covered in Chapter 4.) One anomaly that
seems to offer the hope for the investor is insider trading, since evidence exists that stock
9-6. This question requires that the student apply material from the chapter by locating
fundamental ratios such as P/E and P/S and then compare the ratios for the selected firms. I
PROBLEMS
9-1. According to the dividend-growth model
a.
b.
c.
If the price of the stock is $20, then the individual’s valuations are greater than the price,
and the stock should be bought.
This problem illustrates the components of the dividend-growth model. Parts (a) and (b)
9-2. V = $1(1 + .07) = $21.40
9-3. First determine the dividend paid: $2 X .4 = $.80
a. The value of the stock:
b. If the dividend rises by 20 percent, the new dividend
is D = $.80(1 + .2) = $.96. The value of the stock becomes:
In the last case the required rate of return rose because the firm increased its use of
financial leverage (e.g., debt financing) which increased risk.
9-4. The required rate of return is
9-5. a. kA = .08 + (.15 – .08)1.5 = .185 = 18.5%
b. Valuation of stock A:
c. Valuation of stock B:
d. Valuation of the stock:
9-6. a. Just because stock A offers higher potential growth is insufficient reason to buy it.
b. Just because stock B offers a higher dividend yield is insufficient reason to buy it.
c. Required rate of return for A:
9-7. Required rate of return:
k = .014 + (.08 – .014)1.34 = 10.244%
Valuation of stock QED:
9-8. This problem and the next two problems illustrate the super-growth version of the
dividend-growth model. They illustrate that if the simplifying assumption concerning the
Year Dividend X (Present Value Interest Factor)
1 $1.20(.909) = $1.09
$61.34
9-9. First, determine the investor’s required rate of return.
Year Dividend X (Present Value Interest Factor)
1 $2.50/(1.127) = $2.50(.887) = $2.218
(Notice that the interest factors cannot be found in the interest table, so they must be
calculated. The student may also use a financial calculator.)
Third, determine the value of the stock during the period of normal growth and bring that
amount back to the present.
Value at the beginning of year four:
9-10. This problem illustrates a declining-growth version of the dividend-growth model.
The dividend declines to a level that will be maintained indefinitely. I use the problem to
illustrate that not all firms grow and that declining firms still have value as long as they are
able to generate cash flow (i.e., dividends when applying the dividend-growth model).
Investment Assignment (Part 4)
Part 4 applies the various ratios covered in the chapter to the stocks the individual student
is following and to use the ratios to rank the companies. In Question 6, the student is asked
to determine if based on this information, should any of the stocks be sold.
Teaching Guides for the Financial Advisor’s Case: Blue Jeans and Stock Selection
OBJECTIVES: To perform a ratio analysis of a firm’s financial statements and to explore
difficulties associated with making the dividend-growth model operational. The case
combines Chapters 8 and 9.
BACKGROUND: The investor, H.B. Babalola, is considering purchasing the stock of
Dentex, primarily because he has observed the popularity of its primary product, denim,
with the younger generation. Dentex currently sells for $50, and Babalola wants to know if
the stock is a good purchase at that price. This is the fundamental valuation question facing
investors, since determining whether a stock should be bought or sold requires determining
what the stock is worth.
The case has two distinct parts. The first is a ratio analysis of Dentex’s financial
statements, which should create no difficulties. The second part is the application of the
dividend-growth model. Dentex has experienced a period of rapid growth but has had a
poor year and a large decline in earnings. The case raises questions such as (1) can the
historical information (e.g., the rapid growth of past dividends) forecast future performance
and (2) is the recent fiscal year an aberration or an indication of a new environment
developing for the firm.
Guides for the Questions
1. The first part of the case requires a ratio analysis of the firm’s financial statements. The
ratios and the industry averages are as follows:
2015 2014
(Industry average = 10X)
(Since the income statement does not give earnings before interest and taxes as a separate
line, the analyst must add interest expense to earnings before taxes to determine EBIT.)
The ratio analysis indicates that while Dentex has had a poor year, it is fundamentally
sound as most of the ratios exceed the industry averages. Its current position seems
particularly strong as the firm is more liquid than the industry average and turns over both
Ratio analysis cannot answer such questions as whether the current year’s decline is an
aberration or whether the investor should buy the stock. The analysis does indicate the
historical financial strength of the firm. Since Dentex appears to be a financially strong
2. The current payout ratio is $2.20/$5.87 = 37.4%. The last year the payout ratio exceeded
30% was 2007. For the last five years, the ratio has averaged 22.3%. (The importance of
3. Since ten years have elapsed, the growth rate in earnings may be computed using an
interest table for the future value of $1:
(One weakness with this approach is that it uses only two observations, which could
generate misleading information, especially if one of the years is an aberration.)
The current dividend yield is
4. Prior to 2013, the dividend policy was to distribute less than one fourth of the firm’s
earnings. In 2013, the firm distributed 37 percent of its earnings. Management chose to
maintain the dividend (and even increased it) instead of distributing a given percentage of
5. Many factors may affect the unsystematic risk associated with a firm. This question
a. Dentex is primarily a one-product firm, the manufacture of denim. While this fabric may
be popular, any change in demand will certainly have an impact on Dentex. While many
b. Dentex uses a modest amount of financial leverage as its debt ratio is less than the
c. Foreign competition is fierce in textiles, so the investor needs to determine if foreign
6. The P/E ratio for Dentex is $50/$5.87 = 8.5, which is low. Interpreting this ratio,
however, is difficult. Some analysts believe that low P/E ratios are a harbinger of lower
future earnings (and perhaps lower dividends). These analysts would avoid this stock.
Other follows of the market suggest buying low P/E stocks on the grounds that bad news
7. The growth rate for Dentex cannot continue indefinitely in excess of 15 percent,
because the earnings cannot sustain that growth. In addition, the company has increased
8. The dividend-growth model for stock valuation is
9. In the capital asset pricing model, the required return is
k = Rf + (Rmm – Rf)beta.
SUMMARY
Based on the ratio analysis, Dentex may offer an opportunity if the current decline in
earnings has severely depressed the price of the stock and created a buying opportunity.
However, the firm may have changed, and several years may lapse before the financial
statements mirror this fundamental change in the firm. If such a change has occurred, the
stock may not be undervalued, and the ratio analysis does not forecast the future of the
firm.
The stock is no longer overvalued and should be purchased. (The instructor may wish to
Teaching Guides for Financial Advisor’s Case: Determining the Value of a Business
Valuing a privately held business is exceedingly important for at least two reasons. The
first is the determination of the value for estate purposes. Overvaluation will lead to the
1. The value based on the P/E is
lowest valuation: 9 x $8.50 = $76.50
highest valuation: 17 x $8.50 = $144.50
Given these per share valuations, the value of the firm is
2. The growth rate depends on the technique used to estimate the rate. For the purpose of
this case, use the future value of a dollar, so that the interest factor for the growth rate
based on the increase in earnings from $6.70 to $8.50 is
3. The valuation based on the dividend-growth model also requires an estimate of the
required rate of return. Since the return on the market is expected to exceed the risk-free
rate by 6 percent and the appropriate beta is 0.85, the required rate of return is
Required rate of return = .052 + (.112 – .052)0.85 = 10.3%
4. These valuations are built on the assumption that infor-mation concerning publicly held
firms is applicable to this firm. Specifically the P/E and beta coefficient used in the above
valuations were for publicly held firms. This information is not available for privately held
firms.
5. a. If the anticipated market return rises, that should increase the required return, which
decreases the value of the stock.
6. Large estates may be subject to a substantial tax. It the estate tax rate is 35%, a
reduction in the valuation of $1,000,000 translates into a tax savings of $350,000.