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the projects, leaving shareholders to invest the dividends in other opportunities at a fair mar-
dividend payout ket rate of only 12.5%. Suppose, therefore, Growth Prospects chooses a lower dividend
ratio payout ratio (the fraction of earnings paid out as dividends), reducing payout from 100% to
Percentage of
earnings paid out as Actually, we are referring here to earnings net of the funds necessary to maintain the productivity of the firm™s cap-
dividends. ital, that is, earnings net of “economic depreciation.” In other words, the earnings figure should be interpreted as the
maximum amount of money the firm could pay out each year in perpetuity without depleting its productive capacity.
For this reason, the net earnings number may be quite different from the accounting earnings figure that the firm re-
ports in its financial statements. We will explore this further in the next chapter.
Bodie’Kane’Marcus: IV. Security Analysis 12. Equity Valuation © The McGraw’Hill
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Fifth Edition

12 Equity Valuation

F I G U R E 12.1
Low reinvestment
Dividends per share ($) Dividend growth for
High reinvestment
10 two earnings
reinvestment policies




0 10 20 30

40%, and maintaining a plowback ratio (the fraction of earnings reinvested in the firm) of plowback ratio
60%. The plowback ratio also is referred to as the earnings retention ratio. or earnings
The dividend of the company, therefore, will be $2 (40% of $5 earnings) instead of $5. Will retention ratio
the share price fall? No, it will rise! Although dividends initially fall under the earnings rein- The proportion of the
vestment policy, subsequent growth in the assets of the firm because of reinvested profits will firm™s earnings that is
generate growth in future dividends, which will be reflected in today™s share price. reinvested in the
business (and not paid
Figure 12.1 illustrates the dividend streams generated by Growth Prospects under two div-
out as dividends).
idend policies. A low reinvestment rate plan allows the firm to pay higher initial dividends but
results in a lower dividend growth rate. Eventually, a high reinvestment rate plan will provide
higher dividends. If the dividend growth generated by the reinvested earnings is high enough,
the stock will be worth more under the high reinvestment strategy.
How much growth will be generated? Suppose Growth Prospects starts with plant and
equipment of $100 million and is all-equity-financed. With a return on investment or equity
(ROE) of 15%, total earnings are ROE $100 million 0.15 $100 million $15 million.
There are 3 million shares of stock outstanding, so earnings per share are $5, as posited above.
If 60% of the $15 million in this year™s earnings is reinvested, then the value of the firm™s cap-
ital stock will increase by 0.60 $15 million $9 million, or by 9%. The percentage increase
in the capital stock is the rate at which income was generated (ROE) times the plowback ratio
(the fraction of earnings reinvested in more capital), which we will denote as b.
Now endowed with 9% more capital, the company earns 9% more income and pays out 9%
higher dividends. The growth rate of the dividends, therefore, is3
g ROE b 15% 0.60 9%
If the stock price equals its intrinsic value, and this growth rate can be sustained (i.e., if the
ROE and payout ratios are consistent with the long-run capabilities of the firm), then the stock
should sell at
D1 $2
P0 $57.14
k g 0.125 0.09

We can derive this relationship more generally by noting that with a fixed ROE, earnings (which equal ROE Book
value) will grow at the same rate as the book value of the firm. Abstracting from net new investment in the firm, the
growth rate of book value equals reinvested earnings/book value. Therefore,

Reinvested earnings Reinvested earnings Total earnings
g b ROE
Book value Total earnings Book value
Bodie’Kane’Marcus: IV. Security Analysis 12. Equity Valuation © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

422 Part FOUR Security Analysis

When Growth Prospects pursued a no-growth policy and paid out all earnings as dividends,
the stock price was only $40. Therefore, you can think of $40 as the value per share of the as-
sets the company already has in place.
When Growth Prospects decided to reduce current dividends and reinvest some of its earn-
ings in new investments, its stock price increased. The increase in the stock price reflects the
fact that planned investments provide an expected rate of return greater than the required rate.
In other words, the investment opportunities have positive net present value. The value of the
firm rises by the NPV of these investment opportunities. This net present value is also called
the present value of growth opportunities, or PVGO.
present value
Therefore, we can think of the value of the firm as the sum of the value of assets already in
of growth
place, or the no-growth value of the firm, plus the net present value of the future investments
the firm will make, which is the PVGO. For Growth Prospects, PVGO $17.14 per share:
Net present value of a Price No-growth value per share PVGO
firm™s future
$57.14 $40 $17.14 (12.6)

We know that in reality, dividend cuts almost always are accompanied by steep drops in
stock prices. Does this contradict our analysis? Not necessarily: Dividend cuts are usually taken
as bad news about the future prospects of the firm, and it is the new information about the
firm”not the reduced dividend yield per se”that is responsible for the stock price decline. The
stock price history of Microsoft proves that investors do not demand generous dividends if they
are convinced that the funds are better deployed to new investments in the firm.
In one well-known case, Florida Power & Light announced a cut in its dividend, not be-
cause of financial distress, but because it wanted to better position itself for a period of dereg-
ulation. At first, the stock market did not believe this rationale”the stock price dropped 14%
on the day of the announcement. But within a month, the market became convinced that the
firm had in fact made a strategic decision that would improve growth prospects, and the share
price actually rose above its preannouncement value. Even including the initial price drop, the
share price outperformed both the S&P 500 and the S&P utility index in the year following the
dividend cut.
It is important to recognize that growth per se is not what investors desire. Growth en-
hances company value only if it is achieved by investment in projects with attractive profit op-
portunities (i.e., with ROE k). To see why, let™s now consider Growth Prospects™
unfortunate sister company, Cash Cow. Cash Cow™s ROE is only 12.5%, just equal to the re-
quired rate of return, k. Therefore, the NPV of its investment opportunities is zero. We™ve seen
that following a zero-growth strategy with b 0 and g 0, the value of Cash Cow will be
E1/k $5/0.125 $40 per share. Now suppose Cash Cow chooses a plowback ratio of b
0.60, the same as Growth Prospects™ plowback. Then g would be
g ROE b 0.125 0.60 0.075
but the stock price is still
D1 $2
P0 $40
k g 0.125 0.075
no different from the no-growth strategy.
In the case of Cash Cow, the dividend reduction that frees funds for reinvestment in the firm
generates only enough growth to maintain the stock price at the current level. This is as it
Bodie’Kane’Marcus: IV. Security Analysis 12. Equity Valuation © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

12 Equity Valuation

should be: If the firm™s projects yield only what investors can earn on their own, shareholders
cannot be made better off by a high reinvestment rate policy. This demonstrates that “growth”
is not the same as growth opportunities. To justify reinvestment, the firm must engage in proj-
ects with better prospective returns than those shareholders can find elsewhere. Notice also that
the PVGO of Cash Cow is zero: PVGO P0 E1/k 40 40 0. With ROE k, there is
no advantage to plowing funds back into the firm; this shows up as PVGO of zero. In fact, this
is why firms with considerable cash flow, but limited investment prospects, are called “cash
cows.” The cash these firms generate is best taken out of or “milked from” the firm.

Takeover Target is run by entrenched management that insists on reinvesting 60% of its earn-
ings in projects that provide an ROE of 10%, despite the fact that the firm™s capitalization rate
is k 15%. The firm™s year-end dividend will be $2 per share, paid out of earnings of $5 per
share. At what price will the stock sell? What is the present value of growth opportunities? Growth
Why would such a firm be a takeover target for another firm? Opportunities
Given current management™s investment policy, the dividend growth rate will be
g b
ROE 10% 0.6 6%
and the stock price should be
P0 $22.22
0.15 0.06
The present value of growth opportunities is
PVGO Price per share No-growth value per share
$22.22 $22.22 $5/0.15 $11.11
PVGO is negative. This is because the net present value of the firm™s projects is negative: The
rate of return on those assets is less than the opportunity cost of capital.
Such a firm would be subject to takeover, because another firm could buy the firm for the
market price of $22.22 per share and increase the value of the firm by changing its invest-
ment policy. For example, if the new management simply paid out all earnings as dividends,
the value of the firm would increase to its no-growth value, E1/k $5/0.15 $33.33.

3. a. Calculate the price of a firm with a plowback ratio of 0.60 if its ROE is 20%. Concept
Current earnings, E1, will be $5 per share, and k 12.5%.
b. What if ROE is 10% less than the market capitalization rate? Compare the
firm™s price in this instance to that of a firm with the same ROE and E1, but a
plowback ratio of b 0.

Life Cycles and Multistage Growth Models
As useful as the constant growth DDM formula is, you need to remember that it is based on a
simplifying assumption, namely, that the dividend growth rate will be constant forever. In fact,
firms typically pass through life cycles with very different dividend profiles in different
phases. In early years, there are ample opportunities for profitable reinvestment in the com-
pany. Payout ratios are low, and growth is correspondingly rapid. In later years, the firm ma-
tures, production capacity is sufficient to meet market demand, competitors enter the market,
and attractive opportunities for reinvestment may become harder to find. In this mature phase,
the firm may choose to increase the dividend payout ratio, rather than retain earnings. The div-
idend level increases, but thereafter it grows at a slower rate because the company has fewer
growth opportunities.
Bodie’Kane’Marcus: IV. Security Analysis 12. Equity Valuation © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

424 Part FOUR Security Analysis

Return on Payout Growth Rate*
TA B L E 12.2 Assets Ratio 2002“2005
Financial ratios in
two industries
Analog Devices 17.0% 0.0% 27.2%
Cirrus Logic 12.0 0.0 34.6
Intel 22.5 7.0 22.6
LSI Logic Corp. 16.0 0.0 32.8
Micron Technologies 21.5 0.0 22.5
Motorola 10.5 17.0 41.7
National Semiconductor 21.0 0.0 19.8
Novellus 17.0 0.0 14.1
Texas Instruments 10.0 9.0 25.9
Average 16.4% 3.7% 26.8%
Electric utilities
Alleghany Energy 10.0% 32.0% 9.8%
Central Vermont 8.0 49.0 8.3
Consolidated Edison 7.5 67.0 1.5
Energy East 6.5 51.0 5.8
G.P.U. 9.0 58.0 5.6
Green Mountain Power 8.5 54.0 8.7
Northeast Utilities 6.0 51.0 11.2
Nstar 9.0 55.0 4.3
United Illuminating 7.5 63.0 3.1
Average 8.0% 53.3% 6.5%

*Year 2002 earnings for some semiconductor firms were negative, which would make growth rates meaningless.
In these cases, we used an average of recent-year earnings, or longer term growth estimates from Value Line.
Source: From Value Line Investment Survey, 2001. Reprinted by permission of Value Line Investment Survey.

Table 12.2 illustrates this profile. It gives Value Line™s forecasts of return on assets, dividend
payout ratio, and three-year growth rate in earnings per share of a sample of the firms included
in the semiconductor industry versus those of East Coast electric utilities. (We compare return
on assets rather than return on equity because the latter is affected by leverage, which tends to
be far greater in the electric utility industry than in the semiconductor industry. Return on assets
measures operating income per dollar of total assets, regardless of whether the source of the
capital supplied is debt or equity. We will return to this issue in the next chapter.)
Despite recent problems, the semiconductor firms as a group have attractive investment op-
portunities. The average return on assets of these firms is forecast to be 16.4%, and the firms
have responded with quite high plowback ratios. Many of these firms pay no dividends at all.
The high returns on assets and high plowback ratios result in rapid growth. The average


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