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P0 = $2.98 + $22.72 = $25.70
Thus price today should be about $25.70 per share.
United Bird Seed is looking forward to several years of very rapid growth, so you
could not use the constant-growth formula to value United™s stock today. But the for-
mula may help you check your estimate of the terminal price in Year 3 when the com-
pany has settled down to a steady rate of growth. From then on dividends are forecast
to grow at a constant rate of g = .05 (5 percent). Thus the expected dividend in Year 4
DIV4 = 1.05 — DIV3 = 1.05 — $1.44 = $1.512
and the expected terminal price in Year 3 is
DIV4 $1.512
P3 = = = $30.24
r “ g .10 “ .05
the same value we found when we used the P/E ratio to predict P3. In this case our two
approaches give the same estimate of P3, though you shouldn™t bet on that always being
the case in practice.

Suppose that another stock market analyst predicts that United Bird Seed will not set-
Self-Test 7
tle down to a constant 5 percent growth rate in dividends until after Year 4, and that div-
idends in Year 4 will be $1.73 per share. What is the fair price for the stock according
to this analyst?

Growth Stocks and Income Stocks
We often hear investors speak of growth stocks and income stocks. They seem to buy
growth stocks primarily in the expectation of capital gains, and they are interested in the
future growth of earnings rather than in next year™s dividends. On the other hand, they
Valuing Stocks 297

buy income stocks principally for the cash dividends. Let us see whether these distinc-
tions make sense.
Think back once more to Blue Skies. It is expected to pay a dividend next year of $3
(DIV1 = 3), and this dividend is expected to grow at a steady rate of 8 percent a year (g
= .08). If investors require a return of 12 percent (r = .12), then the price of Blue Skies
should be DIV1/(r “ g) = $3/(.12 “ .08) = $75.
Suppose that Blue Skies™s existing assets generate earnings per share of $5.00. It
pays out 60 percent of these earnings as a dividend. This payout ratio results in a div-
idend of .60 — $5.00 = $3.00. The remaining 40 percent of earnings, the plowback
of earnings paid out as
ratio, is retained by the firm and plowed back into new plant and equipment. (The
plowback ratio is also called the earnings retention ratio.) On this new equity invest-
ment Blue Skies earns a return of 20 percent.
If all of these earnings were plowed back into the firm, Blue Skies would grow at 20
Fraction of earnings retained
percent per year. Because a portion of earnings is not reinvested in the firm, the growth
by the firm.
rate will be less than 20 percent. The higher the fraction of earnings plowed back into
the company, the higher the growth rate. So assets, earnings, and dividends all grow by
g = return on equity plowback ratio
= 20% — .40 = 8%
What if Blue Skies did not plow back any of its earnings into new plant and equip-
ment? In that case it would pay out all its earnings as dividends but would forgo any
growth in dividends. So we could recalculate value with DIV1 = $5.00 and g = 0:
P0 = = $41.67
.12 “ 0
Thus if Blue Skies did not reinvest any of its earnings, its stock price would not be $75
but $41.67. The $41.67 represents the value of earnings from the assets that are already
in place. The rest of the stock price ($75 “ $41.67 = $33.33) is the net present value of
the future investments that Blue Skies is expected to make. This is reflected in the
market-value balance sheet, Table 3.6.
What if Blue Skies kept to its policy of reinvesting 40 percent of its profits but the
forecast return on this new investment was only 12 percent? In that case the expected
growth in dividends would also be lower:
g = return on equity — plowback ratio
= 12% — .40 = 4.8%
If we plug this new value for g into our valuation formula, we come up again with a
value of $41.67 for Blue Skies stock:
DIV1 $3.00
P0 = = = $41.67
r“g .12 “ .048

(all quantities on a per-share basis)
Assets Liabilities and Shareholders™ Equity
Assets in place $41.67 Shareholders™ equity $75
Investment opportunities 33.33 Debta 0

a We assume the firm is all-equity financed.

Plowing earnings back into new investments may result in growth in earnings
and dividends but it does not add to the current stock price if that money is
expected to earn only the return that investors require. Plowing earnings
back does add to value if investors believe that the reinvested earnings will
earn a higher rate of return.

To repeat, if Blue Skies did not plow back earnings or if it earned only the return that
investors required on the new investment, its stock price would be $41.67. The total
value of Blue Skies stock is $75. Of this figure, $41.67 is the value of the assets already
in place, and the remaining $33.33 is the present value of the superior returns on assets
Net present
to be acquired in the future. The latter is called the present value of growth opportu-
value of a firm™s future
nities, or PVGO. (Remember that investors expected Blue Skies to earn 20 percent on
its new investments, well above the 12 percent expected return necessary to attract in-
By the way, growth rates calculated as
g = return on equity — plowback ratio
rate at which firm can grow;
return on equity — plowback
are often referred to as sustainable growth rates.

Suppose that instead of plowing money back into lucrative ventures, Blue Skies™s man-
Self-Test 8
agement is investing at an expected return on equity of 10 percent, which is below the
return of 12 percent that investors could expect to get from comparable securities.
a. Find the sustainable growth rate of dividends and earnings in these circumstances.
Assume a 60 percent payout ratio.
b. Find the new value of its investment opportunities. Explain why this value is nega-
tive despite the positive growth rate of earnings and dividends.
c. If you were a corporate raider, would Blue Skies be a good candidate for an at-
tempted takeover?

The superior prospects of Blue Skies are reflected in its price-earnings ratio. With a
stock price of $75.00 and earnings of $5.00, the P/E ratio is $75/$5 = 15. If Blue Skies
had no growth opportunities, its stock price would be only $41.67 and its P/E would be
$41.67/$5 = 8.33. The P/E ratio, therefore, is an indicator of the prospects of the firm.
To justify a high P/E, one must believe the firm is endowed with ample growth oppor-

Be careful when you look at price-earnings ratios. In our discussion, “expected future
earnings” refers to expected cash flow less the true depreciation in the value of the as-
sets. What is “true” depreciation? It is the amount that the firm must reinvest simply to
offset any deterioration in its assets. In practice, however, when accountants calculate
the earnings that are reported in the company™s income statement, they do not attempt
to measure true depreciation. Instead reported earnings are based on generally accepted
accounting principles, which use rough-and-ready rules of thumb to calculate the de-

“New Paradigm” View
for Stocks Is Bolstered
future are not so implausible,” Leonard Nakamura, eco-
Maybe all the new-economy hype isn™t just hype after
nomic adviser at the Federal Reserve Bank of Philadel-
phia says.
Almost everyone agrees the revolution in information
Mr. Nakamura estimates that after treating R&D as
technology has probably played some part in the ex-
regular investment and removing inflation™s distorting
traordinary valuations that stocks have reached this
impact on inventories and depreciation, the market™s
P/E ratio is only a little higher than in 1972, whereas un-
But figuring out how big a part has proved elusive.
adjusted, it is 41% higher.
Skeptics look on “new paradigm” arguments as the sort
Federal Reserve Chairman Alan Greenspan ac-
of fuzzy-minded thinking that usually accompanies
knowledged two weeks ago that the economy™s shift to
speculative bubbles in the stock market.
“idea-based value added,” where investment is ex-
Now, some researchers have found compelling evi-
pensed immediately rather than depreciated over time,
dence that conventional accounting understates the
has understated earnings, although that is offset by the
earning power of today™s companies”earning power
increased use of stock options in place of wages. But
that the stock market correctly recognizes.
he added, “It does not seem likely . . . that such [ac-
The research, if correct, goes a long way toward ex-
counting] adjustments can be the central explanation of
plaining how stocks, in particular of technology compa-
the extraordinary increase in stock prices.”
nies, could sensibly trade at such unprecedented mul-
Mr. Nakamura says, “It could be that some propor-
tiples of earnings.
tion of what™s going on now is a bubble . . . It™s impor-
Friday, those trends were well in force. The Dow
tant not to be complacent about the stock market and
Jones Industrial Average eased 50.97 points to
think it will do this forever. On the other hand, it™s im-
11028.43. But the Nasdaq Composite Index, loaded
portant to recognize we™re in fact saving and investing
with technology stocks, climbed 35.04 to a record
a lot more than it appears on the surface.”
2887.06, passing its previous high of 2864.48 set on
The economic establishment is beginning to accept
July 16. The Standard & Poor™s 500-stock index, which
some of these arguments”but only some. The Bureau
added 4 to 1351.66, now stands at a near-record 33
of Economic Analysis is about to change how it calcu-
times trailing earnings.
lates economic output by reclassifying software pur-
But does such a high price-to-earnings ratio mean
chases as investments rather than current spending,
stocks are overvalued? Earnings would be higher and
which it estimates would have boosted the level of out-
P/E ratios lower if companies weren™t spending so
put in 1996 by 1.5% (although the boost to output
heavily on “intangible assets” such as research and de-
growth would be far smaller). But for now it isn™t reclas-
velopment, software, marketing and computer training.
sifying databases, or literary or artistic works as invest-
Intangible assets fuel future profits just as surely as
ments, as international guidelines suggest.
would a “tangible asset” such as a piece of equipment
or a factory. But intangibles are expensed against cur-
rent earnings, while “tangible” assets are added to the Source: Republished with permission of Dow Jones, from “ ˜New
balance sheet and gradually depreciated. Paradigm™ View for Stocks Is Bolstered,” by Greg Ip, The Wall Street
This “helps explain the rising value of U.S. equities. Journal, September 13, 1999: Permission conveyed through Copy-
That explanation, in turn, suggests that continued right Clearance Center, Inc.
strong economic growth and strong profit growth in the

preciation of the firm™s assets. A switch in the depreciation method can dramatically
change reported earnings without affecting the true profitability of the firm.
Other accounting choices that can affect reported earnings are the method for valu-
ing inventories, the decision to treat research and development as a current expense
rather than as an investment, and the way that tax liabilities are reported.


A Small Spat about $1.6 Billion

extreme position only if each could be sure that the
Company valuation is not a precise science. When two
other side would do so also. Conversely, a more mid-
companies dispute the price that one should pay for the
dle-of-the-road posture made sense if each could be
other, a battle between their investment bankers can be
confident that the other would provide a middle-of-the-
road valuation.
AT&T bought McCaw Cellular in 1994. As a result it
When the two parties met at Morgan Stanley™s of-
acquired McCaw™s 52 percent stake in the shares of a
fices to examine each other™s valuations, there was a
cellular communications company, LIN Broadcasting,
stunned silence, and then Bear Stearns™s team began
and assumed an obligation to buy the remaining 48 per-
to laugh. Morgan Stanley™s valuation was $100 a share,
cent of the shares at their fair value. The process for de-
while Lehman Brothers and Bear Stearns came up with
termining fair value was laid down when McCaw ac-
a figure of $162 a share. Since AT&T was proposing to
quired its initial stake in LIN. AT&T and LIN had 30 days
buy 25 million LIN shares, the disagreement amounted
to come up with an initial valuation of the shares and


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