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 Unitedâ€™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 Ă— DIV3 = 1.05 Ă— $1.44 = $1.512
and the expected terminal price in Year 3 is
P3 = = = $30.24
r â€“ g .10 â€“ .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 shouldnâ€™t bet on that always being
the case in practice.
Suppose that another stock market analyst predicts that United Bird Seed will not set-
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 yearâ€™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 â€“ g) = $3/(.12 â€“ .08) = $75.
Suppose that Blue Skiesâ€™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 Ă— $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% Ă— .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 â€“ 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 â€“ $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 Ă— plowback ratio
= 12% Ă— .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:
P0 = = = $41.67
râ€“g .12 â€“ .048
MARKET-VALUE BALANCE SHEET FOR BLUE SKIES
(all quantities on a per-share basis)
Assets Liabilities and Shareholdersâ€™ Equity
Assets in place $41.67 Shareholdersâ€™ equity $75
Investment opportunities 33.33 Debta 0
a We assume the firm is all-equity financed.
298 SECTION THREE
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
to be acquired in the future. The latter is called the present value of growth opportu-
value of a firmâ€™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 Ă— plowback ratio
rate at which firm can grow;
return on equity Ă— plowback
are often referred to as sustainable growth rates.
Suppose that instead of plowing money back into lucrative ventures, Blue Skiesâ€™s man-
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-
THE PRICE-EARNINGS RATIO
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-
WHAT DO EARNINGS MEAN?
Be careful when you look at price-earnings ratios. In our discussion, â€śexpected future
earningsâ€ť refers to expected cash flow less the true depreciation in the value of the as-
sets. What is â€śtrueâ€ť 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 companyâ€™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-
FINANCE IN ACTION
â€śNew Paradigmâ€ť View
for Stocks Is Bolstered
future are not so implausible,â€ť Leonard Nakamura, eco-
Maybe all the new-economy hype isnâ€™t just hype after
nomic adviser at the Federal Reserve Bank of Philadel-
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 inflationâ€™s distorting
traordinary valuations that stocks have reached this
impact on inventories and depreciation, the marketâ€™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 â€śnew paradigmâ€ť arguments as the sort
Federal Reserve Chairman Alan Greenspan ac-
of fuzzy-minded thinking that usually accompanies
knowledged two weeks ago that the economyâ€™s shift to
speculative bubbles in the stock market.
â€śidea-based value added,â€ť 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 todayâ€™s companiesâ€”earning power
increased use of stock options in place of wages. But
that the stock market correctly recognizes.
he added, â€śIt 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.â€ť
nies, could sensibly trade at such unprecedented mul-
Mr. Nakamura says, â€śIt could be that some propor-
tiples of earnings.
tion of whatâ€™s going on now is a bubble . . . Itâ€™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, itâ€™s im-
11028.43. But the Nasdaq Composite Index, loaded
portant to recognize weâ€™re in fact saving and investing
with technology stocks, climbed 35.04 to a record
a lot more than it appears on the surface.â€ť
2887.06, passing its previous high of 2864.48 set on
The economic establishment is beginning to accept
July 16. The Standard & Poorâ€™s 500-stock index, which
some of these argumentsâ€”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 werenâ€™t spending so
put in 1996 by 1.5% (although the boost to output
heavily on â€śintangible assetsâ€ť such as research and de-
growth would be far smaller). But for now it isnâ€™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 â€śtangible assetâ€ť such as a piece of equipment
or a factory. But intangibles are expensed against cur-
rent earnings, while â€śtangibleâ€ť assets are added to the Source: Republished with permission of Dow Jones, from â€ś â€˜New
balance sheet and gradually depreciated. Paradigmâ€™ View for Stocks Is Bolstered,â€ť by Greg Ip, The Wall Street
This â€śhelps 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 firmâ€™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.
FINANCE IN ACTION
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-
AT&T bought McCaw Cellular in 1994. As a result it
When the two parties met at Morgan Stanleyâ€™s of-
acquired McCawâ€™s 52 percent stake in the shares of a
fices to examine each otherâ€™s valuations, there was a
cellular communications company, LIN Broadcasting,
stunned silence, and then Bear Stearnsâ€™s team began
and assumed an obligation to buy the remaining 48 per-
to laugh. Morgan Stanleyâ€™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