With both historical and analyst estimates, growth is an
exogenous variable that affects value but is divorced from the operating
details of the firm. The soundest way of incorporating growth into value is to
make it endogenous, i.e., to make it a function of how much a firm reinvests
for future growth and the quality of its reinvestment. We will begin by
considering the relationship between fundamentals and growth in equity income,
and then move on to look at the determinants of growth in operating income.
When
estimating cash flows to equity, we usually begin with estimates of net income,
if we are valuing equity in the aggregate, or earnings per share, if we are
valuing equity per share. In this section, we will begin by presenting the
fundamentals that determine expected growth in earnings per share and then move
on to consider a more expanded version of the model that looks at growth in net
income.
The
simplest relationship determining growth is one based upon the retention ratio
(percentage of earnings retained in the firm) and the return on equity on its
projects. Firms that have higher retention ratios and earn higher returns on
equity should have much higher growth rates in earnings per share than firms
that do not share these characteristics. To establish this, note that
where,
gt = Growth Rate in Net Income
NIt = Net Income in year t
Given
the definition of return on equity, the net income in year t1 can be written
as:
where,
ROEt1 = Return on equity in year t1 _{}
The
net income in year t can be written as:
Assuming
that the return on equity is unchanged, i.e., ROEt = ROEt1 =ROE,
where
b is the retention ratio. Note that the firm is not being allowed to raise
equity by issuing new shares. Consequently, the growth rate in net income and
the growth rate in earnings per share are the same in this formulation.
In
this illustration, we will consider the expected growth rate in earnings based
upon the retention ratio and return on equity for three firms Ð Consolidated
Edison, a regulated utility that provides power to New York City and its
environs, Procter & Gamble, a leading brandname consumer product firm and
Reliance Industries, a large Indian manufacturing firm. In Table 11.5, we
summarize the returns on equity, retention ratios and expected growth rates in
earnings for the three firms.
Table
11.5: Fundamental Growth Rates in Earnings per Share

Return on Equity 
Retention Ratio 
Expected Growth Rate 
Consolidated
Edison 
11.63% 
29.96% 
3.49% 
Procter & Gamble 
29.37% 
49.29% 
14.48% 
Reliance
Industries 
19.43% 
82.57% 
16.04% 
If
we relax the assumption that the only source of equity is retained earnings,
the growth in net income can be different from the growth in earnings per
share. Intuitively, note that a firm can grow net income significantly by
issuing new equity to fund new projects while earnings per share stagnates. To
derive the relationship between net income growth and fundamentals, we need a
measure of how investment that goes beyond retained earnings. One way to obtain
such a measure is to estimate directly how much equity the firm reinvests back
into its businesses in the form of net capital expenditures and investments in
working capital.
Equity
reinvested in business = (Capital Expenditures Ð Depreciation + Change in
Working Capital Ð (New Debt Issued Ð Debt Repaid))
Dividing
this number by the net income gives us a much broader measure of the equity
reinvestment rate:
Equity
Reinvestment Rate =
Unlike
the retention ratio, this number can be well in excess of 100% because firms
can raise new equity. The expected growth in net income can then be written as:
Expected
Growth in Net Income =

Net Income 
Net Cap Ex 
Change in Working Capital 
Net Debt Issued (paid) 
Equity Reinvestment Rate 
ROE 
Expected Growth Rate 
Coca
Cola 
$ 2177 m 
468 
852 
$104.00 
65.41% 
23.12% 
15.12% 
Nestle 
SFr 5763m 
2470 
368 
272 
44.53% 
21.20% 
9.44% 
Sony 
JY 30.24b 
26.29 
4.1 
3.96 
60.28% 
1.80% 
1.09% 
Both
earnings per share and net income growth are affected by the return on equity
of a firm. The return on equity is affected by the leverage decisions of the
firm. In the broadest terms, increasing leverage will lead to a higher return
on equity if the preinterest, aftertax return on capital exceeds the
aftertax interest rate paid on debt. This is captured in the following
formulation of return on equity:
where,
t
= Tax rate on ordinary income
The
derivation is simple[1]. Using this expanded version of ROE, the
growth rate can be written as:
The
advantage of this formulation is that it allows explicitly for changes in
leverage and the consequent effects on growth.
To
consider the components of return on equity, we look, in Table 11.7, at Con Ed,
Procter & Gamble and Reliance Industries, three firms whose returns on
equity we looked at in Illustration 11.5.

ROC 
Book D/E 
Book Interest rate 
Tax Rate 
ROE 
Consolidated
Edison 
8.76% 
75.72% 
7.76% 
35.91% 
11.63% 
Procter
& Gamble 
17.77% 
77.80% 
5.95% 
36.02% 
28.63% 
Reliance 
10.24% 
94.24% 
8.65% 
2.37% 
11.94% 
Average
and Marginal Returns
The
return on equity is conventionally measured by dividing the net income in the
most recent year by the book value of equity at the end of the previous year.
Consequently, the return on equity measures both the quality of both older
projects that have been on the books for a substantial period and new projects
from more recent periods. Since older investments represent a significant
portion of the earnings, the average returns may not shift substantially for
larger firms that are facing a decline in returns on new investments, either
because of market saturation or competition. In other words, poor returns on
new projects will have a lagged effect on the measured returns. In valuation,
it is the returns that firms are making on their newer investments that convey
the most information about a quality of a firmÕs projects. To measure these
returns, we could compute a marginal return on equity by dividing the change in
net income in the most recent year by the change in book value of equity in the
prior year:
Marginal Return on Equity = _{}
For example, Reliance Industries reported net income of Rs 24033 million in 2000 on book value
of equity of Rs 123693
million in 1999, resulting
in an average return on equity of 19.43%:
Average Return on Equity = 24033/123693 = 19.43%
The marginal return on equity is computed below:
Change in net income from 1999 to 2000 = 24033 17037 = Rs
6996 million
Change in Book value of equity from 1998 to 1999 = 123693 Ð
104006 = Rs 19,687 million
Marginal Return on Equity = 6996/19687 = 35.54%
So
far in this section, we have operated on the assumption that the return on equity
remains unchanged over time. If we relax this assumption, we introduce a new
component to growth Ð the effect of changing return on equity on existing
investment over time. Consider, for instance, a firm that has a book value of
equity of $100 million and a return on equity of 10%. If this firm improves its
return on equity to 11%, it will post an earnings growth rate of 10% even if it
does not reinvest any money. This
additional growth can be written as a function of the change in the return on
equity.
Addition
to Expected Growth Rate = _{}
where
ROE_{t} is the return on equity in period t. This will be in addition
to the fundamental growth rate computed as the product of the return on equity
in period t and the retention ratio.
Total
Expected Growth Rate =
While
increasing return on equity will generate a spurt in the growth rate in the
period of the improvement, a decline in the return on equity will create a more
than proportional drop in the growth rate in the period of the decline.
It
is worth differentiating at this point between returns on equity on new
investments and returns on equity on existing investments. The additional
growth that we are estimating above comes not from improving returns on new investments
but by changing the return on existing investments. For lack of a better term,
you could consider it Òefficiency generated growthÓ.
Just as equity income growth is determined by the equity
reinvested back into the business and the return made on that equity
investment, you can relate growth in operating income to total reinvestment
made into the firm and the return earned on capital invested.
When a firm has a stable return on
capital, its expected growth in operating income is a product of the
reinvestment rate, i.e., the proportion of the aftertax operating income that
is invested in net capital expenditures and noncash working capital, and the
quality of these reinvestments, measured as the return on the capital invested.
Expected Growth_{EBIT} =
Reinvestment Rate * Return on Capital
where,
Return
on Capital =
In
making these estimates, you use the adjusted operating income and reinvestment
values that you computed in Chapter 4. Both measures should be forward looking
and the return on capital should represent the expected return on capital on
future investments. In the rest of this section, you consider how best to
estimate the reinvestment rate and the return on capital.
The reinvestment rate measures how much a
firm is plowing back to generate future growth. The reinvestment rate is often
measured using the most recent financial statements for the firm. Although this
is a good place to start, it is not necessarily the best estimate of the future
reinvestment rate. A firmÕs
reinvestment rate can ebb and flow, especially in firms that invest in
relatively few, large projects or acquisitions. For these firms, looking at an
average reinvestment rate over time may be a better measure of the future. In
addition, as firms grow and mature, their reinvestment needs (and rates) tend
to decrease. For firms that have expanded significantly over the last few
years, the historical reinvestment rate is likely to be higher than the
expected future reinvestment rate. For these firms, industry averages for
reinvestment rates may provide a better indication of the future than using
numbers from the past. Finally, it is important that you continue treating
R&D expenses and operating lease expenses consistently. The R&D
expenses, in particular, need to be categorized as part of capital expenditures
for purposes of measuring the reinvestment rate.
The return on capital is often based upon
the firm's return on existing investments, where the book value of capital is
assumed to measure the capital invested in these investments. Implicitly, you
assume that the current accounting return on capital is a good measure of the
true returns earned on existing investments and that this return is a good
proxy for returns that will be made on future investments. This assumption, of
course, is open to question for the following reasons.
á
The book
value of capital might not be a good measure of the capital invested in
existing investments, since it reflects the historical cost of these assets and
accounting decisions on depreciation. When the book value understates the
capital invested, the return on capital will be overstated; when book value
overstates the capital invested, the return on capital will be understated.
This problem is exacerbated if the book value of capital is not adjusted to
reflect the value of the research asset or the capital value of operating
leases.
á
The
operating income, like the book value of capital, is an accounting measure of
the earnings made by a firm during a period. All the problems in using
unadjusted operating income described in Chapter 4 continue to apply.
á
Even if the
operating income and book value of capital are measured correctly, the return
on capital on existing investments may not be equal to the marginal return on
capital that the firm expects to make on new investments, especially as you go
further into the future.
Given these concerns, you should consider
not only a firmÕs current return on capital, but any trends in this return as
well as the industry average return on capital. If the current return on
capital for a firm is significantly higher than the industry average, the
forecasted return on capital should be set lower than the current return to
reflect the erosion that is likely to occur as competition responds.
Finally, any firm that earns a return on
capital greater than its cost of capital is earning an excess return. The
excess returns are the result of a firmÕs competitive advantages or barriers to
entry into the industry. High excess returns locked in for very long periods
imply that this firm has a permanent competitive advantage.
In this Illustration, we will estimate
the reinvestment rate, return on capital and expected growth rate for Embraer,
the Brazilian aerospace firm, and Amgen. We begin by presenting the inputs for
the return on capital computation in Table 11.8.
Table 11.8:
Return on Capital

EBIT 
EBIT (1t) 
BV of Debt 
BV of Equity 
Return on Capital 
Embraer 
945 
716.54 
1321.00 
697.00 
35.51% 
Amgen 
$1,996 
$1,500 
$323 
$5,933 
23.98% 
We use the effective tax rate for
computing aftertax operating income and the book value of debt and equity from
the end of the prior year. For Amgen, we use the operating income and book
value of equity, adjusted for the capitalization of the research asset, as
described in Illustration 9.2. The aftertax returns on capital are computed in
the last column.
We follow up by estimating capital expenditures,
depreciation and the change in noncash working capital from the most recent
year in Table 11.9.
Table 11.9: Reinvestment
Rate

EBIT(1t) 
Capital expenditures 
Depreciation 
Change in Working Capital 
Reinvestment 
Reinvestment Rate 
Embraer 
716.54 
182.10 
150.16 
173.00 
141.06 
19.69% 
Amgen 
$1,500.32 
$1,283.00 
$610.00 
$121.00 
$794.00 
52.92% 
Here again, we treat R&D as a capital
expenditure and the amortization of the research asset as part of depreciation
for computing the values for Amgen. In the last column, we compute the
reinvestment rate by dividing the total reinvestment (cap ex Ð depreciation +
Change in working capital) by the aftertax operating income. Note that
EmbraerÕs reinvestment rate is negative because of noncash working capital
dropped by 173 million in the most recent year.
Finally, we compute the expected growth
rate by multiplying the aftertax return on capital by the reinvestment rate in
Table 11.10
Table 11.10:
Expected Growth Rate in Operating Income

Reinvestment Rate 
Return on Capital 
Expected Growth Rate 
Embraer 
19.69% 
35.51% 
6.99% 
Amgen 
52.92% 
23.98% 
12.69% 
If Amgen can maintain the return on capital and reinvestment
rate that they had last year, it would be able to grow at 12.69% a year. EmbraerÕs growth rate is negative
because its reinvestment rate is negative. In the Illustration that follows, we
will look at the reinvestment rate in more detail.