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 t-1 can be written
as:

where,

ROEt-1 = Return on equity in year t-1 _{}

The
net income in year t can be written as:

Assuming
that the return on equity is unchanged, i.e., ROEt = ROEt-1 =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.

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 =

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 pre-interest, after-tax return on capital exceeds the
after-tax 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.

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.

You will consider three separate scenarios, and examine how
to estimate growth in each, in this section. The first is when a firm is
earning a high return on capital that it expects to sustain over time. The
second is when a firm is earning a positive return on capital that is expected
to increase over time. The third is the most general scenario, where a firm
expects operating margins to change over time, sometimes from negative values
to positive levels.

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 after-tax operating income that
is invested in net capital expenditures and non-cash 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.

The reinvestment rate for a firm can be
negative if its depreciation exceeds its capital expenditures or if the working
capital declines substantially during the course of the year. For most firms,
this negative reinvestment rate will be a temporary phenomenon reflecting lumpy
capital expenditures or volatile working capital. For these firms, the current
yearÕs reinvestment rate (which is negative) can be replaced with an average
reinvestment rate over the last few years. (This is what we did for Embraer in
the Illustration above.) For some firms, though, the negative reinvestment rate
may be a reflection of the policies of the firms and how we deal with it will
depend upon why the firm is embarking on this path:

á
Firms that
have over invested in capital equipment or working capital in the past may be
able to live off past investment for a number of years, reinvesting little and
generating higher cash flows for that period. If this is the case, we should
not use the negative reinvestment rate in forecasts and estimate growth based
upon improvements in return on capital. Once the firm has reached the point
where it is efficiently using its resources, though, we should change the
reinvestment rate to reflect industry averages.

á
The more
extreme scenario is a firm that has decided to liquidate itself over time, by
not replacing assets as they become run down and by drawing down working
capital. In this case, the expected growth should be estimated using the
negative reinvestment rate. Not surprisingly, this will lead to a negative
expected growth rate and declining earnings over time.

The analysis in the previous section is
based upon the assumption that the return on capital remains stable over time.
If the return on capital changes over time, the expected growth rate for the
firm will have a second component, which will increase the growth rate if the
return on capital increases and decrease the growth rate if the return on
capital decreases.

Expected Growth Rate = _{}

For
example, a firm that sees its return on capital improves from 10% to 11% while
maintaining a reinvestment rate of 40% will have an expected growth rate of:

Expected Growth Rate =

In
effect, the improvement in the return on capital increases the earnings on
existing assets and this improvement translates into an additional growth of
10% for the firm.

So
far, you have looked at the return on capital as the measure that determines
return. In reality, however, there are two measures of returns on capital. One
is the return earned by firm collectively on all of its investments, which you
define as the average return on capital. The other is the return earned by a
firm on just the new investments it makes in a year, which is the marginal
return on capital.

Changes
in the marginal return on capital do not create a second-order effect and the
value of the firm is a product of the marginal return on capital and the
reinvestment rate. Changes in the average return on capital, however, will
result in the additional impact on growth chronicled above.

What
types of firms are likely to see their return on capital change over time? One
category would include firms with poor returns on capital that improve their
operating efficiency and margins, and consequently their return on capital. In
these firms, the expected growth rate will be much higher than the product of
the reinvestment rate and the return on capital. In fact, since the return on
capital on these firms is usually low before the turn-around, small changes in
the return on capital translate into big changes in the growth rate. Thus, an
increase in the return on capital on existing assets of 1% to 2% doubles the
earnings (resulting in a growth rate of 100%).

The other category would include firms
that have very high returns on capital on their existing investments but are
likely to see these returns slip as competition enters the business, not only
on new investments but also on existing investments.

The
third and most difficult scenario for estimating growth is when a firm is
losing money and has a negative return on capital. Since the firm is losing
money, the reinvestment rate is also likely to be negative. To estimate growth
in these firms, you have to move up the income statement and first project
growth in revenues. Next, you use the firmÕs expected operating margin in
future years to estimate the operating income in those years. If the expected
margin in future years is positive, the expected operating income will also
turn positive, allowing us to apply traditional valuation approaches in valuing
these firms. You also estimate how much the firm has to reinvest to generate
revenue growth, by linking revenues to the capital invested in the firm.

Many
high growth firms, while reporting losses, also show large increases in
revenues from period to period. The first step in forecasting cash flows is
forecasting revenues in future years, usually by forecasting a growth rate in
revenues each period. In making these estimates, there are five points to keep
in mind.

á
The rate of
growth in revenues will decrease as the firmÕs revenues increase. Thus, a
ten-fold increase in revenues is entirely feasible for a firm with revenues of
$2 million but unlikely for a firm with revenues of $2 billion.

á
Compounded
growth rates in revenues over time can seem low, but appearances are deceptive.
A compounded growth rate in revenues of 40% over ten years will result in a
40-fold increase in revenues over the period.

á
While
growth rates in revenues may be the mechanism that you use to forecast future
revenues, you do have to keep track of the dollar revenues to ensure that they
are reasonable, given the size of the overall market that the firm operates in.
If the projected revenues for a firm ten years out would give it a 90% or 100%
share (or greater) of the overall market in a competitive market place, you
clearly should reassess the revenue growth rate.

á
Assumptions
about revenue growth and operating margins have to be internally consistent.
Firms can post higher growth rates in revenues by adopting more aggressive
pricing strategies but the higher revenue growth will then be accompanied by
lower margins.

- In coming
up with an estimate of revenue growth, you have to make a number of
subjective judgments about the nature of competition, the capacity of the
firm that you are valuing to handle the revenue growth and the marketing
capabilities of the firm.

Before
considering how best to estimate the operating margins, let us begin with an
assessment of where many high growth firms, early in the life cycle, stand when
the valuation begins. They usually have low revenues and negative operating
margins. If revenue growth translates low revenues into high revenues and
operating margins stay negative, these firms will not only be worth nothing but
are unlikely to survive. For firms to be valuable, the higher revenues
eventually have to deliver positive earnings. In a valuation model, this
translates into positive operating margins in the future. A key input in
valuing a high growth firm then is the operating margin you would expect it to
have as it matures.

In
estimating this margin, you should begin by looking at the business that the
firm is in. While many new firms claim to be pioneers in their businesses and
some believe that they have no competitors, it is more likely that they are the
first to find a new way of delivering a product or service that was delivered
through other channels before. Thus, Amazon might have been one of the first
firms to sell books online, but Barnes and Noble and Borders preceded them as
book retailers. In fact, one can consider online retailers as logical
successors to catalog retailers such as L.L. Bean or Lillian Vernon. Similarly,
Yahoo! might have been one of the first (and most successful) internet portals
but they are following the lead of newspapers that have used content and
features to attract readers and used their readership to attract advertising.
Using the average operating margin of competitors in the business may strike
some as conservative. After all, they would point out, Amazon can hold less
inventory than Borders and does not have the burden of carrying the operating
leases that Barnes and Noble does (on its stores) and should, therefore, be
more efficient about generating its revenues and subsequently earnings. This
may be true but it is unlikely that the operating margins for internet
retailers can be persistently higher than their brick-and-mortar counterparts.
If they were, you would expect to see a migration of traditional retailers to
online retailing and increased competition among online retailers on price and
products driving the margin down.

While
the margin for the business in which a firm operates provides a target value,
there are still two other estimation issues that you need to confront. Given
that the operating margins in the early stages of the life cycle are negative,
you first have to consider how the margin will improve from current levels to
the target values. Generally, the improvements in margins will be greatest in
the earlier years (at least in percentage terms) and then taper off as the firm
approaches maturity. The second issue is one that arises when talking about
revenue growth. Firms may be able to post higher revenue growth with lower
margins but the trade off has to be considered. While firms generally want both
higher revenue growth and higher margin, the margin and revenue growth assumptions
have to be consistent.