There
is no other ingredient in discounted cash flow valuation that evokes as much
angst as estimating future growth. Unlike cash flows and discount rates, where
we often have the security of historical data, growth rates require us to
grapple with the future. In this section, we will look first at why growth
rates can be different for equity and operating earnings, examine two of the
standard approaches for estimating growth (by looking at the past and using
analyst estimates) and close with a discussion of the fundamentals that
determine growth.
As
with cashflows and discount rates, a contrast has to be drawn between growth in
equity earnings and growth in operating earnings. To make the distinction,
consider the simplified version of an income statement in table 2.3:
Table 2.3: An Income Statement – Revenues to Earnings per Share
Item 
Factors
that explain differences in growth 
Revenues 

 Operating Expenses 
1.
Changes in
operating efficiency/ performance 2.
Operating
leverage 
EBITDA 

 Depreciation & Amortization 
1.
Changes
in depreciation schedules/ rules 2.
Amortization
of intangibles 
EBIT 

 Interest Expenses + Income from cash holdings  Taxes 
1.
Changes
in financial leverage (debt) 2.
Changes
in cash holdings/ interest rates 3.
Changes
in tax rates/ rules 
Net
Income 

/ Number of Shares 
1.
Stock
buybacks and issues 2.
Exercise
of past option grants 
Earnings
per share 

We are assuming that the firm has no minority holdings in
other companies, which would result in an additional line item, just above the
net income line, for income from these holdings.
The growth rates in different
measures of earnings (operating income, net income and earnings per share) will
generally be different for most firms, and especially so for growth firms or
firms in transition.
á
Share issues and Buybacks: If the number
of shares remains fixed, the growth rate in earnings per share should be the
same as the growth rate in net income. Firms that generate excess cash flows
and use these cash flows to buy back stock will register higher growth rates in
earnings per share than in net income. Conversely, firms that make a practice
of raising new equity (issuing new shares) to fund investments or acquisitions
can have higher growth rates in net income than in earnings per share.
á
Financial Leverage: The growth rates in
operating and net income can diverge if the net interest expense (interest
expense – interest income) grows at a rate different from operating
income. Firms that use increasing amounts of debt to fund their operations will
generally report higher growth rates in operating income than net income.
However, if that debt is used to buy back shares, the earnings per share growth
will reflect the fewer shares outstanding.
á
Operating Leverage: The growth in
operating income can also be very different from the growth in revenues,
primarily because some operating expenses are fixed and others are variable.
The higher the proportion of the costs that are fixed costs (higher operating
leverage), the greater will be the growth rate in operating income relative to
the growth in revenues.
In effect, when asked to estimate growth rates, the first
question that an analyst has to ask is ÒIn what item?Ó If our task is to estimate growth in
operating income, we cannot use growth rates in earnings per share as
substitutes.
When
confronted with the task of estimating growth, it is not surprising that
analysts turn to the past. In effect, they use growth in revenues or earnings
in the recent past as a predictor of growth in the future. Before we put this
practice under the microscope, we should add that the historical growth rates
for the same company can yield different estimates n
for the following reasons:
1.
Earnings measure: As we noted above, the
growth rates in earnings per share, net income, operating income and revenues
can be very different for the same firm over a specified time period.
2.
Period of analysis: For firms that have
been in existence for long periods, the growth rates can be very different if
we look at ten years of history as opposed to five years.
3.
Averaging approach: Even if we agree on
an earnings measure and time period for the analysis, the growth rates we
derive can be different, depending upon how we compute the values. We could,
for instance, compute the growth rate in each period and average the growth
rates over time, yielding an arithmetic average. Alternatively, we could use
just the starting and ending values for the measure and compute a geometric
average. For firms with volatile earnings, the latter can generate a very
different (and lower) value for growth than the former.
A debate how best to estimate historical growth makes sense
only if it is a good predictor of future growth. Unfortunately, studies that
have looked at the relationship have generally concluded that (a) the
relationship between past and future growth is a very weak one, (b) scaling
matters, with growth dropping off significantly as companies grow and (c) firms
and sectors grow through growth cycles, with high growth in one period followed
by low growth in the next.
If
historical growth is not a useful predictor of future growth, there is another
source that we can use for future growth. We can draw on those who know the
firm better than we do – equity research analysts who have tracked the
firm for years or the managers in the firm – and use their estimates of
growth. On the plus side, these forecasts should be based upon better
information than we have available to us. After all, managers should have a
clearer sense of how much they will reinvest in their own businesses and what
the potential returns on investments are when they do, and equity research
analysts have sector experience and informed sources that they can draw on for
better information. On the minus side, neither managers nor equity research
analysts are objective about the future; managers are likely to over estimate
their capacity to generate growth and analysts have their own biases. In
addition, both analysts and managers can get caught up in the mood of the
moment, over estimating growth in buoyant times and under estimating growth in
down times. As with historical growth, studies indicate that neither analyst
estimates nor management forecasts are good predictors of future growth.
If
we cannot draw on history or trust managers and analysts, how then do we
estimate growth? The answer lies in the fundamentals within a firm that
ultimately determine its growth rate. In this section, we will consider the two
sources for growth – new investments that expand the business and
improved efficiency on existing investments.
The best way to consider earnings
growth is to break it down algebraically into its constituent parts. Define E_{t}
to be the earnings in period t, I_{t} to be
the investment at the start of period t and ROI_{t} as the return on
that investment. Thus, we can rewrite E_{t} as:
E_{t} = ROI_{t} * I_{t}
The change in earnings from period t1 to t, , DE, can then be
written as follows
DE = E_{t} – E_{t1}=
ROI_{t} * I_{t}  ROI_{t1} * I_{t1}
The growth rate is written in terms of DE and E_{t1}:
g = DE/
E_{t1} = (ROI_{t} * I_{t}  ROI_{t1} * I_{t1})/
E_{t1}
Consider the simplest scenario,
where the ROI is stable and does not change from period to period (ROI = ROI_{t}
= ROI_{t1}). The expected growth rate in earnings for this firm is:
g = DE/
E_{t1} = ROI ( I_{t}
 I_{t1})/ E_{t1}
=
ROI * (DI/E_{t1})
In other words, the growth rate for this firm will be a
function of only two variables – the return it makes on new investments
(ROI) and the proportion of itÕs earnings that are put into new investments (DI/E_{t1}).
The
more general scenario is one where the return on investment does change from
period to period. In this case, the expected growth rate can be written as:
g = DE/ E_{t1} = ROI_{t} * (DI/E_{t1}) + (ROI_{t} – ROI_{t1})/ ROI_{t1}
This equation is based on the assumption that the return on
new investments in period t is identical to the return earned on existing
investments in that period. In fact, this can be generalized even further, if
we allow the return on new investments, ROI_{New,t},
to be different from the return on existing assets, ROI_{Existing,t},
the expected growth rate can be written as:
g = DE/ E_{t1} = ROI_{New,t} * (DI/E_{t1}) + (ROI_{Existing,t} – ROI_{Existing,t1})/ ROI_{Existing,t1}
The first term
in this equation captures the growth from new investments, determined by the
marginal return on those investments and the proportion invested in these
investments. The second term captures
the effect of changes in the return on investment on existing assets, a
component that we will title Òefficiency growthÓ. Increasing the return on
investment (improving efficiency) will create additional earnings growth,
whereas declining efficiency (with drops in the return on investment) will
reduce earnings growth.
While
investment and return on investment are generic terms, the way in which we
define them will depend upon whether we are looking at equity earnings or
operating income. When looking at equity earnings, our focus is on the
investment in equity and the return is the return on equity. When looking at
operating earnings, the focus is on the investment in capital and the return is
the return on capital. In the cash flow definitions introduced at the start of
this chapter, the change in investment is computed as the reinvestment, with
the measurement of the reinvestment again varying depending upon the cash flow
being discounted. In dividend discount models, reinvestment is defined as
retained earnings (i.e.. any income not paid out as dividends). In free cash
flow to equity (firm) models, reinvestment is defined in terms of the equity
reinvestment rate (reinvestment rate).
Central to any estimate of
fundamental growth is the estimate of return on capital or equity. Table 2.4 summarizes the inputs for each
measure depending on the measure of cash flow that we are focused on:
Table 2.4: Measuring Investment and Return on Investment

Change
in Investment 
Return
on Investment 
Operating Income 
Reinvestment Rate = 
Return on Invested Capital (ROC or ROIC) 
Net Income (Noncash) 
Equity Reinvestment Rate = 
Noncash Return on Equity (NCROE) 
Earnings per share 
Retention Ratio = 
Return on Equity (ROE) 
It is conventional practice to use
accounting measures of investment and return on investment. Thus, the book
values of equity and invested capital and accounting earnings are used to
compute returns on equity and capital:
The problem with accounting measures on both dimensions is
well documented, with accounting choices on restructuring charges, amortization
and capitalization all making a difference in the final numbers.[1]
The
final issue that we have to consider is the difference between marginal and
average returns. Note that the return on investment that we use to compute the
growth from new investments should be the return earned on those investments
alone, i.e, a marginal return. The return on existing assets is an average
return on a portfolio of investments already made. While we often use the same
value for both numbers in valuation, they can be different, in fact, very
different in practice.
For
many mature firms with limited investment opportunities, the potential for
growth from new investments is limited. These firms cannot maintain a high
reinvestment rate and deliver a high return on capital with that reinvestment.
However, they can still grow at healthy rates if they can improve the returns
that they earn on existing assets. Conversely, declines in returns on existing
assets can translate into drops in earnings growth rates. Stated again in terms
of different measures of earnings, efficiency growth can be written in table
2.5, as follows:
Table 2.5: Measuring Investment and Return on Investment

Measure of return on existing
assets 
Efficiency
growth 
Operating Income 
Return on Capital 

Net Income (Noncash) 
Noncash Return on Equity 

Earnings per share 
Return on Equity 

When
valuing companies, efficiency growth is pure gravy in terms of value created,
since the growth comes with no concurrent cost. Unlike growth from new
investments, where the positive effects of growth have to be offset against the
negative effect of more investment, improving the return on capital on existing
assets increases the growth rate without adversely affecting the cash flows. It
should as come as no surprise, then, that analysts who want to increase the
value of a company draw on the efficiency argument to justify much higher
growth rates than those estimated using fundamentals.
While
the potential for efficiency growth is always there, we should put some common
sense constraints on how much we can draw on this growth.
1.
There is more potential for efficiency growth at
mature firms, with poor returns on capital (equity), than there is at firms
that are performing well, for two reasons. First, improving the return on
capital is a much more feasible option for a firm that generates a return on
capital that is well below the sector average than at a firm that already
outperforms the sector. Second, the
effect of an improvement in returns on growth is much greater when the return
on capital is low than when it is high. A firm that improves its return on
capital from 5% to 6% will report a 20% growth rate from efficiency in that
period, whereas a firm that improves its return on capital from 25% to 26% will
generate a 4% growth rate from efficiency in that period.
2.
You can draw on increased efficiency to justify
growth only for finite periods. After all, a firm cannot be infinitely
inefficient. Once the inefficiencies, no matter how significant, are fixed, the
firm will have to revert back to its sustainable growth rate, based upon new
investments. In discounted cash flow valuation, this has a practical
consequence: you can draw on both efficiency and new investments to justify
growth during the high growth period, but only on new investments to justify
growth forever (in the terminal value computation).
In closing, growth in a specific firm can come from new
investments or improved efficiency, but it has to be earned either way. None of
us has the power to endow companies with higher growth rates, just because we
like the managers or want to make it value increase.
[1]
To get a sense of the problems with using accounting numbers, and how best to
correct for them, see: Damodaran, A., 2007, Return on capital, Return on
Invested Capital and Return on Equity: Measurement and Implications, Working
Paper, SSRN.