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growth rates much lower than the growth rate in the economy will become smaller in

proportion to the economy over time. Since there is no economic basis for arguing that

this cannot happen, there is no reason to prevent analysts from using a stable growth rate

much lower than the nominal growth rate in the economy. In fact, the stable growth rate

can be a negative number. Using a negative stable growth rate will ensure that your firm

peaks in your last year of high growth and becomes smaller each year after that.

There is one rule of thumb that works well in setting a cap on the stable growth

rate. The stable growth rate should generally not exceed the riskfree rate used in a

valuation. Why should the two be related? The riskfree rate can be decomposed into an

expected inflation rate and an expected real interest rate. If we assume that the real

growth rate of an economy will be equal to the real interest rate in the long term, the

riskfree rate becomes a proxy for the nominal growth rate in the economy.

12.2 â˜ž: Cyclical firms and Constant Growth Rates

Models that are built on the assumption of an expected constant growth rate over time

cannot be used for cyclical firms, whose earnings growth is likely to be very volatile over

time - high during economic booms, and very low or negative during recessions.

a. True

b. False

Explain.

Estimation in DCF Models

While all discounted cashflow models require the same four ingredients â€“

cashflows, a discount rate, a period of high growth and a growth rate during the period,

there are different estimation challenges we face with each model. In this section, we will

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begin by estimating these inputs to the simplest of the three models, the dividend

discount model, and then extend the discussion to cashflow to equity and firm valuation

models.

I. Dividend Discount Models

When an investor buys stock, he generally expects to get two types of cash flows -

dividends during the holding period and an expected price at the end of the holding

period. Since this expected price is itself determined by future dividends, the value of a

stock is the present value of just expected dividends. The dividend discount model is

therefore the most direct and the most conservative way of valuing a stock since it counts

only those cashflows that are actually paid out.

Setting up the Model

In itâ€™s most general form, the value of a stock in the dividend discount model is

the present value of the expected dividends on the stock in perpetuity.

t ="

Expected Dividends in period t

#

Value per share of stock =

(1 + Cost of Equity) t

t =1

Since we cannot estimate dividends in perpetuity, we

Terminal Value: This is the

generally allow for a period where dividends can grow at expected price of a stock (or

!

extraordinary rates but we allow for closure in the model equity) at the end of a

specified holding period.

by assuming that the growth rate will decline to a stable

rate that can be sustained forever at some point in time in

the future. By assuming stable growth at some point in time in the future, we can stop

estimating dividends and estimate what we think the stock will be worth at the end of the

extraordinary growth period.

t =n

E(Dividends) t Terminal Value n E(Dividends)n +1

"

Value 0 = + where Terminal Value n =

(1 + r) t (1 + r) n (rn - g n )

t =1

!

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where r is the cost of equity and gn is the expected growth rate in dividends in perpetuity

after year n.2 Note that it is possible for a firm to already be in stable growth, in which

case this model collapses into itls simplest form:

Value of a stock in stable growth = Expected Dividends next year/ (Cost of equity â€“ gn)

This model is called the Gordon Growth model and is a special case of the dividend

discount model. It can be used only for firms that are already in stable growth.3

Estimating Model Inputs

Breaking down the general version of the dividend discount model, there are four

basic components. The first is the length of the high growth period, during which the firm

can sustain extraordinary growth. The second is the expected dividends each year during

the high growth period. The third is the cost of equity that stockholders will demand for

holding the stock, based upon their assessments of risk. The final input is the expected

price at the end of the high growth period â€“ the terminal value. In this section, we will

consider the challenges associated with estimating each of these components.

a. Length of High-Growth Period

The question of how long a firm will be able to sustain high growth is perhaps the

most difficult of all to answer in a

High Growth Period: This is a period during which

valuation, but two points are worth a companyâ€™s earnings or cash flows are expected to

keeping in mind. One is that it is not a grow at a rate much higher than the overall growth

rate of the economy.

question of whether but when; all firms

will ultimately be stable growth firms, because high growth makes firms larger, and the

firmâ€™s size will eventually become a barrier to further high growth. The second is that

high growth in valuation, at least high growth that creates value, comes from firms

earning high returns on their marginal investments. Using the terminology that we have

used before in investment analysis, it comes from firms having a return on equity

(capital) that is well in excess of the cost of equity (capital). Thus, when we assume that a

2 The cost of equity can be different for the high growth and stable growth periods. Hence, rn is the cost of

equity for the stable growth period.

3 When the Gordon Growth model is used to value high growth companies, it is entirely possible that g>r

and the model will yield a negative value. The problem is not with the model but in its msapplication to a

high growth firm.

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firm will experience high growth for the next 5 or 10 years, we are also implicitly

assuming that it will earn excess returns (over and above the cost of equity or capital)

during that period. In a competitive market, these excess returns will eventually draw in

new competitors, and the excess returns will disappear.

We should look at three factors when considering how long a firm will be able to

maintain high growth.

1. Size of the firm: Smaller firms are much more likely to earn excess returns and

maintain these excess returns than otherwise similar larger firms. This is so because

they have more room to grow and a larger potential market. When looking at the size

of the firm, we should look not only at its current market share, but also at the

potential growth in the total market for its products or services. Thus, Microsoft may

have a large market share of the computer software market, but it may be able to

grow in spite of it because the entire software market is growing. On the other hand,

Boeing dominates the market for commercial airliners, but we do not expect the

overall market for airliners to increase substantially. Boeing, therefore, is far more

constrained in terms of future growth.

2. Existing growth rate and excess returns: Although the returns we would like to

estimate are the marginal returns on new investments, there is a high correlation

between the returns on current investments and these marginal returns. Thus, a firm

earning excess returns of 20% on its current investments is far more likely to have

large positive excess returns and a long growth period than a firm currently earning

excess returns of 2%. There are cases where this rule will not work, such as in new

industries going through major restructuring.

3. Magnitude and Sustainability of Competitive Advantages: This is perhaps the most

critical determinant of the length of the high growth period. If there are significant

barriers to entry and sustainable competitive advantages, firms can maintain high

growth for longer periods. If, on the other hand, there are no or minor barriers to

entry, or if the firmâ€™s existing competitive advantages are fading, we should be far

more conservative about allowing for long growth periods. The quality of existing

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management also influences growth. Some top managers4 have the capacity to make

the strategic choices that increase competitive advantages and create new ones.

Again, the sensitivity of value to changes in the length of the high growth period can

always be estimated. While some analysts use growth periods greater than 10 years, the

combination of high growth rates and long growth periods creates a potent mix in terms

of increasing the size of the firm, in many cases well beyond the realm of what is

reasonable. Looking back, there are very few firms that have been able to grow at high

rates for more than 10 years.

Illustration 12.1: Length of High Growth Period

To assess how long high growth will last at Disney, Aracruz and Deutsche Bank,

we assessed their standings on each of the above characteristics in Table 12.1:

Table 12.1: Assessment of Length of High Growth Period

Disney Aracruz Deutsche Bank

Firm Size/Market Size Firm is one of the Firm has a small market Firm has a significant

largest players in the share of the paper/pulp market share of a mature

entertainment and theme business, but the business.

park businesses but the business is mature.

businesses are

redefining themselves

and expanding.

Current Excess Returns Firm is earning less than Returns on capital are Firm has a return on

its cost of capital, and largely a function of equity that has lagged its

has done so for last few paper/pulp prices but, on cost of equity in recent

years average, have been less years.

than the cost of capital.

Competitive Advantages Has some of the most Cost advantages because Has an edge in the

recognized brand names of access to Brazilian commercial banking

in the world. Knows rainforests. Has invested business in Germany but

more about operating in newer, updated plants this advantage is

theme parks than any and has skilled dissipating in the EU.

other firm in the world. workforce.

Has skilled animation

studio staff.

Length of High Growth 10 years, entirely 5 years, largely due to 5 years, mostly to allow

period because of its strong access to cheap raw firms to recover to pre-

competitive advantages material. downturn levels.

(which have been

wasted over the last few

years) but the excess

returns are likely to be

4 Jack Welch at GE and Robert Goizueta at Coca Cola are good examples of CEOs who made a profound

difference in the growth of their firms.

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small.

What about Bookscape? The single biggest competitive advantage possessed by the firm

is its long-term lease, at favorable terms, in a superb location in New York City. It is

unlikely that the firm will be able to replicate this advantage elsewhere. Adding to this

the fact that this is a private firm leads us to conclude that there will be no high growth

period.

12.3. â˜ž: Length of High Growth Period and Barriers to Entry

Assume that you are analyzing two firms, both of which are enjoying high growth. The

first firm is Earthlink Network, an internet service provider, which operates in an

environment with few barriers to entry and extraordinary competition. The second firm is

Biogen, a biotechnology firm which is enjoying growth from two drugs to which it owns

patents for the next decade. Assuming that both firms are well managed, which of the two

firms would you expect to have a longer high growth period?

a. Earthlink Network

b. Biogen

c. Both are well managed and should have the same high growth period

b. Expected Dividends during High Growth Period

The first step in estimating expected dividends during the high growth period is to

estimate the expected earnings for each year. This can be done in one of two ways â€“ you

can apply an expected growth rate to current Historical Growth Rate (in Earnings): This is

the growth rate over the past few periods in

earnings or you can begin by estimating future

earnings - it can be calculated either by

revenues first and then estimate net profit

averaging the year-specific growth rates

margins in each year. The first approach is

(arithmetic average) or by estimating at the

easier but the second approach provides for compounded growth rate over the whole

period.

more flexibility since margins can change over

time. The resulting expected earnings are

paired with estimated dividend payout ratios in each period, which may change over the

high growth period. This may seem like an awkward procedure, since expected dividends

could well be estimated using the current dividends and applying a dividend growth rate,

but it is used for two reasons. First, most analyst projections for growth are stated in

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terms of revenues and earnings rather than dividends. Second, separating earnings

forecasts from dividend payout provides more flexibility in terms of changing dividend

payout ratios as earnings growth rates change. In particular, it allows us to raise dividend

payout ratios as earnings growth rates decline.

The growth rate in earnings can be estimated using one of three approaches. The

first is to look at the past and measuring the historical growth rate in earnings over

previous years. In measuring earnings growth, we will have to consider both how far

back to go in time and whether to use arithmetic average or geometric average growth

rates. In general, geometric growth rates yield more meaningful values than arithmetic

average growth rates. The second is to look at estimates made by others following the

same stock. In fact, growth estimates made by equity research analysts following a stock

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