
Chapter 4 Valuation of assets, shares and companies 107
public in 1980 at an issue price of $22, its share price plummeted to $7 in 1998, soaring
to nearly $70 in the dotcom bubble before receding to $15 in 2003. However, this firm
is enjoying a ‘second bite at the cherry’ with the spectacular success of the iPod digi-
tal music player. Its product, iTunes, registered its 200 millionth download in
December 2004, just ten months after launch, making Apple the world leader in legal-
ly downloaded music. During 2004, its shares rose from $20 to $65, including a 20 per-
cent jump in November on the announcement of its first quarter 2004 results.
A distressed company like Apple, in its ‘dog days’, would have a positive value so
long as its management were thought capable of staging a corporate recovery, i.e. the
market is valuing more distant dividends on hopes of a turn-around in earnings. If
recovery is thought unlikely, the company is valued at its break-up value.
For inveterate non-dividend payers, the market is implicitly valuing the liquidating
dividend when the company is ultimately wound up. Until this happens, the compa-
ny is adding to its reserves as it reinvests, and continually enhancing its assets, its
earning power and its value. In effect, the market is valuing the stream of future earn-
ings that are legally the property of the shareholders.
■ Will there always be enough worthwhile projects in the future?
The DGM implies an ongoing supply of attractive projects to match the earnings avail-
able for retention. It is most unlikely that there will always be sufficient attractive proj-
ects available, each offering a constant rate of return, R, sufficient to absorb a given
fraction, b, of earnings in each future year. While a handful of firms do have very
lengthy lifespans, corporate history typically parallels the marketing concept of the
product life cycle – introduction, (rapid) growth, maturity, decline and death – with
paucity of investment opportunities a very common reason for corporate demise. It is
thus rather hopeful to value a firm over a perpetual lifespan. However, remember that
the discounting process compresses most of the value into a relatively short lifespan.
■ What if the growth rate exceeds the discount rate?
The arithmetic of the model shows that if g k
e
, the denominator becomes negative
and value is infinite. Again, this appears nonsensical, but, in reality, many companies
do experience periods of very rapid growth. Usually, however, company growth settles
down to a less dramatic pace after the most attractive projects are exploited, once the
firm’s markets mature and competition emerges. There are two ways of redeeming the
model in these cases. First, we may regard g as a long-term average or ‘normal’ growth
rate. This is not totally satisfactory, as rapid growth often occurs early in the life cycle
and the value computed would thus understate the worth of near-in-time dividends.
Alternatively, we could segment the company’s lifespan into periods of varying growth
and value these separately. For example, if we expect fast growth in the first five years
and slower growth thereafter, the expression for value is:
Note that the second term is a perpetuity beginning in year 6, but we have to find its
present value. Hence it is discounted down to year zero as in the following expression:
where g
f
is the rate of fast growth during years 1–5 and g
s
is the rate of slow growth
beginning in year 6 (i.e. from the end of year 5).
a
5
t 1
D
o
11 g
f
2
11 k
e
2
t
a
q
t 6
D
5
11 g
s
2
11 k
e
2
t
P
o
D
o
11 g
f
2
11 k
e
2
D
o
11 g
f
2
2
11 k
e
2
2
p
D
o
11 g
f
2
5
11 k
e
2
5
¢
D
5
11 g
s
2
1k
e
g
s
2
1
11 k
e
2
5
≤
3Present value of all further dividends4
P
o
3Present value of dividends during year 1–54
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