The Dividend Growth Model, while possessing some convenient properties, has some major limitations.
■ What if the company pays no dividend?
The company may be faced with highly attractive investment opportunities that cannot be financed in other ways. According to the model, such a company would have no value at all! Total retention is fairly common, either because the company has suffered an actual or expected earnings collapse, or because, as in some European economies (e.g. Switzerland), the expressed policy of some firms is to pay no dividends at all. The American computer software firm Microsoft paid its first dividend only in 2003, while two other computer firms, Dell and Apple, have yet to pay dividends at all. Yet we observe that shares in such companies do not have zero values. Indeed, nothing could be further from the truth.
In the case of Dell, $100 invested in its initial public offering in June 1988, would have been worth about $38,000 by January 2005 following 100 per cent profits reten- tion. After seven stock splits, 100 shares of Dell was equivalent to 9,600 shares. Apple’s history is more chequered. It managed to survive the major strategic blunder of omitting to license out the Macintosh operating system to other manufacturers. Having gone
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 ke, 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 gas 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 gfis the rate of fast growth during years 1–5 and gsis the rate of slow growth beginning in year 6 (i.e. from the end of year 5).
a
5 t1
Do11gf2
11ke2t a
q
t6
D511gs2 11ke2t PoDo11gf2
11ke2 Do11gf22
11ke22 pDo11gf25
11ke25 ¢D511gs2
1kegs2 1
11ke25≤ 3Present value of all further dividends4
Po 3Present value of dividends during year 1–54
However, we may note here that valuation of the dividend stream implies a known dividend policy. Because dividends are not controlled by shareholders, but by the firm’s directors, the DGM is more applicable to the valuation of small investment stakes in companies than to the valuation of whole companies, as in takeover situa- tions. When company control changes hands, control of dividend policy is also trans- ferred. It seems particularly unrealistic, therefore, to assume an unchanged dividend policy when valuing a company for takeover.
■ The P:E ratio and the Constant Dividend Valuation Model
If we examine the P:E ratio more closely, we find it has a close affinity with the growth version of the DVM. The P:E ratio is defined as price per share (PPS) divided by earnings per share (EPS). In its reciprocal form, it measures the earnings yieldof the firm’s shares:
This equals the dividend yield plus retained earnings (bE) per share. As in the DGM, the growth version of the DVM, we define the fraction of earnings retained as b. We can then write:
E
VD
VbE V 1
P:EEPS
PPS Earnings
Company value E V
The DGM may be used to examine the impact of changes in dividend policy, i.e.
changes in b. Detailed analysis of this issue is deferred to Chapter 17.
Example: the case of unequal growth rates
Consider the case of dividend growth of 25 per cent for years 1–5 and 7 per cent thereafter.
Assuming shareholders require a return of 10 per cent, and that dividend in year zero is 10p, the value of the share is calculated as follows:
For years 1–5
Year Dividend (p) Discount factor at 10% PV (p)
1 10(1.25) 12.5 0.909 11.4
2 12.50(1.25)215.6 0.826 12.9
3 etc. 19.5 0.751 14.6
4 24.4 0.683 16.7
5 30.5 0.621 18.9
Total 74.5
For later years, we anticipate a perpetual stream growing from the year 5 value at 7 per cent p.a. The present value of this stream as at the end of year 5 is:
This figure, representing the PV of all dividends following year 5, is now converted into a year zero present value:
PV £10.88 (PVIF10.5) (£10.88 0.621) £6.76
Adding in the PV of the dividends for the first five years, the PV of the share right now is:
PV (£0.745 £6.76) £7.51 D6
kegs D5117%2
110%7%2 30.5p11.072
0.03 32.64p
0.03 £10.88
earnings yield
The earnings per share (EPS) divided by market share price
SHAREHOLDER VALUE
Cash flow from operations
Cost of capital
Business strategy
Investment strategy
Financing strategy Sales growth
Margin
Planning horizon
Capital investment Working capital Acquisitions
Credit rating Tax rate Capital structure Dividend policy Corporate
objective
Value drivers
Strategic focus Figure 4.2
Shareholder value analysis framework
The ratio E/Vis the overall rate of return currentlyachieved. If this equals R, the rate of return on reinvested funds, then bE/Vis equivalent to the growth rate gin the DGM.
In other words, the earnings yield, E/V, comprises the dividend yield plus the growth rate or ‘capital gains yield’ for a company retaining a constant fraction of earnings and investing at the rate R. The two approaches thus look very similar. However, this apparent similarity should not be over-emphasised for three important reasons:
1 The earnings yield is expressed in terms of the current earnings, whereas the DGM deals with the prospectivedividend yield and growth rate, i.e. the former is historic in its focus, while the latter is forward-looking.
2 The DGM relies on discounting cash returns, while the earnings figure is based on accounting concepts. It does not follow that cash flows will coincide with account- ing profit, not least due to depreciation adjustments.
3 For the equivalence to hold, the current rate of return, E/V, would have to equal the rate of return expected on future investments.
Despite these qualifications, it is still common to find the earnings yield presented as the rate of return required by shareholders, and hence the cut-off rate for new investment projects. Unfortunately, this confuses a historical accounting measure with a forward-looking concept.