# Dividend theory

Dividends and share price growth are the two ways in which wealth can be provided to shareholders. This article looks at some theories on dividend payments, as well as the practical matters that have to be taken into account and a discussion on dividend policies.

Dividends and share price growth are the two ways in which wealth can be provided to shareholders. There is an interaction between dividends and share price growth: if all earnings are paid out as dividends, none can be reinvested to create growth, so all profitable companies have to decide on what fraction of earnings they should pay out to investors as dividends and what fraction of earnings should be retained.

This article will deal first with some theories on dividend payments. It will then look at practical matters that have to be taken into account and will also discuss particular dividend policies.

### Theories

The relevant theories are:

• The dividend valuation model
• The Gordon growth model
• Modigliani and Miller’s dividend irrelevancy theory.

#### The dividend valuation model

This states that the value of a company’s shares is sustained by the expectation of future dividends. Shareholders acquire shares by paying the current share price and they would not pay that amount if they did not think that the present value of future inflows (ie dividends) matched the current share price. The formula for the dividend valuation model provided in the formula sheet is:

P0 = D0 (1+ g)/(re – g)

Where:

P0 = the ex-div share price at time 0 (ie the current ex div share price)
D0 = the time 0 dividend (ie the dividend that has either just been paid or which is about to be paid)
re = the rate of return of equity (ie the cost of equity)
g = the future annual dividend growth rate.

Note the following carefully:

P0 is the ex div market value. The formula is based on an investment costing P0 and which produces the first inflow after one year and then every year thereafter. If the first income arises after one year the share value must be ex-div as a cum-div share would pay a dividend very soon indeed.

The top line of the formula represents the dividend that will be paid at Time 1 and which will then grow at a rate g. The use of the expression D0(1 + g) has an implicit assumption that the growth rate, g, will also apply between the current dividend and the Time 1 dividend – but it need not apply if a change in dividend policy is planned.

The formula can be usefully rewritten as.

P0 = D1 /(re – g)

Where D1 is the Time 1 dividend.

It cannot be emphasised enough that g is the future growth rate from Time 1 onwards. Of course, the growth rate isn’t guaranteed and the future growth rate is always an estimate. In the absence of other information, the future growth rate is assumed to be equal to the historic growth rate, but a change in dividend policy will undermine that assumption.

#### The Gordon growth model

This model examines the cause of dividend growth. Assuming that a company makes neither a dramatic trading breakthrough (which would unexpectedly boost growth) nor suffers from a dreadful error or misfortune (which would unexpectedly harm growth), then growth arises from doing more of the same, such as expanding from four factories to five by investing in more non-current assets. Apart from raising more outside capital, expansion can only happen if some earnings are retained. If all earnings were distributed as dividend the company has no additional capital to invest, can acquire no more assets and cannot make higher profits.

It can be relatively easily shown that both earnings growth and dividend growth is given by:

g = bR

where b is the proportion of earnings retained and R is the rate that profits are earned on new investment. Therefore, (1 – b) will be the proportion of earnings paid as a dividend. Note that the higher b is, the higher is the growth rate: more earnings retained allows more investment to that will then produce higher profits and allow higher dividends.

So, if earnings at time 1 are E1, the dividend will be E1(1 – b) so the dividend growth formula can become:

P0 = D1 /(re – g) =  E1 (1 – b)/(re – bR)

If b = 0, meaning that no earnings are retained then P0 = E1/re, which is just the present value of a perpetuity: if earnings are constant, so are dividends and so is the share price.

If we consider that the dividend policy is represented by b and (1-b), the proportions of earnings retained and paid out, it looks as though the formula predicts that the share price will change if b changes, but that is not necessarily the case as we will see below.

#### Modigliani and Miller’s dividend irrelevancy theory

This theory states that dividend patterns have no effect on share values. Broadly it suggests that if a dividend is cut now then the extra retained earnings reinvested will allow futures earnings and hence future dividends to grow. Dividend receipts by investors are lower now but this is precisely offset by the increased present value of future dividends.

However, this equilibrium is reached only if the amounts retained are reinvested at the cost of equity.

Example 1: earnings are all paid as dividend
Current position: Earnings = \$0.8 per share (all paid out as dividend); RE =20%, the price per share. would be

P0 = 0.8/0.2 = \$4  (the PV of constant dividends received in perpetuity).

Example 2: earnings are reinvested at the cost of equity
So, what would happen if, from Time 1 onwards, half the earnings were paid out as dividend and half retained AND re = R = 0.2 (meaning that the return required by investors is the return earned on new investment)?

P0 = E1 (1 – b)/(re – bR)

P0 = 0.8(1 – 0.5)/(0.2 – 0.5 x 0.2) = \$4

So, no change in the share value, and so the dividends are irrelevant.

Example 3: earnings are reinvested at more than the cost of equity
For example, the company has made a technological breakthrough and invests the retained earnings to make use of the enhanced opportunities. As you might be able to predict, this piece of good fortune must increase the share price.

re = 0.2 (as before) and R = 0.3

P0 = 0.8(1 – 0.5)/(0.2 – 0.5 x 0.3) = \$8

In this case, the share price rises because the extra earnings retained have been invested in a particularly valuable way.

Example 3: earnings are reinvested at less than the cost of equity
For example, the company invests the retained earnings in a way that turns out to be poor. It has messed up. As you might be able to predict, this piece of bad luck or carelessness must decrease the share price.

re = 0.2 (as before) and R = 0.1

P0 = 0.8(1 – 0.5)/(0.2 – 0.5 x 0.1) = \$2.67

In summary:

• If the company retains earnings and uses those to ‘do more of the same’ then the share price should not be affected.
• If the company retains earnings and uses those to produce higher returns than demanded by investors (and that could be through expanding current operations to become more efficient and cost effective) then dividends should be cut as that will increase shareholder value.
• If the company retains earnings and uses those to produce lower returns than demanded by investors (and that could be through keeping excess cash in the bank, earning very little) then dividends should be increased to avoid the share price falling. If the company can think of no good use for its earnings, it should distribute them to shareholders who can then decide for themselves what to do with them.

### Practical considerations

As so often occurs, theoretical outcomes do not always match practical considerations. So too with dividend irrelevancy. Perhaps this is because investors do not understand or believe the theory or perhaps it is because, to derive the theory, simplifying assumptions have to be made, such as the existence of perfect markets with no transaction costs and perfect information.

The practical matters are:

• Signalling. The announcement of a dividend is the release of a piece of publically available information. The semi-strong form of the efficient market hypothesis says that the share price will react to this information. The problem is: what signal does a change in dividend give out and therefore how should share prices move? For example, does a cut in dividend mean that the company is conserving cash because it expects hard times or does it mean that the company sees a great investment opportunity? There is inevitably information asymmetry as the directors will almost certainly be in possession of information that is not in the public domain. Almost always shareholders will be unsettled by abrupt changes in dividend policy.
• Lack of trust in directors’ forecasts or justifications for dividend cuts. Really, this point follows on from above. Directors might have been very open about a dividend policy but if investors do not share directors’ optimism about the future success of the company, the share price will be affected.
• Investors’ preference for current consumption rather than future promises (the ‘bird in the hand’ argument). Here, it is argued that a current dividend means that investors have safely received cash. Whereas, if the dividend were deferred they are at the mercy of future events and risks. This argument is very persuasive, but it is incorrect. Market forces should mean that a share price has been correctly set for the level of risk and returns made. If more cash is paid out as dividend the investor has to decide how to invest that cash. It could be spent on another investment which has higher returns and higher risk or on one where both returns and risks are lower. In either case, diversified investors should be happy with the deal because the capital asset pricing model states that extra risk is correctly compensated for by extra returns.
• The clientele effect. This idea suggests that investors buy shares that ‘suit’ their needs. So, a pension fund will base much of its investment portfolio on its need to produce income to pay to pensioners. It will therefore invest heavily in shares that pay regular, relatively predictable dividends. Similarly, tax can affect investment decisions if gains are taxed less severely than income. If a company abruptly changes its dividend policy it will disturb investors’ carefully constructed portfolios and investors will have to adjust their mix of shares incurring transaction costs. It is sometimes argued that if a cut in dividend reduces an investor’s income, the investor can sell some shares to manufacture ‘income’. Of course, this will again incur transaction costs and different tax treatment.
• Company liquidity. Irrespective of all the potential share price movements that a change in dividend policy might cause, companies have to ensure that their liquidity is sound and might have dividend reductions forced on them if they are to stay solvent.
• Borrowing covenants. Sometimes lenders put clauses in loan agreements which limit dividend payments, for example to a certain fraction of earnings. This is the lender trying to ensure that the loan is more secure. If less cash is paid as dividends, liquidity might be better (though, of course, cash can still be consumed on the purchase of non-current assets).
• Legal constraints. No distributable reserves means no dividends.

Here is perhaps a good place to mention scrip dividends. These allow shareholders to choose to receive shares as full or partial replacement of a cash dividend. The number of shares received is linked to the dividend and the market price of the shares so that roughly equivalent value is received. This choice allows investors to acquire new shares (if they don’t need the cash dividend) without transactions costs and the company can conserve its cash and liquidity. There can also be beneficial tax effects in some countries.

### Dividend payment policies

• Constant dividends: in this approach dividends are predictable but shareholders might be dissatisfied if they see earnings rising but they are stuck will low dividends. If a larger and larger fraction of earnings is retained, shareholders might begin to question whether the company can find enough investment opportunities of the right quality.
• Constant growth: again, predictable and very attractive to shareholders. However, the dividend growth rate might not match earnings growth rate.
• Constant pay-out ratio: for example, (1 – b) = 25%. A clear and presumably logical link between dividends and earnings. However, in some circumstances this policy might produce signals that are mis-interpreted. Directors know that shareholders prefer predictable dividends and shareholders know that directors know their preference. Therefore, shareholders might interpret the cut as signalling that earnings are poor and will not improve any time soon. If, however, earnings fall yet the directors maintain the dividend, this is often interpreted as signalling that the fall in earnings is temporary and the directors feel sufficiently confident in the company’s future to maintain the dividend in absolute terms.
• Dividends as residuals: relating back to what was covered in the first section of the article, before paying dividends, directors should first spend earnings on investments in the company that yield:

• Investments that yield more than the cost of equity (this will increase shareholder value)
• Investments that yield the cost of equity.

Only after these investment opportunities run out should the company pay dividends from the residual earnings, thus allowing shareholders to make the best use they can of their receipts.

• No dividend: Microsoft and Apple both went many years without paying a dividend. It is difficult to use the dividend valuation model in these circumstance without making very contentious assumptions about what future dividends might be. Nevertheless, share values rose dramatically as both companies were immensely successful and, on a P/E approach to valuation, they were plainly very valuable indeed.

### Conclusion

Dividends and dividend policy will be a continuing cause of debate and comment. The theoretical position is clear: provided retained earnings are reinvested at the cost of equity, or higher, shareholder wealth is increased by cutting dividends. However, in the real world, where not necessarily all investors are logical and where transaction costs and other market imperfections intervene, determining a successful and popular dividend policy is rather more difficult.