You will also recall from Chapter Three that even if Gordon's model is mathematically definable (Ke>g as well as D1>0) he argues that a fall in dividends should produce a rise in the equity capitalisation rate, causing share price to fall. However, MM refute this argument.

If a company's reduction in dividends fails to match shareholders' expectations, they can always create home-made dividends by selling part of their holdings (or borrowing) to satisfy their consumption preferences, without affecting their overall wealth.

To understand MM's proposition, let us develop the data from Activity 1 using Equation (18) assuming that the number of shares currently owned by an individual shareholder is defined by (n) to represent their holding.

Activity 2

Assume you own a number of shares (n = 10,000) in Jovi plc and expect an initial policy of full dividend distribution. From the previous Activity and Equation (19) it follows that your current stock of wealth is worth:

Now assume that the firm withholds all dividends for reinvestment. What do you do, if your income requirements (consumption preferences) equal the dividend foregone (£1,000)?

According to MM, the ex-div price should increase by the reduction in dividends. So, your holding is now valued as follows, with no overall change:

However, you still need to satisfy your income preference for £1,000 at time period one.

So, why not sell 250 shares for £41,000 / 10,000 at £4.10 each?

You now have £1,025, which means that you can take the income of £1,000 and reinvest the balance of £25 on the market at your desired rate of return (Ke=2.5%). And remember you still have 9,750 shares valued at £4.10.

To summarise your new stock of wealth:

Shareholding 9,750: Market value £39,975: Homemade Dividends £1,000: Cash £25

Have you lost out?

According to MM, of course not, since future income and value are unchanged:

To summarise, MM conclude that if shareholders do not like the heat they can get out of the kitchen by selling an appropriate proportion of their holdings, borrowing (or lending) to match their consumption (income) preferences.

4.3. The MM Hypothesis: A Corporate Perspective

Let us now turn to the company and what is now regarded as the proof of the MM dividend irrelevancy hypothesis. Usually, it is lifted verbatim from the mathematics of their original article and relegated to an Appendix in the appropriate chapter of most modern financial texts, with little, if any, numerical explanation.

So, where do we start?

According to MM, dividends and retentions are perfect economic substitutes, leaving shareholder wealth unaffected by changes in distribution policy. For its part too, a firm can resort to new issues of equity to finance any shortfall in its investment plans without compromising its current ex-div price.

To illustrate MM's corporate proposition, assume a firm's total number of shares currently in issue equals (n). We can define its total market capitalisation of equity as follows:

Now assume the firm decides to distribute all earnings as dividends. If investment projects are still to be implemented, the company must therefore raise new equity capital equivalent to the proportion of investment that is no longer funded by retentions.

According to MM, the number of new shares (m) issued at an ex-div price (P1) must therefore equal the total dividend per share retained (nD1) defined by:

Based on all shares outstanding at time period one (nP1+mP1) MM then rewrite Equation (19) to represent the total market value of original shares in issue as follows:

And because mP1 = nD1 this equation simplifies to:

MM therefore conclude that because the dividend term disappears from their market capitalisation, it is impossible to assert that share price is a function of dividend policy.

To illustrate the corporate dynamics of MM's argument, let us develop the data from Activity 2, using the preceding equations where the company's total number of shares in issue equals (n).

Activity 3

Assume Jovi plc begins the period with a maximum retention policy (nil distribution) and a given investment policy. Shares are therefore valued currently at £4.00 with an ex-div price of £4.10 at time period one as follows:

If Jovi has one million shares in issue, we can also derive the company's total market capitalisation of equity:

But now assume that the firm decides to distribute all earnings as dividends (10 pence per share on one million issued) without compromising investment (i.e. it is still a "given")

Confirm that this policy leaves Jovi's share price unchanged, just as MM hypothesize.

If investment projects are still to be implemented, the company must raise new equity capital equal to the proportion of investment that is no longer funded by retained earnings. According to MM, the number of new shares (m) issued ex-div at a price (P1) must therefore equal the total dividend per share retained (nD1) defined by the following equation.

Based on all shares outstanding at time period one (nP1+mP1) we can rewrite Equation (19) representing the total market value of original shares in issue as follows:

This simplifies to the following equation where the dividend term disappears.

Since there is also only one unknown in the equation (P1) dividing through by the number of shares originally in issue (n = one million) and rearranging terms, we revert to:

And simplifying, then solving for P1:

Pj = £4.00

Thus, as MM hypothesize:

- The ex-div share price at the end of the period has fallen from its initial value of £4.10 to £4.00, which is exactly the same as the 10 pence rise in dividend per share, therefore leaving P0 unchanged.

- Because the dividend term has disappeared from the equations, it is impossible to conclude that share price is a function of dividend policy.

Review Activity

To reaffirm the logic of the MM dividend irrelevancy hypothesis, revise the Jovi data set for a nil distribution to assess the implications for both the shareholders and the company if management now adopt a policy of partial dividend distribution, say 50 per cent?

Summary and Conclusions

MM criticize the Gordon growth model under conditions of uncertainty from both a proprietary (shareholder) and entity (corporate) perspective. The current value of a firm's equity is independent of its dividend distribution policy, or alternatively its retention policy, because they are perfect economic substitutes:

- The quality of earnings (business risk), rather than how they are packaged for distribution (financial risk), determines the shareholders' desired rate of return and management's cut-off rate for investment (project discount rate) and hence its share price.

- If a company chooses to make a dividend distribution it can always meet its investment requirements by a new issue of equity, rather than use retained earnings, so that the effect on shareholders' wealth is neutral.

- As a corollary, dividend policy should therefore be regarded as a passive residual, whereby management return unused funds to shareholders (the agency principle) because their search for new investment opportunities cannot maintain shareholder wealth.

It therefore seems reasonable to conclude Part Two with the following practical observation on our analyses of share valuation theories.

The P/E ratios associated with business risk, rather than dividend yields associated with financial risk, which are published in the financial press that we first outlined in Chapter Two, should encapsulate all the investment community needs to know about corporate economic performance.

We shall see.

Selected References

1. Gordon, M. J., The Investment, Financing and Valuation of a Corporation, Irwin, 1962.

2. Miller, M. H. and Modigliani, F., "Dividend policy, growth and the valuation of shares", The Journal of Business of the University of Chicago, Vol. XXXIV, No. 4 October 1961.

3. Hill, R.A., Strategic Financial Management (2008).

4. Fisher, I., The Theory of Interest, Macmillan (New York), 1930.

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