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Exercise 4.2: The MM Dividend Irrelevancy Hypothesis

Chapter Four of CVT presents a comprehensive theoretical exposition and practical illustrations of the MM dividend irrelevancy hypothesis from both a proprietary (shareholder) and entity (managerial) perspective. Based on a sequential case study of different dividend-retention policies, initially applied to Gordon's growth model in Chapter Three, we developed a data set for an all equity firm (Jovi plc) with one million ordinary shares (common stock) in issue and an individual investor holding 40,000 shares. We observed that if Jovi adopts a nil dividend distribution policy, its current ex-div price per share was defined as follows using the MM one period model:

(18) P0 = D, + P, / 1 + K = 0 + £4.10 / 1.025 = £4.00


If you return to the companion text (CVT) and the Review Activity for Chapter Four, you will find the following question, for which I did not provide an answer.

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?

Let us now work through this together, given the assumption that profits are reinvested in projects of similar business risk with an equivalent yield of 2.5 per cent:

An Indicative Outline Solution

Our answer to the CVT Review Activity reinforces why MM hypothesized that dividends and retentions may be perfect substitutes in an all-equity firm, leaving shareholder wealth unaffected by changes in dividend distribution policy.

1. Dividend Irrelevancy

For a given investment policy of equivalent risk, a change in dividend policy (either way) does not alter current share price. The future ex-div price falls by the rise in the dividend for a given investment policy of equivalent business risk and vice versa, leaving the current ex-div price unchanged.

2. The Shareholders' Reaction

The MM case for dividend neutrality suggests that if a firm reduces its dividend payout, then shareholders can always satisfy their current income (consumption) preferences by creating home-made dividends. As we observed in Chapter Four, either they sell a requisite proportion of their holdings at an enhanced ex-div price, or borrow at the prevailing market rate of interest.

In our question, the company has moved from a zero distribution to a partial distribution. So, do shareholders who stay with the firm have a problem?

Using Equation (18) and our data where the Jovi company retains all earnings and Ke = 2.5%.

Assuming that the firm pursues a 50 per cent retention policy to reinvest in projects of equivalent business risk (i.e. Ke = 2.5 per cent).

MM would redefine:

So, no shareholder is worse off.

3. The Company's Reaction

For their part too, firms can resort to new equity issues in order to finance any shortfall in their investment plans, or if they wish to pay a dividend.

Reconsider Jovi with an original nil distribution and dedicated investment policy, whose shares are currently valued at £4.00 with an ex-div price of £4.10 at time period one:

The company has now decided to distribute 50 per cent of its earnings as dividends (5 pence per share on one million shares currently in issue).

If investment projects are still to be implemented, the company must raise new equity equivalent to the proportion of investment that is no longer funded by retained earnings. From our equations for the MM proof in Chapter Four, this equals:

The substitution of this figure into the equation for the total market value of the original shares, based on all the shares outstanding at time period one (nP1+mP1), defines the total market value of original shares in issue as follows:

And because the term (mP1 = nD1 ) disappears from this equation, it simplifies to:

Since P1 is the only unknown, dividing through by the number of Jovi's shares originally in issue (n = one million) and using Equation (18)

And solving for P1:

P1 = £4.05

So, as MM hypothesise:

Share price movements compensate for revisions to dividend-retention policy.

In our example, the ex-div share price at the end of the period has fallen from its initial value of £4.10 to £4.05, which is exactly the same as the 5 pence rise in dividend per share, leaving P0 unchanged.

Because the dividend term disappears from the MM equation for the market capitalisation of equity, it is impossible to assert that share price is a function of dividend policy.

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