In a world of uncertainty, but reasonably efficient markets, Gordon presents a plausible hypothesis to explain why movements in share price relate to corporate dividend policy using the following growth model.

Because rational, risk-averse investors prefer their returns in the form of dividends now, rather than later (a "bird in the hand" philosophy), the overall shareholder return (yield) or managerial cut-off rate for investment, is not a constant but a function of the timing and size of the dividend payout ratio. Expressed mathematically:

Consequently, share price is a positive function of the dividend payout ratio.

As we explained in Chapter Three, Gordon and others who tested his model empirically were unable to prove this proposition categorically, even for all-equity firms, because of the statistical problem of multicolinearity. Explained simply, change D1 and all the other variables on the right hand side of Equation (17) are also affected (i.e. not only Ke but g).

Fortunately, two of Gordon's American academic contemporaries, Franco Modigliani and Merton H. Miller (MM henceforth) provided the investment community with a lifeline.

According to MM (1961 onwards) the equity capitalisation rate (Ke) conforms to the company's class of business risk, so that under conditions of certainty share price is indeed a function of corporate investment and not dividends, just as Gordon predicts.

However, under conditions of uncertainty, MM maintain that the statistical significance of the Gordon model is inconclusive because it confuses dividend policy with investment policy.

- Any increase in the dividend payout ratio, without any additional finance, reduces a firm's operating capability and vice versa.

- Because uncertainty is non-quantifiable, it is logically impossible to capitalise a multi-period future stream of dividends, where K < K < K ...etc. according to the investors' perception of the unknown.

MM therefore define a current ex-div share price using the following one period model:

where Ke equals the shareholders' desired rate of return (yield) and managerial cut-off rate for investment, which correspond to the "quality" of a company's periodic earnings (class of business risk). The greater their variability, the higher the risk, the higher Ke , the lower the price and vice versa.

MM then proceed to prove that because dividends and earnings are perfect economic substitutes in reasonably efficient markets:

For a given investment policy of equivalent business risk, a change in dividend (D1) cannot alter a company's current ex-div share price (P0) because Ke remains constant.

The next ex-div price (P1) increases by any corresponding reduction in dividend (D1) and vice versa, leaving P0 unchanged

Exercise 4.1: Dividend Irrelevancy

Before we rehearse the MM dividend irrelevancy hypothesis more fully, let us benchmark the inter-relationship between shareholder wealth maximisation, the supremacy of investment policy and dividend irrelevancy in a perfect capital market characterized by Fisher (op cit).

Suppose the Winehouse Company, an all equity firm generates a net annual cash flow of £100 million to be paid out as dividends in perpetuity. The yield and corporate cut-off (discount rate) correspond to a 10 per cent market rate of interest commensurate with the degree of business risk. Thus, the constant dividend valuation model, based on the capitalisation of a level perpetuity gives a total equity value (market capitalisation):

Now assume that the company intends to finance a new project of equivalent risk by retaining the next dividend to generate an incremental net cash inflow of £200 million twelve months later, all paid out as an additional dividend. Thereafter, a full distribution policy will still be adhered to.

Required:

1. Calculate the revised value for V

E

2. Evaluate whether management is correct to retain earnings and whether shareholders should continue to invest in the company?

An Indicative Outline Solution

Our answer reviews the investment and financial criteria that underpin the normative objective of shareholder wealth maximisation, using NPV maximisation as a determinant of share price.

1. The Revised Equity Value (VE)

The first question we must ask ourselves is how the incremental investment (a new project financed by the non-payment of a dividend) affects the shareholders' wealth?

We can present the managerial retention decision in terms of the revised dividend stream:

If we now compare total equity values using the discounted value of future dividends: VE (existing) = £100 million / 0.10 = £1,000 million

VE (revised) = £300 million / (1.1)2 + (£100 million / 0.10) / (1.1)2 = £1,074.4 million

Thus, once the project is accepted the present value (PV) of the firm's equity capital will rise and the shareholders will be £74.4million better off.

For those of you familiar with DCF analysis and the NPV concept, it is also worth noting that the same wealth maximisation decision can be determined from a managerial perspective without even considering the fact that the pattern of dividends has changed.

The increase in total value is simply the new project's net present value (NPV) given by the corporate DCF capital budgeting model.

2. An Evaluation of the Data

In our example, management is correct to retain earnings for reinvestment. The shareholders relinquish their next dividend. However, they gain an increase in the current ex-div value of their ordinary shares, which not only conforms to Fisher's Separation Theorem but also the MM dividend irrelevancy hypothesis.

In perfect capital markets, where the firm's investment decisions can be made independently of the consumption decisions of shareholders: