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3.2. Gordon's 'Bird in the Hand' Model

Gordon's initial analysis of the determinants of share price depends critically on the assumptions of certainty. For example, our previous Activity data incorporated a constant equity capitalisation rate (Ke) equivalent to a managerial assessment of a constant return (r) on new projects financed by a constant retention (b). This ensured that wealth remained constant (effectively Fisher's Separation Theorem). We then applied this mathematical logic to demonstrate that share price and hence shareholder wealth stays the same, rises or falls only when:

But what if the future is uncertain?

According to Gordon (1962 onwards) rational, risk averse investors should prefer dividends earlier, rather than later (a "bird in the hand" philosophy) even if retentions are more profitable than distributions (i.e. r > Ke). They should also prefer high dividends to low dividends period by period. Thus, shareholders will discount near dividends and higher payouts at a lower rate (K now dated) and require a higher overall average return on equity (Ke) from firms that retain higher earnings proportions, with obvious implications for share price. Expressed mathematically:

The equity capitalisation rate is no longer a constant but an increasing function of the timing and size of a dividend payout. So, an increased retention ratio results in a rise in the discount rate (dividend yield) and a fall in the value of ordinary shares:

To summarise Gordon's plausible hypothesis in a world of uncertainty, where dividend policy, rather than investment policy, determines share price:

The lower the dividend, the higher the risk, the higher the yield and the lower the price.

Review Activity

According to Gordon, the theoretical policy prescription for an all-equity firm in a world of uncertainty is unambiguous.

Maximise the dividend payout ratio and you minimise the equity capitalisation rate, which maximises share price and hence shareholder wealth.

But from 1959 to 1963 Gordon published a body of theoretical and empirical work using real world stock market data to prove his "bird in the hand philosophy" with conflicting statistical results.

To understand why, analyse the two data sets below for Jovi plc in a world of uncertainty. The first represents a dividend policy of full distribution. The second reflects a rational managerial decision to retain funds, since the company's return on investment exceeds the shareholders' increased capitalisation rate (Fisher's theorem again).

- Explain why the basic requirements of the Gordon growth model under conditions of uncertainty are satisfied.

- Confirm whether the corresponding share prices are positively related to the dividend payout ratio, as Gordon predicts.

Dividend Policy, Growth and Uncertainty

Dividend Policy, Growth and Uncertainty

- The Basic Requirements

Under conditions of certainty Gordon asserts that movements in share price relate to the profitability of corporate investment and not dividend policy. However, in a world of uncertainty the equity capitalisation rate is no longer constant but an increasing function of the timing of dividend payments. Moreover, an increase in the retention ratio results in a further rise in the periodic discount rate.

So far so good, since our data set satisfies these requirements. Moving from full distribution to partial distribution elicits a rise in Ke even though withholding dividends to finance investment accords with Fisher's wealth maximisation criterion (r > ke ) and also satisfies the mathematical constraint of the Gordon growth model (Ke > rb).

- Has share price fallen with dividend payout?

Rational, risk averse investors may prefer their returns in the form of dividends now, rather than later (a "bird in the hand" philosophy that values them more highly). But using the two data sets, which satisfy all the requirements of the Gordon model under conditions of uncertainty, reveals that despite a change in dividend policy, share price remains unchanged!

Summary and Conclusions

The series of variables in the previous table were deliberately chosen to ensure that share price remained unchanged. But the important point is that they all satisfy the requirements of Gordon's model, yet contradict his prediction that share price should fall. Moreover, it would be just as easy to provide another data set that satisfies these requirements but produces a rise in share price. No wonder Gordon and subsequent empirical researchers have often been unable to prove with statistical significance that real world equity values are:

Positively related to the dividend payout ratio Inversely related to the retention rate Inversely related to the dividend growth rate

Explained simply, Gordon confuses dividend policy (financial risk) with investment policy (business risk). For example, an increase in the dividend payout ratio, without any additional finance, reduces a firm's operating capability and vice versa.

Using Equation (17)

the weakness of Gordon's hypothesis is obvious. Change D1, then you change Ke and g. So, how do investors unscramble their differential effects on price (P0) when all the variables on the right hand side of the equation are now affected? And in our example cancel each other out!

For the moment, suffice it to say that Gordon encountered a very real world problem when testing his theoretical model empirically. What statisticians term multicolinearity. Fortunately, as we shall discover, two other academic researchers were able to provide the investment community with a more plausible explanation of the determinants of share price behaviour.

Selected References

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

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

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