We began Part Two with an overview of share price valuation theory as a basis for stock market analysis using the dividend yield, dividend cover and the P/E ratio The following Exercises focus on the impact of managerial dividend and reinvestment policies on current share price, the market capitalisation of equity and shareholders' wealth, as a prelude to whether dividends (yields) and earnings (P/E ratios) are equally valued by investors.

Exercise 3.1:The Gordon Growth Model

Throughout the late 1950's, Myron J. Gordon (initially working with Ezra Shapiro) formalized the impact of distribution policies and their associated returns on current share price using the derivation of a constant growth formula, the mathematics for which are fully explained in the CVT text.

What is now termed the Gordon dividend growth model determines the current ex-div price of a share by capitalizing next year's dividend at the amount by which the shareholders' desired rate of return exceeds the constant annual rate of growth in dividends.

Required:

1. Present a mathematical summary of the Gordon Growth Model under conditions of certainty.

2. Comment on its hypothetical implications for corporate management seeking to maximise shareholder wealth.

An Indicative Outline Solution

These questions not only provide an opportunity to test your understanding of the companion text, but also to practice your written skills and ability to editorialize source material.

1. The Gordon Model

According to Gordon (1962) movements in ex-div share price (P0) under conditions of certainty relate to the profitability of corporate investment and not dividend policy.

Using Gordon's original notation and our Equation numbering from CVT (Chapter Three) where Ke represents the equity capitalisation rate; E1 equals next year's post-tax earnings; b is the proportion retained; (1-b) E1 is next year's dividend; r is the return on reinvestment and r.b equals the constant annual growth in dividends:

subject to the proviso that Ke > r.b for share price to be finite.

You will also recall that in many Finance texts today, the equation's notation is simplified with D1 and g representing the dividend term and growth rate, subject to the constraint that Ke > g

2. The Implications

In a world of certainty, Gordon's analysis of share price behavior confirms the importance of Fisher's relationship between a company's return on reinvestment (r) and its shareholders' opportunity cost of capital rate (Ke).

Because investors can always borrow, or sell part of their holding to satisfy any income requirements, movements in share price relate to the profitability of corporate investment opportunities and not alterations in dividend policy. To summarize the dynamics of Equation (16):

1. Shareholder wealth (price) will stay the same if r is equal to Ke

2. Shareholder wealth (price) will increase if r is greater than Ke

3. Shareholder wealth (price) will decrease if r is lower than Ke

Exercise 3.2: Gordon's 'Bird in the Hand' Model

Moving into a world of uncertainty, Gordon (op cit) explains why rational-risk averse investors are no longer indifferent to managerial decisions to pay a dividend or reinvest earnings on their behalf, which therefore impacts on share price.

Required:

1. Present a mathematical summary of the difference between the Gordon Growth Model under conditions of certainty and uncertainty.

2. Comment on its hypothetical implications for corporate management seeking to maximise shareholder wealth.

An Indicative Outline Solution

Again, these questions provide opportunities to test your understanding of the companion text and practice your written and editorial skills.

1. The Gordon Model and Uncertainty

According to Gordon (ibid) movements in share price under conditions of uncertainty relate to dividend policy, rather than investment policy and the profitability of corporate investment. He begins with the basic mathematical growth model:

subject to the proviso that Ke > r.b for share price to be finite.

This again simplifies to:

But now, the overall shareholder return (equity capitalisation rate) is no longer a constant but a function of the timing and size of the dividend payout. Moreover, an increase in the retention ratio also results in a further rise in the periodic capitalisation rate. Expressed mathematically:

2. The Implications

According to Gordon's uncertainty hypothesis, rational, risk averse investors adopt a "bird in the hand" philosophy to compensate for the non-payment of future dividends.

They prefer dividends now, rather than later, even if retentions are more profitable than distributions (i.e. r > Ke). They prefer high dividends to low dividends period by period. (i.e. Dj> D2 ). Near dividends and higher payouts are discounted at a lower rate (Ket now dated) ,

Thus, investors require a higher overall average return on equity (Ke) from firms that retain a higher proportion of earnings with obvious implications for share price. It will fall.

Gordon presents a plausible hypothesis in a world of uncertainty, where dividend policy, rather than investment policy, determines share price.

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 ex-div value of ordinary shares: Share prices are:

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

To summarize Gordon's position:

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

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