For simplicity, so far we have assumed that if a share is held indefinitely and future dividends and earnings per share remain constant, the current ex-div price can be expressed using the capitalisation of a perpetual annuity based on its current dividend or earnings yields. The purpose of this Chapter is to refine the constant valuation model by considering two inter-related questions.

- What happens to a share's current price if its forecast dividends or earnings are not constant in perpetuity?

- When valuing a company's shares, do investors value current dividends more highly than earnings retained for future investment?

3.1. The Gordon Growth Model

Chapter One began with a discussion of investment principles in a perfect capital market characterised by certainty. According to Fisher's Separation Theorem (1930), it is irrelevant whether a company's future earnings are paid as a dividend to match shareholders' consumption preferences at particular points in time. If a company decides to retain profits for reinvestment, shareholder wealth will not diminish, providing that:

- Management's minimum required return on a project financed by retention (the discount rate, r) matches the shareholders' desired rate of return (the yield, Ke) that they can expect to earn on alternative investments of comparable risk in the market place, i.e. their opportunity cost of capital.

- In the interim, shareholders can always borrow at the market rate of interest to satisfy their income requirements, leaving management to invest current unpaid dividends on their behalf to finance future investment, growth in earnings and future dividends.

From the late 1950's, Myron J. Gordon developed Fisher's theory that dividends and retentions are perfect substitutes by analysing the impact of different dividend and reinvestment policies (and their corresponding yields and returns) on the current share price for all-equity firms using the application of a constant growth formula.

What is now termed the Gordon dividend-growth model defines 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.

Using Gordon's original notation 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:

Today, in many Finance texts the equation's notation is simplified with Dj and g representing the dividend term and growth rate, now subject to the constraint that Ke > g

In a certain world, Gordon confirms Fisher's relationship between corporate reinvestment returns (r) and the shareholders' opportunity cost of capital (Ke). Share price only responds to profitable investment opportunities and not changes in dividend policy because investors can always borrow to satisfy their income requirements. To summarize the dynamics of Equation (16).

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

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

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

Activity 1

To confirm the impact of retention financed investment on share price defined by Gordon under conditions of certainty, use the following stock exchange data for Jovi plc with an EPS of 10 pence and a full dividend distribution policy to establish its current share price.

Dividend Yield 2.5%

Now recalculate price, with the same EPS forecast of 10 pence, assuming that Jovi revises its dividend policy to reinvest 50 percent of earnings in projects with rates of return that equal its current yield.

Comment on your findings. - Full Distribution (Zero Growth)

Without future injections of outside finance, a forecast EPS of 10 pence and a policy of full distribution (i.e. dividend per share also equals 10 pence) Jovi currently has a zero growth rate. Shareholders are satisfied with a 2.5 per cent yield on their investment. We can therefore define the current share price using either a constant dividend or earnings valuation for the capitalisation of a perpetual annuity, rather than a growth model, because they are all financially equivalent.

- Partial Distribution (Growth)

Now we have the same EPS forecast of 10 pence but a reduced dividend per share, so that 50 percent of earnings can be reinvested in projects with rates of return equal to the current equity capitalisation rate of 2.5 percent.

According to Gordon, dividends will grow at a constant rate in perpetuity. Thus, Jovi's revised current ex-div share price is determined by capitalizing next year's dividend at the amount by which the desired rate of return exceeds the constant annual growth rate of dividends.

Using Equations (16) or (17):

- Commentary

Despite abandoning a constant share valuation in favour of the growth model to accommodate a change in economic variables relating to dividends retention, reinvestment and growth, Jovi's share price remains the same.

According to Gordon, this is because movements in share price relate to the profitability of corporate investment opportunities and not alterations to dividend policy. So, if the company's rate of return on reinvestment (r) equals the shareholders' yield (Ke) price will not change. It therefore follows logically that:

(i) Shareholder wealth (price) will only increase if r is greater than Ke

(ii) Shareholder wealth (price) will only decrease if r is lower than Ke

Activity 2

Can you confirm that if Ke = 2.5%, b = 0.5 but r moves from 2.5% to 4.0%, or down to 1.0%, then P0 moves from £4.00 to £10.00 or £2.50 respectively, just as Gordon's model predicts.

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