# General Dividend Valuation

If distributions tend to infinity, then by definition the final term of Equation (9) disappears altogether because the share is never sold. This is the general dividend valuation model:

# Constant Dividend Valuation

Finally, if we assume that dividends are constant in perpetuity (Dt = Dt = D2 = D3 ...= Dw) and Ke is constant then the general model simplifies to the constant dividend valuation model.

# The Dividend Yield and Corporate Cost of Equity

We stated earlier that an appreciation of equity valuation models is a pre-requisite for understanding why shareholder returns provide the management of an all-equity firm with its cut-off rate for investment. To prove the point, let us rearrange the terms of Equation (12).

We have now defined the dividend yield published daily by the financial press throughout the world from stock exchange listings. Whilst the yield is based on an abstract constant dividend model, its use by investors as a corporate performance indicator is rational.

In an uncertain world where future dividend or price movements are unknown, it is reasonable to assume that without information to the contrary, future returns should at least equal today's ratio of a company's latest dividend to current share price. As a percentage, this dividend yield also enables investors to compare a company's performance over time, with its competitors, or the market, to establish whether its shares are over or under valued.

A "golden" investment rule is the higher the risk, the higher the return and lower the price. For example, a firm declares a 20 pence dividend on shares currently trading at £2.00. The yield is 10 per cent. But shareholders interpret the dividend as "bad" news and after panic selling, price falls to £1.00. So, the yield doubles, not because of improved performance but increased risk. Investors are now paying less for the same dividend.

Management ignore dividend yields at their peril

Because dissatisfied shareholders can always seek investment opportunities elsewhere, the percentage dividend for every £100 they invest in a company should represent a managerial benchmark for accepting new projects of equivalent risk. The yield also represents a minimum project return if management retain profits for reinvestment, rather than pay a dividend. Recalling Fisher's Separation Theorem and Agency Theory, firms that cannot maintain yields should distribute profits for shareholders to reinvest on the capital market. To summarise:

The current dividend yield is an opportunity cost of capital which equals the minimum cut-off (discount) rate for new investment in an all-equity firm.

# Dividend Growth and the Cost of Equity

For a company, the shareholder concept of maintainable yield based on the constant dividend model provides a convenient discount rate. Unfortunately, it is too simplistic. Assuming D1 = D2 = D3 and so on, implies either a 100 percent dividend pay-out ratio or zero-growth, both of which are rarely observed in the real world. Most firms retain a proportion of earnings for profitable reinvestment to enhance shareholder wealth through dividend growth and capital gains. So, how does this affect the yield as a cut-off rate for investment?

Beginning with a valuation model let us assume that through retention financed investment dividends now grow at a constant annual compound rate (g) in perpetuity. Leaving aside the detailed mathematics (that you can download elsewhere) M.J. Gordon (1958) proved that the current ex-div price becomes:

The Gordon constant growth dividend mode/ defines the current ex-div share price by capitalizing next year's dividend at the amount by which the desired equity return exceeds the constant rate of growth in dividend.

For example, if we assume that the next dividend per share is 20 pence, the shareholders' rate of return is 10 percent per annum and the annual growth rate is five percent

Activity 2

Take growth out of the previous equation or use Equation (12) for the constant dividend model to confirm that P0 is only £2.00. What does this reveal?

The two equations illustrate an important consideration for rational investors when buying shares, namely how growth potential can uplift equity value.

Rearrange the terms of Equation (14) and we can also isolate the impact of constant growth on the shareholders overall return.

So now, the cost of equity as a managerial discount rate equals a dividend expectation divided by current share price, plus a premium for growth. Using our previous example: