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Exercise 3.3: Growth Estimates and the Cut-Off Rate

The derivation of variables that comprise the Gordon model under conditions of certainty based on Equation (17) is not problematical. With zero growth, the model is equivalent to Equation (8), the constant dividend valuation model explained in Chapter Two, which simply discounts the next dividend (D1) at a constant equity capitalisation rate (Ke) using the current yield.

If growth is positive, Gordon 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 (g) the constant annual rate of growth in dividends. This growth rate (g = r.b)) is equivalent to the multiplication of a constant return (r) on new projects financed by a constant retention rate (b).

Subject to the mathematical proviso that Ke> g, it follows that if

Then shareholder wealth, measured by ex-div share price, stays the same, rises or falls, which confirms Fisher's Separation Theorem (1930) outlined at the beginning of our study.

So far so good, but if management finance future projects by retaining profits and shareholders wish to incorporate this data into their analysis of corporate performance in their quest for wealth, how do they calculate the growth rate?

In the real world, dividend-retention policies are rarely constant. Even if they are uniform, management and those to whom they are ultimately responsible still need annual growth estimators. A simple solution favored by the investment community, even if the future is uncertain, is to assume that the past and future are interdependent. Without information to the contrary, Gordon (op cit) also believed that a company's anticipated growth could be determined from its financial history and incorporated into his model.

Consider the following data available from the published accounts for the Adele company.

Year Dividend per Share

2008 20.00

2009 22.00

2010 24.20

2011 26.62

2012 29.28


1. Using a mathematical growth formulae of your choice, calculate the company's average periodic growth rate, as a future estimator of g

2. Use your answer to derive the forecast dividend for 2013 and assuming the company's shares are currently trading at $268.40 ex-div, calculate the dividend yield, namely the equity capitalisation rate (managerial cut­off rate for new investment) according to the Gordon Growth model.

An Indicative Outline Solution

1. The Annual Growth Rate

Using the formula (Dt - Dt 1)/Dt 1 or alternatively (Dt - Dt 1) -1, we can determine annual dividend growth rates.

Year Annual Growth Rate

2008-9 (22.00/20.00) -1 = 0.1

2009-10 (24.20/22.00) -1 = 0.1

2010-11 (26.62/24.20) -1 = 0.1

2011-12 (29.28/26.62) -1 = 0J_ Total 0.4

The average periodic growth rate, as an estimator of g, is therefore given by the sum of annual growth rates divided by the number of observations.

g = 0.4 / 4 = 10%

Alternatively, we can calculate dividend growth by solving for g in the following equation and rearranging terms.

2. The Forecast Dividend and Yield

Using the previous data and the appropriate equations:

The forecast dividend per share for 2013 should be

$29.28 (1.1) = $32.21

If Adele's shares are currently priced at $268.40 and dividends are expected to grow at ten per cent per annum beyond 2013, the current yield is 22 per cent. This is derived by solving for Ke in the Gordon Growth model as follows:

Rearranging terms:

Summary and Conclusions

Our Exercises have focused on the inter-relationships between dividend policy, the behaviour of the dividend yield and the price of a company's shares in the presence of growth financed by retentions. They illustrate why Myron J. Gordon believed that movements in share price relate to:

1. Corporate investment policy, rather than dividend policy under conditions of certainty.

2. Dividend policy, rather than corporate investment policy, under conditions of uncertainty.

According to his "bird in the hand" hypothesis, the policy objective for an all-equity firm in a real world of uncertainty is unambiguous:

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

But as we explained in CVT, when Gordon published empirical evidence designed to test his hypothesis and theoretical conclusions, his results were inconclusive. The reasons for which, we shall now analyse in Chapter Four

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.

3. Hill, R.A., Corporate Valuation and Takeover: Parts One and Two (2011).

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