Question 4 (a)

Gordon's model and Walter's model on the relevance of dividends

6 marks

Time to write: About 12 minutes
Topic: Dividend theories and dividend policy

Question

Question 4 (a) · 6 marks

How is Gordon’s Model different from Walter’s Model to relevance of dividends? Also discuss their similarities.

Reworded from the university paper; the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.

Before you write

Read off the question and its marks

12 minfor 6 marks

Read from the question

How…?Discuss…Two asks in one question: answer both.
differSet the differences out in a table, basis by basis, not as two separate essays.

What the paper leaves open

"Different from... to relevance of dividends" is read as "different on the relevance of dividends".

Write it in this order

Read; underline the asks; jot your points 1 min
1 Walter's model: formula and the r-against-ke rule 1 mark 2 min
2 Gordon's model: formula and the bird-in-hand argument 1 mark 2 min
3 Differences between the two models 2 marks 3 min
4 Similarities: relevance view and common assumptions 2 marks 3 min
Check: every ask answered, key terms underlined 1 min

1234

Short on time? Trim steps 3 and 4 evenly rather than skip one: each is capped at its own marks.

Try it first. About 12 minutes for 6 marks. Write it out, then open the solution.

Solution

Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.

Both models belong to the relevance school: the dividend decision affects the value of the share. They reach that conclusion by different routes.

Walter's model. The share price is P = [D + (r ÷ ke)(E − D)] ÷ ke, where D is dividend per share, E earnings per share, r the firm's internal rate of return and ke the cost of equity. The value depends on comparing r with ke: if r > ke (a growth firm) the optimum payout is zero; if r < ke (a declining firm) it is 100%; if r = ke the dividend policy does not affect the price.

Gordon's model. The share price is P = E(1 − b) ÷ (ke − br), where b is the retention ratio, so br is the growth rate. Its distinctive argument is the "bird-in-hand": investors are risk averse, they are more certain of a dividend received now than of capital gains later, and so they discount future gains at a higher rate. On this argument a firm that pays more now is valued more highly. With r and ke held constant, as the model assumes, the formula itself leads to the same conclusions as Walter's: the value rises with retention when r > ke, falls when r < ke, and is unaffected by the payout when r = ke.

Differences

Point	Walter	Gordon
Basis of relevance	The relation between the return on investment (r) and the cost of capital (ke)	Investors' preference for current dividends over uncertain future gains (bird-in-hand)
Risk	ke is taken as a given constant, though a firm's risk pattern does not stay constant (a criticism of the model)	Uncertainty is central: capital gains are riskier than current dividends and are discounted at a higher rate
Growth	Not modelled separately; retained earnings earn r	Growth rate g = br is part of the formula, and ke must exceed br
Formula	P = [D + (r ÷ ke)(E − D)] ÷ ke	P = E(1 − b) ÷ (ke − br)
Effect of payout	Optimum payout is zero, 100%, or irrelevant, depending on r against ke	With r and ke constant, the same as Walter: retain when r > ke, pay out when r < ke, payout irrelevant at r = ke; the bird-in-hand argument adds that investors value a certain dividend more than an uncertain gain

Similarities

Both treat dividends as relevant to the value of the share.
Both assume an all-equity firm whose investment is financed only by retained earnings, with no external financing.
Both assume r and ke are constant.
Both assume a firm with a perpetual life.
Both capitalise the expected returns at the cost of equity: Walter's formula divides by ke, Gordon's by (ke − br).
Both reach the same conclusions on payout when r and ke are constant: retention adds value when r > ke, payout adds value when r < ke, and the payout does not matter when r = ke.

Where the 6 marks sit

#	Component	Marks
1	Walter's model: formula and the r-against-ke rule	1
2	Gordon's model: formula and the bird-in-hand argument	1
3	Differences between the two models	2
4	Similarities: relevance view and common assumptions	2
	Total	6

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