# Finance Assignment Help With Dividend Walter Model

## 9.2.1. Walter's Model

Walter J.E. supports the view that the dividend policy has a bearing on the market price of the share and has presented a model to explain the relevance of dividend policy for valuation of the firm based on the following assumptions:

• All investment proposals of the firm are to be financed through retained earnings only and no external finance is available to the firm.
• The business risk complexion of the firm remains same even after fresh investment decisions are taken. In other words, the rate of return on investment i.e. ‘r’ and the cost of capital of the firm i.e. ke, are constant.
• The firm has an infinite life.

This model considers that the investment decisions and dividend of a firm are interrelated. A firm should or should not pay dividends upon whether it has got the suitable investment opportunities to invest the retained or not.

The model is presented below:

If a firm pays dividend to shareholders, they in turn, will invest this income to get further returns. This expected return to shareholder is the opportunity cost of the firm and hence the cost of capital, ke, to the firm. On the other hand, if the firm does not pay dividends, and instead retains, then these retained earnings will be reinvested by the firm to get return on these retained earnings will be reinvested by the firm to get return on these investment. This rate of return on the investment, r. Of the firm must be at least equal to the cost of capital, ke. If r= ke, the firm is earning a return just equal to what the shareholders could have earned had the dividends been paid to them.

However, what happen if the rate of return, r, is more than the cost of capital, ke? In such case, the firm can earn more by retaining the profits, than the shareholders can earn by investing their dividend income. The Walter’s model, thus says that if r>ke, the firm should refrain from should reinvest the retained earnings and thereby increase the wealth of the shareholders. However, if the investment opportunities before the firm to reinvest the retained earnings are expected to give a rate of return which is less than the opportunity cost of the shareholders of the firm, then the firm should better distribute the entire profits. This will give opportunity to the shareholders to reinvest this dividend income and get higher returns.

In a nutshell, therefore, the dividend policy of a firm depends upon the relationship between r & k. If r>ke (a case of a growth firm), the firm should have zero payout and reinvest the entire profits to earn more than the investors. If however, r<ke, then the firm should have 100% payout ratio and let the shareholders reinvest their dividend income to earn higher returns, if ‘r’ happens to be just equal to ke, the shareholders will be indifferent whether the firm pays dividends or retain the profits. In such a case, the returns of the firm from reinvesting the retained earnings will be just equal to the earnings available to the shareholders on their investment of dividend income.

Thus, a firm can maximise the market value of its share and the value of the firm by adopting a dividend policy as follows:

• If r>ke, the payout ratio should be zero
• If r<ke, the payout ratio should be 100% and the firm should not retain any profit, and
• If r=ke, the dividend is irrelevant and the dividend policy is not expected to affect the market value of the share.

In order to testify the above, Walter has suggested a mathematical valuation model i.e.,

P = D + (r/ke) (E-D)

Ke ke

Where,

P = Market price of equity share

D = Dividend per share paid by the firm.

R = Rate of return on investment of the Firm

Ke = Cost of Equity share capital, and

E = Earnings per share of the firm.

As per the above formula, the market price of a share is the sum of two components i.e.,

• The present value of an infinite stream of dividends, and
• The present value of an infinite stream of return from retained earnings.

Thus, the Walter’s formula shows that the market value of a share is the present value of the expected stream of dividends and capital gains. The effect of varying payout ratio on the market price of the share under different rate of returns, r, have been shown below:

The following information is available in respect of Axis Ltd.

Earning per share (EPS or E) \$ 10

Cost of Capital, ke, 10%

Find out the market price of the share under different rate of return, r, of 8%, 10%, and 15% for different payouts of 0%, 40%, 80% and 100%.

The market price of the share as per Walter’s Model may be calculated for different combinations of rates and dividend payout ratios (the earnings per share, E, and the cost of capital, ke, taken as constant) as follows:

If the rate of return, r= 15% and the dividend payout ratio is 40%, then

P = D + (r/ke) (E-D)

Ke ke

= 40 + 90

= 130

Similarly, if r= 8% and dividend Payout ratio = 80%, then

P = 80+ 16

= 96

The expected market price of the share under different combinations of ‘r’ and ke have been calculated and presented in the table below:

r = 15% 10% 8%

D/P Ratio \$150 \$100 \$80

40% 130 100 88

80% 110 100 96

100% 100 100 100

It may be seen from the table that for a growth firm (r= 15% and r>ke), the market price is highest at \$ 150 when the firm adopts a zero payout and retains the entire earnings. As the payout increases gradually from 0% to 100%, the market price tends to decrease from \$ 150 to \$ 100 and the firm retains no profit. However if r=ke= 10%, then the price is constant at \$ 100 for different payouts ratios. Such a firm does not have any optimum ratio and every payout ratio is good as any other.

### Critical Appraisal

The Walter’s model provides a theoretical and simple frame work to explain the relationship between policy and value of the firm. As far as the assumptions underlying the model hold well, the behaviour of the market price of the share in response to the dividend policy of the firm can be explained with the help of this model.

However, the limitation of this model is that these underlying assumptions are too unrealistic. The financing of investments proposals only by retaining earnings and no external financing is seldom found in real life. The assumption of constant ‘r’ and constant ‘ke’ is also unrealistic and does not hold good. As more and more investment is made, the risk complexion of the firm will change and consequently the ke may not remain constant.