Walter and Gordon’s Model of Dividend

Walter’s Model, developed by Professor James E. Walter, suggests that the dividend policy of a firm is closely linked to its profitability, growth opportunities, and cost of capital. The model argues that dividend decisions are an integral part of the company’s investment decisions. It emphasizes that the choice between paying dividends and retaining earnings depends on whether the firm can generate higher returns from reinvested earnings than what shareholders could earn by investing the same amount elsewhere.

Assumptions of Walter’s Model:

• Internal Financing Only:

The firm uses only retained earnings to finance its investment opportunities and does not issue new equity or debt.

• Constant Rate of Return (r):

The firm’s rate of return on investments remains constant.

• Constant Cost of Capital (k):

The firm’s cost of equity (k) or required rate of return remains constant.

• No External Financing:

The model assumes that the firm relies solely on retained earnings for financing investments.

• Perpetual Life of the Firm:

The firm has an infinite life, meaning the decision to reinvest or pay dividends affects long-term returns.

• No Taxes or Transaction Costs:

The model ignores taxes and transaction costs, making it easier to isolate the effects of dividend policy on value.

Formula of Walter’s Model:

The relationship between the firm’s dividend policy and its market price per share is given by the following equation:

P = [D + r / k(E−D)] / k

Where:

• P: Market price per share
• D: Dividend per share
• r: Rate of return on retained earnings
• k: Cost of capital or required rate of return by shareholders
• E: Earnings per share

The formula shows that the price of the share depends on dividends (D), earnings (E), the rate of return on investment (r), and the cost of equity (k). Based on the values of r and k, Walter’s model classifies firms into three categories:

1. Growth Firms (r > k)

• When the firm’s rate of return (r) exceeds its cost of capital (k), it is considered a growth firm. In such cases, it is more beneficial to retain earnings and reinvest in the business because the firm can generate higher returns than shareholders can earn elsewhere.
• Dividend payout should be minimized as retaining earnings and reinvesting will increase the firm’s market value.
• Policy: Low or zero dividend payout.
• Impact on Share Value: Retention of earnings leads to an increase in the market price of shares.

2. Normal Firms (r = k)

• In a normal firm, the rate of return (r) equals the cost of capital (k). The company’s internal investments generate the same returns as shareholders can earn by investing externally.
• In this case, dividend policy becomes irrelevant as both retention and distribution of earnings will have the same effect on shareholder wealth.
• Policy: Dividend payout can be moderate.
• Impact on Share Value: The dividend policy has no significant impact on the market price of shares.

3. Declining Firms (r < k)

• For firms where the rate of return (r) is less than the cost of capital (k), it is better to distribute earnings as dividends. This is because shareholders can achieve higher returns by investing their dividends elsewhere.
• Retaining earnings and reinvesting in such firms will reduce shareholder wealth.
• Policy: High dividend payout.
• Impact on Share Value: Higher dividends will lead to an increase in market price.

Criticism of Walter’s Model:

• Ideal Assumptions:

The model assumes no external financing, constant returns, and an infinite firm life, which are unrealistic in the real world.

• Tax and Transaction Costs:

It ignores taxes, transaction costs, and market imperfections that significantly affect dividend policies.

• Static Assumptions:

The model assumes constant r and k, while in reality, returns and costs of capital fluctuate due to changes in market conditions and risk factors.

Gordon’s Model of Dividend Policy:

Gordon’s model, developed by Professor Myron J. Gordon, also proposes that the dividend policy is relevant to the market value of a firm. Similar to Walter’s model, Gordon’s model emphasizes the relationship between dividend policy and stock prices, but it also factors in the perception of risk and the behavior of investors.

Assumptions of Gordon’s Model:

1. All Equity Financing: The firm is financed entirely through equity, with no debt.
2. Constant Rate of Return and Cost of Capital: The firm’s rate of return on new investment (r) and cost of capital (k) remain constant.
3. Retention Ratio: A portion of earnings is retained, and the rest is distributed as dividends.
4. Risk Aversion: Investors are risk-averse and prefer dividends (immediate returns) to capital gains (future returns), due to the uncertainty associated with the latter.
5. Perpetual Earnings: The firm’s earnings are expected to continue indefinitely, growing at a constant rate.
6. No Taxes: The model assumes no corporate or personal taxes.
7. No New Stock Issues: All investments are financed from retained earnings, without issuing new shares.

Formula of Gordon’s Model

The price of a share according to Gordon’s model is given by:

P = [E(1−b)] / [k−br]

Where:

• P: Market price per share
• E: Earnings per share
• b: Retention ratio (the proportion of earnings retained for reinvestment)
• k: Cost of equity or required rate of return by shareholders
• r: Rate of return on retained earnings

In Gordon’s model, the retention ratio (b) plays a key role in determining the price of the stock. If the firm retains more earnings (higher b), it reduces immediate dividends, but increases future growth, assuming the firm can reinvest earnings at a rate higher than the cost of equity.

1. Growth Firms (r > k)

• For firms with a high return on investment (r) relative to the cost of capital (k), it is better to retain earnings and reinvest.
• This will lead to higher future dividends and capital appreciation, thus maximizing the stock price.

2. Normal Firms (r = k)

• In a normal firm, where the return on investment equals the cost of capital, dividend payout does not significantly affect the stock price.
• Investors are indifferent between receiving dividends or seeing earnings reinvested.

3. Declining Firms (r < k)

• When the return on investment is less than the cost of capital, it is better to distribute earnings as dividends.
• Investors can achieve better returns by reinvesting the dividends elsewhere, and thus the stock price is maximized by paying higher dividends.

Criticism of Gordon’s Model:

• No Debt Consideration:

The assumption that the firm is entirely equity-financed is unrealistic.

• Ignoring Market Fluctuations:

The model does not consider fluctuations in cost of capital or the impact of risk on investment decisions.

• Risk Aversion Assumption:

Gordon assumes that investors are risk-averse and always prefer dividends over capital gains, which may not be true for all investors.