The formula $P_0=\frac{D}{K}+\frac{\frac{R}{K}(E-D)}{K}$ (Where P0 is market price of shares, E is earning per share, D is dividend per share, R is rate of Return and K is cost of equity) for determining the dividend of the firm has been given by: :

Question

Prepp Team · Accepted Answer

Understanding the Dividend Valuation Formula and its Contributor

The question asks to identify the economist or financial expert who provided the specific formula for determining the market price of shares based on dividends, earnings, return, and cost of equity.

The formula provided is:

$P_0=\frac{D}{K}+\frac{\frac{R}{K}(E-D)}{K}$

Let's understand the variables used in this dividend valuation formula:

$P_0$: Market price of shares
$E$: Earnings per share (EPS)
$D$: Dividend per share (DPS)
$R$: Rate of Return the firm earns on its investments
$K$: Cost of equity capital or required rate of return by shareholders

This formula can be simplified as:

$P_0 = \frac{D}{K} + \frac{R(E-D)}{K^2}$

This formula is a well-known model in corporate finance used to determine the theoretical market price of a share based on the firm's dividend policy and investment decisions. It suggests that the market price is the present value of expected future dividends plus the present value of capital gains resulting from the firm's retained earnings (E-D) reinvested at rate R, discounted by the cost of equity K.

Let's examine the options provided and their contributions to finance:

Myron Gordon: Gordon is known for the Gordon Growth Model, another dividend discount model, but it typically assumes dividends grow at a constant rate (g). The basic Gordon Growth Model formula is $P_0 = \frac{D_1}{K-g}$.
James E Walter: James E. Walter developed a model that emphasizes the relationship between a firm's rate of return on investments (R) and its cost of equity (K) in determining the optimal dividend payout ratio that maximizes firm value. The formula provided in the question is precisely Walter's model. Walter's model posits that if R > K, the firm should retain earnings and reinvest them; if R < K, the firm should distribute earnings as dividends; and if R = K, the dividend policy is irrelevant.
Modigliani - Miller: Modigliani and Miller (M&M) are famous for their dividend irrelevance theory, which states that in a perfect market (without taxes, transaction costs, etc.), a firm's market value is not affected by its dividend policy. Their work is more about the irrelevance principle under specific assumptions, not a valuation formula like the one given.
David Durrand: David Durrand contributed to the understanding of capital structure theories, specifically related to the net income approach and net operating income approach to valuation and the cost of capital, not typically this specific dividend valuation model.

Based on the analysis of the formula and the contributions of the listed individuals, the formula $P_0=\frac{D}{K}+\frac{\frac{R}{K}(E-D)}{K}$ for share valuation is attributed to James E. Walter.

Detailed Explanation of Walter's Model

Walter's model is a theoretical model used to determine the share price of a company. It suggests that the price of a company's share depends on:

The dividend per share (D)
The earnings per share (E)
The firm's internal rate of return on investments (R)
The cost of equity (K)

The formula essentially discounts the expected future cash flows available to shareholders. It splits the value into two parts: the present value of perpetual dividends ($\frac{D}{K}$) and the present value of the capital gains generated by reinvesting retained earnings ($\frac{R(E-D)}{K^2}$).

Walter's model implies that the relationship between R and K is crucial for dividend policy decisions aiming at maximizing shareholder wealth. When R > K, the firm creates value by retaining earnings and reinvesting them. When R < K, the firm destroys value by reinvesting earnings, so distributing them as dividends is better. When R = K, the dividend policy has no impact on share price.

Comparing Walter's Model with other Theories

Feature	Walter's Model	Gordon's Model	M&M Theory
Focus	Relationship between R & K and dividend policy impact on value	Constant dividend growth rate impacting value	Dividend irrelevance under perfect market conditions
Key Formula for P0	$P_0 = \frac{D}{K} + \frac{R(E-D)}{K^2}$	$P_0 = \frac{D_1}{K-g}$	Value depends on earnings, not dividend payout ratio
Assumption on Reinvestment	Explicitly links value creation to reinvestment return (R vs K)	Implicitly assumes reinvestment supports growth rate (g)	Assumes investment decisions are independent of financing/dividend decisions
Market Assumptions	Assumes cost of equity (K) is constant, firms can fund investments internally or externally at K	Assumes cost of equity (K) is constant, constant growth (g) < K	Perfect capital markets, no taxes, no transaction costs, symmetric information, rational investors

Conclusion on the Formula's Origin

The specific dividend valuation formula provided in the question, which incorporates earnings (E), dividends (D), rate of return (R), and cost of equity (K) to determine the market price ($P_0$), is attributed to James E. Walter. His model highlights how a firm's investment opportunities (reflected by R) relative to its cost of equity (K) influence the impact of its dividend policy on share value.

Revision Table: Key Dividend Concepts

Concept	Description	Associated Theorist(s)
Walter's Model	Stock value depends on dividend policy and profitability of investments (R vs K).	James E. Walter
Gordon Growth Model	Stock value is the present value of future dividends growing at a constant rate.	Myron Gordon
Dividend Irrelevance Theory	Under perfect market conditions, dividend policy does not affect firm value.	Modigliani and Miller
Dividend Payout Ratio	Proportion of earnings paid out as dividends ($D/E$).	All models implicitly or explicitly consider this

Additional Information on Dividend Policy

Dividend policy is a critical decision for a company's management. It involves deciding how much of the company's earnings should be distributed to shareholders as dividends and how much should be retained for reinvestment in the business. Different theories offer varying perspectives on the impact of dividend policy on a firm's value and shareholder wealth.

Relevance Argument: Proponents like Walter and Gordon argue that dividend policy is relevant and affects firm value. They suggest that investors prefer current dividends over future capital gains, or that the firm's reinvestment opportunities dictate the optimal payout.
Irrelevance Argument: M&M argue that in a perfect market, investors are indifferent between receiving dividends and realizing capital gains from reinvested earnings. They can create their own "dividends" by selling shares. This theory rests on strong assumptions not always present in the real world.
Factors Influencing Policy: In reality, companies consider many factors when setting dividend policy, including profitability, liquidity, investment opportunities, access to capital markets, contractual obligations, and shareholder preferences (e.g., tax implications).

Understanding models like Walter's helps in analyzing the theoretical link between a firm's investment efficiency, its payout decisions, and its market valuation.