## The Benchmark Case An Illustration of the Irrelevance of Dividend Policy

A powerful argument can be made that dividend policy does not matter. This will be illustrated with the Bristol Corporation. Bristol is an all-equity firm that has existed for 10 years. The current financial managers know at the present time (date 0) that the firm will dissolve in one year (date 1). At date 0 the managers are able to forecast cash flows with perfect certainty. The managers know that the firm will receive a cash flow of \$10,000 immediately and another \$10,000 next year. They believe that Bristol has no additional positive NPV projects it can use to its advantage.4

Current Policy: Dividends Set Equal to Cash Flow

At the present time, dividends (Div) at each date are set equal to the cash flow of \$10,000. The value of the firm can be calculated by discounting these dividends. This value is expressed as

Div1

where Div0 and Div! are the cash flows paid out in dividends, and rS is the discount rate. The first dividend is not discounted because it will be paid immediately. Assuming rS = 10%, the value of the firm is

\$10,000

If 1,000 shares are outstanding, the value of each share is

To simplify the example, we assume that the ex-dividend date is the same as the date of payment. After the imminent dividend is paid, the stock price will immediately fall to \$9.09 (\$19.09 — \$10). Several members of the board of Bristol have expressed dissatisfaction with the current dividend policy and have asked you to analyze an alternative policy.

Alternative Policy: Initial Dividend Is Greater than Cash Flow

Another policy is for the firm to pay a dividend of \$11 per share immediately, which is, of course, a total dividend payout of \$11,000. Because the cash runoff is only \$10,000, the extra \$1,000 must be raised in one of a few ways. Perhaps the simplest would be to issue \$1,000 of bonds or stock now (at date 0). Assume that stock is issued and the new stockholders will desire enough cash flow at date 1 to let them earn the

4Bristol's investment in physical assets is fixed.

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Chapter 18 Dividend Policy: Why Does It Matter? 499

required 10-percent return on their date 0 investment.5 The new stockholders will demand \$1,100 of the date 1 cash flow,6 leaving only \$8,900 to the old stockholders. The dividends to the old stockholders will be

Date 0 Date 1

Aggregate dividends to old stockholders \$11,000 \$8,900

Dividends per share \$ 11.00 \$ 8.90

The present value of the dividends per share is therefore

Students often find it instructive to determine the price at which the new stock is issued. Because the new stockholders are not entitled to the immediate dividend, they would pay \$8.09 (\$8.90/1.1) per share. Thus, 123.61 (\$1,000/\$8.09) new shares are issued.

### The Indifference Proposition

Note that the values in equations (18.1) and (18.2) are equal. This leads to the initially surprising conclusion that the change in dividend policy did not affect the value of a share of stock. However, upon reflection, the result seems quite sensible. The new stockholders are parting with their money at date 0 and receiving it back with the appropriate return at date 1. In other words, they are taking on a zero NPV investment. As illustrated in Figure 18.3, old stockholders are receiving additional funds at date 0 but must pay the new stockholders their money with the appropriate return at date 1. Because the old stockholders must pay back principal plus the appropriate return, the act of issuing new stock at date 0 will not increase or decrease the value of the old stockholders' holdings. That is, they are giving up a zero NPV investment to the new stockholders. An increase in dividends at date 0 leads to the necessary reduction of dividends at date 1, so the value of the old stockholders' holdings remains unchanged.

This illustration is based on the pioneering work of Miller and Modigliani (MM).7 Although our presentation is in the form of a numerical example, the MM paper proves that investors are indifferent to dividend policy in the general algebraic case. MM make the following assumptions:

1. There are neither taxes nor brokerage fees, and no single participant can affect the market price of the security through his or her trades. Economists say that perfect markets exist when these conditions are met.

2. All individuals have the same beliefs concerning future investments, profits, and dividends. As mentioned in Chapter 10, these individuals are said to have homogeneous expectations.

3. The investment policy of the firm is set ahead of time, and is not altered by changes in dividend policy.

5The same results would occur after an issue of bonds, though the argument would be less easily resolved.

6Because the new stockholders buy at date 0, their first (and only) dividend is at date 1.

7M. H. Miller and F. Modigliani, "Dividend Policy, Growth and the Valuation of Shares," Journal of Business (October 1961). Yes, this is the same MM who gave us a capital-structure theory.

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Corporate Finance, Sixth Dividend Policy Does It Matter? Companies, 2002

Edition

Part IV Capital Structure and Dividend Policy

■ Figure 18.3 Current and Alternative Dividend Policies

Current dividend policy:

Old shareholders receive \$10,000 at both date 0 and date 1

Dividends

Alternative policy:

Dividends

10,000

11,000

8,900

Time

Date 0 Date 1

Date 0 Date 1

Time

Alternative policy: New shareholders pay in \$1,000 at date 0 and receive \$1,100 in dividends at date 1

Cash flows

1,100

1,000

Date 0

- '

Time

To illustrate the indifference investors have toward dividend policy in our example, we used present-value equations. An alternative and perhaps more intuitively appealing explanation avoids the mathematics of discounted cash flows.

Suppose individual investor X prefers dividends per share of \$10 at both dates 0 and 1. Would she be disappointed when informed that the firm's management is adopting the alternative dividend policy (dividends of \$11 and \$8.90 on the two dates, respectively)? Not necessarily, because she could easily reinvest the \$1 of unneeded funds received on date 0, yielding an incremental return of \$1.10 at date 1. Thus, she would receive her desired net cash flow of \$11 - \$1 = \$10 at date 0 and \$8.90 + \$1.10 = \$10 at date 1.

Conversely, imagine investor Z preferring \$11 of cash flow at date 0 and \$8.90 of cash flow at date 1, who finds that management will pay dividends of \$10 at both dates 0 and 1. Here he can sell off shares of stock at date 0 to receive the desired amount of cash flow. That is, if he sells off shares (or fractions of shares) at date 0 totaling \$1, his cash flow at date 0 becomes \$10 + \$1 = \$11. Because a sale of \$1 stock at date 0 will reduce his dividends by \$1.10 at date 1, his net cash flow at date 1 would be \$10 - \$1.10 = \$8.90.

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Corporate Finance, Sixth Dividend Policy Does It Matter? Companies, 2002

Edition

Chapter 18 Dividend Policy: Why Does It Matter? 501

■ Figure 18.4 Homemade Dividends:A Trade-Off between Dividends at Date 0 and Dividends at Date 1

The graph illustrates both (1) how managers can vary dividend policy and (2) how individuals can undo the firm's dividend policy.

Managers varying dividend policy. A firm paying out all cash flows immediately is at point A on the graph. The firm could achieve point B by issuing stock to pay extra dividends or achieve point C by buying back old stock with some of its cash.

Individuals undoing the firm's dividend policy. Suppose the firm adopts the dividend policy represented by point B: dividends of \$11 at date 0 and \$8.90 at date 1. An investor can reinvest \$1 of the dividends at 10 percent, which will place her at point A. Suppose, alternatively, the firm adopts the dividend policy represented by point A. An individual can sell off \$1 of stock at date 0, placing him at point B. No matter what dividend policy the firm establishes, a sharholder can undo it.

The graph illustrates both (1) how managers can vary dividend policy and (2) how individuals can undo the firm's dividend policy.

Managers varying dividend policy. A firm paying out all cash flows immediately is at point A on the graph. The firm could achieve point B by issuing stock to pay extra dividends or achieve point C by buying back old stock with some of its cash.

Individuals undoing the firm's dividend policy. Suppose the firm adopts the dividend policy represented by point B: dividends of \$11 at date 0 and \$8.90 at date 1. An investor can reinvest \$1 of the dividends at 10 percent, which will place her at point A. Suppose, alternatively, the firm adopts the dividend policy represented by point A. An individual can sell off \$1 of stock at date 0, placing him at point B. No matter what dividend policy the firm establishes, a sharholder can undo it.

The example illustrates how investors can make homemade dividends. In this instance, corporate dividend policy is being undone by a potentially dissatisfied stockholder. This homemade dividend is illustrated by Figure 18.4. Here the firm's cash flows of \$10 at both dates 0 and 1 are represented by point A. This point also represents the initial dividend payout. However, as we just saw, the firm could alternatively pay out \$11 at date 0 and \$8.90 at date 1, a strategy represented by point B. Similarly, by either issuing new stock or buying back old stock, the firm could achieve a dividend payout represented by any point on the diagonal line.

The previous paragraph describes the choices available to the managers of the firm. The same diagonal line also represents the choices available to the shareholder. For example, if the shareholder receives a dividend distribution of (\$11, \$8.90), he or she can either reinvest some of the dividends to move down and to the right on the graph or sell off shares of stock and move up and to the left.

The implications of the graph can be summarized in two sentences:

1. By varying dividend policy, the managers can achieve any payout along the diagonal line in Figure 18.4.

2. Either by reinvesting excess dividends at date 0 or by selling off shares of stock at this date, any individual investor can achieve any net cash payout along the diagonal line.

Thus, because both the corporation and the individual investor can move only along the diagonal line, dividend policy in this model is irrelevant. The changes the managers make in dividend policy can be undone by an individual who, by either reinvesting dividends or selling off stock, can move to a desired point on the diagonal line.

Ross-Westerfield-Jaffe: IV. Capital Structure and Corporate Finance, Sixth Dividend Policy Edition

18. Dividend Policy: Why Does It Matter?

Part IV Capital Structure and Dividend Policy

A Test

You can test your knowledge of this material by examining these true statements:

1. Dividends are relevant.

### 2. Dividend policy is irrelevant.

The first statement follows from common sense. Clearly, investors prefer higher dividends to lower dividends at any single date if the dividend level is held constant at every other date. In other words, if the dividend per share at a given date is raised while the dividend per share for each other date is held constant, the stock price will rise. This act can be accomplished by management decisions that improve productivity, increase tax savings, or strengthen product marketing. In fact, you may recall in Chapter 5 we argued that the value of a firm's equity is equal to the discounted present value of all its future dividends.

The second statement is understandable once we realize that dividend policy cannot raise the dividend per share at one date while holding the dividend level per share constant at all other dates. Rather, dividend policy merely establishes the trade-off between dividends at one date and dividends at another date. As we saw in Figure 18.4, an increase in date 0 dividends can be accomplished only by a decrease in date 1 dividends. The extent of the decrease is such that the present value of all dividends is not affected.

Thus, in this simple world, dividend policy does not matter. That is, managers choosing either to raise or to lower the current dividend do not affect the current value of their firm. The above theory is a powerful one, and the work of MM is generally considered a classic in modern finance. With relatively few assumptions, a rather surprising result is shown to be perfectly true.8 Because we want to examine many real-world factors ignored by MM, their work is only a starting point in this chapter's discussion of dividends. The next part of the chapter investigates these real-world considerations.

### Dividends and Investment Policy

The preceding argument shows that an increase in dividends through issuance of new shares neither helps nor hurts the stockholders. Similarly, a reduction in dividends through share repurchase neither helps nor hurts stockholders.

What about reducing capital expenditures to increase dividends? Earlier chapters show that a firm should accept all positive net-present-value projects. To do otherwise would reduce the value of the firm. Thus, we have an important point:

Firms should never give up a positive NPV project to increase a dividend (or to pay a dividend for the first time).

This idea was implicitly considered by Miller and Modigliani. As we pointed out, one of the assumptions underlying their dividend-irrelevance proposition was, "The investment policy of the firm is set ahead of time and is not altered by changes in dividend policy."

Questions fc ro-----• How can an investor make homemade dividends?

0 j • What assumptions are needed to show that dividend policy is irrelevant?

8One of the real contributions of MM has been to shift the burden of proof. Before MM, firm value was believed to be influenced by its dividend policy. After MM, it became clear that establishing a correct dividend policy was not obvious at all.

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Corporate Finance, Sixth Dividend Policy Does It Matter? Companies, 2002

Edition

Chapter 18 Dividend Policy: Why Does It Matter?

■ Figure 18.5 Firm Issues Stock in Order to Pay a Dividend

No taxes Firm

Dividend (\$100)

No taxes Firm

Dividend (\$100)

Cash from issue of stock (\$100)

Cash from issue of stock (\$100)

A personal tax rate of 30%

Firm

Cash from issue of stock (\$100)

Dividend (\$100)

Entrepreneur Entrepreneur

In the no-tax case, the entrepreneur receives the \$100 in dividends that he gave to the firm when purchasing stock. The entire operation is called a wash; in other words, it has no economic effect. With taxes, the entrepreneur still receives \$100 in dividends. However, he must pay \$30 in taxes to the IRS. The entrepreneur loses and the IRS wins when a firm issues stock to pay a dividend.

A personal tax rate of 30%

Firm

Dividend (\$100)

Cash from issue of stock (\$100)

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