# The Relationship between Dividend Payouts and Systematic Risk: A Mathematical Approach

## Article excerpt

ABSTRACT

The traditional approach to evaluating dividend policy centers on how the payment of dividends ultimately affects a firm's stock price. The theoretical and empirical work in this area provides mixed results because firms have different motives for paying, not paying, or changing their dividends. In order to better understand how the dividend affects the firm, this paper focuses on how dividends affect a firm's level of systematic risk. Previous studies have used empirical analysis to show an inverse relationship between the payment of dividends and systematic risk. These studies, however, lack a theoretical explanation to accompany their findings. We provide a mathematical model that illustrates the relationship between dividends and systematic risk. In addition, we provide a further empirical analysis that is consistent with our model as well as previous studies.

INTRODUCTION

A primary area of research in the field of corporate finance centers on the relationship between dividends and stock prices. Early literature (Graham and Dodd 1951, and Durrand 1955) focuses on how the dividend payout ratio affects common stock prices, and it concludes that firms can affect the market value of their common stock by altering their dividend policy. Subsequent studies reveal that the relationship between dividends and stock prices is enormously complex and inconclusive. This paper isolates one component of stock price determination, systematic risk, and presents a mathematical model that illustrates how it is affected by a firm's dividend policy. By isolating the impact on systematic risk, we can draw conclusions about how firm value is affected by dividend policy in the absence of other mitigating factors. We also provide a statistical analysis that supports our model.

EARLY LITERATURE

In contrast to the earlier work of Graham and Dodd (1951) and Durrand (1955), Miller and Modigliani (1961) argue that dividends are irrelevant in a world with efficient capital markets, no taxes, and no transaction costs. Dividends, according to Miller and Modiglianai (hereafter M&M), simply reduce the value of the firm's stock by the amount of the dividend. In the absence of taxes and transaction costs, investors should be completely indifferent with regard to the firm's payment of dividends. From the firm's perspective, the key to their argument is that investment decisions are completely independent of dividend policy. If the amount of investment funds remaining after the dividend payout is not enough to meet desired investment outlays, the firm may seek external financing to compensate for their shortage of funds. Therefore, the level of dividends will never affect the investment decision.

Many studies concur with the finding that dividends are an irrelevant determinate of firm value, even after relaxing the restrictive assumptions imposed by M&M. Farrar and Selwyn (1967), for example, show that the irrelevance of dividend policy exists in a world with corporate income taxes but no personal income taxes. If both personal income taxes and corporate income taxes are considered, and capital gains are taxed at a lower rate, they argue that a zero dividend policy is optimal.

Miller and Scholes (1978) show that Farrar and Selwyn may be mistaken in arguing for a zero dividend policy when divergent tax rates on dividends and capital gains exist. When the marginal tax rate on capital gains is lower than the marginal tax rate on dividends received, personal income taxes can be avoided by sheltering taxable dividend income. As a result, investors will be indifferent between dividend income and capital gains, and the original M&M argument that dividends are irrelevant holds.

Without denying the theoretical irrelevancy of dividend policy, Bhattacharya (1979) tries to explain why firms actually do pay dividends. Bhattacharya looks at the favorable signal conveyed by unexpected dividend increases. …

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