Question

what is the connection between the value of share and a Dividend

Answer 1

The analysis of the relationship between a stock's intrinsic value and its dividend can be based on the type of the stock whose price is being analyzed. There are two broad classifications of stock type, namely: value stocks and growth stocks. The former has low price multiples, high dividends and is largely believed to be undervalued with respect to its fundamentals. The latter has high multiples, much lower dividends and grows in price at a rapid pace owing to its earnings capability. Value stock as would be understandable act as a source of high regular dividends for investors whereas growth stocks are majorly held for capital gains in the form of the stock's price appreciation.

Value stock prices are related to its dividend according to the following relationship:

P0 (Current Stock Price) = D1 / (1+ke) + D2/(1+ke)^(2) + D3/(1+ke)^(3) ....................... where Dt is the expected dividend at the end of year t and ke is the stock's cost of equity. As is understandable, the stock's price is directly related to the firm's expected future dividends. Value stock's with high expected dividends have higher prices as compared to other value stocks which pay comparatively lower dividends, cost of equity being the same in both cases. It is, however, another matter that the present value of expected dividends (sum of these present values is the stock's price) is affected to a great extent by the firm's cost of equity or minimum required rate of return. Discussion of the firm's cost of equity impact on share value has not been asked in this question and hence will not be discussed.

Growth Stock Prices do not have a very obvious mathematical relationship with their expected dividends largely because growth stocks usually do not pay any dividends and even if paid they are minuscule in magnitude. Growth stock prices are enhanced by what is known as the present value of growth opportunities (PVGO). Growth companies plow back a major part or their entire earnings as capital to grow their business, earnings and hence their stocks book values. The relationship between growth, plow back of earnings and return generated on capital employed is governed by the following relationship:

Growth = Return on Equity (ROE) x Retention Ratio = ROE x (1- Payout Ratio) = ROE x [1 - {Dividends per Share / Earnings per Share]

As is observable lesser the dividend, greater is the retention and for a given value of ROE, greater is the growth of the firm which is reflected in the firm's elevated stock prices. In such a scenario it will not be wrong to assume that lower dividends followed by a meaningful plow back of earnings into the business pushes growth and enhances stock price. The value generated by these plowed back earnings creates what is known as PVGO. This can be further explained by considering a growth firm and assuming that it does not plow back any earnings and pays out the entire amount as dividends. The value of such a firm should be V = Earnings / ke. However, the growing firm has an actual market value of say T. The difference between the firm's actual value T and value without earnings retention V is the PVGO, which in turn is created by lowering dividends, plowing earnings into growth opportunities and creating value for the firm. One important condition however, for retained earnings to create growth is that the firm's ROE ((the measure of the efficiency with which retained earnings generate value) is greater than the firm's cost of equity.