# How would you respond? “You say stock price equals the present value of future dividends? That’s crazy! All the investors I know are looking for capital gains.”

When hearing the stock price equals the present value of future, dividends it tells me, it is a simplified stock valuation model based on the general principle that the price of a common stock equals the present value of its future dividends (Fuller & Chi-Cheng, 1984). According to Pearson Education, Inc. (2011), The Law of One Price states that the value of a stock is equal to the present value of the dividends and future sale price the investor receives. This is because cash flows are risky and must be discounted at the equity cost of capital, which is the expected return of other securities available in the market with equivalent risk to the firm’s equity. The total return of a stock is equal to the dividend yield plus the capital gain rate. The expected total return of a stock should equal its equity cost of capital. If the stock eventually pays dividends and is never acquired, the dividend-discount model implies that the stock price equals the present value of all future dividends.

The constant dividend growth model assumes that dividends grow at a constant expected rate g. In that case, g is also the expected capital gain rate. Future dividends depend on earnings, shares outstanding, and the dividend payout rate. If the dividend payout rate and the number of shares outstanding is constant, and if earnings change only as a result of new investment from retained earnings, then the growth rate of the firm’s earnings, dividends, and share price. Cutting the firm’s dividend to increase investment will raise the stock price if, and only if, the new investments have a positive NPV.

If the firm has a long-term growth rate of g after the period N+1, then we can apply the dividend-discount model and use the constant dividend growth formula to estimate the terminal stock value PN. The dividend-discount model is sensitive to the dividend growth rate, which is difficult to estimate accurately. If the firm undertakes share repurchases, it is more reliable to use the total payout model to value the firm. In this model, the value of equity equals the present value of future total dividends and repurchases. To determine the stock price, we divide the equity value by the initial number of shares outstanding of the firm. The growth rate of the firm’s total payout is governed by the growth rate of earnings, not earnings per share. When a firm has leverage, it is more reliable to use the discounted free cash flow model. In this model, the firm’s enterprise value (the market value of equity plus debt, less excess cash) equals the present value of the firm’s future free cash flow.

The corporate can estimate the firm’s future free cash flow where Net Investment equals the firm’s capital expenditures in excess of depreciation. The company discount cash flows using the weighted average cost of capital, which is the expected return the firm must pay to investors to compensate them for the risk of holding the firm’s debt and equity together. Then the company can estimate a terminal enterprise value by assuming free cash flow grows at a constant rate, which is usually equal to the rate of long-run revenue growth. Then the company can determine the stock price by subtracting debt and adding cash to the enterprise value, and then dividing by the initial number of shares outstanding of the firm. Even though the company can value stocks by using valuation multiples based on comparable firms, it is best to use several methods to identify a reasonable range for the value. Stock prices aggregate the information of many investors. Therefore, if our valuation disagrees with the stock’s market price, it is most likely an indication that our assumptions about the firm’s cash flows are wrong. According to Brealey-Myers-Allen (2011), “The discounted-cash-flow (DCF) formula for the present value of a stock is just the same as it is for the present value of any other asset” (para.1). When investors buy stocks, they expect to receive a dividend and make a capital gain. According to Brealey-Myers-Allen (2011), the of return that investors expect from their share over the next year is defined as the expected dividend per share DIV1 plus the expected price appreciation per share P1  P0, all divided by the price at the start of the year P0. The cash payoff to owners of common stocks comes in two forms: (Brealey-Myers-Allen, 2011).

(1) Cash dividends and

(2) Capital gains or losses

References:

Brealey-Myers-Allen (2011). Principles of Corporate Finance, 2nd Concise Edition [0] (VitalSource Bookshelf), Retrieved from http://online.vitalsource.com/books/9780390240149/page/86

Fuller, R. J., & Chi-Cheng, H. (1984). A Simplified Common Stock Valuation Model. Financial Analysts Journal, 40(5), 49-56.

Pearson Education, Inc. (2011). Valuing Stocks. Retrieved March 14, 2012 from http://wps.prenhall.com/bp_berk_cf_2_core/136/34997/8959387.cw/index.html