Foundations of Financial Management: An Analysis (part 36)

“Wealth is the ability to fully experience life.” 

– Henry David Thoreau

Valuation and Rates of Return (part F)

by

Charles Lamson

Valuation of Common Stock

The value of a share of common stock may be interpreted by the shareholder as the present value of an expected stream of future dividends. Although in the short-run stockholders may be influenced by a change in earnings or other variables, the ultimate value of any holding rests with the distribution of earnings in the form of dividend payments. Though the stockholder may benefit from the retention and reinvestment of earnings by the corporation, at some point the earnings must be translated into cash flow for the stockholder. The stock valuation model based on future expected dividends, which is termed a dividend valuation model, can be stated as:

No Growth in Dividends

Under the no-growth circumstance, common stock is very similar to preferred stock. The common stock pays a constant dividend each year. For that reason, we merely translate the terms in Formula 4 from last post which applies to preferred stock, to apply to common stock. This is shown as new Formula 7.

Constant Growth in Dividends 

A firm that increases dividends at a constant rate is a more likely circumstance. Perhaps the firm decides to increase its dividends by 5 or 7 percent per year. The general valuation approach is shown in Formula 8.

To find the price of the stock, we take the present value of each year's dividend. This is no small task when the formula calls for us to take the present value of an infinite stream of growing dividends. Fortunately Formula 8 above can be compressed into a much more usable form if two circumstances are satisfied.

For most introductory courses in finance, these assumptions are usually made to reduce the complications in the analytical process. This then allows us to reduce or rewrite Formula 8 as Formula 9. Formula 9 is the basic equation for finding the value of common stock and is referred to as the constant growth dividend valuation model.

Thus, given that the stock has a $2 dividend at the end of the first year, a discount rate of 12 percent, and a constant growth rate of 7 percent, the current price of the stock is $40.

Let's take a closer look at Formula 9 above and the factors that influence valuation. For example, what is the anticipated effect on valuation if the required rate of return or discount rate increases as a result of inflation or increased risk? Intuitively, we would expect the stock price to decline if investors demand a higher return and the dividend and growth rate remain the same. This is precisely what happens.

We should not be surprised to see that an increasing growth rate has enhanced the value of the stock.

Determining the Required Rate of Return from the Market Price 

The first term represents the dividend yield the stockholder will receive, and the second term represents the anticipated growth in dividends, earnings, and stock price. While we have been describing the growth rate primarily in terms of dividends, it is assumed the earnings and stock price will also grow at that same rate over the long term if all else held constant. You should also observe that the formula above represents total return concept. The stockholder is receiving a current dividend plus anticipated growth in the future. If the dividend yield is low the growth rate must be high to provide the necessary return. Conversely, if the growth rate is low, a high dividend yield will be expected. The concepts of dividend yield and growth are clearly interrelated.

The Price-Earnings Ratio Concept and Valuation

The price-earnings ratio (the ratio of a company's share price to the company's earnings per share) represents a multiplier applied to current earnings to determine the value of a share of stock in the market. It is considered a pragmatic everyday approach to valuation. If a stock has earnings per share of $3 and a price-earnings (P/E) ratio of 15 times, it will carry a market value of $45. Another company with the same earnings but a P/E ratio of 20 times will enjoy a market price of $60.

The price-earnings ratio is influenced by the earnings and sales growth of the firm, the risk (or volatility in performance), the debt-equity structure of the firm, the dividend policy, the quality of management, and a number of other factors. Firms that have bright expectations for the future tend to trade at high P/E ratios while the opposite is true for low P/E firms. But beware, a high P/E can also mean the stock is overvalued.

Variable Growth and Dividends

In the discussion of common stock variation, we have considered procedures for firms that had no growth in dividends and for firms that had a constant growth. Most of the discussion and literature in finance assumes a constant growth dividend model. However, there is also a third case, and that is one of variable growth in dividends. The most common variable growth model is one in which the firm experiences supernormal (very rapid) growth for a number of years and then levels off to more normal, constant growth. The supernormal growth pattern is often experienced by firms in emerging Industries, such as the early days of electronics or microcomputers. 

In evaluating a firm with an initial pattern of supernormal growth, we first take the present value of dividends during the exceptional growth period. We then determine the price of the stock at the end of the supernormal growth period by taking the present value of the normal, constant dividends that follow the supernormal growth period. We discount this price to the present and add it to the present value of the super normal dividends. This gives us the current price of the stock.

A numerical example of a supernormal growth rate evaluation model is presented in the next post.

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 281-281*

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