## D

Because the dividend is always the same, the stock can be viewed as an ordinary perpetuity with a cash flow equal to D every period. The per-share value is thus given by:

where R is the required return.

For example, suppose the Paradise Prototyping Company has a policy of paying a \$10 per share dividend every year. If this policy is to be continued indefinitely, what is the value of a share of stock if the required return is 20 percent? The stock in this case amounts to an ordinary perpetuity, so the stock is worth \$10/.20 = \$50 per share.

Constant Growth Suppose we know that the dividend for some company always grows at a steady rate. Call this growth rate g. If we let D0 be the dividend just paid, then the next dividend, D1, is:

The dividend in two periods is:

We could repeat this process to come up with the dividend at any point in the future. In general, from our discussion of compound growth in Chapter 6, we know that the dividend t periods into the future, Dt, is given by:

An asset with cash flows that grow at a constant rate forever is called a growing perpetuity. As we will see momentarily, there is a simple expression for determining the value of such an asset.

The assumption of steady dividend growth might strike you as peculiar. Why would the dividend grow at a constant rate? The reason is that, for many companies, steady growth in dividends is an explicit goal. For example, in 2000, Procter and Gamble, the Cincinnati-based maker of personal care and household products, increased its dividend by 12 percent to \$1.28 per share; this increase was notable because it was the 44th in a row. The subject of dividend growth falls under the general heading of dividend policy, so we will defer further discussion of it to a later chapter.

Dividend Growth

The Hedless Corporation has just paid a dividend of \$3 per share. The dividend of this company grows at a steady rate of 8 percent per year. Based on this information, what will the dividend be in five years?

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

III. Valuation of Future Cash Flows

8. Stock Valuation