Computing the Price of Common Stock

Common stock is the principal way that corporations raise equity capital. Holders of common stock own an interest in the corporation consistent with the percentage of outstanding shares owned. This ownership interest gives stockholders—those who hold stock in a corporation—a bundle of rights. The most important are the right to vote and to be the residual claimant of all funds flowing into the firm (known as cash flows), meaning that the stockholder receives whatever remains after all other

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claims against the firm's assets have been satisfied. Stockholders are paid dividends from the net earnings of the corporation. Dividends are payments made periodically, usually every quarter, to stockholders. The board of directors of the firm sets the level of the dividend, usually upon the recommendation of management. In addition, the stockholder has the right to sell the stock.

One basic principle of finance is that the value of any investment is found by computing the value today of all cash flows the investment will generate over its life. For example, a commercial building will sell for a price that reflects the net cash flows (rents - expenses) it is projected to have over its useful life. Similarly, we value common stock as the value in todays dollars of all future cash flows. The cash flows a stockholder might earn from stock are dividends, the sales price, or both.

To develop the theory of stock valuation, we begin with the simplest possible scenario: You buy the stock, hold it for one period to get a dividend, then sell the stock. We call this the one-period valuation model.

The One-Period Suppose that you have some extra money to invest for one year. After a year, you will

Valuation Model need to sell your investment to pay tuition. After watching CNBC or Wall Street Week on TV, you decide that you want to buy Intel Corp. stock. You call your broker and find that Intel is currently selling for $50 per share and pays $0.16 per year in dividends. The analyst on Wall Street Week predicts that the stock will be selling for $60 in one year. Should you buy this stock?

To answer this question, you need to determine whether the current price accurately reflects the analysts forecast. To value the stock today, you need to find the present discounted value of the expected cash flows (future payments) using the formula in Equation 1 of Chapter 4. Note that in this equation, the discount factor used to discount the cash flows is the required return on investments in equity rather than the interest rate. The cash flows consist of one dividend payment plus a final sales price. When these cash flows are discounted back to the present, the following equation computes the current price of the stock:

where P0 = the current price of the stock. The zero subscript refers to time period zero, or the present. Div1 = the dividend paid at the end of year 1.

ke = the required return on investments in equity. P1 = the price at the end of the first period; the assumed sales price of the stock.

To see how Equation 1 works, let's compute the price of the Intel stock if, after careful consideration, you decide that you would be satisfied to earn a 12% return on the investment. If you have decided that ke = 0.12, are told that Intel pays $0.16 per year in dividends (Div1 = 0.16), and forecast the share price of $60 for next year (Px = $60), you get the following from Equation 1:

Based on your analysis, you find that the present value of all cash flows from the stock is $53.71. Because the stock is currently priced at $50 per share, you would choose to buy it. However, you should be aware that the stock may be selling for less than $53.71, because other investors place a different risk on the cash flows or estimate the cash flows to be less than you do.

The Generalized Dividend Valuation Model

Using the same concept, the one-period dividend valuation model can be extended to any number of periods: The value of stock is the present value of all future cash flows. The only cash flows that an investor will receive are dividends and a final sales price when the stock is ultimately sold in period n. The generalized multi-period formula for stock valuation can be written as:

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