## Cash Flows

Imagine that you are considering buying a share of stock today. You plan to sell the stock in one year. You somehow know that the stock will be worth $70 at that time. You predict that the stock will also pay a $10 per share dividend at the end of the year. If you require a 25 percent return on your investment, what is the most you would pay for the stock? In other words, what is the present value of the $10 dividend along with the $70 ending value at 25 percent?

If you buy the stock today and sell it at the end of the year, you will have a total of $80 in cash. At 25 percent:

Therefore, $64 is the value you would assign to the stock today.

More generally, let P0 be the current price of the stock, and assign P1 to be the price in one period. If D1 is the cash dividend paid at the end of the period, then:

where R is the required return in the market on this investment.

Notice that we really haven't said much so far. If we wanted to determine the value of a share of stock today (P0), we would first have to come up with the value in one year (Pj). This is even harder to do, so we've only made the problem more complicated.

What is the price in one period, P1? We don't know in general. Instead, suppose we somehow knew the price in two periods, P2. Given a predicted dividend in two periods, D2, the stock price in one period would be:

If we were to substitute this expression for P1 into our expression for P0, we would have:

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