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# CASH FLOWS

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?

Here we have a \$3 current amount that grows at 8 percent per year for five years. The future amount is thus:

\$3 × 1.085 = \$3 × 1.4693 = \$4.41

The dividend will therefore increase by \$1.41 over the coming five years.

If the dividend grows at a steady rate, then we have replaced the problem of forecasting an infinite number of future dividends with the problem of coming up with a single growth rate, a considerable simplification. In this case, if we take D0 to be the dividend just paid and g to be the constant growth rate, the value of a share of stock can be written as:

As long as the growth rate, g, is less than the discount rate, r, the present value of this series of cash flows can be written simply as:

This elegant result goes by a lot of different names. We will call it the dividend growth model. By any name, it is easy to use. To illustrate, suppose D0 is \$2.30, R is 13 percent, and g is 5 percent. The price per share in this case is:

dividend growth model A model that determines the current price of a stock as its dividend next period divided by the discount rate less the dividend growth rate.

We can actually use the dividend growth model to get the stock price at any point in time, not just today. In general, the price of the stock as of time t is:

In our example, suppose we are interested in the price of the stock in five years, P5. We first need the dividend at Time 5, D5. Because the dividend just paid is \$2.30 and the growth rate is 5 percent per year, D5 is:

D5 = \$2.30 × 1.055 = \$2.30 × 1.2763 = \$2.935

From the dividend growth model, we get the price of the stock in five years: