## The Two Period Growth Model

The simplest extension of the one-period model is to assume that a period of extraordinary growth (good or bad) will continue for a certain number of years, after which growth will change to a level at which it is expected to continue indefinitely.

The assumption that growth is constant after some point in time follows from the following line of reasoning. After some point in time (5 years, 10 years, 15 years) the analyst has no ability to differentiate between firms on the basis of growth. Many current high-growth firms will no longer have high growth and many firms that are currently viewed as stodgy will be the dynamic high-growth firms of the future. Thus after some years it is sensible to not differentiate between firms but simply to assume they all grow at the same rate. At this point the constant growth model is used.

Let us assume that the length of the first period is N years, that the growth rate in the first period is and that PN is the price at the end of period N. We can write the value of the firm as13

d, A(i+gi) A(i+g,)2 , q(i+g,r l + k (1 + kf (1 + *)3 (! + £)"

I3Many authors write the first term's dividend as DQ(l + gx). In this case, the dividend is the current dividend rather than next period's dividend.

This can, of course, be simplified using the formula for the sum of a geometric progression. The result is p0 = A

In the two-period model we are assuming that after N periods the firm exhibits a constant infinite growth. Thus, the model developed in the earlier section describes PN. If g2 is the growth in the second period and DjV+ , is the dividend in the N + 1 period, we have p -—

The dividend in the N + 1 period can be expressed in terms of the dividend in the first period

With these substitutions we have