## Dividend Discouni Modets

Dividend discount models are designed to compute the intrinsic value of a share of common stock under specific assumptions as to the expected growth pattern of future dividends and the appropriate discount rate to employ. Merrill Lynch, CS First Boston, and a number of other investment banks routinely make such calculations based on their own particular models and estimates. What follows is an examination of such models, beginning with the simplest one.

Constant Growth. Future dividends of a company could jump all over the place; but, if dividends are expected to grow at a constant rate, what implications does this hold for our basic stock valuation approach? If this constant rate is g, then becomes

V + + where D0 is the present dividend per share. Thus the dividend expected at the end of period n is equal to the most recent dividend times the compound growth factor, (1 + g)". This may not look like much of an improvement over. However, assuming that ke is greater than g (a reasonable assumption because a dividend growth rate that is always greater than the capitalization rate would imply an infinite stock value), can be reduced to

V = D1/(keg)

Rearranging, the investor's required return can be expressed as

ke = (D1/V) + g

The critical assumption in this valuation model is that dividends per share are expected to grow perpetually at a compound rate of g. For many companies this assumption may be a fair approximation of reality. To illustrate the use of, suppose that LKN, Inc.'s dividend per share at t=1 is expected to be \$4, that it is expected to grow at a 6 percent rate forever, and that the appropriate discount rate is 14 percent. The value of one share of LKN stock would be

V= \$4/(0.14 − 0.06) = \$50

For companies in the mature stage of their life cycle, the perpetual growth model is often reasonable.