84 Part One Value
bre44380_ch04_076-104.indd 84 09/30/15 12:46 PM
where ∞ indicates infinity. This formula is the DCF or dividend discount model of stock
prices. It’s another present value formula.^7 We discount the cash flows in this case the divi-
dend stream—by the return that can be earned in the capital market on securities of equivalent
risk. Some find the DCF formula implausible because it seems to ignore capital gains. But we
know that the formula was derived from the assumption that price in any period is determined
by expected dividends and capital gains over the next period.
Notice that it is not correct to say that the value of a share is equal to the sum of the dis-
counted stream of earnings per share. Earnings are generally larger than dividends because
part of those earnings is reinvested in new plant, equipment, and working capital. Discounting
earnings would recognize the rewards of that investment (higher future earnings and divi-
dends) but not the sacrifice (a lower dividend today). The correct formulation states that share
value is equal to the discounted stream of dividends per share. Share price is connected to
future earnings per share but by a different formula, which we cover later in this chapter.
Although mature companies generally pay cash dividends, thousands of companies do not.
For example, Amazon has never paid a dividend, yet it is a successful company with a market
capitalization in December 2014 of $137 billion. Why would a successful company decide
not to pay cash dividends? There are at least two reasons. First, a growing company may
maximize value by investing all its earnings rather than paying out any. The shareholders
are better off with this policy, provided that the investments offer an expected rate of return
higher than shareholders could get by investing on their own. In other words, shareholder
value is maximized if the firm invests in projects that can earn more than the opportunity cost
of capital. If such projects are plentiful, shareholders will be prepared to forgo immediate
dividends. They will be happy to wait and receive deferred dividends.^8(^7) Notice that this DCF formula uses a single discount rate for all future cash flows. This implicitly assumes that the company is all-
equity-financed or that the fractions of debt and equity will stay constant. Chapters 17 through 19 discuss how the cost of equity
changes when debt ratios change.
◗ FIGURE 4.1
As your horizon recedes, the present value of the future price (shaded area) declines but the present
value of the stream of dividends (unshaded area) increases. The total present value (future price and
dividends) remains the same.
10050201043210
0
50
$100
Present value, dollars
Horizon period, years
PV (dividends for 100 years)
PV (price at year 100)