Chapter 4 The Value of Common Stocks 99
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firms, near-term growth is unsustainably high. In that case, you may wish to use a two-stage DCF
formula, where near-term dividends are forecasted and valued, and the constant-growth DCF for-
mula is used to forecast the value of the shares at the start of the long run. The near-term dividends
and the future share value are then discounted to present value.
The general DCF formula can be transformed into a statement about earnings and growth
opportunities:
P 0 =EPS 1
_____r + PVGOThe ratio EPS 1 /r is the present value of the earnings per share that the firm would generate under
a no-growth policy. PVGO is the net present value of the investments that the firm will make in
order to grow. A growth stock is one for which PVGO is large relative to the present value of EPS,
assuming no growth. Most growth stocks are stocks of rapidly expanding firms, but expansion
alone does not create a high PVGO. What matters is the profitability of the new investments.
The same formulas that we used to value common shares can also be used to value entire busi-
nesses. In that case, we discount not dividends per share but the entire free cash flow generated by
the business. Usually a two-stage DCF model is deployed. Free cash flows are forecasted out to a
horizon and discounted to present value. Then a horizon value is forecasted, discounted, and added
to the value of the free cash flows. The sum is the value of the business.
Valuing a business is simple in principle but not so easy in practice. Forecasting reasonable
horizon values is particularly difficult. The usual assumption is moderate long-run growth after
the horizon, which allows use of the growing-perpetuity DCF formula at the horizon. Horizon
values can also be calculated by assuming “normal” price–earnings or market-to-book ratios at the
horizon date.
The dividend discount models derived in this chapter work best for mature firms that pay regu-
lar cash dividends. The models also work when companies pay out cash by share repurchases as
well as dividends. That said, it is also true that the dividend discount model is difficult to use if the
company pays no dividends at all or if the split of payout between cash dividends and repurchases
is unpredictable. In that case, it is easier to get price per share by forecasting and valuing the com-
pany’s total free cash flow and then dividing by the current number of shares outstanding.
Select problems are available in McGraw-Hill’s Connect.
Please see the preface for more information.BASIC
- True/false True or false?
a. All stocks in an equivalent-risk class are priced to offer the same expected rate of return.
b. The value of a share equals the PV of future dividends per share.
- Dividend discount model Respond briefly to the following statement:
“You say stock price equals the present value of future dividends? That’s crazy! All the inves-
tors I know are looking for capital gains.”- Dividend discount model Company X is expected to pay an end-of-year dividend of $5 a
share. After the dividend its stock is expected to sell at $110. If the market capitalization rate
is 8%, what is the current stock price? - Dividend discount model Company Y does not plow back any earnings and is expected
to produce a level dividend stream of $5 a share. If the current stock price is $40, what is the
market capitalization rate? - Dividend discount model Company Z’s earnings and dividends per share are expected to
grow indefinitely by 5% a year. If next year’s dividend is $10 and the market capitalization
rate is 8%, what is the current stock price?
● ● ● ● ●PROBLEM
SETS