Chapter 4 The Value of Common Stocks 89
bre44380_ch04_076-104.indd 89 09/30/15 12:46 PM
Investors in year 3 will view Growth-Tech as offering 8% per year dividend growth. So we can
use the constant-growth formula to calculate P 3 :
P 3 =
DIV 4
______
r − .08P 0 =DIV 1
_____
1 + r+DIV 2
_______
(1 + r)^2+DIV 3
_______
(1 + r)^3+ _______^1
(1 + r)^3×DIV 4
______
r − .08= _____.50
1 + r+ _______.60
(1 + r)^2+ _______ 1.15
(1 + r)^3+ _______^1
(1 + r)^3× ______1.24
r − .08We have to use trial and error to find the value of r that makes P 0 equal $50. It turns out that
the r implicit in these more realistic forecasts is approximately .099, quite a difference from
our “constant-growth” estimate of .21.
Our present value calculations for Growth-Tech used a two-stage DCF valuation model. In
the first stage (years 1 and 2), Growth-Tech is highly profitable (ROE = 25%), and it plows
back 80% of earnings. Book equity, earnings, and dividends increase by 20% per year. In the
second stage, starting in year 3, profitability and plowback decline, and earnings settle into
long-term growth at 8%. Dividends jump up to $1.15 in year 3, and then also grow at 8%.
Growth rates can vary for many reasons. Sometimes growth is high in the short run not
because the firm is unusually profitable, but because it is recovering from an episode of low
profitability. Table 4.5 displays projected earnings and dividends for Phoenix Corp., which is
gradually regaining financial health after a near meltdown. The company’s equity is growing
at a moderate 4%. ROE in year 1 is only 4%, however, so Phoenix has to reinvest all its earn-
ings, leaving no cash for dividends. As profitability increases in years 2 and 3, an increasing
dividend can be paid. Finally, starting in year 4, Phoenix settles into steady-state growth, with
equity, earnings, and dividends all increasing at 4% per year.
Assume the cost of equity is 10%. Then Phoenix shares should be worth $9.13 per share:
P 0 = ___^0
1.1+ _____.31
(1.1)^2+ _____.65
(1.1)^3+ _____^1
(1.1)^3× _________ .67
(.10 − .04)= $9.13PV (first-stage dividends) PV (second-stage dividends)
Year
1 2 3 4
Book equity 10.00 12.00 14.40 15.55
Earnings per share (EPS) 2.50 3.00 2.30 2.48
Return on equity (ROE) 0.25 0.25 0.16 0.16
Payout ratio 0.20 0.20 0.50 0.50
Dividends per share (DIV) 0.50 0.60 1.15 1.24
Growth rate of dividends (%) — 20 92 8❱ TABLE 4.4 Forecasted earnings and dividends for Growth-Tech. Note the changes in year 3:
ROE and earnings drop, but payout ratio increases, causing a big jump in dividends. However,
subsequent growth in earnings and dividends falls to 8% per year. Note that the increase in equity
equals the earnings not paid out as dividends.BEYOND THE PAGEmhhe.com/brealey12eTry it! Table 4.4:
Valuing
Grow th-Tech