92 Part One Value

bre44380_ch04_076-104.indd 92 09/30/15 12:46 PM

In general, we can think of stock price as the capitalized value of average earnings under a

no-growth policy, plus PVGO, the net present value of growth opportunities:

P 0 =

EPS 1

_____r + PVGO

The earnings–price ratio, therefore, equals

EPS____

P 0

= r (^) ( 1 − PVGO__
P 0
(^) )
It will underestimate r if PVGO is positive and overestimate it if PVGO is negative. The latter
case is less likely, since firms are rarely forced to take projects with negative net present values.
Calculating the Present Value of Growth Opportunities
for Fledgling Electronics
In our last example both dividends and earnings were expected to grow, but this growth made
no net contribution to the stock price. The stock was in this sense an “income stock.” Be care-
ful not to equate firm performance with the growth in earnings per share. A company that
reinvests earnings at below the market capitalization rate r may increase earnings but will
certainly reduce the share value.
Now let us turn to that well-known growth stock, Fledgling Electronics. You may remem-
ber that Fledgling’s market capitalization rate, r, is 15%. The company is expected to pay a
dividend of $5 in the first year, and thereafter the dividend is predicted to increase indefi-
nitely by 10% a year. We can use the simplified constant-growth formula to work out Fledg-
ling’s price:
P 0 =
DIV 1

r − g
= ____^5
.15 − .10
= $10 0
Suppose that Fledgling has earnings per share of EPS 1  = $8.33. Its payout ratio is then
Payout ratio =
DIV 1

EPS 1

5.00

8.33
= .6
In other words, the company is plowing back 1 – .6, or 40% of earnings. Suppose also that
Fledgling’s ratio of earnings to book equity is ROE  =  .25. This explains the growth rate
of 10%:
Growth rate = g = plowback ratio × ROE = .4 × .25 = .10
The capitalized value of Fledgling’s earnings per share if it had a no-growth policy would be
EPS 1

r
= _ 8.33
.15
= $55.56
But we know that the value of Fledgling stock is $100. The difference of $44.44 must be the
amount that investors are paying for growth opportunities. Let’s see if we can explain that
figure.
Each year Fledgling plows back 40% of its earnings into new assets. In the first year Fledg-
ling invests $3.33 at a permanent 25% return on equity. Thus the cash generated by this invest-
ment is .25 × 3.33 = $.83 per year starting at t = 2. The net present value of the investment
as of t = 1 is
NPV 1 = −3.33 + .83
.15
= $2.22