236 CHAPTER 6 The Cost of Capital
the payout ratio: Retention ration (1 Payout ratio). ROE is the return on equity,
defined as net income available for common stockholders divided by common equity.
Although we don’t prove it here, you should find it reasonable that the growth rate of
a firm will depend on the amount of net income that it retains and the rate it earns on
the retentions. Using this logic, we can write the retention growth model:
g ROE (Retention ratio). (6-6)
Equation 6-6 produces a constant growth rate, but when we use it we are, by implica-
tion, making four important assumptions: (1) We expect the payout rate, and thus the
retention rate, to remain constant; (2) we expect the return on equity on new invest-
ment to remain constant; (3) the firm is not expected to issue new common stock, or, if
it does, we expect this new stock to be sold at a price equal to its book value; and (4) fu-
ture projects are expected to have the same degree of risk as the firm’s existing assets.
NCC has had an average return on equity of about 14.5 percent over the past
15 years. The ROE has been relatively steady, but even so it has ranged from a
low of 11.0 percent to a high of 17.6 percent. In addition, NCC’s dividend payout
rate has averaged 0.5 2over the past 15 years, so its retention rate has averaged 1.0
0.520.48. Using Equation 6-6, we estimate g to be 7 percent:
g 14.5% (0.48) 7%.Analysts’ Forecasts A third technique calls for using security analysts’ forecasts.
Analysts publish growth rate estimates for most of the larger publicly owned compa-
nies. For example, Value Line provides such forecasts on 1,700 companies, and all of
the larger brokerage houses provide similar forecasts. Further, several companies
compile analysts’ forecasts on a regular basis and provide summary information such
as the median and range of forecasts on widely followed companies. These growth
rate summaries, such as the ones compiled by Zack’s or by Thomson Financial Net-
work, can be found on the Internet.
However, these forecasts often involve nonconstant growth. For example, some an-
alysts were forecasting that NCC would have a 10.4 percent annual growth rate in earn-
ings and dividends over the next five years, but a growth rate beyond that of 6.5 percent.
This nonconstant growth forecast can be used to develop a proxy constant growth
rate. Computer simulations indicate that dividends beyond Year 50 contribute very
little to the value of any stock—the present value of dividends beyond Year 50 is vir-
tually zero, so for practical purposes, we can ignore anything beyond 50 years. If we
consider only a 50-year horizon, we can develop a weighted average growth rate
and use it as a constant growth rate for cost of capital purposes. In the NCC case, we
assumed a growth rate of 10.4 percent for 5 years followed by a growth rate of
6.5 percent for 45 years. We weight the short-term growth by 5/50 10% and the
long-term growth by 45/50 90%. This produces an average growth rate of
0.10(10.4%) 0.90(6.5%) 6.9%.
Rather than convert nonconstant growth estimates into an approximate average
growth rate, it is possible to use the nonconstant growth estimates to directly estimate
the required return on common stock. See the Web Extension to this chapter for an
explanation of this approach; all calculations are in the file Ch 06 Tool Kit.xls.Illustration of the Discounted Cash Flow Approach
To illustrate the DCF approach, suppose NCC’s stock sells for $32; its next expected
dividend is $2.40; and its expected growth rate is 7 percent. NCC’s expected and re-
quired rate of return, hence its cost of common stock, would then be 14.5 percent:For example, see
http://www.zacks.com,
http://www.thomsonfn.
com, or http://www.
finance.yahoo.com.