Dividend-Yield-plus-Growth-Rate, or Discounted Cash Flow (DCF), Approach 235
Dividend-Yield-plus-Growth-Rate, or
Discounted Cash Flow (DCF), Approach
In Chapter 5, we saw that if dividends are expected to grow at a constant rate, then the
price of a stock is
(6-4)
Here P 0 is the current price of the stock; D 1 is the dividend expected to be paid at the
end of Year 1 and rsis the required rate of return. We can solve for rsto obtain the re-
quired rate of return on common equity, which for the marginal investor is also equal
to the expected rate of return:
(6-5)
Thus, investors expect to receive a dividend yield, D 1 /P 0 , plus a capital gain, g, for a
total expected return of rˆs. In equilibrium this expected return is also equal to the re-
quired return, rs. This method of estimating the cost of equity is called the dis-
counted cash flow, or DCF, method. Henceforth, we will assume that equilibrium
exists, hence rsˆrs, so we can use the terms rsandrˆsinterchangeably.
Estimating Inputs for the DCF Approach
Three inputs are required to use the DCF approach: the current stock price, the cur-
rent dividend, and the expected growth in dividends. Of these inputs, the growth rate
is by far the most difficult to estimate. The following sections describe the most com-
monly used approaches for estimating the growth rate: (1) historical growth rates,
(2) the retention growth model, and (3) analysts’ forecasts.
Historical Growth Rates First, if earnings and dividend growth rates have been rel-
atively stable in the past, and if investors expect these trends to continue, then the past
realized growth rate may be used as an estimate of the expected future growth rate.
We explain several different methods for estimating historical growth in the Web
Extension to this chapter, found on the textbook’s web site; the spreadsheet in the file
Ch 06 Tool Kit.xlsshows the calculations. For NCC, these different methods produce
estimates of historical growth ranging from 4.6 percent to 11.0 percent, with most es-
timates fairly close to 7 percent.
As the Ch 06 Tool Kit.xlsshows, one can take a given set of historical data and, de-
pending on the years and the calculation method used, obtain a large number of quite
different growth rates. Now recall our purpose in making these calculations: We are
seeking the future dividend growth rate that investors expect, and we reasoned that, if
past growth rates have been stable, then investors might base future expectations on
past trends. This is a reasonable proposition, but, unfortunately, we rarely find much
historical stability. Therefore, the use of historical growth rates in a DCF analysis
must be applied with judgment, and also be used (if at all) in conjunction with other
growth estimation methods as discussed next.
Retention Growth Model Most firms pay out some of their net income as div-
idends and reinvest, or retain, the rest. The payout ratio is the percent of net income
that the firm pays out as a dividend, defined as total dividends divided by net income;
see Chapter 10 for more details on ratios. The retention ratio is the complement of
rsrˆs
D 1
P 0
Expected g.
P 0
D 1
rsg
.
232 The Cost of Capital
