Principles of Corporate Finance_ 12th Edition

Chapter 4 The Value of Common Stocks 87

bre44380_ch04_076-104.indd 87 09/30/15 12:46 PM

If Northwest earns 11% of book equity and reinvests 40% of income, then book equity will
increase by .40 × .11 = .044, or 4.4%. Earnings and dividends per share will also increase by 4.4%:

Dividend growth rate = g = plowback ratio × ROE = .40 × .11 = .044

That gives a second estimate of the market capitalization rate:

r =

DIV 1

_____

P 0

+ g = .041 + .044 = .085, or 8.5%

Although these estimates of Northwest’s cost of equity seem reasonable, there are obvious
dangers in analyzing any single firm’s stock with the constant-growth DCF formula. First, the
underlying assumption of regular future growth is at best an approximation. Second, even if it
is an acceptable approximation, errors inevitably creep into the estimate of g.
Remember, Northwest’s cost of equity is not its personal property. In well-functioning
capital markets investors capitalize the dividends of all securities in Northwest’s risk class at
exactly the same rate. But any estimate of r for a single common stock is “noisy” and subject
to error. Good practice does not put too much weight on single-company estimates of the cost
of equity. It collects samples of similar companies, estimates r for each, and takes an average.
The average gives a more reliable benchmark for decision making.
The next-to-last column of Table  4.3 gives DCF cost-of-equity estimates for Northwest
and seven other gas distribution companies. These are all stable, mature companies for which
the constant-growth DCF formula ought to work. Notice the variation in the cost-of-equity
estimates. Some of the variation may reflect differences in the risk, but some is just noise. The
average estimate is 8.9%.
Estimates of this kind are only as good as the long-term forecasts on which they are based.
For example, several studies have observed that security analysts are subject to behavioral
biases and their forecasts tend to be over-optimistic. If so, such DCF estimates of the cost of
equity should be regarded as upper estimates of the true figure.

Stock

Price Dividend a

Dividend

Yield

Long-Term

Growth Rate

DCF Cost

of Equity

Multistage DCF

Cost of Equity b

Atmos Energy Corp. $55.01 $1.66 3.0% 6.1% 9.1% 7.8%

The Laclede Group Inc. 52.53 1.98 3.8 7.5 11.3 9.0

New Jersey Resources Corp. 59.97 1.87 3.1 4.0 7.1 7.0

NiSource Inc. 41.95 1.14 2.7 9.3 12.0 8.0

Northwest Natural Gas Co. 49.43 2.00 4.1 7.7 11.8 9.3

Piedmont Natural Gas Co. 38.91 1.33 3.4 3.8 7.2 7.8

South Jersey Industries Inc. 58.35 2.16 3.7 7.5 11.2 8.9

Southwest Gas Corp. 60.10 1.54 2.6 5.7 8.3 7.3

WGL Holdings Inc. 53.22 1.85 3.5 5.3 8.7 8.2

Average: 8.9 8.2

❱ TABLE 4.3 Cost-of-equity estimates for local gas distribution companies at the start of 2015.

The long-term growth rate is based on security analysts’ forecasts. In the multistage DCF model,

growth after five years is assumed to adjust gradually to the estimated long-term growth rate of

Gross Domestic Product (GDP).

a Forecasted dividend per share for the coming year. Note the DCF formula calls for DIV 1 , the dividend paid at date 1.

b Long-term growth of GDP was forecasted at 4.5%.

Source: The Brattle Group, Inc.