The real cost of equity

The real cost of equity
The inflation-adjusted cost of equity has been remarkably stable for
40 years, implying a current equity risk premium of 3.5 to 4 percent
Marc H. Goedhar t, Timothy M. Koller, and Zane D. Williams
As central as it is to every decision at premium would fall to zero, that the Dow
the heart of corporate finance, there has
Jones industrial average would reach 36,000
never been a consensus on how to estimate the
and that stocks would earn the same returns
cost of equity and the equity risk premium.1
as government bonds. While these views were
at the extreme end of the spectrum, it is still
Conflicting approaches to calculating risk have
easy to get seduced by complex logic and data.
led to varying estimates of the equity risk
premium from 0 percent to 8 percent—
We examined many published analyses and
although most practitioners use a narrower
developed a relatively simple methodology that
range of 3.5 percent to 6 percent. With
is both stable over time and overcomes the
expected returns from long-term government
shortcomings of other models. We estimate
bonds currently about 5 percent in the US and
that the real, inflation-adjusted cost of equity
UK capital markets, the narrower range
has been remarkably stable at about 7 percent
implies a cost of equity for the typical
in the US and 6 percent in the UK since the
company of between 8.5 and 11.0 percent.
1960s. Given current, real long-term bond
This can change the estimated value of a
yields of 3 percent in the US and 2.5 percent
company by more than 40 percent and have
in the UK, the implied equity risk premium is
profound implications for financial decision
around 3.5 percent to 4 percent for both
making.
markets.
Discussions about the cost of equity are often
The debate
intertwined with debates about where the
stock market is heading and whether it is over-
There are two broad approaches to estimating
or undervalued. For example, the run-up in
the cost of equity and market risk premium.
stock prices in the late 1990s prompted two
The first is historical, based on what equity
contradictory points of view. On the one
investors have earned in the past. The second
hand, as prices soared ever higher, some
is forward-looking, based on projections
investors expected a new era of higher equity
implied by current stock prices relative to
returns driven by increased future productivity
earnings, cash flows, and expected future
and economic growth. On the other hand,
growth.
some analysts and academics suggested that
the rising stock prices meant that the risk
The latter is conceptually preferable. After all,
premium was declining. Pushed to the
the cost of equity should reflect the return
extreme, a few analysts even argued that the
expected (required) by investors. But forward-
The real cost of equity | 11

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looking estimates are fraught with problems,
Exhibit 1. US median P/E vs. inflation
the most intractable of which is the difficulty
of estimating future dividends or earnings
15%
25
Inf lation
Median
growth. Some theorists have attempted to
P/E ratio
meet that challenge by surveying equity
12%
20
analysts, but since we know that analyst
projections almost always overstate the long-
9%
term growth of earnings or dividends,2 analyst
15
objectivity is hardly beyond question. Others
6%
have built elaborate models of forward-
looking returns, but such models are typically
10
3%
so complex that it is hard to draw conclusions
or generate anything but highly unstable
0%
results. Depending on the modeling
5
1962 1966
1970 1974
1978 1982 1986
1990
1994 1998
assumptions, recently published research
Source: McKinsey analysis
suggests market risk premiums between 0 and
4 percent.3
developed a simple, objective, forward-looking
Unfortunately, the historical approach is just as
model that, when applied retrospectively to
tricky because of the subjectivity of its
the cost of equity over the past 40 years,
assumptions. For example, over what time
yielded surprisingly stable estimates.
period should returns be measured—the
previous 5, 10, 20, or 80 years or more? Should
Forward-looking models typically link current
average returns be reported as arithmetic or
stock prices to expected cash flows by
geometric means? How frequently should
discounting the cash flows at the cost of
average returns be sampled? Depending on the
equity. The implied cost of equity thus
answers, the market risk premium based on
becomes a function of known current share
historical returns can be estimated to be as
values and estimated future cash flows (see
high as 8 percent.4 It is clear that both
sidebar, “Estimating the cost of equity”).
historical and forward-looking approaches, as
Using this standard model as the starting
practiced, have been inconclusive.
point, we then added three unique
characteristics that we believe overcome the
shortcomings of many other approaches:
Overcoming the typical failings of
economic models
1. Median stock price valuation. For the US,
In modeling the behavior of the stock market
we used the value of the median company in
over the last 40 years,5 we observed that many
the S&P 500 measured by P/E ratio as an
real economic variables were surprisingly
estimate of the market’s overall valuation at
stable over time (including long-term growth
any point in time. Most researchers have used
in corporate profits and returns on capital)
the S&P 500 itself, but we argue that the
and that much of the variability in stock
S&P 500 is a value-weighted index that has
prices related to interest rates and inflation
been distorted at times by a few highly valued
(Exhibit 1). Building on these findings, we
companies, and therefore does not properly
12 | McKinsey on Finance Autumn 2002

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Exhibit 2. Return on book equity (ROE)
Exhibit 3. Annual estimates of the real cost of equity
18%
15%
14%
Average UK ROE
16%
13%
12%
14%
11%
12%
10%
9%
Median
10%
US ROE
8%
US real cost of equity
7%
8%
6%
6%
5%
4%
UK real cost of equity
4%
3%
2%
2%
1%
0%
0%
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002
Source: McKinsey analysis
Source: McKinsey analysis
reflect the market value of typical companies in
have been funded. These are what we term
the US economy. During the 1990s, the median
“dividendable” cash flows to investors that
and aggregate P/E levels diverged sharply.
might be paid out through share repurchases
Indeed by the end of 1999, nearly 70 percent
as ordinary dividends, or temporarily held as
of the companies in the S&P 500 had P/E ratios
cash at the corporate level.
below that of the index as a whole. By using
the median P/E ratio, we believe we generate
We estimate dividendable cash flows by
estimates that are more representative for the
subtracting the investment required to sustain
economy as a whole. Since UK indices have not
the long-term growth rate from current year
been similarly distorted, our estimates for the
profits. This investment can be shown to equal
UK market are based instead on aggregate UK
the projected long-term profit growth (See
market P/E levels.
sidebar, “Estimating the cost of equity”)
divided by the expected return on book
2. Dividendable cash flows. Most models use
equity. To estimate the return on equity
the current level of dividends as a starting
(ROE), we were able to take advantage of the
point for projecting cash flows to equity.
fact that US and UK companies have had fairly
However, many corporations have moved from
stable returns over time. As Exhibit 2 shows,
paying cash dividends to buying back shares
the ROE for both US and UK companies has
and finding other ways to return cash to
been consistently about 13 percent per year,6
shareholders, so estimates based on ordinary
the only significant exception being found in
dividends will miss a substantial portion of
UK returns of the late 1970s.
what is paid out. We avoid this by discounting
not the dividends paid but the cash flows
3. Real earnings growth based on long-term
available to shareholders after new investments
trends. The expected growth rate in cash flow
The real cost of equity | 13

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Exhibit 4. Decomposition of the inflation-adjusted
cost of equity
The stability of the implied inflation-
adjusted cost of equity is striking.
US
UK
7.2%
6.7%
Despite a handful of recessions and
5.7%
5.8%
financial crises over the past
3.6%
Market risk
5.0%
3.0%
40 years . . . equity investors have
premium
4.3%
continued to demand about the
3.1%
2.8%
Real risk-
2.2%
1.4%
free rate
same cost of equity in inflation-
1962–1979
1990–2000
1962–1979
1995–2000
adjusted terms.
Source: McKinsey analysis
and earnings was estimated as the sum of
2001 for the UK (Exhibit 3). In the US, it
long-term real GDP growth plus expected
consistently remains between 6 and 8 percent
inflation. Corporate profits have remained a
with an average of 7 percent. For the UK
relatively consistent 5.5 percent of US GDP
market, the inflation-adjusted cost of equity
over the past 50 years. Thus, GDP growth
has been, with two exceptions, between
rates are a good proxy for long-term corporate
4 percent and 7 percent and on average
profit growth. Real GDP growth has averaged
6 percent.
about 3.5 percent per year over the last
80 years for the US and about 2.5 percent
The stability of the implied inflation-adjusted
over the past 35 years for the UK. Using GDP
cost of equity is striking. Despite a handful of
growth as a proxy for expected earnings
recessions and financial crises over the past
growth allows us to avoid using analysts’
40 years including most recently the dot.com
expected growth rates.
bubble, equity investors have continued to
demand about the same cost of equity in
We estimated the expected inflation rate in
inflation-adjusted terms. Of course, there are
each year as the average inflation rate
deviations from the long-term averages but
experienced over the previous five years.7 The
they aren’t very large and they don’t last very
nominal growth rates used in the model for
long. We interpret this to mean that stock
each year were the real GDP growth combined
markets ultimately understand that despite ups
with the contemporary level of expected
and downs in the broad economy, corporate
inflation for that year.
earnings and economic growth eventually
revert to their long-term trend.
Results
We also dissected the inflation-adjusted cost of
We used the above model to estimate the
equity over time into two components: the
inflation-adjusted cost of equity implied by
inflation-adjusted return on government bonds
stock market valuations each year from
and the market risk premium. As Exhibit 4
1963 to 2001 in the US and from 1965 to
demonstrates, from 1962 to 1979 the expected
14 | McKinsey on Finance Autumn 2002

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that using an equity risk premium of 3.5 to
Estimating the cost of equity
4 percent in the current environment better
To estimate the cost of equity, we began with a standard perpetuity model:
reflects the true long-term opportunity cost
CFt 1
Pt
(1)
for equity capital and hence will yield more
k
g
e
accurate valuations for companies. MoF
where P is the price of a share at time t, CF
is the expected cash flow per
t
t
1
share at time t
1, k is the cost of equity, and g is the expected growth rate
e
of the cash flows. The cash flows, in turn, can be expressed as earnings, E,
multiplied by the payout ratio:
Marc H. Goedhar t (Marc_Goedhar t@McKinsey.com)
CF
E (payout ratio)
is associate principal in McKinsey’s Amsterdam
Since the payout ratio is the share of earnings lef t af ter reinvestment,
replacing the payout ratio with the reinvestment rate gives:
of fice, Timothy M. Koller (Tim_Koller@McKinsey.com)
CF
E (1
reinvestment rate)
is a principal in McKinsey’s New York of fice, and
The reinvestment rate, in turn, can be expressed as the ratio of the growth
Zane D. Williams (Zane_Williams @McKinsey.com) is
rate, g, to the expected return on equity:
g
a consultant in McKinsey’s Washington, D.C., of fice,
reinvestment rate
ROE
And thus the cash flows can be expressed as:
Copyright © 2002 McKinsey & Company. All rights
g
reser ved.
CF
E
(2)
(1 ROE )
1
We then combined formulas (1) and (2) to get the following:
Defined as the dif ference between the cost of equity and the
g
returns investors can expect from supposedly risk-free
1
government bonds.
P
ROE
g
t
Et 1
(3)
c k
(1 ROE ) g
e
2
E
k
g
t
e
P
1
t
See Marc H. Goedhar t, Brendan Russel, and Zane D.
If the inflation embedded in k and g is the same, we can then express
Williams, “Prophets and profits?” McKinsey on Finance,
e
equation 3 as:
Number 2, Autumn 2001.
E
g
t
1
k
(1 ROE ) g
3
e r
r
(4)
See, for example, Eugene Fama and Kenneth French, “The
Pt
Equity Premium,” Journal of Finance, Volume LVII, Number 2,
Where k and g are the inflation-adjusted cost of equity and real growth rate,
er
r
2002; and Rober t Arnott and Peter Bernstein, “What Risk
respectively. We then solved for k for each year from 1963 through 2001,
e r
using the assumptions described in the text of the article.
Premium is ‘Normal’,” Financial Analysts Journal, March/
April, 2002; James Claus and Jacob Thomas, “Equity premia
as low as three percent?” Journal of Finance, Volume LVI,
Number 5, 2001.
inflation-adjusted return on government bonds
4 See, for example, Ibbotson and Associates, Stock, Bonds,
appears to have fluctuated around 2 percent in
Bills and Inflation: 1997 Yearbook.
the US and around 1.5 percent in the UK. The
5 See Timothy Koller and Zane Williams, “What happened to the
implied equity risk premium was about
bull market?” McKinsey on Finance, Number 1, Summer 2001.
5 percent in both markets.8 But in the 1990s, it
6 One consequence of combining a volatile nominal growth rate
appears that the inflation-adjusted return on
(due to changing inflationar y expectations) with a stable
both US and UK government bonds may have
ROE is that the estimated reinvestment rate varies tremen-
dously over time. In the late 1970s, in fact, our estimates
risen to 3 percent, with the implied equity risk
are near 100 percent. This is unlikely to be a true represen-
premium falling to 3 percent and 3.6 percent in
tation of actual investor expectations at the time. Instead,
the UK and US respectively.
we believe it likely that investors viewed the high inflation of
those years as temporar y. As a result, in all of our estimates,
we capped the reinvestment rate at 70 percent.
7 This assumption is the one that we are least comfor table
We attribute this decline not to equities
with, but our analysis seems to suggest that markets build in
becoming less risky (the inflation-adjusted cost
an expectation that inflation from the recent past will
of equity has not changed) but to investors
continue (witness the high long-term government bond yields
of the late 1970s).
demanding higher returns in real terms on
8 There is some evidence that the market risk premium is
government bonds after the inflation shocks of
higher in periods of high inflation and high interest rates, as
the late 1970s and early 1980s. We believe
was experienced in the late 1970s and early 1980s.
The real cost of equity | 15

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