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CALCULATING THE "CORRECT" OR TARGET PRICE
EARNINGS RATIO ("P/E")
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Investors are often faced with the problem of
understanding whether or not the P/E of a stock makes it a buy or a sell.
The Price / Earnings ratio that a stock can justifiably support depends on a
number of factors and varies quite dramatically with growth, interest
rates, risks and even the dividend pay-out ratio. The following will help
you understand exactly how much growth is required to support a given P/E
ratio. |
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I have calculated the justifiable present value of shares
to an investor using certain assumptions. I use an assumption that an
unusually high growth rate can be sustained for ten years. After that the
growth continues for 10 more years at a more sustainable level of 4% to 8% per year. I
then assume that the company is liquidated at the end of 50 years and the
retained earnings distributed to the investor. While different results can
be obtained using other assumptions, I believe the table below provides a
useful indicator of roughly the growth level that is required to support
various P/E levels. I analyzed a situation where there is no dividend and
one where 50% of earnings are paid out each year. The required investor
return is held at a constant level of 8% which is arguably a reasonable
and realistic target return today. |
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Justifiable P/E Ratio |
Required Return |
First 10 Years Growth |
Subsequent Growth |
Di vidend pay-out ratio |
PEG Ratio |
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8 |
8% |
4% |
8% |
0% |
2.11
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12 |
8% |
8% |
8% |
0% |
1.53
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16 |
8% |
11% |
8% |
0% |
1.46
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21 |
8% |
14% |
8% |
0% |
1.49
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35 |
8% |
20% |
8% |
0% |
1.74
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12 |
8% |
4% |
4% |
50% |
3.06
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17 |
8% |
8% |
4% |
50% |
2.09
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21 |
8% |
11% |
4% |
50% |
1.92
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27 |
8% |
14% |
4% |
50% |
1.90
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42 |
8% |
20% |
4% |
50% |
2.11
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This table shows that P/E ratios of over 20 require a
healthy growth rate of at least 11%, P/E ratios of over 30 are very
difficult to justify because the growth has to be over about 20%. Assuming
that any company can grow at over 20% per year for a ten year period is
very optimistic (perhaps even irrationally exuberant?). If the company has
a high dividend pay-out ratio, then a somewhat lower growth is needed to
justify a given P/E. This table can be used to compare the growth of a
company to its P/E to see if it is justifiable. Please note that this
table is only relevant when the beginning earnings figure used to
calculate the P/E is representative. The table also is not relevant if the
earnings are near zero (say an R.O.E. less than 5%) since the P/E ratio
starts to become large and such a low earning is not representative of a
stable situation. As rule of thumb, it appears that a stock with no
dividend should have a PEG ratio (P/E divided by growth) of no higher than
1.50 while a stock with a 50% dividend can support a PEG ratio as high as
2.00. |
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The reader who is interested in exploring the relationship
between growth, interest rates, risk and supportable P/E ratios should
benefit by studying the following tables and discussion. |
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Study the following to learn exactly why a growth stock
with a P/E of 30 may be a bargain while a stable company with a P/E of 15
may be over-priced. Learn exactly how expected future inflation, interest
rates, earnings growth rates, the risks associated with a particular
stock, and the dividend pay-out ratio all determine the
"correct" P/E for a stock. |
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The following calculations show price earnings ratios that
would result by taking the "present value" of a very long term
cash flow stream under various assumptions about interest rates, earnings
growth, inflation, company specific risk premiums. Most of the scenarios
are for bond like investments where all earnings are paid out to the
investor each year. The final example illustrates a "stock" type
investment where earnings are retained by the company. Note that some
scenarios include high growth rates but only for the first ten years. It
would not be realistic to forecast abnormally high growth to occur for
more than about ten years. A careful review of this data will give an
investor a much better "feel" for the "correct" level
of the price earnings ratio. The investor will then be in a much better
position to judge whether the P/E on a particular stock signals
"buy" or "sell". |
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Calculated impacts of inflation on the Price Earnings
Ratio for Long term bonds |
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Scenario |
1 |
2 |
3 |
4 |
5 |
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First 10 years profit growth rate |
0% |
0% |
0% |
0% |
0% |
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Subsequent 990 years profit growth rate |
0% |
0% |
0% |
0% |
0% |
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Risk free real return required |
4% |
4% |
4% |
4% |
4% |
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Expected inflation rate |
0% |
2% |
4% |
6% |
8% |
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Risk premium required |
0% |
0% |
0% |
0% |
0% |
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Total discount interest rate required |
4% |
6% |
8% |
10% |
12% |
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Theoretical Price equals present value of the 1000 years
of earnings |
$ 25.00 |
$ 16.67 |
$ 12.50 |
$ 10.00 |
$ 8.33 |
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Resulting Price Earnings Ratio |
25 |
17 |
13 |
10 |
8 |
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Year 1 Earnings and pay-out |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
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Year 2 Earnings and pay-out |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
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Year 3 Earnings and pay-out |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
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etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
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Here a risk free government bond paying a steady $1.00 per
year for 1000 years is worth $25 with no inflation but only $8 if
inflation rises to 8%. Illustrates that the appropriate price earnings
ratio for a "risk free" investment drops dramatically with even
a moderate level of inflation. For example if inflation increases from 2%
to 6% the P/E drops 70% from 17 to 10. Long term bond prices drop
dramatically when inflation rises. Long term "risk free"
government bonds are actually very risky when inflation is considered. |
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Calculated impacts of inflation on the P/E Ratio for an
Inflation Indexed long term bond |
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Scenario |
1 |
2 |
3 |
4 |
5 |
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First 10 years profit growth rate |
0% |
2% |
4% |
6% |
8% |
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Subsequent 990 years profit growth rate |
0% |
2% |
4% |
6% |
8% |
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Risk free real return required |
4% |
4% |
4% |
4% |
4% |
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Expected inflation rate |
0% |
2% |
4% |
6% |
8% |
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Risk premium required |
0% |
0% |
0% |
0% |
0% |
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Total discount interest rate required |
4% |
6% |
8% |
10% |
12% |
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Theoretical Price equals present value of the 1000 years
of earnings |
$ 25.00 |
$ 25.00 |
$ 25.00 |
$ 25.00 |
$ 25.00 |
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Resulting Price Earnings Ratio |
25 |
25 |
25 |
25 |
25 |
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Year 1 Earnings and pay-out |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
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Year 2 Earnings and pay-out |
$ 1.00 |
$ 1.02 |
$ 1.04 |
$ 1.06 |
$ 1.08 |
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Year 3 Earnings and pay-out |
$ 1.00 |
$ 1.04 |
$ 1.08 |
$ 1.12 |
$ 1.17 |
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etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
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Here a risk free "real return" "bond"
pays $1.00 in the first year and the payment rises with inflation in
future years. The indexing completely compensates for inflation and the
value of the bond remains steady at $25. This also implies that a rise in
inflation should not decrease the value of a company as long as that
company is able to increase its prices and profits in lock-step with
inflation. A Government real return (inflation indexed) bond is a true
risk free investment. Today actual real return bonds do in fact earn only
about 4%. Investors should keep this in mind as an important reference
level. Investments with an expected returns above about 4% will involve
risk. |
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Calculated impacts on P/E ratio of an increase in
"real" interest rates |
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Scenario |
1 |
2 |
3 |
4 |
5 |
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First 10 years profit growth rate |
2% |
2% |
2% |
2% |
2% |
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Subsequent 990 years profit growth rate |
2% |
2% |
2% |
2% |
2% |
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Risk free real return required |
4% |
5% |
6% |
8% |
10% |
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Expected inflation rate |
2% |
2% |
2% |
2% |
2% |
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Risk premium required |
2% |
2% |
2% |
2% |
2% |
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Total discount interest rate required |
8% |
9% |
10% |
12% |
14% |
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Theoretical Price equals present value of the 1000 years
of earnings |
$ 16.67 |
$ 14.29 |
$ 12.50 |
$ 10.00 |
$ 8.33 |
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Resulting Price Earnings Ratio |
17 |
14 |
13 |
10 |
8 |
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Year 1 Earnings and pay-out |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
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Year 2 Earnings and pay-out |
$ 1.02 |
$ 1.02 |
$ 1.02 |
$ 1.02 |
$ 1.02 |
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Year 3 Earnings and pay-out |
$ 1.04 |
$ 1.04 |
$ 1.04 |
$ 1.04 |
$ 1.04 |
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etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
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I n these examples inflation, growth and risk premium are
constant at 2%. The P/E drops sharply from 17 to 8 as the real return rate
increases from 4% to 10%. When the real interest rate available on
inflation indexed risk free investments rises then the value of all future
cash flow streams from all investments must decline. Unfortunately
governments can increase the real market interest rate almost at will.
When the market real interest rate increases there can be no expectation
that companies' earnings will grow to compensate as there would (arguably)
be for an increase in interest rates due to inflation. In this example the
value of the cash flow stream falls by 14% when the risk free rate rises
from 4% to 5%. This explains exactly why the stock market and bond prices
inevitably drop sharply whenever the government even hints it might raise
interest rates. The stock market and the value of long term bonds are in
fact always very vulnerable to a rise in interest rates at any time. |
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Calculated impacts of risk free growth on the P/E ratio |
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Scenario |
1 |
2 |
3 |
4 |
5 |
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First 10 years profit growth rate |
2% |
5% |
10% |
25% |
50% |
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Subsequent 990 years profit growth rate |
2% |
2% |
2% |
2% |
2% |
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Risk free real return required |
4% |
4% |
4% |
4% |
4% |
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Expected inflation rate |
2% |
2% |
2% |
2% |
2% |
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Risk premium required |
0% |
0% |
0% |
0% |
0% |
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Total discount interest rate required |
6% |
6% |
6% |
6% |
6% |
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Theoretical Price equals present value of the 1000 years
of earnings |
$ 25.00 |
$ 31.78 |
$ 47.42 |
$152.12 |
$875.91 |
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Resulting Price Earnings Ratio |
25 |
32 |
47 |
152 |
876 |
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Year 1 Earnings and pay-out |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
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Year 2 Earnings and pay-out |
$ 1.02 |
$ 1.05 |
$ 1.10 |
$ 1.25 |
$ 1.50 |
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Year 3 Earnings and pay-out |
$ 1.04 |
$ 1.10 |
$ 1.21 |
$ 1.56 |
$ 2.25 |
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etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
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This shows the impact of a growing cash flow over the
first 10 years. The risk free rate, inflation rate and risk factor and the
cash flow growth after ten years are all held constant. The present value
of this cash flow stream increases dramatically with growth. If we can
predict with certainty that an investment's cash return will grow at a
high rate for the next ten years then we are justified in paying a large
amount for the security compared to its current earnings. This explains
why very high P/E ratios are usually exhibited by growth companies. Next
though, we look at how risk impacts the analysis. |
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Calculated impacts on the Price Earnings ratio of
required risk premiums |
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Scenario |
1 |
2 |
3 |
4 |
5 |
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First 10 years profit growth rate |
25% |
25% |
25% |
25% |
25% |
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Subsequent 990 years profit growth rate |
2% |
2% |
2% |
2% |
2% |
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Risk free real return required |
4% |
4% |
4% |
4% |
4% |
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Expected inflation rate |
2% |
2% |
2% |
2% |
2% |
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Risk premium required |
2% |
5% |
10% |
15% |
25% |
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Total discount interest rate required |
8% |
11% |
16% |
21% |
31% |
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Theoretical Price equals present value of the 1000 years
of earnings |
$ 91.39 |
$ 52.73 |
$ 27.43 |
$ 16.89 |
$ 8.40 |
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Resulting Price Earnings Ratio |
91 |
53 |
27 |
17 |
8 |
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Year 1 Earnings and pay-out |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
$ 1.00 |
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Year 2 Earnings and pay-out |
$ 1.25 |
$ 1.25 |
$ 1.25 |
$ 1.25 |
$ 1.25 |
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Year 3 Earnings and pay-out |
$ 1.56 |
$ 1.56 |
$ 1.56 |
$ 1.56 |
$ 1.56 |
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etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
etcetera |
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In this example the earnings grow at a compounded 25% for
10 years. The market real return and inflation remain low. The example
shows the impact of various required risk premiums. For real companies
there can be no guarantee that a predicted 25% growth rate will occur. We
need to add a premium to our expected return to account for the risk that
the growth will not materialize. As the risk premium rises the theoretical
P/E ratio quickly falls. If the risk premium rises to equal the growth
then we have essentially indicated that we place no value on the predicted
growth and the company's worth is based on its current earnings. |
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Calculated impacts on the Price Earnings ratio of 0%
dividend pay-out stock |
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Scenario |
1 |
2 |
3 |
4 |
5 |
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First 10 years profit growth rate |
4% |
8% |
11% |
14% |
20% |
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Dividend pay-out ratio |
0% |
0% |
0% |
0% |
0% |
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Subsequent future years growth rate |
8% |
8% |
8% |
8% |
8% |
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Risk free real return required |
4% |
4% |
4% |
4% |
4% |
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Expected inflation rate |
2% |
2% |
2% |
2% |
2% |
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Risk premium required |
2% |
2% |
2% |
2% |
2% |
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Total discount interest rate required |
8% |
8% |
8% |
8% |
8% |
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Theoretical Price equals present value of the 1000 years
of earnings |
$ 8.43 |
$ 12.23 |
$ 16.04 |
$ 20.89 |
$ 34.75 |
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Resulting Price Earnings Ratio |
8 |
12 |
16 |
21 |
35 |
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PEG Ratio, P/E divided by Growth |
2.11 |
1.53 |
1.46 |
1.49 |
1.74 |
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Year 1 Pay-out |
$ - |
$ - |
$ - |
$ - |
$ - |
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Year 2 Pay-out |
$ - |