# CALCULATING THE “CORRECT” OR TARGET PRICE EARNINGS RATIO (“P/E”)

 CALCULATING THE “CORRECT” OR TARGET PRICE EARNINGS RATIO (“P/E”) 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. 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 40 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.
Justifiable P/E Ratio Required Return First 10 Years Growth Subsequent Growth Dividend pay-out ratio PEG Ratio
8 8% 4% 8% 0% 2.11
12 8% 8% 8% 0% 1.53
16 8% 11% 8% 0% 1.46
21 8% 14% 8% 0% 1.49
35 8% 20% 8% 0% 1.74
12 8% 4% 4% 50% 3.06
17 8% 8% 4% 50% 2.09
21 8% 11% 4% 50% 1.92
27 8% 14% 4% 50% 1.9
42 8% 20% 4% 50% 2.11
 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. 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. 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. 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”.

Calculated impacts of inflation on the Price Earnings Ratio for Long term bonds
Scenario 1 2 3 4 5
First 10 years profit growth rate 0% 0% 0% 0% 0%
Subsequent 990 years profit growth rate 0% 0% 0% 0% 0%
Risk free real return required 4% 4% 4% 4% 4%
Expected inflation rate 0% 2% 4% 6% 8%
Risk premium required 0% 0% 0% 0% 0%
Total discount interest rate required 4% 6% 8% 10% 12%
Theoretical Price equals present value of the 1000 years of earnings \$25.00 \$16.67 \$12.50 \$10.00 \$8.33
Resulting Price Earnings Ratio 25 17 13 10 8
Year 1 Earnings and pay-out \$1.00 \$1.00 \$1.00 \$1.00 \$1.00
Year 2 Earnings and pay-out \$1.00 \$1.00 \$1.00 \$1.00 \$1.00
Year 3 Earnings and pay-out \$1.00 \$1.00 \$1.00 \$1.00 \$1.00
etcetera etcetera etcetera etcetera etcetera etcetera
 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.
Calculated impacts of inflation on the P/E Ratio for an Inflation Indexed long term bond
Scenario 1 2 3 4 5
First 10 years profit growth rate 0% 2% 4% 6% 8%
Subsequent 990 years profit growth rate 0% 2% 4% 6% 8%
Risk free real return required 4% 4% 4% 4% 4%
Expected inflation rate 0% 2% 4% 6% 8%
Risk premium required 0% 0% 0% 0% 0%
Total discount interest rate required 4% 6% 8% 10% 12%
Theoretical Price equals present value of the 1000 years of earnings \$25.00 \$25.00 \$25.00 \$25.00 \$25.00
Resulting Price Earnings Ratio 25 25 25 25 25
Year 1 Earnings and pay-out \$1.00 \$1.00 \$1.00 \$1.00 \$1.00
Year 2 Earnings and pay-out \$1.00 \$1.02 \$1.04 \$1.06 \$1.08
Year 3 Earnings and pay-out \$1.00 \$1.04 \$1.08 \$1.12 \$1.17
etcetera etcetera etcetera etcetera etcetera etcetera
 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.
Calculated impacts on P/E ratio of an increase in “real” interest rates
Scenario 1 2 3 4 5
First 10 years profit growth rate 2% 2% 2% 2% 2%
Subsequent 990 years profit growth rate 2% 2% 2% 2% 2%
Risk free real return required 4% 5% 6% 8% 10%
Expected inflation rate 2% 2% 2% 2% 2%
Risk premium required 2% 2% 2% 2% 2%
Total discount interest rate required 8% 9% 10% 12% 14%
Theoretical Price equals present value of the 1000 years of earnings \$16.67 \$14.29 \$12.50 \$10.00 \$8.33
Resulting Price Earnings Ratio 17 14 13 10 8
Year 1 Earnings and pay-out \$1.00 \$1.00 \$1.00 \$1.00 \$1.00
Year 2 Earnings and pay-out \$1.02 \$1.02 \$1.02 \$1.02 \$1.02
Year 3 Earnings and pay-out \$1.04 \$1.04 \$1.04 \$1.04 \$1.04
etcetera etcetera etcetera etcetera etcetera etcetera
 In 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.

Calculated impacts of risk free growth on the P/E ratio
Scenario 1 2 3 4 5
First 10 years profit growth rate 2% 5% 10% 25% 50%
Subsequent 990 years profit growth rate 2% 2% 2% 2% 2%
Risk free real return required 4% 4% 4% 4% 4%
Expected inflation rate 2% 2% 2% 2% 2%
Risk premium required 0% 0% 0% 0% 0%
Total discount interest rate required 6% 6% 6% 6% 6%
Theoretical Price equals present value of the 1000 years of earnings \$25.00 \$31.78 \$47.42 \$152.12 \$875.91
Resulting Price Earnings Ratio 25 32 47 152 876
Year 1 Earnings and pay-out \$1.00 \$1.00 \$1.00 \$1.00 \$1.00
Year 2 Earnings and pay-out \$1.02 \$1.05 \$1.10 \$1.25 \$1.50
Year 3 Earnings and pay-out \$1.04 \$1.10 \$1.21 \$1.56 \$2.25
etcetera etcetera etcetera etcetera etcetera etcetera
 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.
Calculated impacts on the Price Earnings ratio of required risk premiums
Scenario 1 2 3 4 5
First 10 years profit growth rate 25% 25% 25% 25% 25%
Subsequent 990 years profit growth rate 2% 2% 2% 2% 2%
Risk free real return required 4% 4% 4% 4% 4%
Expected inflation rate 2% 2% 2% 2% 2%
Risk premium required 2% 5% 10% 15% 25%
Total discount interest rate required 8% 11% 16% 21% 31%
Theoretical Price equals present value of the 1000 years of earnings \$91.39 \$52.73 \$27.43 \$16.89 \$8.40
Resulting Price Earnings Ratio 91 53 27 17 8
Year 1 Earnings and pay-out \$1.00 \$1.00 \$1.00 \$1.00 \$1.00
Year 2 Earnings and pay-out \$1.25 \$1.25 \$1.25 \$1.25 \$1.25
Year 3 Earnings and pay-out \$1.56 \$1.56 \$1.56 \$1.56 \$1.56
etcetera etcetera etcetera etcetera etcetera etcetera
 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.
Calculated impacts on the Price Earnings ratio of 0% dividend pay-out stock
Scenario 1 2 3 4 5
First 10 years profit growth rate 4% 8% 11% 14% 20%
Dividend pay-out ratio 0% 0% 0% 0% 0%
Subsequent future years growth rate 8% 8% 8% 8% 8%
Risk free real return required 4% 4% 4% 4% 4%
Expected inflation rate 2% 2% 2% 2% 2%
Risk premium required 2% 2% 2% 2% 2%
Total discount interest rate required 8% 8% 8% 8% 8%
Theoretical Price equals present value of the 1000 years of earnings \$8.43 \$12.23 \$16.04 \$20.89 \$34.75
Resulting Price Earnings Ratio 8 12 16 21 35
PEG Ratio, P/E divided by Growth 2.11 1.53 1.46 1.49 1.74
Year 1 Pay-out \$ – \$ – \$ – \$ – \$ –
Year 2 Pay-out \$ – \$ – \$ – \$ – \$ –
Year 3 Pay-out \$ – \$ – \$ – \$ – \$ –
etcetera etcetera etcetera etcetera etcetera etcetera
 In all previous examples the cash flow or earnings were paid out to the investor annually. This example is similar to the previous one except that the earnings are retained by the company and assumed for calculation purposes to paid out only at the end of the 50 year analysis period. The assumption is that in the long run (after ten years) the growth rate will stabilize at a moderate sustainable level. The theoretical P/E ratio then varies with the growth in the first ten years.  Note that if the growth is 8% which is a health growth rate, and the company retains all earnings then a P/E of only 12 is justified if the investor is to earn an 8% return.
Calculated impacts on the Price Earnings ratio of 50% dividend pay-out stock
Scenario 1 2 3 4 5
First 10 years profit growth rate 4% 8% 11% 14% 20%
Dividend pay-out ratio 50% 50% 50% 50% 50%
Subsequent future years growth rate 4% 4% 4% 4% 4%
Risk free real return required 4% 4% 4% 4% 4%
Expected inflation rate 2% 2% 2% 2% 2%
Risk premium required 2% 2% 2% 2% 2%
Total discount interest rate required 8% 8% 8% 8% 8%
Theoretical Price equals present value of the 1000 years of earnings \$12.23 \$16.71 \$21.11 \$26.66 \$42.26
Resulting Price Earnings Ratio 12 17 21 27 42
PEG Ratio, P/E divided by Growth 3.06 2.09 1.92 1.9 2.11
Year 1 Pay-out \$0.50 \$0.50 \$0.50 \$0.50 \$0.50
Year 2 Pay-out \$0.52 \$0.54 \$0.56 \$0.57 \$0.60
Year 3 Pay-out \$0.54 \$0.58 \$0.62 \$0.65 \$0.72
etcetera etcetera etcetera etcetera etcetera etcetera
 This example is identical to the last one except that the dividend pay-out ratio is increased to 50% and the long term growth rate is reduced to 4%. The theoretical P/E ratios increase in each case. In general, we should be willing to pay a higher P/E ratio for a company that pays out a higher percentage of its earnings, if the growth rates are similar. In general a company with a higher dividend pay-out ratio cannot grow as fast as a similar company that retains all of its earnings. A company with a 50% dividend pay-out that can grow at 8% per year for 10 years and which then stabilizes to a 4% growth thereafter justifies a P/E of 17 if the required return is 8%.

Last Updated on August 24, 2001

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