Even the most common price to earnings ratio is not as simple as you think.

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There is an understandable tendency to put the different valuation methodologies into different baskets; each method does have its pros and cons. But at the end of the day, investors should remember that each method is just a different lens of looking at a company. There is only one intrinsic value. Theoretically, each method should arrive at the same value. At the very least, a proper calculation of intrinsic value should be agreeable across all methods of valuation. In other words, common sense should prevail at the end of the day.

To illustrate my point, let's think a little deeper about the common price to earnings ratio.

#### A perpetual bond example

Consider a bond that pays 10% coupon in perpetuity – this means that it provides a 10% return on capital – what is the maximum P/E multiple that you should pay? If the bond costs \$100, the earnings that you would get is \$10. This corresponds to a P/E of 10x and that is the maximum that you should pay if you have a company which is identical to the perpetual bond with no growth potential.

#### Factoring return on equity and cost of equity

You may not have realised, but the above example has an implied return on equity of 10% (10/100). By paying a P/E of 10x, you, as an investor, are locking yourself into a 10% return for your equity.

What if your cost of equity is 20%? That is, your required return on equity due to the next best alternative forgone is actually 20%. In that case, what is the maximum P/E that you should pay? In order to double your returns, you will have to pay half of the initial amount. That's a P/E of 5x.

Conversely, if your cost of equity is now 5%, you would be willing to a maximum P/E of 20x. Common sense therefore tells us that the fair value P/E of a company depends on the return on equity and cost of equity of the company and investor respectively. If you are an investor with a 20% cost of equity, a 10% ROE company trading at 10x P/E will not be cheap. But it's a different story if you have a 5% cost of equity.

#### Final words

To keep things simple, in a no growth situation, an investor should never pay more than the inverse of his cost of equity in price to earnings. For example, if he has a cost of equity of 5% (5/100), he should never pay more than 20x P/E (100/5). There is a formula that relates P/E into return on equity and cost of equity. We will cover it in a subsequent article when we talk about how about growth factors into the equation.

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