Many of you understand one of the most basic concepts in investments, the P/E ratio. For those who don’t, I’ll give you a brief explanation because you’ll hear “P/E” in almost any discussion on market or company valuation. “P/E” stand for Price-to-Earnings. It’s a ratio of what it costs to own a share of stock in a company, versus the annual earnings of the company that are attributable to that one share. In other words, PE = stock price ÷ annual profit per share. Annual profit is usually referred to as “Earnings Per Share” or “EPS”, so we can simplify a bit and say that PE = stock price ÷ EPS. It’s a measure of how expensive a stock is, relative to the earnings that one share of the company represents. For example, let’s take a look at Apple. The stock is trading at $92 per share. In the year ending Sep 2014, Apple is forecast to earn $6.88 per share (that’s about $41 Billion in profits divided by about 6 Billion shares outstanding). Thus, the PE for Apple is 92/6.88 = 13.37. Is that high or low? How do you determine a fair PE for a company?

To answer that, I like to take the mystery and complication of the stock market out of play and think about a small business, something that you can probably relate to a lot easier. Let’s say you and four friends start a business that earns a steady $50k per year in net profits. When you started the company, you decided you’d each own an equal 20% of the company. In case one of you wanted to sell a part of your share to someone else, you decided you’d each own 200 shares of a 1000 share total (still 20% of the company). If the company earns $50k per year, and there are 1000 shares outstanding, how much does each share of company earn? $50. That is, the EPS for your company is $50. Now, how much is your company worth (how much would someone being willing to pay for one share of your company)? Surely it’s more than $50k ($50 per share) right, because it’s earning $50k per year consistently, so someone who paid only $50 per share for it would get their money back in just a year. You would be highly unlikely to sell a share for such a low price… you’d just keep the share and earn the $50 over the next 12 months from profits instead. On the other hand, the company can’t be worth a billion dollars ($1 million per share), because even though someone paying $1M per share will eventually get their money back by earning $50 per year, 1) it would take several lifetimes, 2) there’s more risk that something happens to the business to reduce its earnings when you need to go farther out in the future to make back your investment, and 3) (most importantly) that $1M can be invested in something else that pays well north of $50 per year so no one would ever pay a million dollars for $50 per year even if it was guaranteed forever. Somewhere in between $50 and $1M per share there is a fair price though. Perhaps the best way to estimate is by using the third rationale above… how much money do I need to invest to earn $50 per year on something with a similar amount of risk? I can put $7700 in a 1-year CD and earn $50 at 0.65% interest. Clearly though, buying future profits of a business is higher risk than a CD so a buyer would want to earn more than the going rate for a CD. There’s also the chance that a buyer may not be able to re-sell the business in a year, so we should look at something that locks up money for a longer time period to compare. How about a 10-year investment-grade (BBB) rated corporate bond? That pays about 5% and has some real risk in it (the company could go bankrupt within 10 years and you wouldn’t get your money back). It would take a $1000 investment in that bond to earn $50 per year. There’s probably still more risk in the small business though because the only way you wouldn’t get your money back in a bond is if the company literally has no money and is forced to liquidate or file bankruptcy. In the small business, even if it just starts to breakeven for a while, there are no profits for the owners, so you may never get your money back. A buyer could argue that she would want a 5% higher return on an investment in your company than he/she could get from the corporate bond. The buyer would be willing to pay $500 per share then, since a 10% annual return on $500 is the $50 per share that your company is generating. $500 per share then might be a fair price for the business. A $500 price for a company earning $50 per year means a PE of 10.

What if your company was growing rapidly and your earnings were expected to increase considerably over the next few years? If $500 (PE of 10) was a fair price for a stable company, surely a buyer would be willing to pay more than $500 (higher than a PE of 10) for a rapidly growing company right? Of course, because he’s not only going to get just $50 per year, he’s going to get $50 this year and more than $50 next year and much more than $50 the year after that. That has to be worth more than the stable company that’s not growing. So now we know that PE’s should be higher for higher growth companies. This should seem pretty intuitive.

There’s another factor that can have a dramatic impact in a fair PE. What happens if interest rates fall and investment grade bonds start to pay 3.33% instead of the original 5%? If investors in a small business like yours still demand a 5% premium to what corporate bonds are paying, they’ll want an 8.33% return from an investment in your company. Since the company is still generating its consistent $50 per share per year, the only way to make that seem like a lower return is to push the value of the company higher. At $600 per share, the $50 in annual profits would be an 8.33% return. The reduction in interest rates pushed the PE (600/50 = 12) higher. So, we can generalize that lower interest rates lead to higher PEs. This may be less intuitive, so I’ll give another way of thinking about it. Instead of looking at the PE ratio, let’s look at its reciprocal. That’s the EPS / stock price. We can call this the “earnings yield”. For our small business above, the earnings yield would be 10% if the stock price was $500 (50/500), it would be 8.33% if the stock price was $600 (50/600) and it would be 5% if the stock price was $1000 (50/1000). If you could get 5% in a savings account or CD, would you ever purchase a company with a 5% earnings yield (remember, steady payments, not expected to grow)? I hope your answer is no, because there’s a lot more risk in the company than there would be in a savings account. So, if bank interest rates were 5%, there’s no way the small business could be worth $1000 per share (5% earnings yield, PE = 20). The price must be < $1000 per share. What if bank interest rates were only 1%? Now you might be willing to take 5% earnings yield in a riskier investment because you’re getting an extra 4% return over what you’d get in the bank. It should seem clearer that lower interest rates in general would make lower earnings yields seem more attractive. If lower rates lead to lower earnings yields, the lower rates must lead to higher PEs, because PE is just the reciprocal of earnings yield.

To summarize, remember that the P/E ratio is the price of a share divided by earnings per share. The reciprocal of the P/E ratio is earnings per share divided by share price and that’s called the “earnings yield”. The stronger the expected growth in earnings, the higher the P/E. The lower the level of overall interest rates, the lower the earnings yield, and the higher the P/E.