Editor’s note: Calcbench recently published a column from Jason Apollo Voss on analyzing EPS and price-to-earnings metrics. Allison Kays, assistant professor of accounting at Emory University, wrote the following rebuttal. We welcome her feedback and post her analysis in its entirety.

By Allison Kays, PhD CPA

In his July 6 column titled, “Is it Really Earnings, or Just Financial Engineering?” Jason Apollo Voss makes the important point that readers of financial statements always need to think critically when interpreting ratios. After starting with ratio analysis, one should dig deeper into a firm’s financial statements to determine why a ratio increased or decreased over time or is higher or lower than a competing firm’s ratio.

Voss’s column  focuses on earnings per share (EPS) and its susceptibility to manipulation  by managers. I wholeheartedly agree and would even go so far as to say that on its own, EPS is a completely useless ratio. Which is especially interesting since EPS is the only ratio that is explicitly defined by U.S. GAAP and required to be reported within a firm’s financial statements.

The reason that EPS is useless on its own is because a firm’s number of common shares outstanding is arbitrary. Two firms of the same size (similar assets and revenue), profitability, and level of common equity funding can have completely different numbers of common shares outstanding. That will result in the two firms reporting completely different EPS ratios. This is because the number of shares outstanding is a measure of how many slices we cut the pie into (which is, of course, arbitrary) rather than a measure of how big the pie is.

To make EPS a more informative metric, it is often compared to the price of a share of a firm’s common stock in a price-to-earnings ratio:

The great thing about the P/E ratio is that both the numerator and the denominator are per share numbers; that allows the fraction to become independent of the number of shares outstanding. To further emphasize this fact, the ratio can also be calculated at the firm level (rather than per share):

In his column, Voss argues that the latter version of the ratio is superior to the former version. It’s important to realize, however, that the two ratios are identical. That can be proven with a simple proof:

Dividing by a fraction is the same as multiplying by its reciprocal:

This proof begs the question: why does Voss’s calculation differ from a traditional P/E ratio when he applies it to S&P 500 companies?

The answer lies in the details. As I mentioned before, EPS is the only ratio explicitly defined by U.S. GAAP and reported on a firm’s financial statements. U.S. GAAP defines EPS as:

My guess is that the difference in Voss’s ratios lies in using the number of shares outstanding at year-end rather than the weighted average number of shares outstanding in the traditional calculation. (A footnote: Very few firms have preferred dividends, but this adjustment could also make a difference in your calculation. It is important to subtract out preferred dividends as that portion of income is not earned by common shareholders.)

The weighted average number of shares outstanding calculates the average shares outstanding over the course of the year, weighted by the length of time the shares are outstanding.

One might argue that since price is a year-end number, we should use the number of shares outstanding at year-end. That’s perfectly fine as long as you understand the choice you are making and its implications.

The reason that U.S. GAAP requires the use of a weighted average is because earnings are earned over a period of time. To make the numerator and the denominator comparable, the weighted average number of shares outstanding is designed to capture the common equity funding available over the same period of time.

The logic here is that when a firm issues more shares, it receives more funding — funding which will likely be used to buy income-producing assets which increases the firm’s income earning ability. On the other hand, if a firm buys back stock, it uses assets to buy that stock back, which makes the firm smaller and reduces the firm’s ability to earn income. (Another footnote: Even if the company uses new funding to pay off debt (or uses debt to fund a share buyback), interest expense will go down (up) which will increase (decrease) net income.)

If the shares are issued or bought back halfway through the year, the company’s ability to earn income is only affected for half of the year. Thus, the denominator takes this effect into account by weighting the shares outstanding accordingly. (One more footnote: This method also makes it harder for a manager to make a last minute manipulation of EPS. If the manager buys back shares right at year end to inflate EPS, there will be very little weight on this reduction to shares outstanding as it only existed for 1/365 days of the year.)

Voss finds that the S&P 500’s P/E ratio is consistently higher when calculated with the number of shares outstanding at year-end rather than using the weighted average. This suggests that on average, firms have more shares outstanding at year-end than over the course of the year.

Lastly, in Part II of Voss’column, he argues that comparing growth in net income over time versus growth in EPS over time is a measure of the level of managerial manipulation of EPS.  It’s important, howevever, also to consider the relationship I describe above: if a company issues more shares, it receives more capital. If it receives more capital, it should use that capital to invest in incom- producing assets, which should produce more income.

Thus, you would expect a company with growing shares outstanding also to have growing income, because the firm is growing. If you look at growth in net income you are measuring growth without considering the amount of funding provided by equity holders.

Voss shows that Google’s net income is growing more quickly than its EPS. This comparison suggests that the company is not using its new funding as efficiently. Voss also shows that Apple’s net income is growing more slowly than its EPS. This comparison suggests that even though the company is buying back shares (spending money on a nonproductive investment) it is still able to grow its business. The key is to understand why the ratio changes, by looking at changes in both the numerator and denominator rather than making any assumptions.

In conclusion, there is not one right way to define any ratio. The internet is full of different definitions of the same ratio. That said, it’s also important to understand the different choices and their implications so that the ratios can be properly interpreted.

A reply from Jason Voss: I love this, and that the author took the time to poke holes in my thinking! As financial due-diligence professionals it is important that we constantly be on a quest to get better. I think that Dr. Kays’ post helps all of us improve our understanding of financial statements, and that is a very good thing. Well done.