Last week we looked at basic EPS. In most cases, this metric will work just fine to unpacking a firm’s earnings and present value. But in many cases, we need to go deeper and look at diluted EPS.
Before I explain why, let me explain how this is calculated. If you remember from last week, we calculated basic EPS with the following simple formula:
N-Pd/Wa = Basic EPS
Where:
N = net income
Pd = preferred dividends
Wa = Weighted average number of common shares outstanding
For diluted EPS, we need to add a couple of factors to our calculation. Specifically, we need to look at convertible debt and stock options.
In doing so, our formula becomes a lot more complex—but it’s still pretty easy to calculate when we unpack everything:
(N-Pd)+(Cpd+Cdi*(1-t))/Wa+Scc+Scd+So = Diluted EPS
Where:
N = net income
Pd = preferred dividends
Cpd = convertible preferred dividends
Cdi = convertible debt interest
t = tax rate
Wa = Weighted average number of common shares outstanding
Scc = Shares from converted preferred shares
Scd = Shared from converted debt
So = New shares from stock options
There’s a lot here, but it’s actually really easy to calculate if we unpack the entire thing—although there are admittedly a lot of steps involved.
Let’s imagine a company reports net income of $100,000 with 200,000 shares of common stock. The company also had 1,000 shares of 10% preferred stock valued at $100 each outstanding. A year ago, the company issued 600 bonds with a 7% coupon which are convertible to 100 shares of common stock each at the start of the year. The tax rate is 10%. The company also issued stock options that converted to 2,500 shares in total at the start of the year.
Okay—all the info we need. Now let’s do this step by step.
We have net income (100,000) and preferred dividends are 1,000 * 100 *.10, or $10,000. So our first bit of the equation is:
(100,000-10,000)+(Cpd+Cdi*(1-t))/Wa+Scc+Scd+So
The Cpd is 0 because the 600 bonds were already converted to stock, so no coupon payments were made.
The Cdi is also 0 because those bonds were converted to stock.
Remember the tax rate is 10%, but we’re multiplying that by 0 so that doesn’t matter either.
Now it’s getting easier:
(100,000-10,000)+(0+0*1-.10)/Wa+Scc+Scd+So
Now to the denominator—things are a bit trickier.
We’re not dealing with common stock issuances, so Wa = 200,000. Scc comes from preferred shares converted, but we’re not told any preferred convert, so that’s 0. Now our formula looks like this:
(100,000-10,000)+(0+0*1-.10)/200,000+0+Scd+So
Just two more to go!
Scd is new shares made from converted debt, and we are told there are 600 bonds that convert to 100 shares each at the start of the year (which is nice—we won’t have to weight average by 12 months of the year). Thus Scd is 600 * 100, or 60,000. Finally, we’re told there are 2,500 stock options exercised at the start of the year. Now we have:
(100,000-10,000)+(0+0*1-.10)/200,000+0+60,000+2,500
Or 34.28 cents per share ($0.34).
Now that we’ve gone through this, let’s quickly do a basic EPS calculation for the same company. We just need net income ($100,000), preferred dividends ($10,000), and weighted average of common shares outstanding (200,000). That gives us:
(100,000-10,000)/200,000
Or $0.45 per share. That’s a 9 cent difference from diluted shares, or a difference of 26%!
Obviously, this calculation is important when we’re dealing with a company that is giving a lot of stock options to, say, the firm’s executive board, or a company that is using a lot of convertible debt to fund investments. Many companies use convertible debt specifically to prop up basic EPS and keep investors happy—but when we use diluted EPS, we can uncover when a firm is gorging on debt and trying to hide that from casual investors.
When deciding whether to track basic or diluted EPS, you need to take a close look at the company’s stock option program, its debt load, and the capital structure of its debt load—i.e., how many convertible bonds are there, how many preferred shares are there, and so on.
I have some good news for you: investors don’t need to calculate the diluted EPS! A lot of this information isn’t readily available in SEC filings, and firms are required to report diluted EPS according to GAAP standards. Therefore, analysts should rather take a close look at basic and diluted EPS as reported over time and note if there’s a divergence. If there is, they should look a bit deeper into why by tracking the company’s debt load, and then determining whether that widening gap is a cause for concern—or an opportunity for investors.