You don't need to be a mathematician to be able to calculate Square, Inc.'s (SQ) valuation. You do need to circle back on your assumptions about whether PayPal Holdings, Inc. (PYPL) provides a good point of comparison. When Square is held up next to PayPal, it shows that though their business models may differ in some ways, they give a good reference. It then points SQ likely undervalued relative to PYPL. However, PYPL itself is overvalued.

A PayPal Comparison

It's been proposed that PayPal offers a good point of comparison for Square. They both operate as payment service providers that allow businesses to accept payments. SQ hit the scene with their easy-to-use dongle that turned your phone into a payment processor. PYPL operates almost exclusively online. In fact, for years they remained unchallenged until startups like Stripe decided to disrupt their business model.

Where the two differ, comes in where they operate. Square firmly sits in the real world while PayPal lives in the digital. These trends are changing with SQ actively working on establishing their online platform and PYPL's acquisition of iZettle.

However, you get the sense Square is more interested in becoming the true one-stop-shop for payment processing than PayPal. Both make things easier such as payroll. However, PYPL seems to point to existing ways of using their program (IE mass payments) rather than SQ Payroll which made a specific application for payroll.

Price to Sales Growth Rate Normalization

It's been pointed out Square trades at a much higher P/S multiple than competitors like eBay (EBAY). But, that makes sense considering how much faster SQ continues to grow. PYPL is no slouch. Their 5-year average is 18.26%, and their most recent YOY was 20.77% with the latest quarter at 22.99%.

Source: Morningstar PayPal Analysis

That's not the same thing as SQ. People pay more for it because the company threw up a 5-year average of 61.20%, and the most recent YOY of 29.59% with the latest quarter at 47.77%.

Source: Morningstar Square Analysis

At the moment you have the P/S for PayPal at 6.7x and Square at 11.32x. Well, that kind of makes sense. If you assume PYPL at fair value, then if SQ puts up 2x-3x their growth pretty consistently over the years, you would expect the P/S to be double that of PYPL.

In fact, you really could only make the argument it's overvalued based on the 2017 numbers. At the paltry 29.59% growth YOY, they should only be 1.42x the P/S ratio of PYPL instead of the 1.69x they're at now, or a 9.51x P/S and $62 a share.

But if you took the 3-year average, you would be at 2.12x the value of PayPal or 14.2x for an equivalent P/S, and using the 5-year average you would be 3.35x the value of PYPL, or at 22.46x for an equivalent P/E. That would put the share prices at $93 and $147 per share. Where their growth will land is debatable. But, when you compare the valuation to that of PYPL unless the overall market itself changes, it would be tough to see share prices drop much below $60.

P/E Normalization

Let's consider what the P/E ratio would look like for Square if they hit operating margins similar to those of PayPal. Right now PYPL runs an 18.82% margin. If that margin is applied to SQ's TTM, they will put out Net Income of $505 million. That equates to $1.28 per share. At the current price, you end up with 57.86x P/E. That's a good bit higher than PYPL which sits at 44.33x.

If you consider these companies equivalent and ignore the growth aspects, then a similar valuation of Square would give a share price of $56.74. That's not too far below the low end of what was noted above for the P/S analysis. Again, let's consider what happens when you account for the higher growth. Using the 3-year growth rate, you'd take 44.33 x 2.12 = 93.98 P/E, and the 5-year 44.33 x 3.35 = 148.5 P/E. That would give share prices of $120 and $190, respectively.

It's fair to point out that the business models between the two don't work in the same way. Square actually manages not just software, but hardware devices. PayPal is only just moving into that area.

Source: Morningstar Square Analysis

Source: Morningstar Square Analysis

Why PayPal Doesn't Deserve It's Premium

So far the article discussed why the valuation of Square relative to PayPal is not outlandish, as well as where potential floors and ceilings might exist. However, that relies on the assumption of PYPL being fairly valued.

Referring to the PayPal financials, you can see the expansion most years. Current margins sit near 18.82%, up from 17.3% the prior year. It would be very unlikely that operating margins will get much higher than 20%. The costs of the business simply make this prohibitive (unless you decided to redefine revenues and expenses which is another discussion for another day).

Take a step back to the growth rates that PayPal currently sees. Right now they've seen averages that sit between 18%-20% per year. Let's consider the S&P 500. The S&P 500 trades at a P/S of 2.14x, and a P/E of 22.60x. The earnings growth rate ranged from 6.0% to 14.41% for 5-year and 3-year periods, respectively. Just using the 18% point, you would get a multiplier for PYPL of 1.24x - 3.0x.

Using these multipliers, you would expect to get a range of P/S on PayPal between 2.65x-6.42x, and a P/E of 28.02x-67.8x. Considering that the current earnings growth rate for the S&P 500 sits at 17.75%, on a relative and short-term basis, the stock is overvalued. But in considering the median for the S&P 500 sits at 12.28%, you'd be looking at a P/S of 3.17x and P/E of 33.12x. That would give you a P/E derived price of $55.64 and a P/S price of $40.12.

However, the story doesn't end there. Remember that PayPal has been expanding their operating margin. That gives another multiplier to consider. The PEG ratio for PYPL sits at 2.24x. The S&P 500 sits at 1.25x. This would imply that PYPL is being overvalued, and better priced at $47.32.

Conclusion

If you consider Square relative to PayPal, it appears to be fairly valued, if not somewhat underpriced. However, PYPL itself seems to be trading at a premium and has further to fall. This would indicate that SQ also has further to fall. That would mean it likely to find a stable value base around $60. The easiest way to trade these pairs is to take a long/short on any oscillations that cause compression in values. If SQ trades lower to PYPL, or PYPL higher to SQ, it becomes a no-brainer.