In two previous articles, I demonstrated why exceptional returns for a company like Under Armour (NYSE:UA) could be difficult to formulate. This reasoning held whether the share price was in the low-$100s or closer to today's bids in the mid-$80s. The idea was simple: the business is expected to do exceptionally well, yet investors might not capture all of this excellent business performance due to the possibility of a declining earnings multiple in the future.

As a for instance, if the business grew by 20% annually for the next decade and shares were to trade at say 20 times, investors would "only" see gains on the magnitude of 4% per annum. As Ben Graham would have it: "obvious prospects for physical growth in a business do not translate to obvious profits for investors." The prospects for Under Armour's growth are apparent, but the current valuation multiple certainly reflects this.

This brings up a natural question: "If not 80 times earnings, then what might be a "reasonable" valuation to pay?" Obviously, this is highly unknown, but I think it can be instructive to work through the process. We never know the future, so the best we can do is come up with cautious and/or logical assumptions and work from there. Let's work through some scenarios to see if we can get a better handle on what might be "reasonable."

Over the intermediate-term, analysts are expecting 20%+ annual growth. Let's scale it back slightly, just to leave a bit of room for caution. We'll use 20%, 15% and 10% as our growth assumptions for the next decade. In addition, we need to come up with some type of end earnings multiple. Once more this is unknown, but let's come up with a baseline.

Nike (NYSE:NKE) is likely the best comparison, as it's in the same industry and has already exhibited exceptional growth characteristics over the years. Today, the company is still expected to provide double-digit growth, but the security's valuation multiple is much lower. Over the past decade, shares have traded in a wide 15 to 30 P/E ratio range, with something in the 20s being characteristic in the last few years. It's conceivable that the valuation could jump much higher. Yet, this at least gives us a historical idea of what the going rate has been for a much larger but still growing company in the same industry.

So let's look at growth rates ranging from 10% to 20% over the next decade for Under Armour along with end P/E ratios ranging from 15 to 30. Here's what that could look like:

Here you have a wide range of potential future prices based on the assumptions above. The idea is not to figure out the exact price in the future. The idea is to think about the process and see what some prudent assumptions lead to. If you suspect that the company can grow by 20% annually and trade with a 30 multiple 10 years from now, the $195 price looks reasonably attractive against today's $85. Of course, if you suspect that say 15% yearly growth and a 20 multiple is a more prudent assumption, your annualized gain would be roughly 0%. It all comes down to your expectations.

Here's a table illustrating the same growth rates and end P/E ratios, with the added information of the required earnings multiple to provide a 10% annualized return:

If you suspect that the company can "only" grow by 10% annually for a decade, you need the starting and ending P/E ratio to be the same in order to achieve 10% annualized gains. As such, I'd contend that starting at 80 times earnings could be a bit troublesome. On the other hand, if you see greater than 20% annualized growth for the decade, you could make a reasonable case for a much higher multiple.

What's equally interesting is that you can pay a well above average multiple and still do okay if the company delivers. For instance, if the company grows by 15% annually and later trades at 25 times earnings, you could pay 39 times earnings and still see 10% annualized gains. Of course, shares are closer to 80 times trailing earnings, thus significantly inhibiting returns at those assumptions. It's not that Under Armour doesn't deserve a higher valuation for its exceptional growth prospects. Instead, it's simply a matter of: "how high is too high?"

We can do the same sort of exercise over a 20-year period. Here's a look at various growth rates and ending P/E multiples, along with what valuation you would need today in order to generate 10% annualized gains:

Once more this table can be instructive. If Under Armour were able to grow by 20% annually for the next two decades and trade above 20 times earnings, today's valuation would be comparatively "cheap." You could generate 10% annualized gains in this instance even with a starting P/E ratio above 100. Of course, this simultaneously indicates exceptionally robust growth for another 20 years.

If you scale back the assumptions slightly, you begin to see where caution could come into play. If Under Armour "only" grows by 10% or 15% - a still exceptional record for a company that has already performed spectacularly - and trades around 20 times earnings, it's apparent today's valuation could be too lofty. A 10% long-term growth rate would be very solid for a great deal of companies. For Under Armour, it could be quite the unfortunate circumstance.

In short, the appropriate price to pay is naturally unknown. However, it can be useful to work through some assumptions to get a better feel for the process. If you believe Under Armour will show exceptional growth for years and years to come, today's valuation could be more or less reasonable. Alternatively, if the company is "only" able to grow by 10% or 15% over the long term, today's valuation could indeed be a substantial drag on future investment returns.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.