On Monday morning, Deutsche Bank announced a huge upgrade for Eli Lilly (NYSE:LLY). Predicting the Indianapolis-based drugmaker's new Alzheimer's disease drug solanezumab will eventually turn into a $3 billion (annually) moneymaker, and not only $1 billion, the Teutonic megabanker added $14 to its target price and raised its rating on Lilly stock to buy.

Which also raises the question: Has Deutsche Bank gone completely bonkers?

German optimism
At $86 and change, Lilly shares recently surpassed Deutsche's previous estimate of their worth ($85). This presented the German banker with a dilemma. Obviously, it couldn't recommend the shares with that price target. So it was time for Deutsche to either cut its rating, or either up the rating, and the price target, as well.

Deutsche chose the latter.

As StreetInsider.com describes Deutsche's move, the analyst reasoned thusly: "key Phase 3 read-out for [solanezumab] is roughly a year away [and] we expect investor interest to grow ahead of this binary event." Additionally, Deutsche says it is "excited about the prospects for the diabetes product Jardiance."

This latter drug, which competes with Johnson & Johnson's (NYSE:JNJ) Invokana, is said to be "gaining momentum following the recent finding that the product improves cardiovascular outcome." And like solanezumab, it could be a big deal for Lilly. My Foolish colleague Cory Renauer recently pegged Invokana as a likely $1-billion-a-year drug for Johnson & Johnson -- and that's a market that Lilly can compete for.

And overall, Deutsche just sees Lilly as having a good chance of growing revenue and earnings "in 2018 and beyond," thanks to its long pipeline full of "interesting late-stage development candidates."

But at what price?
None of which I'd dispute. But before getting too excited about this upgrade, and the 15% profit that Deutsche seems to be promising new Lilly investors today, it's worth asking: Doesn't Lilly already cost too much?

At today's $86 share price, Lilly stock costs nearly 39 times earnings, which is nearly 50% more than the average valuation in Big Pharma (and nearly twice as much as rival Johnson & Johnson costs). Granted, most analysts who follow Lilly agree the company will grow profits strongly in future years, averaging about 13% annualized growth. That's faster than J&J is pegged for -- but slower than the industry average.

It also happens to give the stock a PEG ratio of almost precisely 3.0. (Value investors tend to prefer stocks that sell for closer to 1.0 -- three times cheaper than Lilly).

Let's go to the tape
I have to say that, seeing these numbers, I'm not at all optimistic about Deutsche's decision to recommend investors buy Lilly shares -- except for one thing that many investors may miss: Deutsche Bank's record.

You see, here at Motley Fool CAPS, we've been tracking Deutsche Bank's performance for nearly a decade now. And what we've learned over that time is that Deutsche Bank is just flat-out one of the best pickers of pharmaceutical stocks on the planet. Historically, more than 58% of this analyst's Big Pharma picks have outperformed the market, and by a combined 1,300 percentage points across 27 recommendations in 10 years.

Winners to date include:



Deutsche Bank Said:

CAPS Says:

Deutsche Bank's Picks Beating S&P By:

Novo Nordisk



410 points

Johnson & Johnson



58 points

Eli Lilly



38 points

That's incredibly good performance. And you'll notice that both Eli Lilly and its rival Johnson & Johnson are stocks that Deutsche Bank has called correctly in the past -- lending further weight to this analyst's argument that it was right before ... and is probably right again this time.

Summing up
Based on its valuation alone, there's no argument whatsoever for thinking Eli Lilly stock is cheap enough to buy. But with an analyst like Deutsche Bank standing behind the stock, I have to admit that despite the high stock price, I'd be really hesitant to short Eli Lilly right now.