It's actually consistent. The point here is that Google Cloud is undervalued, hence the high buy rating with a target of $1.6k. That would imply a market cap of $~1.1 trillion, meaning that the worth of the rest of Alphabet (sans Cloud/Waymo valued @ $335B) would be $775B.
When we say "undervalued", you mean compared to competitors?
When the tech bubble bursts, either everyone gets bailed out, and it does become worth 200B. Or we are going to find out much of this tech money was speculation.
What's hard about running a server farm? Does it lend to this valuation?
I'm not sure what "speculation" is meant to imply here. Deutsche is explicitly giving a speculative valuation here; they speculate that Google Cloud will reach $38 billion of revenue in 2025. But that's not some pie-in-the-sky impossible dream; AWS brought $25B (and operating income of $7B) last year.
There are two direct responses to your last question: all parts of running a server farm are hard, and a cloud platform is more than just a glorified server farm.
I can't find a copy of the analysis (it's unclear to me whether it's even public). But presumably Deutsche either thinks 38B is an an almost sure thing, or expects the business to grow even more after 2025.
No, undervalued means the market valuation of the company is less than what it should be. I.e. Deutsche Bank believes that Google's profits summed up for the future (and discounted to account for inflation/risk) will exceed what people are buying it for. As an example, if a share is $10 and it pays $5 per year then it's undervalued because it's value ≈ $5 + .9($5) + .9²($5) + .9³($5) + .... This is essentially how Deutsche Bank is setting their price target. Since their target exceeds the equilibrium price of Google, they have decided it's undervalued.
Would be interesting to have a similar estimate for AWS. My personal pet theory is that (and was already at a stock price of 1k) that around 80% came from AWS. Since I'm by no means an expert getting real numbers would be nice!
And even if they did know what they were talking about (read JP Morgan), that doesn’t mean their estimates are reliable. There are many forces/interests at play wrt these public statements, see the WeWork case.