I must be missing something here..
Why would any experienced investor give $200 million to a small ASIC startup? ...
You aren't missing anything it makes absolutely no sense (for anyone with independent critical thinking skills).
However I would phrase the question more broadly. Why would anyone invest $200M into bitcoin mining (or bitcoin mining hardware)? It would be like there is some niche disease treatment which potentially could result in $100M in global revenue so a biotech company decides to spend $8394208309483249328 quadrillion to develop a treatment. Even if you win, you lose.
Remember people this is a market where the combined global miner revenue is ~$130M. That doesn't mean $130M in miner profit or even $130M in mining hardware sales, that is $130M in global mining revenue. Some portion of that is going to be electricity so lets say $30M of it. The price of ASICs are far more elastic than the price of electricity so I am being generous but you can look at it this way:
GLOBAL GROSS MINING REVENUE = AMMORTIZED HARDWARE COSTS + ELECTRICAL OPERATING COSTS + LABOR/TIME + PROFIT
Lets assume all miners value their time at $0 and they are all so stupid as to paint themselves into a corner where profit is $0. Likewise lets generously assume that only $30M of the $130M is electrical costs.
So that means ~$100M in ammortized hardware. Say the average ASIC is economcially viable for 18-24 months (due to Moore's law and more efficient units). This means the annual market for hardware is maybe $50M a year in hardware sales. So $50M? Yes (as an upper limit) but that is gross revenue not profit. Even if you could hold margins at say 30% we are talking maybe $15M in profit. For the record I am again being generous. Intel who is pretty much the best semiconductor company on the planet, and one in which the barriers to entry are massive (estimated cost to develop a competitive CPU architecture is on the order of $1B to $5B) has net profit margins in the 15% to 20% range.
Nobody (who is smart enough to have $200M) dumps $200M into a venture that AT BEST worth $15M in profit. Remember this is assuming 100% global marketshare, generous to the point of being rediculous variables, and taking all profit from miners). People that do stupid things like that tend to not end up with $200M
Lastly there is no NEED for $200M. While maybe Avalon (or ASICMiner, or xyz) is getting some deep pocketed VC in the near future they wouldn't even know what to do with $200M. There is a reason that companies tend to go through various growth stages (seed financing, round A, round B, IPO, etc). I mean $20M would be a ton of operating cash. Sure there is the NRE and you need to pay salaries, it likely will take some time to tape out, prototype, and test a 20nm design but it doesn't take take $200M.
Note: before someone "correct" the numbers the point isn't to calculate down to the Satoshi the exact amount of global profit. Who cares. Much like an interview question "how many windows are their in NY city?" the point is to do some quick back of napkin math and say "$200M? is that even within one magnitude of making sense?" The answer is a resounding no. $2M invesment = highly plausible. $20M investment = maybe but we are starting to push it. $200M = stupid.