I am assuming, and I could be very wrong, that Wonder is smaller by market cap than Grubhub.
In this case, GrubHub had taken on a bunch of debt; Wonder agreed to assume it, and GrubHub's owners/investors get $150M in cash.
Private companies have shares. Given a per-share price, you can get a market cap. For a company with debt, like GrubHub, enterprise value is a better metric.
Same way you do for a public company. From trades and valuations. Private shares exchange hands in private transactions as well as almost every time the company raises money. If a company issues incentive stock options, they're required to calculate a 409A price, which while a bullshit number, is indeed a per-share price.
Corporations, by law, have shares.
Company generally has these records. Various other sources, e.g. PitchBook, compile them. In some jurisdictions (e.g. UK and India) they have to be publicly announced, though that's becoming less common.
TL; DR It is incredibly wrong to suggest private companies don't have a market cap. As in finance 101 wrong.
no, it's not the same, because the information is not publicly available. They are the same in that in both cases you multiply two numbers together; they are not the same inasmuch as your ability to know those numbers is vastly different. To say they're the same is misleading.
Did they really go from some big number to some small number in an eyeblink with this latest transaction?