If you can raise at a post-money valuation of $5MM and some company offered to acquired you, how much should you be asking for? I know it depends on a lot of things, but generally is it higher or lower than the potential post-money valuation? And what are some the things to consider?
If you had asked "Should I be acquired or raise money," you'd have a hopeless question there. The only possible answer would be "it depends."
Luckily for you, you asked a different question: if the angel investor's valuation is $5m post, what should be the acquirer's valuation? That's a really interesting theoretical question and one which, I think, I can actually answer!
The theoretical answer
Theoretically, you have to consider how much more (or less) the company is worth as a part of the acquirer compared to its value as a stand-alone entity.
Example: Your company has a technology that makes searching for names of people really, really easy. As a standalone website, it's worth X. But if Google acquires you, they can integrate you into their main search feature. Thus your technology will get used a billion times more often. Thus the value of your company as a part of Google is much higher than its value as a stand-alone entity.
Example 2: Your company has a technology that does nothing whatsoever. Facebook wants to acquire you because they really need engineers and you and your partner are pretty good engineers. Thus the value of your company as a part of Facebook is whatever it costs them to recruit two engineers, which is probably lower than its value as a stand-alone entity.
The practical answer
Practically, both prices are taken from the market.
The "startup financing at $5m post" valuation comes from the fact that that is what well-pedigreed startups with about 3 months of work and about 2 engineers are getting these days in the well-pedigreed world of TechStars, Y-combinator, etc. It's just a number that seems to be "the going rate." In other words it's the valuation that appears to clear the market, nothing more, nothing less.
The valuation you would get from an acquirer comes from their perception of how much value you add to their business, combined, again, with market conditions.
If it's just an HR acquisition... well, these days, well-pedigreed startups that are getting acquired solely for their engineers are going for about $2m per hireable engineer. That's because the acquiring company believes they can offer each engineer a startup bonus of $2m, and very very few working engineers would turn them down. So this sets an upper bound on the acquisition price as an HR acquisition.
If the company actually might have some revenue... well, the only responsible answer is that the valuation is "the net present value of the total sum of future cash flows, discounted," but of course, the real answer is "how much do we want it and who else wants it and how much competition is there and how much will we have to pay."
You have to consider the purpose of each transaction. If you have someone who's looking to invest in you (angel or VC) they're hoping for anything from an above-average reliable return (10-20% per year) to a risky but huge return (10x in 7 years). At best they're paying mostly for your future potential, and depending on their risk tolerance they may be paying quite a bit more than the business is worth now. Other investors may put future potential in the back and only invest if you can give them a good return in 1-2 years.
If another company is acquiring you (excluding the HR buys that Joel mentioned) then there are two possibilities. If it's for financial reasons, they mostly want to get a good return on their investment and moderate growth so they would be looking at the current value more than future value and it's important that they don't overpay. If it's for strategic reasons they might expect the business to be worth more as an acquisition than it is on its own. The multiple there might vary quite a bit but in most cases I would expect it to be fairly low (not every business is worth 10x more as a strategic acquisition than it is for the financial value).
Also remember that strategic acquisitions go both ways. An acquiring company or a connected investor might get more value out of your business because they can help it, but they might also give you less because they're doing work to grow it and you wouldn't be able to do it without them (see Shark Tank/Dragon's Den for countless examples of this). They wouldn't want to lose a good deal over a small difference in valuation but they might throw it into the bargaining.
Based on these categorizations you would need to look at both sides and try to understand their motivations. An investor might buy into your company expecting a lot of future growth, and pay well above the current business value (anywhere from 5x to 100x what it would otherwise be worth), while an acquirer might expect strategic benefits and moderate future growth and give you 3-5x what the financial value would be. Or it could be reversed - maybe the investor is risk-averse and the acquirer sees more strategic value. But right now I would say there are many investors who are betting on a lot of growth potential, which you may not get as much with acquirers.
This assumes you're profitable now, so investors and acquirers can get part of that profit. If you aren't profitable then the investors would be focused more on growth and the acquirers more on costs they can eliminate, which probably leads to higher valuations from investors again.
Things to consider: