I've been raised angel money as CEO several times, and also advised angels on multiple transactions...

Of course the investors understand that you don't want to "give away too much" equity, but of course if they believe in your business then they'll want to acquire a meaningful position.

If you're still pre-revenue (or even if you have revenue but still negative cash-flow), then the thought-process in the angel mind often goes like this:

1. How much money does this company need, to significantly transform itself to the next stage (and either become cash-flow-positive or at least become a serious candidate for a much larger round of funding)?

2. For my risk, I'm going to take around a third. (Maybe 20-40%).

3. Therefore, if I think this company needs $400k to hit its next milestone, and I want to take 40%, then I'm going to give this company a pre-money valuation of $1M.

And then, of course, the question is, "do I think it's ok to risk $400k on this enterprise."

If you were to counter-offer to an investor, "gee, thanks, but we don't want to give away that big a %age — so we're only going to take $200k," the investor would have a huge problem:

The angel would say, "but you just got done telling me that the company absolutely needs $400k to grow! so, if you 'settle' for $200k, won't you be in trouble? or were you lying when you said you needed a full $400k?"

It can become a bit of a catch-22 if you start down this road.

RECOMMENDATION:

Figure out what you truly think the company needs, to really transform itself into something much bigger. Try to raise that much in the round. LISTEN to the feedback you hear from angels. They will drop hints (or tell you explicitly) if they think you're asking too much or too little. If your round is over-subscribed, that is, if you're able to get more investors than you needed, then you can run up the $ valuation. Otherwise, keep it modest and expect the early risk-takers to eat a big chunk of equity.

But don't counter-offer a lower amount of money for the round, because it would discredit your earlier claims about what you need.

Of course I'd be happy to jump onto a call and discuss this further if you like. And above I was pretty much assuming you're pre-revenue; I would change some of what I said if you have positive cash flow or at least some revenue.

Firstly - I think you are in a decent position. Any angel worth their salt will know that this is a negotiation and a fine balance between disincentivizing the management team and getting what they perceive as a 'good deal'.

Their are two sticking points as I see it:

1. The angel believes you are undercapitalising - occasionally you may need a reasonable amount of funds to generate product/market fit or to build the operational infrastructure to make/support sales. If the capital isn't available to reach these inflection points then it presents a serious systemic risk to the business.

2. The angel perceives that you are fixating on is valuation, for valuations sake. You have chosen an arbitrary number and in your head even if Peter Thiel offered you the money you, would still refuse on principle.

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I think what troubles me about the way you've presented your question is it seems like a flick switch. If a then b, if b then a, you are curating a round of funding, that means if this guy gives you options above and beyond money then it's worth understanding and weighing up the associate benefits. He may reduce your marketing spend by x, he may have a black book that gets you into the offices of the key decision makers you are after. If this is the case then you are reducing your slice but ultimately ending up with a far bigger pie.

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I think set out a considered and well worked rational for both scenarios. However, one thing I would say is get back up options in place. The one thing I do know from experience is you have a plan A and a plan B, but if he strings the conversation out till you are running low on cash then you will be wishing you had a plan C. As at that point he can call in any chips he wants.

I really don't think you have a problem though, bootstrapping and lean methodology are all the rage. Just suggest you want to solidify the business before accelerating it.

My last warning would be....if he is fixated and a defined % ownership probably worth questioning why. Investment is about cohesion and an angel that is willing to support you (you being the individual), a one size fits all for anything in life should be treated with suspicion.