The basic rule of thumb (pay 70% of ARV or purchase plus rehab and make a profit of about 15% of ARV) makes a bunch of assumptions:
1) You're paying hard money rates for a 70% of ARV loan -> about 7% of ARV (10% of the loan amount) goes to money costs
2) You hold for about six months
3) You pay typical purchase closing costs of about 2% of the purchase price. Call that 1.5% of ARV, which is a bit high but also covers the misc costs like utilities, lawn maintenance, etc.
4) You pay typical sales closing costs also about 2%
5) You sell for ARV.
6) You pay realtor commissions of 6%
So, that looks like this:
Sell: 100%
Commissions: 6%
Selling costs: 2%
Money costs: 7%
Buy costs: 1.5%
Purchase plus rehab: 70%
Total: 86.5%
Profit: 13.5%
The cash required would typically be the money cost plus the buy costs, 7% + 1.5% = 8.5%. The selling costs and commissions come out of the sale and the loan covers purchase plus rehab. So your ROI SHOULD be 13.5% / 8.5% = 159%.
Now that's in a perfect world, and things often go wrong so the profit will go down and the cost will go up.
If you're paying cash, you eliminate the money costs. So your profit jumps to 20.5% of ARV (assuming everything else is the same). Your investment, though, becomes purchase, rehab, and buy closing costs, 71.5% of ARV. So your ROI is only 28%. Nevertheless, your cash-in-pocket for this deal is about 66% higher than using hard money.
But a better comparison is to ask what gives the best return for your available investment cash.
With hard money, you put in 8.5% of ARV. With cash, you put in 71.5% of ARV. Say you have enough cash to do that all cash deal. An alternative would be to do (71.5% / 8.5% = 8.4) eight deals with hard money. Now, your return on each is only (ONLY?) 13.5% of ARV. With eight of them, your total return is 108% of ARV. That's CONSIDERABLY more cash in your pocket than doing one all cash deal. Over five times the cash of a single all-cash deal.
That's the power of leverage. Its a two-edged sword, though. If things go badly (e.g., the housing market drops like a rock like it did for many fix and flippers in about 2007), you can REALLY get caught holding the bag.
Now, back to your "what if we can get cheap money" question. So, if you can borrow a big chunk of the cash to do a deal at a much lower rate, all the better. I'm a bit unclear on what you intend to do, though. If you can get cash from somewhere other than the property, and use it instead of hard money, then simply adjust the numbers above to reflect the difference in cost. For example, if you can get cash at 8% and no points rather than 15% and four points (net 11.5% of amount borrowed for six months) than your money costs (4% of amount borrowed for six months) is only about a third of the hard money costs. So, your profit goes up by a corresponding amount.
You say its a private lender, and if they're willing to lend at 6% based on the property, and they're aware they're short term loans, then you also have a good deal.
But to your question of "can you pay a higher price". Sure. Maybe it looks like this:
Sell: 100%
Commissions: 6%
Selling costs: 2%
Money costs: 2.5%
Buy costs: 1.5%
Purchase plus rehab: 75%
Total: 87%
Profit: 13%
Here I'm assuming you can still borrow 70% of ARV but at 6% and no points. So that's 3% of the amount borrowed (for the six months), which is 2.1% of ARV. I bumped that up to 2.5%. That still leaves you a profit of 13% of ARV. Your investment is 4% of ARV, so your ROI is 325%! Woo Hoo!
Now, if you can find 70% deals, stick with those. But cheap money is, IMHO, a HUGE boost in your ability to do deals. At least around here, finding a 70% deal is like finding a needle in a haystack. You spend a LOT of time searching. A 75% deal is much easier to find. If you can turn a nice profit on a 75% deal, you'll spend lots more time doing deals.