ARV: After Repair Value. This is the retail "arms-length" value that the property would fetch in 30 to 60 days (at most) if it was in fixed-up move-in condition. This can be calculated by an appraisal or a Broker Price Opinion (BPO). A BPO is about 1/3 the cost of an appraisal, and most lenders will accept an independent 3rd-party (i.e., not
your own broker's) BPO instead of a full appraisal.
AS_IS: ARV - repair_costs. Get itemized estimates from 3 licensed contractors, use either the average or the lowest (the bank will want to see all of the estimates anyway so you won't get away with using the highest estimate).
82% Rule: For FHA and VA (government loans), a cash offer of 82% of the AS-IS value
must be accepted (according to my attorney, but what does he know?). For non-government loans, the lenders have their own rules and timetables for lowering their asking price.
NOTE: The 82% Rule applies to REO (post-foreclosure), but it may not apply to pre-foreclosure. It's a good "rule of thumb" in either case.
btw: If you have a real estate license, you can also subtract your broker commission from the calculated price, but be sure to specify that in the contract addenda and in your cover letter. The contract should state the purchase price reflects subtracting your commission as a Seller concession in purchase price.
UGLY = 70%*(ARV-repairs) = 70%*AS_IS
NICE = 82%*(ARV-repairs) = 82%*AS_IS
Thus, 70% of the AS-IS value is the most you want to pay for ugly houses. If there is little or no fix-up, then your holding costs are much lower (you can immediately flip), and you can consider using the 82% calculation. If you are holding for rent, then you must calculate a price that will cover all of your costs and generate a positive cash flow after expenses and debt service (that's a completely different calculation).
Remember, those calculations do not include costs for acquisition, carrying, disposition. Those extra costs are paid out of your gross margin in the calculations.
Thus, an alternative calculation is:
All_Costs = Repair_costs + acquisition + carrying + disposition
Net_Profit = If ARV > 130K, then 40K. Else 30%*ARV.
Max_Offer = ARV - Net_Profit - All_Costs
You may need to adjust the Net_Profit calculation, depending on how hot or cold your market is, or depending on the median price for a 3 bed, 2 bath, 2 car house in good condition. If prices are significantly higher (like Newport Beach California), then you may want something like:
Net_Profit = If ARV > 500K, then 150K. Else 15%*ARV.
Just work the numbers to be sure you don't lose money if the property stays vacant/unsold for longer than you anticipated, or you encounter unforeseen repairs (like mold remediation).
If the lender won't budge, then just resubmit the offer each month with the date changed until it is accepted, or until some knucklehead comes in with a higher offer and takes the property. (We have a lot knucklehead newbies here in northern Colorado who are paying way too much for REO. They overpay and under-repair, then their properties sit vacant on the market for months. Then they become motivated sellers.

)
btw: Your offer must be for cash and you can include a contingency for 3rd party financing, but be sure to include a pre-approval (not a pre-qualify) letter that is conditioned
only upon the property appraisal (not conditioned upon
you qualifying). Forget about any "creative" financing; the lenders want all cash at closing and they want it fast. Your inspection contingency should be a "go" or "no go" choice; don't come back with a "notice to correct" or a price reduction. You should already know the repair costs and factored that into your original offer. Also include a "property insurance" contingency to get out of the deal if you cannot get satisfactory (in your subjective opinion) property insurance.