Hey Jamarr,
Congrats on your first lead! If you're like me, you're hungry to get that first deal done, and getting leads is a huge step forward.
You could use either number as a legitimate comp. The important part is that you calculate your figures based on a number that reflects today's retail price (not tomorrow's speculative price). You could split the difference and say $145k if you want.
What is the owner's motivation to sell? Despite the condition of the home, and despite the fact that her house has been on the market for a year, does she have any motivating factors to put any urgency on selling the home? She could just be seeing if she can get top dollar for her 100% equity house without having to spend a penny on updates. (Wouldn't you want to do the same?)
If she hasn't told you any motivations, ask her why she put her house in the market a year ago, and why she is responding to your marketing now after a year. Does she need to move out and in with family members, or into an assisted living home? Does she need cash to pay off a debt or lien against the property? Is her family pushing her to sell so they can get the cash for something?
Education might be empowering here too. You want to be a valuable source of information, not just a guy trying to buy her house at a discount. Instruct her on what the property tax appraisal really is (used to calculate property taxes, not market value). Instruct her that property tax appraisal is really a meaningless number to her, because there is no penalty or fee for selling beneath that value. Find some absurdly inaccurate numbers in the area if you feel like it might help tell the story that property tax appraisal does not reflect market value. Also, instruct her on what your repair estimates are (line by line), and how repair costs have inhibited her from selling her home. She may not know a new HVAC system costs $8,000, or kitchen updates might cost $12,000, or bathroom updates might cost $6,500.
After knowing her motivations, and informing her, you'll know what would make her agreeable to selling to you.
"(name), I'd love to help you meet (motivation). You've seen what selling your home with a realtor has gotten you -- after a year, your home is still on the market and nobody has bought. Your realtor may have pushed you to make repairs to find a buyer, and with all the repairs and updates your house needs (list them off), I estimate the total to be around (repair amount). I totally understand why you wouldn't want to pour (repair amount) into a home that you're just going to move out of anyways.
"Here's the service I can offer you -- I work with cash buyers in the area, and we can buy your house today, in as-is condition, and close in 30 days or less. In order to make that happen though, we'll have to make an offer about 30-35% below what you've been listing it at, and minus repairs. Would you like to sell your house quickly, in as-is condition, for (Retail value - 30% - repairs - assignment fee)?"
After giving the offer, wait for her response.
If she's not very motivated, there's likely no price short of full retail that would make her sell. In that case, it might be better to move on to the next lead.
Best of luck!