Advice on Offer for My First Investment - $25k above asking price

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Hi.  I'm just starting out in real estate and trying to learn as fast as I can.  However, I'm not letting the fact that I don't know everything stop me from moving forward.

I found a 4-unit property.  I used the bigger pocket calculator to crunch the numbers and if my numbers are correct, it will allow me to live rent-free while I live in one of the units and cash-flow around $300 - $500 a month after I leave and rent out the 4th.  I plan to keep it for at least 5 years and I view this as the first in my portfolio.

After I put in an offer, the seller came back and said they decided to keep the property and not sell it.  When my agent said we can up the price, they came back with $25k over asking (which is high I think...I was willing to do $15k over asking)0.

The original asking was $400,000. And my realtor estimated around $100,000 for rehab costs. They counter-offered at $425,000, but they are saying it only needs $75k rehab costs. So, it might be a wash. I'll have it appraised to see what the actual ARV is.

My question is ... if the ARV says it will be less valuable than what I paid for it, is it still a good idea to purchase because it has positive cash flow?

I'm wondering if people think this is a good deal or not if I pay $500,000, but the property appraises for $475,000.  Any thoughts or guidance is appreciated.  What would you do?