Cap Rate Confusion

[TJ Woolum]

Can someone please help me understand cap rates? For some reason I can't wrap my head around it. I understand the mathematical equation... that's easy enough. Cap = NOI / Property Value. NOI is pretty straight forward. But how do you determine the property value? Well, one way is to do the math and say Property Value = NOI/CAP. But now I'm left in the same position as before... how do you determine the cap? Around and around we go.

Let me give you an example of what I'm struggling with. I am currently in the process of closing on a small multi-family. The NOI is $33,508. After some negotiating, we settled on a purchase price of $422,500. Higher than I wanted to pay but there is upside with renovating one of the units and drastically increasing the rent. Plus the area is nice and continues to appreciate. Anyway, assuming the property value is $422,500, cap rate would be 7.93%. Great. What does that tell me? I don't know. But... a recent appraisal came back WAY below at $180k. Everyone agrees this valuation is nowhere near reality but my lender won't lend now and I am fine walking away. My realtor asked the selling realtor what comps she used to determine the list price. She gave some examples but then said "The price also reflects the cap rate of the property." Well wait a minute... how can she determine the cap rate of the property if we're debating the property value? Cap rate at $422,500 is 7.93%. Cap rate at $180k is 18.6%. Clearly the $180k doesn't make sense but either does her argument that the list price was set to reflect the cap rate of the building. At least it doesn't really make sense to me.

Any help here would be greatly appreciated.