The After Repair Value (ARV) is the value of a property after completion of a renovation.
For example, if you bought a house for $100,000, invested $50,000 into a cost-effective renovation, and it then appraised for $200,000, the ARV is $200,000. To estimate the ARV of a property, you can look at the comparable home sales and listings ("comps") to see what properties with similar characteristics in a neighborhood are selling for.
Using the BRRR real estate investing method, your budget of purchase price plus rehab would ideally be no higher than 75% of the ARV. For example, let's say you bought a property for $50,000 and invested $25,000 into repairs. That's $75,000 of invested capital. Now, when you go to a lender to refinance the property by taking out a mortgage, the home appraises for $100,000. The ARV in this example is therefore $100,000. Since most lenders require 25% down for non-primary residences and investment properties, you're able to cash out 75% of the appraised value of the property -- that's $75,000 which is is the entire amount you invested in the project.