Need help determining fair amount due brother from real estate owned by my mother and me after her passing.

In 1997, my mother and I purchased and shared a home. She paid cash and I financed my portion. We split all costs for improving the house evenly. When my mother left the home approximately 3-4 years ago for a nursing home, the home was quit deeded to me. After she moved out, I maintained the property, upgraded the kitchen, purchased a new water heater, and painted the interior (did not share the cost). My mother passed away in March and consequently, my brother has a ¼ stake of her portion of the home. He wants his portion paid to him now. I will need to refinance or sell my home in order to pay him, but I don't know if he is due ¼ of the current assessed value if I refinance or ¼ of the sale price if I sell, or if he's due ¼ of the assessed value prior to the upgrades I paid for, or if he's due ¼ of the assessed value at the time the home was quit deeded to me. Basically I don't know how to calculate his portion fairly.