If you are interested in purchasing the rental, consider acquiring estimates from local licensed contractors and then make a determination--as for which is cheaper, much will depend on the property's exact location, size, extensive/cosmetic repairs, etc.

Asside from being a Real Estate Broker, I"m also a licensed contractor. The answer will depend on the house condition itself. In some cases it's better to tear down to a minimum and rebuild, reason being is that if a house is in bad condition it will be more labor intensive to repair. Many times you start with a remodel, and find out that more work is needed. That having been said, if you like the house, you might be able to expand the existing house to suit your needs. I reccommend a good architect to get you started, so that you can determine just how much house you can build based on the property size. In any event bear in mind that completely tearing down and rebuilding may increase your property taxes(there are ways around that)

Sarah - This depends on the price & location. Where we are located it is usually cheaper to renovate than start from scratch.
The Marie Souza Team
Cape Cod, MA
508-790-2000