Is $3,850 to install a gas tankless water heater a fair price?

My wife and I just moved into our new house. We knew going in that we had to replace the water heater soon as it is 10 years old and has corroded connections. My wife is a little worried about going with the $3,850 option, even though it comes from a well-reviewed company. I'm unsure if the 1/2" gas line piping compatibility plays a role in the price variation. From what I can tell, the company is insured based on their website. I'll have to see the length from the gas meter in the house, it might be relatively close. The plumber felt that a permit wasn't needed as he felt it would eventually just lead to an increase in property taxes, but he was fine pulling them if requested. None of the other quotes had permits either.