Charging?

I have a voltmeter plugin in the cig lighter socket. It reads about 11.5 when
I trun on the master. Reads about 12.8 after engine start and after an hour
flight has worked up to maybe 13.7 or so. I plan on taking a known accurate
meter out Sat to check these reading.
My A&P says maybe the alternator needs rebuilt (at about $250). He says that
the voltage reg is solid state and either works or not - ie no adjustment.
I've had a couple of times when the bat needed a boost, so something is wrong.
Any comments before I start throwing money at the problem.

Chuck
Archer 2185B