Tesla Inc. is making an operating profit of more than $3,000 on each sale of the current low-price version of its Model 3 sedan, but would likely lose nearly twice that amount if it sold the vehicle at its long-promised $35,000 price tag, according to a new estimate from UBS Securities LLC.

The Model 3’s profitability is a critical issue for the electric-car maker, which began selling the vehicle a year ago as it sought to move from a luxury niche into the mass market, and end years of losses.

The...