It isn’t every day that a chief executive casually mentions at the end of a call with investors that his chief financial officer is leaving.

While Deepak Ahuja’s motives are unknown, the fact that Tesla is trying to fund its lofty ambitions on the cheap certainly may have contributed to workplace stress. Fourth-quarter results out Wednesday for the cash-strapped auto maker at first glance looked surprisingly strong. Tesla reported sales of $7.2 billion, which topped analyst estimates, and adjusted earnings of $1.93 a share,...