Elon Musk, the billionaire chief executive of Tesla, has said the tweet that cost him and the company $20m (£16m) each in fines by the US Securities and Exchange Commission was “worth it”.

Elon Musk (@elonmusk) Worth it

The tweet, which was posted less than an hour before Musk went on to tweet that he would take a break from Twitter “for a few days”, was in response to a question from a Twitter follower.

The SEC in September charged Musk, 47, with misleading investors with tweets in August that said he was considering taking Tesla private at $420 a share and had “funding secured”. The tweets had no basis in fact, and the ensuing market chaos hurt investors, regulators claimed.

Tesla and Musk have agreed to pay $20m each to financial regulators and, under a settlement, the billionaire will step down as the company’s chairman but remain as chief executive.

Under the settlement agreement, Tesla needs to appoint an independent chairman by 13 November. James Murdoch is seen as a leading contender. Murdoch is set to leave the role of chief executive of 21st Century Fox when the entertainment company completes the sale of the majority of its assets to Disney, and will be succeeded by his brother, Lachlan. He joined Tesla’s board last year as a non-executive director and has reportedly said he wants the job of chair.

Under the SEC settlement, Musk will also have to comply with the company’s communications procedures when tweeting about the firm. The SEC charged Tesla with failing to have required disclosure controls and procedures for Musk’s tweets. The SEC said the company had no way to determine if his tweets contained complete and accurate information.

Tesla last week announced it had made a $312m profit in its third quarter – far more than analysts had been expecting. On a conference call with analysts, Musk said the company had delivered more cars in the past quarter than it did in all of 2016. He also said Tesla expected to remain profitable in the next quarter and for “all quarters going forward”, except those in which large debt payments are due.