Shareholders of the bankrupt Hertz car rental company have, miraculously, avoided being wiped out. Precisely how much they will recover is less clear.

The private equity consortium that will acquire Hertz says the company’s current public stockholders will get a package worth $7.36 for each share. About $2 of that figure is in cash as well as direct new shares in the reorganised Hertz. The balance comes in the form of “warrants”, offering the option to buy into the new Hertz at a given price. These are a derivative security whose valuation comes from the famed Black-Scholes equation, which contains a variety of inputs. With Hertz shares trading at $6 a piece, Wall Street does not seem to agree with the maths involved.

In March, private equity bidders valued Hertz at $4.8bn. Three months on the same group of bidders has prevailed in an auction by valuing the company at $6.9bn. In the original bid, junior bondholders were to get a recovery of 70 cents on the dollar, which included equity in a restructured Hertz. Those bondholders will now be fully repaid and in cash. The bounty is so big that current Hertz shareholders will get cash along with the chance to become shareholders in the new Hertz — a highly unusual bankruptcy outcome.

Private equity bidders and Hertz have used a share price volatility input of 57.5 per cent in the Black-Scholes equation to determine the $5.47 value of warrants. Volatility is typically the swing factor in option valuation. The more volatile a stock, the more likely the option will swing into the money.

Investors, even retail players using the Robinhood app who swarmed into Hertz last year, are sceptical. Hertz shares trading at $6 reflect concerns not just about the warrant valuation but also the theoretical worth of Hertz more generally. Hertz shares, which traded as low as 66 cents this year, have proved a remarkable bargain. If you believe the new private equity backers, they still are. But the calculation has not convinced everyone.

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