By Ronald Barusch

Updated Sept. 5, 2016 7:59 p.m. ET

It is once again time to consider the usefulness of investment-bank fairness opinions. The latest reminder of their dubious value, at least in some deals: Lazard’s fairness analysis for SolarCity ’s special committee relating to the company’s acquisition by Tesla Motors. A securities filing Wednesday disclosed a $400 million arithmetic error in Lazard’s analysis that, when corrected, turned out to have no impact on the opinion. But I would argue that the no harm-no foul result is just more evidence of how little information fairness opinions convey.

Of Lazard’s roughly $10 million fee for its work on the deal, $2 million was specifically allocated and paid in connection with the fairness opinion. Plus the committee may pay Lazard as much as $2 million more in its “sole and absolute discretion.” Unless a competing bid comes in at this late stage (and Lazard has already contacted several potential bidders who so far haven’t bit), none of this compensation would seem to be for acting as a “finder” for the deal; Lazard wasn’t hired until after Tesla announced its takeover proposal.

Fairness opinions became all but mandatory after a 1985 Delaware Supreme Court opinion slammed a board for not doing enough homework on a deal it approved. Ever since, directors selling a company have insisted on what might be called a “getting their ticket punched” exercise by getting an investment bank to wave its magic wand of fairness over a deal.

The true value and usefulness of fairness opinions have often been questioned over the years and indeed, in the case of SolarCity, the opinion doesn’t seem to come with much useful information.

For example, in reaching its determination of fairness, Lazard looked at four different discounted cash-flow valuations. When the special committee was making its decision (before the valuations were corrected for the error), in all of them, the high end of Lazard’s estimate was more than double the low end. In one of them, the top of the range was 400% of the bottom. In another, the low end was about a quarter of the unaffected price. Since investment banks generally take the position that a value at any point in its fairness range is as likely to be accurate as another, the usefulness of these ranges is highly questionable.

Besides, it isn’t clear how the fairness analysis could have made much of a difference. A page-one story in Thursday’s Wall Street Journal reports that SolarCity was facing a cash squeeze, and 15 institutional investors passed on either acquiring SolarCity or injecting equity. That raises the question of what alternatives there were. The seriousness of the problem is highlighted by the fact that management prepared two different sets of projections in connection with the deal: A “Liquidity Management Case,” which was given only to Lazard and the special committee, and a “SolarCity Unrestricted Liquidity Case,” which was also shared with Tesla. The first produced a discounted cash-flow valuation range of $5.04-$20.64 a share in one analysis. Given the market value of the deal was $25.13 a share at the time that it was voted on by the board, it doesn’t sound like too much sophisticated analysis was necessary to find the path forward.

Then there was that “computational error,” which double-counted some of SolarCity’s projected debt in the spreadsheets Lazard used to prepare its fairness opinion. Lazard discovered the error three weeks after the special committee had approved the deal. It resulted in a $400 million overstatement of SolarCity’s debt. Lazard was still able to reaffirm its opinion after the error was discovered, undoubtedly helped by those huge valuation ranges. But $400 million represents more than 20% of SolarCity’s current market capitalization.

This isn’t the first time a significant error has been incorporated into a fairness evaluation. Goldman Sachs Group was involved in one two years ago in connection with Tibco Software Inc. that resulted in litigation and a roughly $30 million settlement payment by the bank.

It isn’t that investment banks don’t provide valuable advice. It’s just that using them to provide the patina of fairness has produced a steady stream of fees in exchange for something that often doesn’t add discernible value.

Mr. Barusch is a retired M&A lawyer who writes about deal making for The Wall Street Journal.