Warning: This piece contains spoilers about Sunday night's episode of "Mad Men."

Well, that was fast. The gang at Sterling Cooper Draper Pryce is thinking about taking their advertising firm public, selling shares of the company at $11 each and using the capital to expand more aggressively and try to become one of the big boys on Madison Avenue.

Would Don, Joan, and Roger get to ring the bell at the NYSE? Maybe, but don't buy the stock. (Stan Honda/AFP/Getty Images)

It’s a stunning turnaround for the "Mad Men" crew, coming just four years after they started the company, three years after the near-death experience of losing the Lucky Strike account and one year after a partner hanged himself in the office. But these are exciting times at SCDP, a time of limitless possibilities. The prospect of a huge payday has put stars in the eyes of Joan Harris, the company’s administrative czarina, who stands to pocket a cool million in 1968 in pre-great inflation dollars, equivalent to $6.7 million today.  (Given how she obtained her partnership, she earned it.) And the ever-smarmy Pete Campbell sees his cashing in on an IPO as a way to coax back his wife, Trudy, (played by official Wonkblog crush object Alison Brie), who would be better off without him, thank you very much.

Alas, we don’t have access to full financials of SCDP (if creator Matthew Weiner ever wants to have the camera linger on Joan’s meticulously prepared income statement and balance sheet, I’d be grateful). But from what we do know, should the company be thinking about going public? The answer gets at some bigger questions in how companies are (and should be) governed.

In modern America, the overwhelming majority of large companies organize themselves as publicly traded corporations, their shares freely available to be bought and sold by anyone with a brokerage account, the stock price a second-by-second referendum on the firm’s prospects. A handful of giant companies, like Cargill and Koch Industries, have remained private (and so have countless smaller firms). In professional services, like law firms and consultancies, the most common ownership structure is a partnership.

Which is better? There’s no right answer, of course, but rather a set of tradeoffs: Large private companies get to keep their detailed financial information secret and don't have to comply with a bunch of laws meant to protect shareholders, but they also can’t tap the highly convenient source of capital that are the public markets.

But professional services firms — whose “product” is ideas, services or advice — are a different animal. And while there may be successful counterexamples, there’s lots of reason to think they have no business being publicly traded companies. Sorry, Joan.

When investors buy shares in a company, they are buying a claim on the future profits the company will earn, and the raw tools that the company will use to earn them. When you buy shares of Procter & Gamble, you are buying an interest in the brand names of Tide detergent and Crest toothpaste and Gilette razors and in the factories and equipment used to make those products. You’re also buying a share in what can loosely be called the organization of P&G — a process for developing, marketing and distributing consumer products that has had great success over the years and manages to funnel the efforts of thousands of people into household name brands.

Now compare that to what you’re getting if you buy shares in a law firm, consultancy or an advertising firm like Sterling Cooper Draper Pryce.

There’s almost zero value in the firm's physical capital; the office space is rented, and the desks and typewriters and (today) computers are of minimal value. The brand name may have some value, but it is intimately linked to the individuals who lead it, which means they could walk out the door any day of the week; Sterling Cooper Draper Pryce wouldn’t be much of a powerhouse without Don Draper.

Moreover, those individuals who are creating value know exactly what they are worth and thus can demand a high share of the money they bring in, meaning that money isn’t going to shareholders. Think of it this way: In a law firm, if a partner has a stellar year, bringing in a new piece of complex litigation business that earns $10 million for the firm, she is going to demand that a large part of that $10 million show up in her own compensation, rather than be funneled to the entire group of partners. And she would threaten to leave if she didn’t get her way.

A corporate entity can own the Crest brand name. It can’t own Don Draper.

The latest episode of "Mad Men" began with an investment banker advising about a possible public offering; yet the remainder of the episode showed why a firm like Sterling Cooper has no business being publicly traded.

First, Don lets his contempt for the sleazy Jaguar dealer Herb Rennet get the better of him and drops the automotive account that the firm spent all last season coveting. Then Pete  bumps into his father-in-law at a brothel, which costs the firm the $9 million Vicks account. The rival firm Cutler Gleason and Chaough is in danger because one of the partners has pancreatic cancer.

So, if you’re a shareholder of SCDP or the version of the firm that is to merge with Cutler Gleason and Chaough, this is your essential dilemma: You will be highly dependent on the performance of a small number of erratic individuals and the arbitrary whims of clients. If the firm does well, the superstars in its employ will demand most of the returns. And if the firm does poorly, there won’t be any profits to go around.

If Sterling Cooper or most any firm like it were to go public, the basic equation would be: Heads the partners win, tails the shareholders lose. SCDP stock is a "Strong Sell."

Update: Ad Age found seven examples of advertising agencies going public in the 1960s, some of them small ones. But this does appear to be a thing of the past. "Just about any sort of agency IPO sounds impossible today, let alone one the size of SCDP," writes Matthew Creamer.