On Wall Street, financial engineering masquerades as vision. When it works, you get to be called the Oracle of somewhere or other. If it works for only a short period, you can still get rich. What a country.

Which brings us to one of the biggest takeover battles in an age: Valeant Pharmaceuticals' unsolicited bid for Allergan.

Valeant is the product of cynicism that doubles, as is frequently the case, as a brilliant business model. It's a drug company that doesn't develop drugs. Instead, it runs a serial takeover operation, furiously buying companies and products to propel its growth. After easily swallowing a bunch of gel caps, Valeant is now trying to wolf down the horse pill of Allergan, the maker of Botox, in a deal valued at around $53 billion in cash and stock, Valeant's biggest acquisition yet.

Valeant's notion is that the pharmaceutical industry is made up of a bunch of dreamers who waste precious shareholder dollars actually researching and developing drugs. There's a kernel of truth here. Whole swaths of the drug industry, especially in biotechnology, have never had a return on capital. Fewer dollars have come out than have gone in.

Valeant's revelation was that it could slash the R.&D. budgets of its newly acquired operations.

"Pharma is a spoiled industry," Valeant's chief financial officer, Howard B. Schiller, told me, spendthrift and reliant on the lavish profit margins from new drugs. And anyway, he points out, most big drug companies do lots of mergers and acquisitions, just as Valeant does. "What differentiates us from other companies is the number of transactions and the speed with which we are moving."

The second cheeky crux of Valeant's business model is to hardly pay any taxes. In one of those is-that-really-legal? maneuvers, the much-larger Valeant bought the much-smaller Biovail in 2010. Scratch that. Technically, Biovail bought Valeant, relocated officially to Canada, and then changed its name to Valeant and left its management in the United States largely intact. This switcheroo allowed Valeant to magically lower its tax rate. Biovail also had a fandango of an operation in the Barbados, which lowered its taxes even further. Valeant now benefits from that as well.

Valeant's stock has risen about 850 percent since the beginning of 2010. Because of that, Valeant's chief executive, J. Michael Pearson, a former McKinsey consultant, became one of those beloved Wall Street comets that streaks across the sky, as analysts look agape and skeptics gather.

So we came to 2014 with Valeant looking for something new to buy. In April, Valeant teamed up with hedge fund manager William A. Ackman to make its hostile Allergan offer. This also came with a seriously-that's-legal? wrinkle: Valeant and Mr. Ackman agreed on a joint bid to buy Allergan, and then the fund manager bought nearly 10 percent of Allergan before the bid. Valeant made its generous proposal public, and Mr. Ackman was sitting on a huge paper profit. (Fear not, this isn't insider trading. The rules are not just that you trade on material, nonpublic information, but that you got it from someone who wasn't supposed to tell you, in exchange for something of value.)

In fighting off the bid, Allergan has engaged in an exaggerated show of disbelief that anyone would deign to offer shares so louche as Valeant's. Last week, in a presentation aided by two forensic accounting firms, Allergan pointed out that gorgeous-looking Valeant appears rather distended and puffy up close, as if it had hit the Botox too many times.

The central question that Allergan and the critics raise is: Does Valeant create any value at all? Nobody really knows if Valeant is doing anything that makes money, or is just engaged in prestidigitation that never gets anywhere.

All serial acquirers are infernally opaque. When Valeant buys something, it incurs costs—for instance, to pay severance to fired workers. It absorbs new assets and revalues them. And it reorganizes its operations. Valeant and its boosters argue that these costs are one-time in nature, while the newly acquired operations generate revenue and profit for many years.

In the first quarter, Valeant reported a loss of $22.6 million, measured by generally accepted accounting principles. The company had negative net income in three of the four years from 2010 to 2013. Wall Street believes that G.A.A.P. net income is only for the hopelessly naïve and prefers an adjusted number that more truly reflects the underlying economic reality. And in the first quarter, Valeant made $600 million on the adjusted number that Valeant and Wall Street prefers.

Mr. Ackman has experience betting against complex financial operations, and he told me Valeant is the real deal.

"Superficially, Valeant has some of the indicia that are suggestive of a short, but when you study the facts, you realize that it is a great company," Mr. Ackman said.

The problem is that it's almost impossible for an outsider to judge whether Valeant is paying the right prices for its new acquisitions or overpaying, whether it is really generating much organic growth from its products, and what its true costs are.

One question is whether the company actually generates much cash. Because it takes over companies serially, an intellectually honest assessment of its business would consider the "one-time" charges not so one-time at all.

J. Edward Ketz, an accounting professor at Penn State University, took the company's cash flow and adjusted it for all the spending from acquiring companies and paying the restructuring costs. By Professor Ketz's reckoning, Valeant has sent more than $1 billion in cash out the door each of the last four years and was negative $5.4 billion in 2013 alone.

Mr. Schiller, the chief financial officer, thinks that's a silly measurement that inherently penalizes any acquisition the company makes. (He also disagrees that Valeant is opaque, pointing out that it breaks out the costs of its acquisitions in great detail.) The company's supporters argue the returns on Valeant's investments have been steadily high, in the midteens.

But then one looks at the company's rising debt. Adding all of its commitments, Valeant discloses that it has $23.4 billion in debt, a number that's been rising steadily. Its operating cash flow was only $1.3 billion over the last 12 months. That's a low 5 percent coverage ratio. One theory why the company wants to buy Allergan is that the target has lots of free cash flow and little debt.

In its eagerness to complete the deal, Valeant is looking more and more like a summery bull market nostrum that requires too much suspension of disbelief.