"Overall there are many, many risks that treasurers have to face, and certainly the economic uncertainty is top of mind," Miarka said during a webinar last month. "The last thing the European economy right now needs is uncertainty. Just believing that there is a meaningful amount of uncertainty, that already has an economic impact now."

Effects of the Prospective Brexit

The EU treaty sets a two-year timeframe for negotiating new agreements if a member decides to leave the union. Given the prospect that other countries might decide to follow the U.K.'s example, the EU would have little motivation to make the new trade arrangements attractive for the U.K.

"Maybe I'm a little too cynical, but I would believe that the EU would make a point not to make it too easy for the U.K. to negotiate," Miarka said, adding that if the U.K. exited the EU but maintained the advantages of EU membership without the obligations, "that would have a huge knock-on effect on any potential countries that want to move out, and that's not in the [EU's] political interest."

The Greenwich survey showed more than half of the treasurers surveyed (52%) say that if the U.K. decides to exit, that exit would not be orderly.

Stephen Chipman, CEO of Radius, a Boston-based consulting company, noted that 50% of multinationals headquartered elsewhere in the world have their EU headquarters in the U.K., and cited transfers and taxation as one area in which a Brexit could pose significant risk for multinationals operating there.

"There is a real possibility of increased withholding taxes on the repatriation of profits and dividends," Chipman, pictured at left, wrote in an email. While an EU directive provides relief in this area, in the case of a Brexit, "a U.K. company with subsidiaries in EU member states would need to rely on the U.K.'s extensive network of double-tax treaties to prevent effective double-taxation on intra-group dividends, interest, and royalties. The potential imposition of withholding taxes on the repatriation of dividends (for example) out of Europe via a historic U.K. holding structure may become an issue for a large number of multinationals."

Richard Johnson, vice president of market structure and technology at Greenwich, noted on the firm's webcast that the EU's passporting system allows companies that set up an office in the U.K. to do business in all the rest of the countries that belong to the EU.

"Presumably that would go away in the event of Brexit, or at least be put considerably at risk," Johnson said. "If the vote is for Brexit, U.S. companies will look to mainland Europe in terms of growing their operations."

Chipman noted that the loss of passporting would also affect financial institutions. "U.S. firms such as Goldman Sachs and JPMorgan have … operated across the EU from their London base," he wrote. "A Brexit would put an end to the passporting arrangements, and any bank operating from the U.K. would need to instead establish a branch or subsidiary in another EU member state."

A Brexit could also complicate multinationals' data operations going forward if U.K. policies on data privacy run counter to those of the EU, according to Chipman.

"For businesses processing large volumes of personal data, this would no longer be viable if the U.K. government's surveillance powers are considered to threaten data privacy rights in the EU in the same way as the activities of the U.S. [National Security Agency] have been construed," he wrote. "If so, then it could well be the case that transfers of EU data to the U.K. are deemed unlawful, which would be a real problem for all the U.S. businesses handling their EU data through or in the U.K."

Currency Impacts

Perhaps the most immediate concern for multinationals operating in the U.K. is the effect the vote will have on the British currency. Since the referendum was announced earlier this year, the British pound has underperformed against the dollar and the euro, and the cost of hedging sterling has risen.

Karl Schamotta, head of enterprise risk management at Cambridge Global Payments, a Toronto-based foreign exchange specialty firm, pointed out that the referendum could trigger FX volatility no matter which way the vote goes.

"There's risk in the event of an exit that sterling falls dramatically and we have a lot of turbulence as a result," said Schamotta, pictured at left. "You also have the risk that if there is a vote to stay, we have a big relief rally. Both can create a lot of uncertainty for a corporate treasurer."

The FX market suggests there's a 30% to 40% probability of a U.K. exit from the EU, he said. "There has been some depreciation but not nearly as substantial as what we would see in the event the vote goes through."

Companies in the U.S. and Canada have done a substantial amount of hedging of those risks, according to Schamotta. A few months ago, there was "quite a lot of forward activity," as companies locked in their exchange rate on future payments, he said. "More recently, we've seen skyrocketing implied volatility levels, which implies huge demand for hedges against sterling weakness, both against the euro and the U.S. dollar.

"One- and two-month vols on sterling have gone crazy over the last few weeks here, to levels last seen around the financial crisis, around 2009," he added.

Schamotta predicted that sterling could fall 10% to 15% on the news that British voters had voted to leave the EU and the euro would lose about 5%, heading toward the 1.08 level against the dollar. On the other hand, given the decline that's already occurred, sterling could rally 5% to 10% if the British vote to stay.

Schamotta warned that any relief rally would be tempered by the damage the Brexit referendum has already done to the U.K. economy. "Lots of surveys indicated businesses were cutting investment and slowing hiring, or putting on absolute hiring freezes," he said. "The lagging effects of that are likely to hang on the U.K. economy for a while."

He also noted concerns about the possibility of FX market dysfunction in the wake of the British referendum and said big banks are planning for the possibility that liquidity dries up or price discovery becomes difficult when the poll results are announced.

"If a treasurer expects they're going to be able to enter or exit a position very smoothly in the wake of an announcement or even as polls come through, that may be a dangerous assumption," Schamotta said.