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In the beginning, there was a trick. Or, to be more precise, there were several tricks. Banks, stockbrokers and lawyers spent years ensuring that shareholders were refunded money they weren't owed. In particularly egregious cases, they received several refunds on taxes that were only paid once. In industry jargon, the dividend-stripping schemes are known as cum-cum and cum-ex, and according to reporting by ZEIT ONLINE, ZEIT and German public broadcaster ARD, they resulted in the German state losing a vast amount of money.

Total amount lost by the state due to the tricks: at least 31800000000 (31.8 billion)
Of that, damages resulting from legally disputed tax tricks (cum-cum): at least 24.6
Of that, total lost by way of probable organized crime (cum-ex): at least 7.2
Number of people thus far convicted: 0

Individual banks and funds have likewise shorted the state billions of euros. To do so, they engaged in circular trading, repeatedly claiming tax refunds from state coffers.

Total amount of refunds claimed by a single American pension fund from the German state on the basis of repeatedly issued tax credits: 53882080.94
Number of beneficiaries of this pension fund: 1
Amount spent by the fund on short-term German stocks: 6400000000 (6.4 billion)

Number of credits issued to a tax cheat for a tax sum that was only paid once: Up to 10

Experts have long been aware of the tricks, and there were warnings.

1992 was the year in which State Commissioner August Schäfer first warned of such deals.
2012 was the year in which lawmakers first made cum-ex deals illegal.

Number of whistleblowers who warned of criminal activity during that time period: 5

Many large banks likewise earned money from the deals.

Number of German banks that participated in the presumably illegal deals: 40
Banks and funds around the world alleged to have taken part in these activities: more than 100
Amount of money that 7 banks and funds have thus far paid back: about 1000000000 (1 billion)
Number of suspicious cases identified by the Federal Central Tax Office: 100
Number of finance ministers who could have put a stop to the tax theft during their tenures: 4 Theo Waigel (Christian Social Union), Oskar Lafontaine (Social Democratic Party), Hans Eichel (SPD), Peer Steinbrück (SPD)

What the state could have done with €31.8 billion:

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Covered the costs of the refugees who came to Germany over more than one year. The German federal government will spend €21.3 billion on refugees in 2017.

© Miguel Villagran/Getty Images

Doubled payments to Hartz IV welfare recipients for a year. In 2016, the state spent around €34 billion on providing basic financial security to those on welfare, roughly the same amount lost to the tax tricks.

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Built 1,200 kilometers of highways.

How the Damages to Taxpayers Were Calculated

It isn't easy to estimate the damages caused by the financial tricks employed by banks, brokers and lawyers. Many of the transactions were hidden and are difficult to reverse engineer after the fact. The calculations in this graphic are based on computations undertaken by finance expert Christoph Spengel, the chair of international taxation at the University of Mannheim. It is important to differentiate between two financial tricks: cum-cum and cum-ex.

Cum-cum is a legally disputed dividend-stripping practice in which a bank assists foreign investors in receiving a tax refund to which they do not have a claim. Broadly speaking, it looks like this: The bank sells shares belonging to a foreign client one day before the payment of dividends to, for example, a German stockbroker. Once in possession of the shares, that broker can then claim a refund on the dividend withholding tax that the foreign investor would not have been eligible to receive. After the dividend is dispersed, the shares are immediately sold back to the foreign investor. The tax refund is divided among those involved. And the state is poorer as a result.

In the years from 2001 to 2016, taxpayers lost at least €24.6 billion due to this method, Spengel estimates. That averages out to about €1.5 billion per year.

How is this sum calculated? The first step undertaken by the finance expert was to add up all the dividend disbursements paid by German companies to foreign investors: around €311 billion. Assuming a withholding tax of 15 percent (as Germany has agreed to with around 80 countries, with a rate of 25 percent applying to those remaining) along with the 5.5 percent German reunification tax, one arrives at maximum damages of €49.2 billion. If one assumes that every second foreign investor took advantage of the cum-cum scheme, one arrives at a total of €24.6 billion. Spengel considers this assumption to be conservative. "The majority of foreign investors are institutional investors, meaning banks and funds," Spengel says. "They would have been poorly advised not to have used the method." (You can examine the details of Spengel's calculations here.)

A variation of this trick is known as cum-ex. This method is much more complicated and involves a tax bill being paid once and then claimed as a refund from the tax office twice or even more times. The profit thus generated is disbursed among those involved in the deal. (To see exactly how the trick works, click here.) Such deals were made illegal in 2012. To estimate the damages to taypayers, Spengel used data from the securities service provider Clearstream. Accordingly, the damages for the years 2005 to 2012 total around €7.2 billion, for an average of over €1 billion per year. (You can examine details of the calculations here.)

Translation: Charles Hawley