In the baseline computation, on the one side is the sum paid, which is €222 million. On the other side is the sum of expected annual profits, revenues less wages, discounted, over his five-year contract. Using a 1% real discount rate and a 30% corporate tax rate, with 0% risk for injury, and making the revenue to be generated by Neymar as the unknown to be solved for, we can calculate the break-even point.
Under this baseline scenario, Neymar would need to generate €111 million a year for PSG to make zero profits. If the tax rate plus risk of injury rises from 30% to 50%, a more realistic case considering other payments and injury risks, and if we add the commission to the sum paid, this number jumps to €151 million a year. These figures are 38% and 52%, respectively, of the 2016 commercial revenues of the club.
It is highly unlikely that the Neymar deal will yield these numbers. Thus, PSG stands to lose.
One option would have been to offer Neymar a lower wage, but the wage is not the most important factor here. Halving his wage would require him to generate €92 million a year to break even, and even cutting his reported wage by three-quarters would require him to generate €80 million annually for PSG. These are formidable (and unrealistic) amounts.
This means that PSG has been prepared to pay more than Neymar’s expected economic value. One can think of it as a kind of bubble, though stock market bubbles usually arise in other ways, and in different circumstances.
The 2009 transfer of Cristiano Ronaldo makes much more economic sense. Here, again, the numbers are unconfirmed. Ronaldo was reportedly bought by Real Madrid from Manchester United for €94 million. For four years he earned about €11 million a year after tax, and subsequently earned close to €20 million a year after tax.
Plugging in these numbers in the baseline computation, and considering pre-tax wages, Ronaldo needed to generate about €40 million a year for Real Madrid to break even. This is equivalent to about 20% of Real’s commercial revenues at the time, or less than 10% its total revenues. It is probable that Real profited from this investment.
So not all transfers are bubbles. But looking at the top transfers by value, from Neymar’s move to Kevin de Bruyne’s €75 million move from Wolfsburg to Manchester City in 2015, it looks like the majority are bubbles. That means that the price paid was not subsequently justified by the net gains accruing to the purchasing club. Even at the time of purchase, this could have been expected. Why, then, are these trades done?