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The Actuary The magazine of the Institute & Faculty of Actuaries
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Discounting footballers

Football is a funny old game. The transfer market for footballers is even funnier. In August 2003, Juan Sebastian Veron, a Manchester United Football Club player, was ‘sold’ to Chelsea Football Club for payments totalling up to £15m. Two years before this, Veron had signed a five-year contract with Manchester United after transferring from Lazio, an Italian club, for about £28m. The media reported that Manchester United had made a loss of £13m.
This is wrong for many reasons:
– the £28m includes a price to secure Veron’s services for a guaranteed period of five years;
– the £28m also includes an amount to secure five years’-worth of options on re-negotiating Veron’s contract;
– the £28m needs to be written off over five years;
– we should consider Veron’s expected net present value to Manchester United.
So, what was the loss or profit to Manchester United on the transfer of Veron to Chelsea? There are three ways to tackle this question from an accounting perspective, an actuarial perspective, and an economic perspective.

Linear depreciation
The accounting treatment of a footballer requires the use of ‘terminal value’. This is the value of the player after the player’s contract has expired. Until the mid-1990s, it was acceptable for football clubs to pay transfer fees for footballers who were out of contract. In Europe this was found to be in breach of Article 48 of the Treaty of Rome (the Bosman case). The football community had argued that soccer was not an economic activity and that the Treaty of Rome did not apply. The European Court of Justice disagreed. The European Court of Justice added that the practice went against the principle of a free movement of labour.
The Bosman case says that we should equate terminal value to zero pounds. The £28m should be written off by an amount of £5.6m per year and the loss faced by Manchester United would then be £1.8m under simple linear depreciation.

Actuarial smoothing
The accounting treatment fails to take account of the time value of money. The £28m can be written off smoothly using an annuity. The crucial assumption is the interest rate. We know that Manchester United assets are risky. Therefore the interest rate would need a risk premium (see table 1).
Consider an interest rate of 7% per annum. The annuity to spread costs over five years would be 4.100. This would give an annual write down of £6.83m. After three years the future write-downs would be worth £17.92m. Hence the loss (on the transfer fee) would be about £2.92m. This, of course, ignores other cashflows that Veron would generate. Such cashflows also need consideration in a complete test of profitability.

Economic value
When Manchester United secured Veron’s services, presumably they thought that his expected net present value to the club was positive. Veron’s expertise in midfield was expected to bring trophies and cash to Manchester United. His talents would improve the skills of his team mates. Again, higher expected benefits for Manchester United.
Two years down the road and Manchester United felt that £15m cash beat Veron’s future expected net present value to the club. Chelsea felt that Veron would be a good acquisition. This was not odd. The same player could perform differently in another team. A deal was struck.
In essence, Manchester United made an assessment of future cashflows from Veron compared with future cashflows to Veron. This assessment must have included salary costs and bonuses to Veron, as well as competition prize money to Manchester United stemming from Veron.
The historical profit or loss made from Veron was irrelevant. Only the future mattered. Indeed, the actual profit or loss would be extremely difficult to gauge. The primary reason for this would be the difficulty in gauging the prize money to Manchester United attributable to Veron’s skills on the football pitch. Manchester United opted to sell.
This brings up a point about modern financial theory. Footballers’ contracts are littered with options. The employing club has options to renegotiate a new contract. A player may receive options to talk to other clubs for a new contract if a bid of a critical value is received. Such ‘real options’ are important when contracts are designed. However, they are extremely difficult to value.

The Chelsea factor
By assuming that clubs are rational, we can get an insight into transfer markets. The loss on Veron was unlikely to be £13m. And who in their right mind thinks that net present value matters to Chelsea?

Reference
Peter Antonioni and John Cubbin (2000), ‘The Bosman ruling and the emergence of a single market in soccer talent’, European Journal of Law and Economics, Volume 9(2), 2000, pp15773

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