## Darvish - playing with the numbers

Apparently Yu Darvish’s father has recently said that it is “50:50” whether his son posts for the 2012 season.

Playing with a few numbers, it is not clear why he would want to do so.

The current projection is that it will take a \$55 million posting fee and a six year contract at \$75 million to land Darvish.   The posting fee is paid up-front, while the salary is of course paid over time.

Pardon me if I get a bit mathy here.  Money paid in the future is less painful than money paid today.  So econogeeks have created something called “net present value”, which is the amount of money today which equates to a stream of payments in the future.  At a discount rate of (say) 8%, and assuming that the \$75 million is paid at a rate of \$12.5 per year for each of the 6 years, the \$130 million paid to Darvish over 6 years is worth about \$113 million paid today.

That same \$113 million is the value of a six-year contract at \$24.5 million per year.

So, financially, a team that would be willing to pay a \$55 million posting fee and \$12.5 million per year should be equally willing to pay \$24.5 million per year for 6 years with no posting fee.

Darvish is currently making about 500 million yen per year in Japan (roughly US\$ 7 million).  He becomes a free agent after the 2014 season (3 years).

So let’s compare his income for the next 6 years under two scenarios:  he signs for \$12.5 million per year with the Blue Jays now, or he plays 3 years in Japan at \$7 million and then signs for \$24.5 million for 3 years.

all figures in \$millions

Japan               MLB

Salary,              2012                                            7                  12.5

2013                                            7                   12.5

2014                                            7                   12.5

2015                                          24.5                12.5

2016                                          24.5                12.5

2017                                          24.5                12.5

Total                                        \$94.5               \$75.0

Net present value  @ 8%     \$68                  \$58

This calculation is admittedly simplistic.  Darvish’s endorsements in Japan likely substantially increase his income, and the roughly 9% annual increase in baseball salaries would increase his salary in 2015 from \$24.5 to about \$32 million.  On the downside, he could get injured, or his performance could falter, reducing his value in 2015.

Still, this calculation begs the question:  why give the posting fee to the Ham Fighters when, by waiting 3 years, he could effectively keep it for himself?

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