The Bay Deal and the Time Value of Money

One thought process seems to be that Jason Bay and agent Joe Urbon were silly to take what could be a heavily back-loaded contract from the Mets in favor of Boston’s deal which offered more cash upfront. The idea stems from this Peter Gammons piece which includes this nugget of information:

While the Mets offer is four [years] for 65 [million], it’s so backloaded that I’ve been told by Mets people that it’s far less than what the Red Sox were offering in present-day value

Present-day value is important because $100 today is more valuable than $100 a year from today. If the two offers were equal in dollars, however constructed differently, with one deal being front-loaded and the other back-loaded, then the agent should have his player sign the front-loaded contract. That scenario doesn’t match reality though. Boston reportedly offered four years and $60M while the Mets offered four years and $66M. More present-day value or not, Urbon and crew were correct to take the Mets offer. Here’s why.

Let’s assume Boston offered Bay 4/$60M split evenly across the four seasons; which is to say $15M in 2010, 2011, and so on. Meanwhile New York’s offer is more in total dollars, but most of the payout is located in the final two seasons. For our purposes, let’s say the money breakdown is 10/15/20/21. Using the time value of money formula and a discount rate of one’s liking, you can quickly figure the adjusted totals in present-day value. In this example, Boston’s deal is worth roughly $56M while the Mets’ offer is worth nearly $61M, or a spread in $5M, almost identical to the unadjusted spread.

Say one gets really aggressive with the discount rate and bumps it to 10% with the same contract breakdown. The Boston offer would be worth $52M in present-day value while the Mets’ offer worth $56M. Closer, but still no cigar. Keep that discount rate and get creative with the back-loading, say, 7/12/22/25; it’s even tighter at $52M and $55M. Still though, the Mets offer is worth more.

Barring some really ridiculous discount rate or extensive back-loading of the contract, there’s just no way around it. New York offered more dollars.