Baseball Economics: Breaking Down Utley's Contract

In response to Jeff's comments regarding his disproval over the backloading of Utley's contract hurting the ability to trade him after his peak years, I decided to mix my finance background and love of sports to do an analysis of the VALUE of Utley's contract.

First off, the Phillies would never trade Chase Utley, Jeff, and prepare for an afterlife in Phillies purgatory for even mentioning that slander. Second, if Chase were to suffer a career ending injury, we have to pay him the money either way, so it wouldn't matter how much of the contract was left.

Now, let's get into the contract as it was originally signed:

Signing Bonus: 2 Mil
2007: 4.5 Mil
2008: 7.5 Mil
2009: 11 Mil
2010: 15 Mil
2011: 15 Mil
2012: 15 Mil
2013: 15 Mil

Total: 85 Mil/7 years

Now, Chase Utley will never actually see that 85 Mil, and not just because of taxes. To illustrate the VALUE of Utley's contract, I'm going to use the compound interest formula to show what Utley's contract will be worth at the receipt of his last paycheck. Then, I'm going to use the Time Value of Money formula to find the value of the contract in today's dollars. I'll compare that to a balanced contract, as Jeff suggested, and also a contract built around paying the highest dollar for "peak" performance, meaning his 29-32 aged years.

Before we start, we're going to throw out the signing bonus, since it will be a constant for all 3 contract types, and simply make extra work. The compound interest formula will calculate the future value of each contract year, by assuming that every penny is invested. It doesn't matter if Chase invests his money or not, this rate will only serve as a constant and will work both ways (when we find the Present value, too). Otherwise, we could just be boring and adjust the future rate for inflation. Anyway, the generally accepted finance rate of return for standard investments is 8% (11% Stock Market historical average - 3% accepted inflation). Here is the formula for compound interest:

Total = Principal x (1+Rate)^years

The first year, for instance, would read:

Total = 4.5 Mil x (1.08)^7
Total = 4.5 Mil x 1.71
Total = 7.71 Mil

So the first year of the contract will be worth 7.71 Mil in 2013. If you do this for each year, raising it to one less year each time (for example, year two would be raised to the 6th power) and add up all of the totals, you get 108.78 Mil.

Next, we find the Present Value of that sum using the Time Value of Money. The Time Value of Money formula states:

Future Value = Present Value x (1+r)^years

The math works as follows:

108.78 Mil = PV x (1.08)^7
108.78 Mil = PV x 1.71
63.61 Mil = Present Value

That means that if Chase's contract was settled in one lump sum today, he would be entitled to a check for almost 64 Mil, not the 85 Mil reported in the contract. The 85 Mil does not represent an actual number that will ever be realized. It's the addition of 7 static payments, at 7 different times (in actuality, the contract will be paid in hundreds, if not thousands of small increments, and may even be deferred with interest until well after his playing years).

Back to the point, though, on to the other contract types. The balanced payment model is actually a lot easier to compute since it represents an annuity and requires only one calculation for the compound interest instead of 7 (a lot of this could actually be simplified into one calculation, but I've taken the long way to illustrate things better). The annuity formula reads:



Now subtracting the signing bonus from the contract gives us 83 Mil. Over 7 years, that's an average of 11.86 Mil per year. So the math reads like this:

Total = 11.86 Mil x [((1.08)^8 - 1)/.08] - 11.86 Mil
Total = 11.86 Mil x [((1.85) - 1)/.08] - 11.86 Mil
Total = 11.86 Mil x [.85/.08] - 11.86 Mil
Total = 11.86 Mil x 10.63 - 11.86 Mil
Total = 126.15 Mil

We use the same Present Value formula from before to get 73.77 Mil. That means that the Phillies would be paying almost 10 Mil more in today's dollars to sign Utley for a balanced contract. So yes, the Phillies may have trouble trading his 15 Mil per season for the final 4 seasons. The net savings of 10 Mil in today's dollars, however, more than offsets any contract they have to eat down the road. In fact, the value of the final year of his contract in today's dollars is 9.5 Mil, which is less than the money they save by backloading it to being with. That means that they essentially get the final year out of him for FREE compared to a balanced contract that was one year shorter. So if worst came to worst and they had to trade him in the offseason before his final year, they could eat his entire remaining 15 Mil in order to net a few prospects, and still turn a small profit over a balanced contract of one year shorter. Or they could trade him with two years left and pay half his salary, while netting out at 0 or a slight profit and get players in return. All of this ignores the fact that given the market, and Utley's natural abilities, he may still be a bargain in 2012 and 2013 at 15 Mil.

I also did one more calculation, just to round out the picture. If the contract was built around his peak years, maybe resembling this:

2007: 7 Mil
2008: 10 Mil
2009: 12 Mil
2010: 15 Mil
2011: 12 Mil
2012: 10 Mil
2013: 7 Mil

It still adds up to 83 Mil (without the signing bonus) over 7 years. The math for this contract gives you a future value of 121.84 Mil and a Present Value of 71.25 Mil. That is a slight improvement over the balanced contract (because you're paying him less early on) but still doesn't compare to the current contract.

So what does this all mean...that the Phillies have some bright accountants who know how to design a contract. Chase also had no bargaining power and couldn't really squabble over details anyway, but he'll get his money and the Phillies will get their man (right after his wife is finished with him, that is).

On a sadder note, Vern Ruhle, former Phillies pitching coach died at 55 from cancer. That's a tragicly young age for anyone to pass. Vern was only with the Phils for a couple tough years, but reports around baseball say he was outgoing and a good man.