Earlier this week, several sources reported that Jason Bay has agreed to terms on a contract with the Mets. The contract is currently pending a physical, but is reported to run for four years and $66 million, with a vesting option of slightly more than $14 million. Previously, the Red Sox reportedly offered Bay a contract that would have paid $60 million over four years. For the moment, let’s ignore the vesting option (which reportedly vests easily-that’s a discussion for another day). Interestingly, Peter Gammons told WEEI that the Mets offer is “so back-loaded that [he had] been told by Mets people that it’s far less than what the Red Sox were offering in present-day value.” This statement set me off on a quest to make $6 million dollars disappear in the sands of time.

Back-loaded contracts were once all the rage. In the early half of the go-go Noughties, teams back-loaded contracts to postpone the full brunt of the pain. On first glance, this type of contract structure looks like the kind of shoddy amortization that felled the housing market a few years ago. However, when interest rates are high and investments offer strong returns, back-loaded contracts can be useful. Conversely, when interest rates are low and the economy is weak, they are less useful. To understand why, we must understand the concept of present value.

The value of money is a function of, among other things, the time at which it will be acquired. If a team defers payments to a player, it can spend more on current players. On the other hand, a player who receives deferred payment loses the ability to keep that money in his investment account, where it would likely earn interest. Payments later are effectively smaller than payments now.

The amount by which they are smaller depends on our choice of a discount rate. A discount rate is a combination of two separate but not unrelated factors: the expected rate of inflation over the time period in question and the rate of return on the next best investment. The sum of these two numbers is our discount rate. Inflation can be a tricky thing to predict, particularly under current economic conditions. However, one indicator macroeconomists use is the TIPS spread, which is the difference between the interest rates on a Treasury bond and its inflation-protected analog. Jason Bay’s contract is for four years, so we can use the spread on five-year Treasury bonds, which is currently 2.10 percent. This spread suggests an estimate of average inflation over the next five years is slightly more than two percent. In reality, the actual rate of inflation could be higher or lower.

The rate of return on alternate investments is a harder number to estimate. Although the economy has been slow, teams may use the money in any number of ways, including signing players that might put them into the playoffs. Let’s assume a rate of return of three percent, a modest return for a somber economic climate. That would give us an overall discount rate of five percent.

How would the present value of the various contracts be affected by this rate? First, let’s discount the Red Sox offer of $15 million per year for four years. In the first year, we won’t discount at all. In the second year, we’ll discount by five percent. In the third year, we’ll discount by five percent two times, and in the fourth year, we’ll discount by five percent three times. It looks like this: 15+15/1.05+15/1.05^2+15/1.05^3 = 55.8, so $55.8 million will be our baseline of comparison.

Now let’s imagine four different back-loaded contract structures from the Mets (the exact terms have not been reported).

           2010   2011   2012   2013  
Option 1   16.5   16.5   16.5   16.5
Option 2   13.5   15.5   17.5   19.5
Option 3   10.0   13.5   19.5   23.0
Option 4   10.0   10.0   21.0   25.0

And here are the comparisons with the Red Sox’ offer:

            Option 1   Option 2   Option 3   Option 4 
Mets         $61.4      $61.0      $60.4      $60.2
Red Sox      $55.8      $55.8      $55.8      $55.8
Difference    $5.6       $5.2       $4.6       $4.4

For Option 1, the net present value using a five percent discount rate is $61.4 million, which exceeds the Red Sox offer by $5.6 million. For Option 2, the present value is $61 million, which exceeds the Red Sox offer by just less than $5.2 million. For Option 3, we get $60.4 million, which is $4.6 million more. Finally, for the aggressively back-loaded Option 4, we get $60.2 million, which is still $4.3 million more than what the Red Sox were offering. It just doesn’t seem possible to get a contract back-loaded enough to make it worth less than the Red Sox offer unless the payments stretch out for nearly a decade.

However, you may be wondering about my choice of a discount rate. After all, it is the sum of two highly uncertain variables, and therefore it is also highly uncertain. What if we used a different discount rate? In the chart below, I have graphed the four options from above and discounted them each by four percent (blue), five percent (red), six percent (green), and seven percent (purple). I have also overlaid a transparency on each chart that reflects the Red Sox offer, discounted in the same fashion.

Bay Chart

Take a look at Option 4, the most back-loaded of the four. Compare the purple lines for both the transparency and the main series. Now look at the vertical area between the two. On the left, the Boston offer exceeds the New York offer; on the right, the two are reversed. However, the distance between New York and Boston is larger on the right than the difference between Boston and New York on the left. Thus, even assuming a higher discount rate and aggressive back-loading, it does not appear possible to make the contracts equal in value.

It is important to note that the usefulness of back-loading for teams is greatest when salaries are rising at a high rate from year to year, inflation is high, and the economy (and revenues with it) is strong. None of these descriptions fits the current economic climate. Although the Mets ownership, which reportedly invested money with Ponzi artist Bernie Madoff, apparently once believed in the possibility of consistent returns in the 10-13 percent range, that simply isn’t realistic today. Without returns like that, back-loading can lead to contracts that are albatrosses later on. Even in the early 2000s, when the economy was stronger, there were plenty of examples of back-loaded contracts that teams were happy to be free from. Given that Jason Bay is likely entering a slow decline, the Mets will breathe a sigh of relief when this back-loaded deal has run its course.

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Interesting read. There's still examples out there of contracts from the early 2000's. At least one I can think of is the deal Todd Helton signed in 2003: 16.6M in 2010, 19.1M in 2011, and a whopping club option 23M in 2012 (4.6M buyout). I'll say this for the Mets, at least they're not signing Bay to a 9-year contract.
A nice article on the whole, and a good attempt at sharing the concept of present value with a non-technical audience. I'm not sure I agree with your views on discount rates entirely, but that's another matter. Might I suggest that you insert the word "incremental" in your definition of discount rate? Specifically the discount rate would be better defined as the sum of the rate of inflation plus the INCREMENTAL return on the next best investment.
Could there be an even more backloaded option? For example, Albert Pujols has 12M of his current contract deferred until 2020-2029 to be paid in 1.2M annual installments. At 5% and 6% long term average discount rates, the 12M is worth only 4.24M and 3.47M, respectively.
You're right, it's possible. I didn't include such contract structures because they would not be as clear in the visualization. However, here's an example:

2010: 8MM
2011: 10MM
2012: 10MM
2013: 10MM
2014: 10MM
2015: 18MM

Even with a 7% discount rate, that deal is still worth more in present value (54.7MM) and the Red Sox offer (54.4MM).
Good article, Tommy. Not sure whether this is in play with the Bay contract, but "backloading" can also refer to deferred payments after the nominal end of the contract. Manny Ramirez is under such a deal - he'll be receiving payments from the Dodgers 2 years after his current contract expires. And if I'm not mistaken, his deal with Boston called for deferred payments until 2025 or so.

A contract structure that pays Bay $10M/year through 2013 and defers the remaining $26M over the next 5-6 years might give him a lower NPV than a straight-line $15M per year Boston deal.
I always wonder why more teams don't front load contracts, since a) most free agents production will decline over the course of a contract b) they are much more certain of the financial structure and need of the franchise in the coming year then a few years down the line. C) as the players contract goes on, the team actually gets increased payroll flexibility to use as new needs arise. I realize because of inflation front loading means that the money is worth more, but without actually calculating it I imagine the difference would not be huge. Espeically if its a gradual decline instead of a steep one.

See arod's contract as an example of this.
I always thought the same thing, but the MBA=types would call this the opposite of "net-present-value analysis" and call it a bad deal.

Also, getting what you want NOW and paying for it LATER has unfortunately, been the American way for a while (and led us into the economic mess we're in now).

The Dodgers and Mets are apparently on very shaky financial ground and thus are more susceptible to backloading of contracts.
I'm unsure why MLB allows the backloading / deferring of contracts. It can really hamper a team's future. It's similar to a NBA team's trading away future draft picks - something the NBA has limited teams from doing.
Others have caught your oversight w/r/t contracts that backload beyond the end of the nominal contract term.

I think you also might want to consider the way in which the discount rate might be different for Bay and the Mets. They likely have very different "next best investments" and very different risk tolerances.

I'd bet, on that view, that the Mets get more value out of backloading than Bay gives up. So maybe that means it is more efficient to backload these things?

One last comment. You talk about albatrosses. The last year or two of a bad deal never gets paid in full. The team always pawns the guy off on another team for 20 cents on the dollar, 30 cents on the dollar, whatever. So there's an advantage to long-term deals.

Consider Team A's 5 year offer at 10mm AAV versus Team B's 4 year deal for the same total value, 50mm, but an annual AAV of 12.5. Team A may have an albatross at the end of the contract, but if they can get another team to eat ANY part of the player's salary in Year 5, then they've spent less than Team B. And the total outflows aren't the only advantage. They've spend less in the early years, which has a discounting value; they've kept comps down for future free agents and arb cases, which are always keyed to AAV not total contract value; and they've retained a longer control over the player, which is great if he doesn't stink it up at the end of the deal.

You can play the game again with a less charitable example. Team A offers 4 x 10, Team B offers 5 x 9. B is a much bigger contract. Like 22.5% bigger in absolute value. If B can get a team to take HALF of the player's final year contract off their hands, though, it'll be the same absolute $$ going out, but with the advantages of a lower AAV and backdating. And of course, longer control and lower comps.

This is why MLB HATES short, expensive deals. Joe Sheehan, god bless him, doesn't buy this math. In his defense, teams rarely do this as prudently as I have, and instead put way too much cash on the backend.
I've also read ($18 million in year 1, $15 million annually after) that Boston "front-loaded" part of the Lackey deal. Could be the offered the same type of deal to Bay.
My only concern with this analysis is that you are hypothesizing on an "alternative investment" as though it could be equities or bonds or some other investment vehicle; but in fact, we know what the investment vehicle is: an MLB franchise.

I think it would be more worth while to look at the historical trending of MLB franchises in major markets and look at what return they see on their working capital in these large markets to arrive at a truer rate of return. You may also find there is a bump (or not, in the Mets case) when new stadiums are built.

The discount rate is critical and I feel like you glossed over the second aspect of it. While we cannot know precisely what investment in the franchise produced what return, I think a worthwhile secondary analysis would be to determine the overall return on working capital that a MLB franchise is likely to see.
I think it's probably wrong to assume that the alternative investment has to be through the MLB franchise. Nobody owns a major league franchise as their sole business; any money that isn't used towards payroll could be used by the owner of the franchise in any other business. It's a mistake to consider MLB franchises in a vacuum instead of, in essence, as part of a larger conglomerate.
Few owners are 100% owners, so it's wrong to think about them as a part of an identifyable conglomerate (e.g., Stein brenner, Inc.)

As with any PV calc, we should be comparing it to the most likely alternate uses of the money: other player contracts, investments in scouting and development, investments in the parks, marketing, etc...

It's also worth thinking about what the goals of ownership are. If they're in win-now-at-all-costs mode, the only meaningful comp is other player contracts. If they're squeezing as much cash flow out of the franchise as possible in the near-term, this would increase the discount rate (since they value the present dollar out of the franchise more than the future dollar).

Finally, in addition to some of moscow25's points below, there is also the portfolio effect to consider - the Mets have many contracts outstanding, and may be simply unable to afford a level-payment market rate contract. In other words, as above, their discount rate is high because, in 2010, for the Mets, money is scarce.
There's a psychological aspect at play in here, too. We value a real dollar today significantly more than a hypothetical dollar next year, even totally separate from discount rates, expected inflation, and so on. Just a part of human nature.

And don't agents get their total 10% (or whatever) upfront? Sounds odd, but I thought I heard somewhere that that is the common practice. In which instance, agents would want to backload as much as possible in return for a greater raw dollar figure.
In this case there is no "hypothetical dollar;" the contracts are guaranteed. To the extent that you might not get the dollar, an accurate discount rate incorporates that risk. For example, if there is a .1% chance per year that the world will end, the annual discount rate should be 100.1% of what it would be if there were no chance of apocalypse. (Is that math right, finance people?)

Finally, agents are not paid up front, they are paid the same time that the client is. Clients would rarely have the cash to pony up the full commission all at once, and part of the agent's job is to ensure that all the payments (including performance-based incentives) are made in full and on time.

The player's union has a method (incl. discount rate) used to calculate values for all contracts. I am not sure exactly how it works (not straight NPV), because I believe the 1st A-Rod contract was seen as essentially "full value" (worth ~$250M). It might be that it doesn't discount payments, unless salary is deferred based upon the average yearly value of the contract. (In the case of Bay, if the deal went 10-10-10-36, then 6.5 per year would be discounted.)
In light of your added factor that teams can dump bad deals for cents on the dollar and thus have a lower cost for a bad deal, is there any chance you might take a look at some of the contracts that were dumped later (e.g. Pierre or some others that may have more back-loaded) compared to the reported alternate deals the player might have signed when the deal was entered into? And how about those that were not/won't be dumped (e.g. Helton or VWells) to see if the premise holds up? I recognize that Helton was an extension vs. full FA exposure so he's not the best example. Just a thought. And would that lead to some idea of what the market discont is for dumped contracts vs. WAR or VORP or someone other unit of comparison? I better stop as I'm already running wild with this.
As Tom Gorman pointed out - two parties can have significantly different discount rates. In fact there is more than just discount rate involved, there is the simple issue of cashflow. Given various news article about the Mets ownership it may be that the legal entity of the Mets may be in a negative cashflow situation. This may be viewed as a temporary situation and the owners would normally not allow the entity to go bankrupt because of the value of the team. BUT, if ownership lacks cash then it goes to the employees and gets them to defer payments.
The discount rate of money you don't have is quite high!

Secondly, from a financial point of view back-loaded contracts can be handled simply by selling the Company. Sure there is a theoretical reduction to future cashflows which might come in the price but my experience is that in a auction environment these "rounding" numbers get thrown out. What's ten million here or there in a $500 million transaction (really a lot but that is not what people think in the heat of negotiation.) So, back load the contracts, take the cash now (or simply stay in business) to allow you to sell the team!

Enough finance, back to baseball!
What you never mentioned were taxes. I am sure these players have their tax accountants assess the deals, to see if by backloading a contract over several years they wind up paying less in taxes.

Great article!
Perhaps Bay's deal has a Bonnilla-esque 25-year payment plan.
I liked this article the first time...when I read it on fangraphs:
Nice article, but I think you confused a few people with your explanation of why the discount rate exits for the teams. Also, it's worth explaining why the players only care about the total figure, rather than their own discount rate, more so than owners.

Yes, the discount rate has something to do with inflation and re-investing in the team or other businesses, but this confuses the issue somewhat. Rather, anyone with $1M to invest for X years can get a safe nominal dollar return by buying government bonds that are dated for X years, money market funds, or other really safe investments. This rate changes all the time, but is historically around 2-3%. Taking a more aggressive risk profile, investors can get historical returns of around 5% in nominal terms from fixed income (bonds), and of around 10% from equities (stocks). All of this has been written about in "Random Walk on Wall St," and is known by everyone who invests amounts of over $1M. The main point is, the more risk you can take on, the higher your long term rate of return will be. Thus, your discount rate for future nominal dollar commitments is *higher* if you are able to bear more risk with the capital in question.

More than anything, back loaded contracts take advantage of the fact that team owners are wealthier than individual players. As such, they can take on higher risk investments. A player would rather get his $10M now, rather than later, but he loses relatively little to take it two years from now, since he is not rich enough to invest the entire $10M (or $5M after taxes) into the highest returning vehicle. However owners can invest that entire $10M into high-yielding risky assets that (over the long run) return higher nominal returns than treasury bonds. Moreover, the owner might be able to pursue higher returns still from private investments (such as investing in his own ball club, buying out business partners, etc). If he did not think that these investments would yield more than treasuries, he does not need to make them.

Then of course there are taxes. Deferred payments can be a huge win for both players and teams because of uneven taxation. If Bobby Bonilla stands to make $10M per season as a player for the Mets, and roughly $0M after he retires, he might be much better off taking deferred payments for 20 years, even without any interest on those payments! After he retires, Bobby can move to a low-tax state like Florida (or Puerto Rico), get himself a good accountant, and end up paying maybe half as much tax as he would have, earning $10M per year as a New York Met. The owner, of course, would be happy to take the discount rate on Bobby Bo's deferral. The only loser is the state of New York.

Of course, the players and owners would never say that. They will talk about how they are saving money now to get better players and to win a championship for the fans. Which is also good economic sense for both sides, FWIW.

Again, nice article, but I thought I'd point out a few further angles here...
I like the article Tommy, although I'd like to point out a few simplifications that you're leaving out. First off, and this is not a small one, you are leaving out taxes. The difference in tax rates between MA and NY is not inconsequential - and can make the difference of 2-5m by itself. Secondly, you are making the assumption that the salary is paid in annual lump sums, whereas it is more likely (I don't know the exact structure so I could be wrong here) that it is in 12 equal monthly payments each year. This differential actually can make the difference of 2-3m more, depending on your discount rate. Lastly, I made these comments on the similar fangraphs article, and I'll post them here as well, as I feel they are quite relevant:

I agree with the author AJ on his conclusion, that is, if you do a gross simplification of the problem. Using his assumptions of a 10/15/20/21 breakdown versus a 15/15/15/15 split for the Red Sox, I derive a breakeven discount rate of roughly 35%. IF you assume a signing bonus of $10m from the Sox, then assume a contract equally front-loaded as the hypothetical Mets contract is backloaded (basically 21/20/15/10, proportioned for the $10m bonus and the 10% lower overall contract) I get payouts of 10 bonus + 15.9/15.1/11.4/7.6. Even in this extreme scenario, you would need a discount rate of about 9% to make the Red Sox offer better. Yes, the difference in the timing of the payments makes a massive difference.

The question then becomes, what is the proper discount rate that should be considered. I would argue that the opportunity cost of capital is the key metric to consider. For a pension fund or insurance company, the treasury curve would be proper to use – approximately 2.6% or so for 5 years at current rates (although this is a simplification of the actual calc). For a high-net worth individual, you could certainly argue that his opportunity cost would be higher as he could and probably would take on more risk in his portfolio. As a simple solution, you could ask at what rate could Jason Bay borrow money for a personal loan from a bank right now and use this as a proxy for his proper discount rate as it is essentially his cost of capital. I would guess this would be around 7-10%. This seems reasonable to me as a fair-value discount rate for Jason Bay.

Nevertheless, if you decide to include taxes (as you should), everything changes! I estimated roughly 41% NY & 38% MA effective tax rates (I am no tax expert so this could be a false assumption), the key is in the differential here more than the level. This 2.5-3% differential in effective tax rates makes a huge difference in favor of the Red Sox offer. So much so that if you assume any front-loading of the Sox contract at all (almost any signing bonus, or anything better than 15/15/15/15), the Red Sox offer is superior.

So, in the end, I would guess that Peter Gammons, while no financial expert himself, probably spoke to somebody in the Mets organization that knows what he is doing. The Red Sox offer was probably better, although without full details of the contracts offered, it is not possible to tell with certainty.
On a (hopefully minor) point, taxes for MLB players are actually even more brutal than the rest of us. Since the players play one week/year in Minnesota, one week in Detroit, etc, some of those states & cities charge them a tax for that time also. Again not sure this matters, just though I'd point it out. On the other hand, if Jason Bay plays in New York, but *resides* elsewhere, especially during the offseason (he pays even less tax if he can claim that he has not been in NYC for more than half the business days of the year), he pays a lot less tax than a New York resident. This is why some wealthy New Yorkers live in Connecticut. So the difference in taxation might be more or less than the straight NY vs MA figure you quoted. Not sure it matters, but just wanted to point this out.

Your analysis of the discount rate of 7-10% seems about right.
You are right that taxes matter, but that doesn't affect the amount the team actually has to pay. So if the Mets were hoping that by back-loading the contract, they would actually be paying Bay less than the Red Sox were offering, taxes don't move the needle. However, from Bay's perspective, you are correct (although we may want to consider the differential in sponsorships playing in New York).

(By the way, does anyone know the exact top tax brackets in Boston and New York?)

The same is true of the discount rates, because there are actually two different rates: that for Bay and that for the Mets. It's important to keep these separate. For Bay, his discount rate should be similar in New York and Boston. For the teams, however, the discount rates may well be different. On a separate note, I think the "liquidity" concerns are pretty minor, since most of these ownership groups could easily borrow money at a pretty good rate, effectively discounting in the same manner the future cash.

However, your points are well-taken, particularly from Bay's perspective.