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.
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the theorietical that can always be floated is that said player might invest their money wisely/aggressively and outgain the discount rate and then some. in which case it was better to have more money sooner. obviously this derives from the proper time valuation of money but hypothetically could happen. he could also give all of his money to bernie madoff…
It’s not an objective right or wrong decision. It’s entirely based on his personal time preference schedule. Since Bay accepted the deal, it’s obvious that the New York deal ranked higher on his scale of values than the Boston deal.
I thought the Red Sox withdrew their offer when they signed Cameron. That would mean there’s no way to determine which deal ranked higher Bay’s “scale of values”.
Maybe, I’m not really sure if they withdrew it or not. If they did, you’re right, we cannot say which offer was “better” because it is purely a subjective valuation. If Bay has a low time preference schedule, the back loaded $66M may trump the front loaded $60M. For those with a high time preference schedule, they may rank the $60M over the $66M.
We also aren’t privy to the psychic differences between the two. Maybe Bay prefers New York to Boston or the NL to the AL. These would all weigh into his decision and affect how he ranks the two.
The agent should also consider tax rates. NY state taxes are near 9% and MA state taxes are near 5%. That’s a few million dollars difference right their in taxes.
State taxes are deductible from federal taxes, so some of that difference is “regained”, making the gap much less than suggested.
State taxes are deductible to an extent. That extent is exceeded when you are talking millions of dollars.
Players are taxed in every state for games played there so it isn’t that big of a deal.
Not according to the whole fiasco between the State of New York and Derek Jeter. Jeter claimed a Florida residence to reduce his tax liability. Where does Bay claim to live?
I have no idea what address Bay puts on his tax returns, but his off-season home is in Kirkland Washington — one of the few states that has no state income tax. Though if that in itself was enough to significantly evade taxes I suspect you’d have a lot more big-ticket players owning mostly-empty nominal residences in the Evergreen State.
MA tax rate got bumped to 6.25% in August 09.
That’s the sales tax rate, silly. The personal income tax rate in Massachusetts continues to be 5.3%.
Because the team ownership and the player likely have different discount rates, the distribution of the annual payments can be a creative way to make both side feel like they got a good deal. I don’t know what Wilpon’s primary business is, but his discount rate should be something like the rate of return he obtains from reinvesting him money in his own lines business. That could well be more than 10%, for all I know. Jason Bay may be more risk averse with his money, and would invest it in bonds or some other low risk fund. So the deal has a different value for each side. Maybe the Mets’ “source” who said the deal was cheaper than the Red Sox offer was using a high discount rate from the team’s perspective; yet the deal is better for Bay, from his perspective, using his own discount rate.
The rate of return Wilpon has been getting on his reinvestments recently has been roughly negative 100%. Though apparently not enough to force him to sell the team or stop (over?)paying for big name talent.
As far as I knew the Sox offer was withdrawn before the current Mets offer hit the table, once Cameron signed with Boston.
Any money spent of Bay would have been better spent on Holliday, the superior player. That’s final.
Pretty brainy article. I’m tempted to suggest the Wilpons use a negative discount rate given how Madoff ripped them off.
Wilpon was one of a dozen or so large investors that took redemptions at the right time and made money through Madoff.
You could have made it more clearcut and actually solved for the discount rate that would be the breakeven point. Taking MA vs. NY state tax into account for the contract without discounting, Bay is looking at paying an extra 3.6M in taxes in NY for the first 4 years. Given that the difference in the deal is now .4M, he probably should have chosen the front-loaded contract. Getting even further into it, and probably an entirely different argument, we could see some rather high inflation over the next few years if the Fed doesn’t take back all the money they put into circulation. The front-loaded contract becomes much more valuable in that scenario. I think that maybe Bay just valued playing in NY more than he valued playing in Boston.
Again state taxes are paid to the state the game is played in. Its a monstrous headache for a player’s taxes but it makes the difference between state tax rates for salary concerns really hard to calculate.
An exact number is hard to calculate, but, half your games are played at home, half on the road.
A reasonable rough estimate would be Salary * 50% * State Tax Rate for each offer, then compare those numbers. The taxes for the other half of the games will vary based on schedule, but it’s probably reasonable to assume that when comparing multi-year deals, that portion of the taxes will roughly even out over the course of the deal.
Why use a 5 % discount rate when the US dollar declined against most world currencies by 13-14% in 2009, and shows signs of dropping even more in 2010?
And as to the Wilpons, I do not know what discount rate to apply to their Madoff investment:
Amount invested: $ 42MM
Amount taken out in cash (before scandal broke): $ 93 MM
Alleged loss: $$$$$ ????
I was under the impression that athletes have to pay state income taxes to all the states in which they play (and that have income taxes). Then that total amount is deducted from the amount of money they owe to their home state (i.e. they don’t get taxed twice). True?
That’s true…furthermore, all state income taxes are deducted from the Federal. Players whose play in states with lower income taxes do make out better, but much less than people think.
Do we ever see teams front-load a contract? It actually seems like it may be a reasonable approach in certain cases, at least how it’s playing out in my head.
Take a team like the Blue Jays. The reports we hear is that ownership is willing to give them plenty of money to spend, but management feels there’s no reason to spend it now as they won’t catch the Yankees/Red Sox until they have a bunch of new young stars developed, which they hope to acquire through the Doc trade and a new scouting focus, etc, and then they’ll want to go out and spend that money to add to a big core.
What that essentially means though is that in 2010 and 2011, at least, the Jays will be paying out an amount far less than their spending cap. So if that money is there, why not go out and try to grab, say, Matt Holliday (or replace him with another top free agent next year, I’m just using him as a general example). Offer up Holliday a heavily front-loaded contract, which is obviously appealing to Holliday for the reasons in this article. So Holliday gets, say Holliday signs for 6/$120M, but it’s structured so he’ll get $30M the first three years, and $10M the last three. This would give the Jays the increased payroll flexibility in their competing years, while they already have the star player on hand.
I realize typing this out the flaws in my logic – that they’d probably be better off saving the money and just spending it when they’re ready to compete – but it does make sense for a team like the Jays in the sense that being owned by such a big corporation, they’re given a budget, and the assumption is that budget is independent of the next years. If they spend way below this year, they won’t be given that in extra funds to spend afterwards, and vice versa, if they spend the full amount this year, it won’t reduce their cap later.
So maybe it’s an extreme example I’m giving, so perhaps imagine a team a year away from feeling like they can compete offering a 4 year/$40M deal to someone and paying out $30M the first year and next to nothing the next three…
And maybe typing this all out made me realize why my initial thought made no sense.
Not to the extent you’ve described here, but I think the contract that Lackey just signed with the Red Sox is actually front end loaded, 21mm in year 1, followed by 4 years of 15.25mm, total contract of 5 years 82mm
A-Rod’s contract is also somewhat front-loaded, though that will shift if/when he starts hitting his incentive HRs – 08:$27M, 09:$32M, 10:$32M, 11:$31M, 12:$29M, 13:$28M, 14:$25M, 15:$21M, 16:$20M, 17:$20M (Cot’s Contracts).
I’m guessing A-Rod is front-loaded to deal with two possibilities:
1) If he does break the all time home run record, he gets a ton of bonus money along the way. In a backloaded contract, the end of the contract would be insanely expensive.
2) Giambi making ~$20m/year at the end of his dead and having lots of issues was rough on the team, to the point that they looked into ways to get out of his contract or send him to the minors to avoid luxury tax costs. A 40+ year old A-Rod, totally washed up, making $30m+ a year would have a far worse impact on team construction.
Is the Vegas over/under on Bay wanting out of Citifield going to be set in months or years?
At bats.
Really, does Jason Bay care about past, present or future value? If one method gets him an extra million what will he do with it that he couldn’t have done anyway? It’s like me deciding whether I should get the $1.29 coffee at McDonald’s or $1.85 at Starbucks. It doesn’t matter one whit. No doubt it’s all about bragging rights – 65 million is more than 60 million – so there, Red Sox!
plus bay gets an option year that from the reports seems like it will vest pretty easily, so it is more like 5yr instead of 4yr
Hey R.J.,
I think you are making this too simple and probably doing it wrong. You don’t know the Red Sox offer, so you can’t really do this type of analysis, and anyone can make assumptions that make the arguement go in their favor. For example:
What if the Sox offered him salary of 9/15/15/15 plus a 6mm signing bonus? If you do this analysis at 10%, assuming all cash paid monthly, and 6mm in bonus money then the Red Sox offer, in PV terms is worth more using your Mets offer of 10/15/20/21 (also paid monthly). Even at 5% the Red Sox is still worth more.
Did make a bad assumption and treat cash flows as annual? Did you treat all the cash flows as if they were paid at the end of the year or the begining of the year? Is salary paid out over 12 months in even installments? What exactly is the handy time value of money formula you used?
I know that signing bonuses are not that common in baseball, but I think guys like Arod and CC get a large mulit-million bonus at the beginning of each year as part of their contract and get their regularly scheduled salary.
All in all I think it very likely that HoFamer Gammons is correct, the Red Sox offered more money in today’s dollars, and that is without any crazy discount rates, so it is quite possible that may need to change the last line in your post…
10% is way too high. Its closer to a real rate of 3%,
In the nineties the average was a little less than 3%. In the 2000′s even with no inflation the last two years, the average was more like 5.5%.
CC’s bonus was just a one time thing for the first year of his contract.
A-Rod gets payouts every January for the first 5 years, but that’s his signing bonus – it wasn’t paid out at the start.
I remember back in the ’90′s the Mets used to give out contracts with ultra-long term payouts (i.e., the contract’s total value is two years, $10 mill, but $5 mill of that will be payed in 20 annual installments of $250K). If it’s structured that way, the present value could be much, much, much less than is being discussed.
Let’s also remember that the Bush Tax Cuts expire after 2010 (I think that goes from 35 to 39.6%), so anything you don’t get this year will be taxed at a still higher rate.
I think it is a bit of a moot point. It’s not as if Bay had both the Sox and Met’s offer on the table at the same time. The Sox made their offer, Bay declined and thought he’d get more years/money. There just wasn’t the market his agent envisioned.
The proper rate to use in these calculations is usually the risk free interest rate, which would be, for example, the 5 year and 3 year treasury rates in this case. In the current interest rate environment, the present value calculation makes little difference at all. The 3 year treasury is at 1.5% and the 5 year is at 2.5%.
You can maybe argue for an inflation forecast 5 years out of as high as 3%, if you’re a bit of a maverick, but the consensus currently would be around 2.5% for long term inflation. And in the shorter run, we are currently still in a deflation. Leave it to the Mets though, to bring out the time value of money argument in the midst of a deflationary recession.
There’s a huge ongoing argument about discount rates, with lots of lawsuits and the like around the subject. What’s clear is that some discount rates are inappropriate, but it’s not so clear than any particular rate is the only proper rate.
The discount rate to use depends on who is analyzing the PV of the contract.
For the team, this is not just a function of the risk-free rate, but rather the team’s overall cost of capital (which will be at a premium to treasuries). I don’t know the Mets/Sox financial situation one bit, but I imagine the cost of capital for a baseball team is very low given the massive premiums (relative to cash flow) required to buy a baseball team. Anything above 7% is probably too high, and that is probably pushing it.
For the player, I agree, he should use the risk free rate, unless he has other investment opportunities in which he can invest the money to earn a superior return.
Either way, RJ is right here… the contract would have to be ridiculously backloaded, or have deferred salary going out multiple years beyond the length of the contract to consider the Mets’ offer lower.
There are superior returns without risk.
Those rates are artificially low because the Fed is/was buying our own treasuries. A stronger indicator for an inflation outlook is Gold and the yield curve on treasuries (which is historically high).
What is the time value of money formula? That is, the equation?
P / (1+r)^t
where P is the dollar value of the payment
r is the discount rate
t is the time in years
Run this formula for each individual payment the player is going to receive, then add the results together for the present value of the contract as a whole.
thanks!
Typical Gammons Red Sox ballwashing.
The baseball rules utilize something close to the risk free rate for discounting, but that is just a convention for other purposes of the rule, which has absolutely nothing to do with the proper discount rate applicable to the Mets or Jason Bay or any other individual player. Most players have financial advisors who will help them sort through the time value issues; for that reason, I doubt that most players will ignore the issue.
I don’t know if its a *big* deal or not, but Bay’s 2014 salary is at least a little bit dependent on his 2013 salary.
IF the Mets were to offer Bay arbitration after 2013, his back loaded contract would be beneficial because he would be due a raise on that $21 million instead of a front loaded contract where he’ll be due a raise on his hypothetical $15 millon
I feel obligated to comment here given that I work on a fixed-income trading desk at a large bank. There are some comments made above with some questionable math and logic that I feel like somebody should correct.
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.
I assume monthly payments in equal installments for the salary – doing this versus annual payments can make a difference of 2-4m depending on your discount rate. I disagree with Wolf’s assertion that the Sox offer is worth more at 10% and 5% (given a $6m bonus) however. I calc a $6m bonus breakeven discount rate to be 11%. Regardless, his point is well-taken on the monthly versus annual payments.
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 8-10%. 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.
Great article! More journalists, like Peter Gammons, need to have their vague opinions evaluated like this more often. Then maybe they’ll do some math before they state an opinion that is clearly incorrect based on the math. If the present value is still higher in the Mets offer even with that generous discount rate and the dramatically back-loaded contract, then no responsible journalist would ever bring up that argument if they had done their homework. Great work RJ, I hope everyone who reads Gammons’ article finds their way over to this article.
What about deferred money? I am not sure about the Mets but the Cardinals love to use this in contracts.Under Albert Pujols current contract he still will be getting paid in 2029. If you take this into consideration Pujols contract of $100M is closer to $90M in present terms.
That’s just one of the reasons that Gammons should stick to balls and strikes and stop pretending he has a clue about the time value of money.
I would expect a very high discount rate on these deals; FA contracts are anything but risk-free. The Mets are tying up a large amount of capital for 4+ years and whether they see any return on it is a very uncertain proposition.
Just as a point of comparision, VC companies typically use 35-50% discount rates when evaulating whether to invest in a company. That seems pretty high, but 9% seems pretty low.
That rate implies that Jason Bay has an equivalent beta (risk/return) of the S&P 500. I think any FA deal is riskier than putting your money in the market.
VC companies use 35-50% discount rates on FCF analysis because startup companies are incredibly risky. This is an analysis of the present value of the money, not the PV of the contract based on risk profiles.
OK, fair enough. Then 9% seems about right.
And under those assumptions the original post is correct; Bay would have to play for free for the Mets for two years for the PV on the Mets’ offer to be less than the Red Sox.
Looks like Gammons needs to check his figures and not just repeat what he’s been told.
Can someone crunch the numbers and tell me how the Mets were better off paying Bobby Bonilla 1 million every year starting next year until 2025?
How’s that prison food Bernie?
What happens if we look at State income taxes and cost of living in comparing a Boston/New York deal?
If we can look at backloading and total value, I would imagine this can also be calculated. I don’t know the answer, but I am curious the effect.
Finally, personal preference comes into play. I am not saying that Bay prefers Boston over NY, I am just saying his living preference may have some value to him as a person. This cannot really be calulated. Maybe he likes NY more than Boston, or maybe he likes Boston more than NY. I am just saying that may have value to Bay.
To put it in some level of perspective, just ask yourself would you move yourself and your family for a 10% bump?
I’m not sure I agree with the specifics of your analysis RJ, but I agree that the difference in value is probably a wash. I think one thing few commentators point out is that a heavily backloaded contract makes it much more difficult for a team to move a player and his contract due to the salary considerations. Bay, as an aging, declining slugger with decreasing WAR would be an obvious choice to possibly unload toward the 4th or 5th years of the contract, but the difference in a $15M v a $25M salary in those years could make or break any trade.
But if it was strongly front-loaded, say 20/17/15/8 it would easily have surpassed the Mets offer in real value. Plus in a decade like the 70′s you could very well have to discount 12-13 percent a year. Not that this decade would rival the 70′s but it is not impossible either.