No, Shohei Ohtani Did Not Just Sign the Largest Contract Ever

The headlines claim it's $700 million – the biggest contract ever signed in sports history.

That's a $70 million per year, 10-year commitment ?– but with almost all ($68 million a year) of that money deferred for a decade.

It’s worth $46 million a year – if you buy the math used by the MLB Commissioner’s Office.

But that's not the reality. Most of us have an intuitive sense that the large deferrals throw a wrinkle into how we should think about this contract. So how much is Shohei Ohtani’s $700 million really worth?

In today’s (2023) dollars, it comes to $325 million. While impressive, that value doesn’t set any records. In fact, it falls short of the present value for the contract signed by his former teammate, Mike Trout, in 2019.

How do we arrive at such a determination? Ohtani’s unprecedented contract, both in terms of its sheer size and the deferred money, gives a wonderful real-world opportunity to clarify the idea of present value.

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A Present Value Primer

My MBA students know that present value is a well-established method to answer these questions. The basic idea: we should all recognize that a dollar received next year is worth less than a dollar received today. Don’t believe it? Imagine you just won $68 million in the lottery, but there’s a catch. You don’t get a penny of that until July 1, 2034. Would you accept a lesser payment to have your money today? Of course you would. But how much less? Would you be happy with $60 million? $50 million? How about $44 million?

Let’s take a more familiar approach to this problem. “Discounting future cash flows” may seem like a foreign language to some, but most of us have on occasion deposited money into a savings account and earned interest. We deposit $100, earn 5% interest, and one year later our account statement reads $105. I could also frame it to you this way: if you want $105 in one year, you’d better put $100 in the bank today. The $100 deposit is the present value of a $105 cash flow received in one year.

On a dramatically different scale, we can apply this concept to Ohtani’s deferred $68 million per year. As it turns out, $44,081,476 put into a savings account and earning 4.43% interest will grow to exactly $68 million in ten years. An equivalent way to frame it: the present value of $68 million due in 10 years, discounted at 4.43%, is $44 million. If the Dodgers want to pay $68 million in ten years, they’d better set aside around $44 million in today’s dollars.

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A Straightforward Baseball Example

Before delving into Ohtani’s contract, let’s apply this concept to a much more straightforward baseball contract, and clarify the way these contracts are often viewed. In December of 2022, the New York Yankees committed $360 million to retain star outfielder Aaron Judge. This contract pays a straightforward $40 million per year for 9 years. It has a stated value of $360 million, which was the number widely reported by the press. Major League Baseball, for purposes of the Competitive Balance Tax (CBT), values this contract at an Average Annual Value of $40 million per year – a straightforward averaging of the total payout divided by the 9 year term of the contract. But it should be clear by now that $360 million is not the present value of Judge’s contract. We haven’t done any discounting whatsoever to express that amount, spread out over nine years, in today’s dollars. For the baseball nerds, like me, out there, this demonstrates that MLB's concept of the contract value for CBT purposes is very different from the financial concept of present value.

But determining the present value of Judge’s contract is relatively straightforward. We just need to figure out what rate to use for the discounting process[1] , line up the timing of the cash flows (because if a dollar in one year is worth less than a dollar today, then a dollar in two years is worth even less, and a dollar in 9 years… you get the point), and then add up all of those discounted values. As my students can by now quote back to me, “the present value of anything is the sum of its discounted future cash flows.”

If we discount the cash flows to Judge’s contract and express them in today’s dollars – how much would the Yankees have to set aside and invest at the appropriate interest rate, in order to fully pay the future salary obligations – we get a present value of almost exactly $300 million.

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Valuing Ohtani’s Contract: The MLB Process

The Dodgers will pay Ohtani $700 million over the next 20 years. This is structured as $2 million in salary paid each year for the next 10 years while Ohtani is actually wearing Dodger blue, and $68 million in deferred compensation paid every July 1 from 2034 to 2043. Note that for the purposes of determining present value, we don’t care that this money is earned earlier and deferred. We don’t care whether Ohtani is playing for the Dodgers or another team or retired – all we care about is the timing on which the money hits Ohtani’s bank account, and an appropriate discounting thereof back to today’s dollars.

Importantly, however, these deferrals do matter for MLB and for the calculations of its Competitive Balance Tax, which require the value of the deferred payments to be accounted for and spread out over the 10-year term specified in the contract. But this is only for tax considerations, and the process used by MLB is not particularly meaningful to present value in today’s dollars.

So we have the timing of the cash flows: Ohtani will receive $2 million per year from 2024-2033, followed by $68 million per year from 2034-2043. Now, what is the correct discount rate to use? Astute readers will surmise that I didn’t pull the 4.43% number cited earlier out of thin air. That’s a rate which is specified in MLB’s Collective Bargaining Agreement. In a minute, I will argue that this is almost certainly not the correct rate to use for a proper present value calculation. But since it is the rate that MLB utilizes, and is the basis of values widely reported in the media, let’s give the number due consideration.

For the CBT purposes, MLB is valuing Ohtani’s contract at an Average Annual Value (AAV) of $46 million. How do they get to that number? The first step of the MLB process is to determine a value for the deferred money at the time at which the expense is incurred (which is not the present – hence this is partial discounting and not a proper application of present value). So the $68 million paid in 2034, using the 4.43% discount rate, is worth $44,081,476 in 2024. Add that to the $2 million Ohtani actually receives in 2024, and we get $46 million. Next up: the $68 million paid in 2035 is worth… $44,081,476 in 2025, when the expense is incurred. Both payments are deferred by 10 years, so they both have the same value for the MLB process -- even though they obviously have different present values, as $68 million received in 10 years has to be worth more than $68 million received in 11 years. Yet MLB still places a value on the 2025 salary of $46 million. And so on – it’s $46 million each year, all the way down. Each of those deferred sums is valued at $44 million and matched up to the $2 million actually paid. So for the MLB Competitive Balance Tax purposes, the value of Ohtani's contract is approximately $460 million.

On one hand, this is a convenient representation because it matches how we are used to hearing about baseball contracts. We can compare it more directly to Aaron Judge’s $360 million stated value, which had no deferrals. However, as we’ve already seen, the present value of Judge’s contract is not $360 million – there’s no discounting going on there whatsoever. Don't be confused; just because there is some discounting being applied to Ohtani's contract, the $460 million figure is not the present value of the contract, any more than $360 million is the present value for Judge's contract.

So why, then, is the official MLB value on Ohtani’s contract – $460,814,760 across ten years – not the true present value of Ohtani’s contract? As we've seen, there’s some discounting of the deferred money, but not a full treatment. That first $68 million payment is being valued at $44 million – and the final $68 million payment coming in 2043 is being valued at that exact same $44 million. But clearly this can’t be true in a present value sense. A $68 million payment in 2043 is worth considerably less than a $68 million payment in 2034. In fact, it’s worth $14.2 million less – only $29.8 million in today’s dollars.

The calculation of $460 million does some discounting, but not a full discounting. So what, then, is the true present value of the contract? Let’s cut to the chase: using the 4.43% discount rate applied by MLB, and discounting all of the cash flows from the contract back to today, the present value of Ohtani’s contract would be $382 million.

A couple of caveats. First, I am discounting these values to April 1, 2024 – which seems consistent with the treatment by MLB in their AAV calculation. Second, I’m assuming annual payments on April 1 (more or less, the start of each baseball season), which is on average earlier than the payments will actually be received. Finally, and importantly, we need to improve our selection of a discount rate. Even so, we can already see that the true present value is considerably less than the $460 million figure implied by the widely reported AAV calculation.

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But What About That Discount Rate?

Present value calculations are only as accurate as the discount rate we apply. So let’s dig into that 4.43% number that MLB uses. This is the “mid-term imputed interest rate” calculated by the IRS. It represents the rate the IRS will use to estimate taxes due on interest you didn’t, but perhaps should have, received.[2] This includes such things as interest free loans from family members, or implied interest on zero coupon bonds. This is a theoretical interest rate that is used for tax purposes. It’s an inappropriate rate to value Ohtani’s contract for at least three reasons: first, it is not a market-driven rate and understates the true risk-free rate at the time[3] ; second, its mid-term nature of 3 to 9 years does not match the duration of the cash flows to Ohtani’s contract (the average dollar on the contract is paid 14.2 years from today); and third, this rate is based on US Treasuries and therefore assumes zero credit risk.

In order to arrive at a proper present value calculation, we need to select a more appropriate discount rate. This rate should be an appropriate maturity risk-free rate (market US Treasury rates) plus some measure of a risk premium. The first and second shortcomings noted above are easy enough to solve. We can take a current yield from a 10-year US treasury bond[4] – 4.23% as of December 8, 2023. The fact that this yield is below the 4.43% mid-term imputed rate is purely accidental. US Treasury rates fell considerably with positive economic news in November; the opposite could have easily occurred. And in fact, the mid-term IRS imputed rate has bizarrely gone in the other direction – it now sits at 4.82% for December.[5]

The third shortcoming – an estimate of credit risk – is trickier. The IRS imputed interest rate from October was below the prevailing US Treasury rate and therefore implies a negative risk premium, which cannot be correct. We need to determine a rate which matches the riskiness of the cash flows coming from Ohtani’s contract. But how much risk is appropriate?

Some may argue that a risk-free interpretation should apply. Baseball contracts such as Ohtani’s are fully guaranteed, after all. This guarantee does not, however, imply that the cash flows are risk free. Corporate bond payments are contractual obligations that are also guaranteed, often with physical assets posted as collateral. While the Dodgers do not make public their capital structure, I doubt creditors are lining up to loan money to the Dodgers at the same rate as to the US Government, regardless of how many wins they bring to Chavez Ravine. Organizations can and do default on bond payments. Ohtani’s contract is a liability to the Dodgers, just like debt obligations, and would be subject to potential loss of value in a bankruptcy proceeding. I do not at all mean to suggest that Ohtani’s contract will push the Dodgers towards bankruptcy, or even that bankruptcy is a likely outcome – merely that it is a non-zero possibility.

Indeed, there is precedent. The Pittsburgh Penguins defaulted on $26 million in deferred money due to retired center Mario Lemieux in 1998, and entered bankruptcy shortly thereafter. Lemieux never received cash payment of that salary. Instead, the obligation was converted to equity and he emerged from the bankruptcy proceedings with an ownership stake in the recapitalized franchise – a not-uncommon “debt to equity conversion” result from bankruptcy courts.

And an example even closer: the Dodgers themselves, under former owner Frank McCourt, filed for Chapter 11 bankruptcy in 2011. MLB took control of the team and shepherded a sale to new owners at a price of $2 billion. No player salaries were impacted in this situation – but absent a rescue of the franchise by a deep-pocketed buyer, restructuring deferred salary would not have been unthinkable.[6]

Finally, consider the example of the 2020 season, cut short to 60 games due to the COVID pandemic. MLB and the players union negotiated a compromise of pro-rata reduction in player salaries for that season. Risk-sharing happened between the owners and the players, and no player in baseball received their full “guaranteed” payments that year.

So we need some sort of risk premium for our discount rate, but what is the right amount to apply here? Without access to financial data for MLB or the Dodgers, it is difficult to pinpoint a precise rate. We do have a couple points of data, however. The Atlanta Braves are a publicly traded corporation and publish quarterly financial reports. Based on their most recent 10-Q, it seems that creditors are demanding risk premiums anywhere from 1% to 3%, with the cheapest financing coming through MLB itself via the Major League Baseball Facility Fund.[7] Secondly, it may make sense to examine the credit quality of Major League Baseball itself, if we consider them as a backstop to the individual teams. In June 2023, the credit rating agency Fitch Ratings affirmed the MLB Facility Fund at an A- rating, and MLB Trust Securitization at an A rating. Currently, A rated debt across maturities trades at an average risk premium of 0.93% over similar maturity US Treasuries[8] . This is consistent with the 1% premium to treasuries that the Braves paid under the MLB facility fund in 2023. I view the 0.93% premium for A-rated debt as a conservative estimate for the risk premium on Ohtani’s contract.

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And Now, A Proper Valuation of Ohtani's Contract

With a discount rate in place, we can now conduct a proper analysis for the present value of Ohtani’s contract. Taking a 4.23% 10-year US Treasury yield[9] and a 0.93% credit risk premium, I will apply a 5.16% discount rate to the annual cash flows. This results in a present value (sticking with an annual valuation process, and as of April 1, 2024) of $347,399,155. This is dramatically lower than the $460 million number because we are properly discounting all of the cash flows. This number can be directly and fairly compared to Aaron Judge’s $300 million[10] in present value as of the signing of his contract.

Still, we can do a more careful job of discounting the cash flows on a monthly basis and modeling the time at which they are received. Here I will assume that the annual salaries are paid throughout the season on the 1st of the month between April 1 and September 1, in equal installments. The deferred payments arrive on July 1st of the designated year, as specified in the contract. We can apply an accurate maturity-matched US Treasury rate for each period, plus the 0.93% risk premium, and finally value the contract as of the signing date (December 10, 2023) rather than April 1, 2024.

With all this in place, we arrive at a valuation of $325,510,587 for Ohtani’s contract. This is about $22 million lower than the annual valuation. More precise accounting on the timing of the cash flows contributes the largest difference, at $10 million; using maturity-matched rates accounts for $6 million of the difference; and valuing the contract at the signing date rather than at the start of the baseball season accounts for $6 million.

If $325 million is the present value of the contract as written, what would that mean in terms of a contract without such dramatic deferrals? A straight 10-year annuity with the same present value will represent that more typical payment structure. A contract that provided a flat annual payment of $42.4 million for 10 years would be equivalent. This is about 92% of the AAV prescribed by MLB. We could interpret this as a contract with a stated value of $424 million, if you like.

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The Largest Contract Ever? Not So Fast.

Ohtani’s contract is almost certainly not, in present value terms, the largest sports contract ever. That honor still belongs to the €555 million 5-year contract Argentinian football star Lionel Messi signed with FC Barcelona in 2017. A cursory approach (without full contract details) values Messi’s contract in the vicinity of a $580 million USD present value at the time of signing.

As it turns out, Ohtani’s contract may not even be the largest baseball contract in terms of present value. A reasonable analysis shows that former teammate Mike Trout’s 2019 extension had a higher present value, at the time of signing, than Ohtani’s contract.

Trout’s contract guarantees $426.5 million over 12 years, with no deferrals. Already, this stated value is a touch higher than the properly converted 10-year stated value of Ohtani’s contract at $424 million.

But Trout’s contract covers 12 years, while Ohtani’s only covers ten.[11] That matters for present value. The case for Trout in part depends upon the discount rate we apply to these cash flows. A similar monthly analysis, valuing the contract at the time of signing and using the same 5.16% discount rate we applied to Ohtani, values Trout’s contract at $324.4 million in present value – barely below Ohtani’s deal. An uncomplicated interpretation could be that these contracts are, for the most part, equivalent.

However, we should not simply apply the same discount rate to every baseball contract. Rather, we need to use the discount rate that prevailed at the time of the signing. Treasury rates were significantly lower in 2019 – a 10-year US Treasury yielded 2.54%. Adding the prevailing 0.92% A-rated credit spread delivers a 3.46% discount rate. Applying this rate to Trout’s contract gives a present value of $353 million (annual payments) and $350,978,060 with a more judicious monthly accounting and maturity-matched rates. This comes in at about $25 million more than Ohtani’s in present value at the time of signing.

It feels a bit disingenuous to make the claim of superior value primarily due to a differing interest rate environment. Are we to accept the assertion that Trout’s contract is more valuable, not because of anything associated with the player, but rather due to interest rates and economic conditions? That's not a happy thought for most baseball fans. But let’s put some context around this. First, yes – this is exactly how asset prices and discounting works. Every asset – be it the stock market, US Treasury bonds, real estate – sees its present value shift as interest rates change. The tremendous impact of federal reserve action on the stock market, bond market, and real estate throughout 2022 is powerful and recent evidence.

Perhaps more illustrative, however, is the connection from interest rates and inflation to those contract dollars themselves. The Dodgers feel comfortable committing such a large notional sum to Ohtani in part because they know the dollars they pay him back with will be worth considerably less than today’s dollars. The higher the inflation rate, the more willing teams should be to make larger commitments many years in the future. If inflation today was at 1.8% – the prevailing rate in 2019 – would the Dodgers feel quite as generous towards Ohtani? With lower inflation, those future commitments would loom larger; a rational response would be to pare back the amount of that commitment.

Consider this in real, inflation-adjusted, terms: suppose the average ticket price to a Dodger’s game today is a nice, round, $100. At 1.8% inflation, we should expect that ticket to cost $142 in 20 years. At 3.2% inflation (today’s run rate), we should expect the ticket price to be $187. If the Dodgers sell 40,000 tickets per game, it would take 11.9 games worth of ticket sales to pay Ohtani’s $68 million with 1.8% inflation, but only 9.1 games worth to pay the cost at 3.2% inflation. These things matter to team owners! And if inflation had been higher in 2019, shouldn’t the Angels have been willing to pay a higher future cost to retain Mike Trout’s services?

To summarize, it makes sense to apply a lower discount rate to Trout’s contract for one simple reason – if discount rates were the same back then as they are today, the salary payments given to Mike Trout would almost assuredly be different. We need to evaluate the contract given in 2019 using the information we had available at that point in time, rather than retroactively apply an interest rate regime unknown at the time. And doing so shows that the present value of Mike Trout’s contract at the time of signing exceeds that of Ohtani’s by about $25 million.

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And What About Inflation?

This brings us to one last point: so far, we’ve been comparing 2019 dollars to 2023 dollars. As we’ve seen, even without directly considering inflation, Mike Trout signed a contract worth more in present value than Ohtani’s current deal.[12] But we’ve experienced a lot of inflation over the last four years! What price would a 2019-era Mike Trout go for today?

Inflation hits the baseball diamond as hard as anywhere in America. I’m old enough to remember reading (in a printed copy of the Anchorage Daily News!) when the Minnesota Twins signed center fielder Kirby Puckett to a 3-year, $9 million contract, making him the first player to earn $3 million per year. Player salaries have come a long ways since; even with 34 years of inflation, that contract comes to only $7.3 million per year in today’s dollars – about the going rate for a capable back-end bullpen arm in today’s league.

Adjusting the salaries in Mike Trout’s contract for the intervening four and a half years of inflation[13] adds 20.7% to the price of locking up (at least, at that time) the best player in baseball for the rest of his career. In today’s dollars, the Angels would have to pay an additional $88 million for Trout’s signature on the contract. That would make for a hypothetical $514.8 million contract in stated value, in 2023 dollars. This would result in a $376.3 million present value figure.[14]

One last comparison: Trout’s contract is for 12 years, while Ohtani’s covers only ten. Converting Trout’s ?inflation-adjusted numbers into an average annual salary with the same present value in 2023 dollars, Trout’s would come in at $42.8 million while Ohtani’s is $42.4 million – again, Trout comes out ahead but they are essentially identical.

Shohei Ohtani has pushed the game of baseball forward in a myriad of amazing ways. No player has ever accomplished on a baseball field the things he has done. And now we can say that no player has ever been paid, in notional terms, the massive amount of dollars he will receive. Despite this, Ohtani’s record-breaking contract hasn’t broken new ground, when we look at the value paid in today’s dollars. Sure, it’s a well-deserved home run – but he hasn’t hit the ball out of the park.

[1] Here I use a 4.86% discount rate. We will discuss the determination of these discount rates in detail shortly.

[2] I should note that the deferred money in Ohtani’s contract does not collect any interest.

[3] The IRS code states that the rate will be determined by the Secretary of Treasury based upon average yields over a selected prior period. The 4.43% rate is the one published by the IRS for the month of October 2023, a month when rates on US Treasuries maturing between 3 and 7 years ranged from a low of 4.58% to a high of 5.30%. The rate clearly reflects conditions in prior months when interest rates were below rates in October and is a stale number.

[4] Ten years still understates the maturity of Ohtani’s contract, due to the concentration of the cash flow between years 10 and 20; however, there is not a large difference between the 10 year rate and the 20 year rate, and later we will take a more precise approach and match the timing of the cash flows to appropriate treasury rates for each point in time.

[5] Further evidence that this is simply an inappropriate non-market rate.

[6] Baseball as a sport has entered a period of some economic uncertainty, with the collapse of Bally Sports and the impact on team revenues coming from their TV deals with Regional Sports Networks. MLB can take control of one troubled franchise and work to achieve a happy outcome. But what if economic circumstances impact the business of baseball as a whole? What if not one, but five or ten franchises encounter economic troubles simultaneously? Such a smooth outcome is hardly guaranteed. Baseball is not a risk-free business, and even guaranteed contracts must bear a portion of that risk.

[7] Excerpts from the Atlanta Braves’ 10-Q published in August 2023 include: “The interest rate of a Eurodollar loan was one-month LIBOR plus a margin of 1.20% to 1.325%, based on the credit rating of Major League Baseball Trust”; “In June 2020, Braves Facility Fund converted previous borrowings under a revolving credit advance to a $30 million term note with Major League Baseball Facility Fund, LLC (the “MLB facility fund – term”). Interest is payable on June 10 and December 10 of each year at an annual rate of 3.65%. In each of December 2029 and 2030, $15 million of the term note matures” – implying a 3% spread over 10-year treasuries; “Borrowings outstanding under the MLB facility fund – revolver bore interest at a rate of 6.52% per annum as of June 30, 2023” – implying a 1% spread to short-term treasuries; “The term loan agreement bears interest at one-month SOFR plus 2.10% per annum and is scheduled to mature on June 13, 2027”; “The term loan agreement bears interest at daily simple SOFR plus 2.50% per annum and is scheduled to mature on May 18, 2028.”

[8] Taken from the St. Louis Federal Reserve Economic Database.

[9] As of the contract date on December 10, 2023, taken from the US Treasury Department web site.

[10] Also done on an annual basis and using a 4.86% discount rate (3.69% 10-year UST rate and 1.17% credit spread).

[11] Trout’s contract was also an extension, that bought out his last year of team-controlled arbitration, rather than a free agent signing. I ignore that detail here and focus just on the stated cash flows to the contract.

[12] To some extent, applying present value and using the appropriate discount rate already helps correct for inflation. Some level of expected inflation is already included in the discount rates we use. The higher discount rate applied to Ohtani’s contract is, for the most part, a reflection of higher inflation expectations in 2023 than we had in 2019. However, the level of inflation experienced between 2019 and 2023 was far in excess of the expected inflation implied by interest rates when Trout signed his contract. If the actual inflation matched inflation expectations, this additional analysis would not add anything.

[13] Using CPI-All Urban Consumers from the St. Louis Federal Reserve Economic Data.

[14] Since we are using 2023 dollars, and have accounted for the intervening inflation between 2019 and 2023, we should apply the 5.16% prevailing 2023 discount rate to this hypothetical contract.