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Today’s Pinch Hitter is Joe Stief, who grew up in Springfield, Virginia and as a teenager followed his father’s footsteps into becoming a Yankees fan (Joe’s dad grew up just 15 miles outside of New York City). That part of his story is worth knowing, but for this post, this part is most important: Joe is currently a junior studying finance at the Mason School of Business at the College of William & Mary.

For his post, Joe took a look at baseball contracts in a way the rest of use rarely do.

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^{[2]}Every winter, teams give players long-term contracts worth millions. Traditionally we view these contracts in either annual value (Ex: Alex Rodriguez, $27.5 million per year) or total value (Ex: Alex Rodriguez, $275 million). But what if I told you that because of payment scheduling, A-Rod’s current contract is really worth $189 million dollars and averages only $19 million per year?

One of the core concepts in finance is called the time value of money; a dollar today is worth more than a dollar tomorrow. The reason for this is not inflation, but rather because one must consider potential interest forfeited if they are to accept payment later. If you have a retirement fund, you know that the earlier you save, the longer your savings accumulate interest and the more money you have at retirement.

For the same reason that putting $5,000 in your 401(k) is more valuable when you’re 25 than it is at age 55, it is much better for Alex Rodriguez to receive his $275 million earlier rather than later.

Let’s say in 2008 the Yankees had offered Rodriguez $275 million in one lump sum in 2008 or 2018. He’d be crazy to not take the sum immediately because from 2008 to 2018 he could invest and grow the money. If we assume that A-Rod earns 10% on his money annually, the Yankees would have to give him $648 million ($250 x [1+10%]10) in 2018 to match the value of having $250 million in 2008. If we consider inflation, the amount the Yankees would have to give him in 2018 only increases.

But contracts aren’t paid as one lump sum, they are paid by year, so we discount each annual salary of Alex’s contract to arrive at the present value of the deal. We exponentially multiply the discount rate by the number of years from 2008 and divide each payment by the corresponding number. We then add up these annual discounted cash flows to find the net present value of the contract. The discount rate is the annual rate at which Alex’s money grows; I assumed 10%, but also included calculations at 5% and 15%. It is also assumed that the contract was signed on January 1 of 2008 and that each season’s payment is made on January 1 before the respective season.

Below is another table comparing the present value (at signing) of other mega-contracts:

On average, about 30% of the nominal value of a mega-contract is “lost” because of time value of money. Albert Pujols’s contract loses the most because his contract is very backloaded. He will earn $30 million in 2021, but in 2012 dollars, that $30 million is only worth $12.7 million. Joey Votto’s contract is for $4 million more than Prince Fielder’s, but because Fielder’s contract is shorter and not backloaded, his contract is really worth over $10 million more than Votto’s. Fielder and Votto’s contract illustrate my point well: because of time value of money, when a player is paid is just as important as how much.

*Associated Press photo*