## Examining Net Present Value and Its Effects

Going back to January 2016, Dave Cameron wrote an article detailing the breakdown of money owed to Chris Davis over the life of the deal he signed last year. For myself, this provided insight into how teams value long-term contracts, but more importantly it led me to more questions about how money depreciates over time. Fast-forward to the present and we start to see some articles and comments with people speculating about how much money teams are going to throw at Bryce Harper when he reaches free agency in a few years. The numbers have been pretty incredible; \$400 million? \$500 million? Even \$600 million? Then someone threw out an even larger number: \$750 million.

The best thing to do is ignore these numbers because we are still a couple of years away from free agency and he just had a down year where he was “only” worth 3.5 WAR, which gave the team a value of \$27.8 million. At some point the numbers don’t even make sense because the contract values are getting so inflated. But at the same time, good for him, maybe he’ll buy a baseball team once he retires, or a mega-yacht. But unfortunately we will need to wait until after the 2018 season before we find out the value of this contract. In the meantime, speculation will run rampant and the media will throw out inflated numbers for the amusement of the masses.

Now, the purpose of this article is not to predict the value of Bryce Harper’s future contract, but to examine a few scenarios as to the actual value in present-day dollars. To do this I will use the concept of Net Present Value (NPV) from Dave Cameron’s Chris Davis article and then use some of the numbers from his article predicting a contract for Bryce Harper. Let’s set a couple rules; (1) Match the length of contract given to Stanton — 13 years, (2) use nice round numbers and get as close to the total values as possible, (3) use a discount rate of 4%, (4) this is an exercise in futility and not to be taken too seriously and finally (5) to estimate NPV for a massive contract.

Here are the scenarios for a 13-year contract totaling in excess of \$400M, \$500M and \$600M.

 13 Year Contract Structure Year Age 2019 26 \$31,000,000 \$38,500,000 \$46,500,000 2020 27 \$31,000,000 \$38,500,000 \$46,500,000 2021 28 \$31,000,000 \$38,500,000 \$46,500,000 2022 29 \$31,000,000 \$38,500,000 \$46,500,000 2023 30 \$31,000,000 \$38,500,000 \$46,500,000 2024 31 \$31,000,000 \$38,500,000 \$46,500,000 2025 32 \$31,000,000 \$38,500,000 \$46,500,000 2026 33 \$31,000,000 \$38,500,000 \$46,500,000 2027 34 \$31,000,000 \$38,500,000 \$46,500,000 2028 35 \$31,000,000 \$38,500,000 \$46,500,000 2029 36 \$31,000,000 \$38,500,000 \$46,500,000 2030 37 \$31,000,000 \$38,500,000 \$46,500,000 2031 38 \$31,000,000 \$38,500,000 \$46,500,000 Total \$403,000,000.00 \$500,500,000.00 \$604,500,000.00 NPV \$309,555,083.25 \$384,447,442.10 \$464,332,624.87

Over the life of this contract, the value of each in NPV is significantly less than the actual amount signed. That’s because \$5 today won’t buy you as much five years down the road. To get a little more numerical, 13 years from now currency will lose ~40% of its value. Quoting the Chris Davis article again, the league and the MLBPA have agreed to use a 4% discount rate to calculate present-day values of long-term contracts. Since important people within the industry take this into account, that’s likely why we don’t see too many contracts with a significant amount of deferred money.

Since players are taking — and I use this term very lightly — a “hit” when they sign a long-term deal, I wondered what kind of contract structure would benefit a player the most. Again, I wanted to use nice round numbers, so I settled on a 10-year, \$100M contract, looking at an equal payment structure, a front-loaded contract, and a back-loaded contract. Here’s what I came up with:

 Hypothetical 10 Year \$100M Contract Year Equal Front-loaded Back-loaded 1 \$10,000,000 \$14,500,000 \$5,500,000 2 \$10,000,000 \$13,500,000 \$6,500,000 3 \$10,000,000 \$12,500,000 \$7,500,000 4 \$10,000,000 \$11,500,000 \$8,500,000 5 \$10,000,000 \$10,500,000 \$9,500,000 6 \$10,000,000 \$9,500,000 \$10,500,000 7 \$10,000,000 \$8,500,000 \$11,500,000 8 \$10,000,000 \$7,500,000 \$12,500,000 9 \$10,000,000 \$6,500,000 \$13,500,000 10 \$10,000,000 \$5,500,000 \$14,500,000 Total \$100,000,000 \$100,000,000 \$100,000,000 NPV \$81,108,957.79 \$83,726,636.52 \$78,491,279.06

There’s not a huge difference, but a player would gain just over \$5M by signing a front-loaded contract as compared to a back-loaded contract. It seems as though the agents and the MLBPA are more concerned about total dollars rather than NPV since they probably want to drive up total contracts.

And in case you’re wondering what those annual salaries would look like in NPV from the table above, I’ve created another table to show what those salaries actually look like in NPV over the life of our hypothetical 10-year contract.

 NPV Of Hypothetical 10 Year \$100M Contract Year Expected Equal Front-loaded Back-loaded 1 \$10 \$9.62 \$13.94 \$5.29 2 \$10 \$9.25 \$12.48 \$6.01 3 \$10 \$8.89 \$11.11 \$6.67 4 \$10 \$8.55 \$9.83 \$7.27 5 \$10 \$8.22 \$8.63 \$7.81 6 \$10 \$7.90 \$7.51 \$8.30 7 \$10 \$7.60 \$6.46 \$8.74 8 \$10 \$7.31 \$5.48 \$9.13 9 \$10 \$7.03 \$4.57 \$9.48 10 \$10 \$6.76 \$3.72 \$9.80

What I was hoping to show you next was a cool interactive plot similar to the table above, but instead of showing you the annual salaries it will show cumulative earnings as the life of our 10-year/\$100M contract as time progresses. Well unfortunately I am unable to get this plot to show up on this webpage; it has something to do with WordPress being unable to use Javascript. If you’ll bear with me, you can click the link below (it just opens a new window and shows the plot).