## Bobby Bonilla, Financial Genius? August 1, 2011

Posted by tomflesher in Baseball, Economics.
Tags: , , , , ,

When Bobby Bonilla signed a deferred compensation agreement in 2000, the Mets owed him $5.9 million dollars. Basically, the Mets got to hold on to the$6 million or so (and ended up spending it on payroll), but they had to pay Bonilla back a bit more in interest. His yearly payments are $1,193,248.20, which means that in absolute terms, the Mets are paying him$35,797,446 in total over the next 25 years. Of course, the $1.19 million Bonilla gets today is worth much more than the same-size payment he’ll get in 2036. Bonilla’s arrangement mimics a financial instrument called an annuity, where a constant payment is made at specific time periods after a specific present sum is invested. The annuity formula is: $Present Value =Payment \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]$ where r is the annualized interest rate and t is the number of years of payment. Keep in mind, though, that the present value of the annuity isn’t$5.9 million – it’s $5.9 million compounded annually at some rate of interest agreed to by Bonilla and the team for the ten years between the deal and the first payout. In general, that means $5900000\times(1 + r)^{10} = Payment \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]$ Since we know Bonilla’s payout, we can substitute in: $5900000\times(1 + r)^{10} = 1193248.2 \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}]$ and that solves out neatly to the 8% that the team and Bonilla agreed to. The math checks out so far. At the time the deal was made, the 8% was 50 basis points (0.5%) below the Prime Rate, the reference rate used by banks in making loans. The average prime rate over the previous year was about 8.16%, and rates had hovered within 75 basis points since September of 1994*, so while interest rates are expected to move, it was very likely that rates would stay similar, at least in the short term. For the record, a 30-year fixed rate mortgage would have cost between 8.15% and 8.25%, so taking into account the long maturity of the loan, it wasn’t a bad deal. Let’s look at how good a prediction it was. Annualizing prime rates, the Mets could have earned a (full prime) rate of return as follows: $\begin{tabular}{c||cc} Year& Annualized interest rate & Current Value \\ \hline 2000& 0.09233 & 6444766.67 \\ 2001& 0.06922 & 6890851.93 \\ 2002& 0.04675 & 7212999.26 \\ 2003& 0.04123 & 7510355.16 \\ 2004& 0.04342 & 7836429.74 \\ 2005& 0.06187 & 8321243.53 \\ 2006& 0.08133 & 8998038.00 \\ 2007& 0.08050 & 9722380.06 \\ 2008& 0.05088 & 10217006.15 \\ 2009& 0.03250 & 10549058.85 \\ 2010& 0.03250 & 10891903.26 \\ \end{tabular}$ So, the actual value of the$5.9 million on January 1, 2011, was $10,891,903.26, but the agreement pegged the value at $5900000*(1.08)^{10} = 12737657.48$ for a difference of about$1.85 million. Bobby’s already better off because historical interest rates didn’t keep up with 8%.

My biggest question is why the Mets agreed to an 8% interest rate then and there to be in effect for the next 35 years. Since I’m not a finance professional, I don’t know whether that’s an industry standard agreement or not, but it seems like the risk of setting an interest rate that far in the future would be far too high. What if the Mets had agreed to the 8% interest rate for ten years and then offered Bonilla a menu of financially equivalent options? All of them would rely on the payment formula:

$Payment = \frac{r \times PV}{1 - \frac{1}{(1 + r)^t}}$

where t is the number of periods and r is the newly figured interest rate.

One option would be to take the $12,737,657.48 as a lump sum, although that wouldn’t necessarily be a good idea for the Mets. (We know they’re cash strapped.) The current prime rate is 3.25%, so if we took the lump sum$12,737,657.48 from the original agreement and reamortized it today at 2.75%, Bobby could receive a payment of $711,270.46 over the next 25 years. Similarly, at 2.75%,$1,047,789.14 per year for 15 years or $2,761,502.75 for five years would be equivalent options. Each has a different total cash outlay, but the discount rate means that each of them is worth the same$12,737,657.48 in 2011 dollars.

Bringing it all back, that’s why it’s a little silly to talk about the Mets paying $30 million to defer$6 million in compensation. It’s true that they’ll end up putting more dollars into Bonilla’s hands, but that simply represents Bonilla’s forebearing on the ability to invest that money at current interest rates. It doesn’t matter when you pay him – the money is worth the same amount, and that’s all that matters.

* Historical prime rates here, thanks to the St. Louis Fed and Federal Reserve Economic Data