The backgrounds of the webpages are based on actual assignments, research and other thoughts. Read on if you want to know a little more. -- Andy
About Background
About a year and a half before I was engaged to be an expert witness on the Tesla stock option trial (Tornetta v. Musk), I made a quick attempt at valuing the stock options awarded to Elon Musk in 2018 (I chose the word "awarded" on purpose - it technically wasn't "granted" using the ASC 718 definition until the shareholders approved the award). I wanted to see how close I could get to the disclosed pro forma fair value calculated as of January 21, 2018 using the same assumptions that were disclosed. In about 15 minutes, I was able to get within about 5% of the disclosed value using a closed-form barrier option model (Reiner and Rubinstein, 1991) adjusted with an illiquidity discount using the Finnerty model. I thought this was close enough at the time.
The stock options had some nuances that needed to be considered when estimating an accounting fair value -- they would only become exercisable if certain market capitalization hurdles were met (under ASC 718, these are "market conditions") AND certain operational milestones were attained (under ASC 718, these are "performance conditions"). For purposes of calculating an accounting fair value in accordance with ASC 718, only the market conditions would be considered for the per-unit value while the performance conditions were considered as part of the cost recognition - that is, only the units that vested based on the attainment of performance conditions would be recognized. The FASB considered requiring performance conditions be factored into the per-unit valuation, but concluded, based on input from valuation experts, that incorporating performance conditions into the valuation model would not be reliable since a correlation between stock returns and performance conditions would need to be determined reliably.
Little did I know I was going to be engaged as an expert witness and I would need to develop a model to value these options more "precisely" (that is, I needed to attempt to replicate the valuation that was used). The background is a screenshot of the Excel version of the model which I then had a programmer friend help me with some R coding so I could run more simulations. The R version of the model was able to get within 1% of the disclosed value.
I was then asked to see what the impact would be if the operational milestones, ("performance conditions" under ASC 718), were factored into the per-unit valuation, notwithstanding the accounting guidance. This required an assumed correlation matrix that examined stock returns, revenue and adjusted EBITDA. As expected, coming up with reliable correlation assumptions was a challenge, but I was able to incorporate the assumptions (leaving aside the reliability) into the Monte Carlo simulation. The upper left corner provides a Cholesky decomposition to adjust the stochastic variables to reflect correlation between the stock returns and performance measures. The stochastic factors also had to be adjusted to reflect the differences in periodicity between daily stock returns and quarterly revenue and EBITDA reporting. The embedded note provides some algebra to make sure the sum of daily stochastic factors matches the quarterly stochastic factor.
