Many companies offer an Employee Stock Purchase plan — the option to buy shares in the company at at a 15% discount to the price at the beginning or the end of the purchase period.
This seems like a good deal — but how good of a deal is it? Put another way, if we went to Goldman Sachs and told them that we wanted them to sell us a security that behaved like an ESPP, how much would it cost? That's what we're going to find out.
If you want to skip the explanation and make your calculation, start here.
This chart shows the payoff from your ESPP investment (the black 'payoff' line) as well as the payoff of each of the components of the replicating portfolio (i.e., what combination of shares and options combine to match the payoff of the black line).
An Employee Stock Purchase Plan (ESPP) typically has the following features —
Assuming a $28.00 starting price and 1000 shares cap, this scheme's payoff is seen here — from $0, it increases by $150 for each dollar increase in the end of period share price up to the 'shares cap limit' (i.e., where you transition from being limited by the shares cap to being limited by the dollar cap), then flattens out until it hits the price at the beginning of the offering period where it again increases.
If that's confusing don't worry — we'll go through it step by step.
Hover over the yellow circles for more information!
\begin{align} \nonumber \textit{payoff} &= max\_shares \\ \nonumber &\quad \times current\_price \\ \nonumber &\quad \times discount \end{align}
The leftmost section of the chart represents stock prices that are low enough to hit the 1000 shares cap, i.e., when you cannot invest the entire $12,500. Given the 15% purchase discount, this limit kicks in at $12.50 / 85%, or $14.70. At this point, each dollar change in the stock price drives a $150 change in the payoff. E.g., at $5, you purchase 1000 shares for $4.25 (i.e., the 85% discount), locking in a gain of $750 (i.e., 1000 x $5 * 15%).
\begin{align} \nonumber \textit{payoff} &= \frac{1}{1-discount} \\ \nonumber &\quad \times max\_investment \end{align}
The simplest part of the payoff chart to understand is the flat part in the middle. This represents the stock prices where:
In this case, you will invest $12,500 at an 85% discount to the current stock price, yielding a ~17% return, or ~$2205 gain (i.e., (1/1-15%) * $12,500).
\begin{align} \nonumber \textit{payoff} &= ((current\_price / \\ \nonumber &\quad (starting\_price \times \\ \nonumber &\quad (1 - discount))) - 1) \\ \nonumber &\quad \times max\_investment \end{align}
The rightmost section of the chart represents stock prices where the price at the end of the period is greater than the price at the beginning of the period. To understand why, consider our original example:
We know what the payoff looks like, but now we need to put a value on that payoff. Enter the replicating portfolio. Put simply: What combination of stocks and options recreates the same payoff that we observe with the ESPP? And since each of the components of the replicating portfolio can be valued, we will know the value of the ESPP!
Before jumping into each of the individual parts of the replicating portfolio, it'll be good to get an intuitive understanding of how the individual components of the portfolio combine into the payoff chart we explored above.
The chart to the right let's you toggle the three replicating portfolio components on and off so you can see how each contributes to the final payoff line.
We know from earlier that the payoff chart rises by $150 for each $1 increase in the stock price up to the point where we can invest the full $12,500. We can replicate this payoff by buying 150 shares of the stock! I.e., when the price of the stock goes up by $1, we will gain $150 if we have 150 shares.
Once we cross the 1000 share cap mark at about $14.70, we need the payoff chart to flatten out. We do that by selling 150 call options at a strike price of $14.70 such that for each dollar the stock price increases beyond $14.70, we lose $150.
For quick review — a call option is the option to buy a stock at a given price (the 'strike price'). If we have a call option with a strike price of $15, we make a dollar when the stock price is $16, and when the stock price is <= $15, we make $0.
The final upward kink in the payoff happens when the stock price exceeds the starting stock price. We create this kink in the payoff by buying call options with a strike price of the beginning of period stock price (i.e., $28.00). The number of call options is the maximum investment (i.e., $12,500) divided by the maximum purchase price (i.e., .85 * the current price).
Since our starting price is $28, our maximum purchase price is $23.80. $12,500 / $23.80 == ~525.
Now, we have a replicating portfolio consisting of
The mechanics of option pricing are beyond the scope of this website (this tool uses the Black-Scholes model), but what's most important to grasp is that the higher the volatility, the higher the option value. I.e., the ESPP value for companies with steady stock prices is lower than that of highly unpredictable stock prices.
To see why this is, consider the bell curve chart shows a call option with a $28 strike price and the volatility of the underlying stock. Note that as you adjust the volatility upward, the spread of potential outcomes and the value of the ESPP goes up!
To understand why this is, consider the following:
Created by Garrett Edel using Django Rest Framework, ChartJS, and Polygon.io