# Employee Stock Purchase Plan (ESPP) Explained For Engineers (With Formulas!)

## What is an ESPP?

The Employee Stock Purchase Plan (ESPP) is a plan offered to many employees of publicly traded companies to set aside a percentage of their post-tax salary to purchase company shares at a discount, generally twice per year.

## TL;DR: should you participate?

In my opinion, all employees should opt into this plan if offered.

If you take away nothing else from this article, at least understand this:

Assuming you sell

immediately, the absoluteflooron your ESPP investment is an`18%`

pre-tax, semi-annual return.

If the stock goes down, and you sell immediately, you still make money. If it goes up, you’re locking in a much larger return if you sell immediately.

The only reason not to participate in the ESPP is if you can’t (or don’t want to) live on the smaller paycheck until you sell.

## The reasoning

The price you will pay for the stock will be the lower of the following two:

- The end of day trading price on the
*first*day of the period - The end of day trading price on the
*last*day of the period

On top of this price, you will get the stock at a discount up to `15%`

, depending on the employer.

### ESPP Return Formula

Suppose we’re operating under a six-month period and `15%`

discount. Let’s calculate the financial implications of the ESPP.

These are the parameters we’ll be working with:

- half of your annual base pay (since we’ll operate over a six-month window)`p`

- the percentage of your base pay you’ve elected to contribute (e.g.`f`

`0.1`

for`10%`

)- the price of your company’s shares at the start of the window`h`

- the percentage change in your company’s share price over the window (e.g.`d`

`1.07`

for a`7%`

increase, or`0.8`

for a`20%`

drop)

The amount of money we make over a six-month window can be generalized by this formula.

We start by figuring out how much money we have available to purchase, which is just the percentage we’ve elected to contribute multiplied by the six-month salary, * f*p*.

Then, we need the price we’re paying for the stock, which is `85%`

of the lesser of the start and end of the window trading prices, which explains the * min(y,1)*.

- If the stock appreciates over the window (
), then we’ll pay`d > 1`

`85%`

of the starting value ().`0.85*h`

- If the stock depreciates (
), then we’ll pay`d < 1`

`85%`

of the ending value (under a`20%`

price drop, we’d pay).`0.85*0.8*h`

To calculate the actual value of those shares at the time of our purchase, we just multiply by the ending window value, * d*h*.

### Example Scenario

Let’s walk through an example. Suppose our base salary is `$50k`

per year, and we’ve elected to contribute `10%`

to the plan. Let’s say our company share price is `$10`

at the start of the window and ends at `$15`

.

Our parameters would be initialized as follows:

=`p`

`25,000`

=`f`

`0.1`

=`h`

`10`

=`d`

`1.5`

Now, how much money did we make over this six-month window?

This comes out to `$4411.76`

. We invested `$25,000*0.1 = $2,500`

and gained `$1911.76`

. Not bad at all.

### ESPP Minimum ROI

We can simplify the formula into the following:

You might notice that the quantity on the left (* d/(0.85*min(d,1))*) is the amount our contribution (

*) will grow. This is what the plot of that function looks like.*

`f*p`

This plot is a function of * d*, the percentage change in our company’s share price over the window. When

*, we still have a multiplier of*

`d < 1`

`~1.18`

on our contributions, which is a guaranteed `~18%`

return on investment.If * d > 1* and our stock has done well, then we celebrate. For instance, if the stock appreciates by

`30%`

over the six-month window, we’re looking at a return on investment of `50%`

.However, the trading window for employees may fall weeks after the ESPP offering period. This means that the stock has time to fall more than `18%`

, in which case we’d lose money. This is where risk tolerance and confidence comes into play.

It may be advantageous to simply leave our ESPP shares alone if we believe that our company has a bright future. This also allows us to pay long term capital gains rates.