Random Expiration Call Options

When we described the use of the VC method by venture funds to make investment decisions in a startup, the model was solely about the investment decision (VC Method).

The next stage involves deciding in what format the investment will be made—whether it will be preferred shares, convertible preferred shares, or something else. When we reviewed these formats, we demonstrated how Exit Diagrams are created, which visually describe the format and clarify the agreement on what the investor will receive when the startup goes public or is successfully sold (Exit Diagrams).

In this note, I will show how to read the diagram as the sum of sequential, randomly exercisable, European-style Call options.

Let me remind you that the horizontal axis on the exit diagram represents the value of the organization at the time of exit, while the vertical axis represents the fund’s share in that value. (This is not a time-based diagram, but rather a single point in time for different scenarios.)

For example, the diagram below shows that if the organization is valued at up to 20 million at the time of the fund’s exit, the fund’s share is 1/2. In the range of 20 to 30 million, it is 100%, and above 30 million up to 50 million, the fund will receive only 30 million, no matter the outcome, etc.

The diagram depicted on the graph is read from left to right with the following formula:
Exit Equation = 1/2C(0) + 1/2C(20) – C(30) + 1/4C(50) + 1/8*C(80)

Where:
C = Random Expiration Call Option;

Options are calculated at every inflection point of the curve.

Fractions indicate increases or decreases in the slope.

As with regular options, we have all the data to derive the result using a formula, but it is important to understand that we are not talking about regular Call options here:

First, it’s crucial to highlight that these are essentially American Call options, not European ones, because the execution time is not fixed, and the fund can convert at any time. However, as with regular options, American and European ones have the same price here because early conversion is unprofitable (unlike in the case of PUT options).

Now, given that we do not know when the fund will exit and that option pricing requires knowing the time, we must introduce a probability factor. To explain, let’s assume that the probability of the fund exiting in 3 years is 50%, and the probability of it exiting in 5 years is also 50%. Based on this assumption, we can calculate two Calls and multiply them by their respective probabilities.

Now imagine that the fund managers meet weekly to discuss the exit probabilities for all investments. This means the exit is considered 52 times a year, and we must calculate the Call for each case.

We can now reduce these time intervals infinitely and, using the relevant probability distribution function, arrive at a complex formula (similar to how a compound interest formula can be broken down into daily, hourly, or continuous compounding).

The formula resembles Black-Scholes, but it is not the same. The calculations are quite complex, but the book’s authors have created a web version you can successfully use: VCV Tools Option Calculator

Also, you can view an Excel model here: RE Calls – Excel.

P.S. The most complex parameter in the options formulas is Volatility, which was statistically determined to be 89%*.

P.S.
Volatility is the most difficult parameter in option formulas, which is statistically determined up to 89%.

Venture Capital & the Finance of Innovation Andrew Metrick & Ayako Yasuda Second Edition