January 15, 2023

There are several different mathematical models that investors can use to judge whether to invest in an early-stage (seed) startup. Some of the most common models are:

- Net present value (NPV) model: As I mentioned earlier, the NPV model estimates the value of an investment based on the expected cash flows that the investment will generate over time, discounted to the present using a required rate of return. If the NPV is positive, the investment is expected to be profitable. If the NPV is negative, the investment is expected to be unprofitable.
- Internal rate of return (IRR) model: The IRR model is similar to the NPV model, but it focuses on the rate of return that the investment is expected to generate. It estimates the rate of return that would make the NPV of the investment equal to zero. If the IRR is greater than the required rate of return, the investment is considered to be a good one. If the IRR is less than the required rate of return, the investment is considered to be a poor one.
- Payback period model: The payback period model estimates the amount of time it will take for the investment to "pay for itself," or generate sufficient cash flows to cover the initial investment cost. If the payback period is shorter than the required payback period, the investment is considered to be a good one. If the payback period is longer than the required payback period, the investment is considered to be a poor one.
- Discounted cash flow (DCF) model: The DCF model estimates the value of an investment by forecasting the expected cash flows that the investment will generate over time, and then discounting those cash flows back to the present using a required rate of return. The value of the investment is the sum of the present values of all the expected cash flows. If the value of the investment is greater than the initial investment cost, the investment is considered to be a good one. If the value of the investment is less than the initial investment cost, the investment is considered to be a poor one.
- Probabilistic model: A probabilistic model estimates the likelihood of different outcomes occurring, and assigns probabilities to each outcome. This can be useful for investments with a high degree of uncertainty, such as early-stage startups. The investor can use the probabilities to calculate the expected value of the investment, which is the sum of the values of all the possible outcomes, multiplied by the probability of each outcome occurring. If the expected value is positive, the investment is considered to be a good one. If the expected value is negative, the investment is considered to be a poor one.

There are many other mathematical models that investors can use to judge whether to invest in an early-stage startup, and the most appropriate model will depend on the specific circumstances of the investment.

It is difficult to say which statistical models are used most frequently for each stage of a startup's development, as it will depend on the specific circumstances of each startup and the preferences of the investors evaluating it. However, some common models that are often used to evaluate startups at different stages of development include:

- Seed stage: During the seed stage, startups are typically in the very early stages of development and may not have any revenue or even a fully developed product. In this case, investors may rely more on qualitative assessments and less on quantitative models. They may look at factors such as the team, market opportunity, and competitive landscape to assess the potential of the startup.
- Early stage: As a startup begins to generate revenue and establish itself in the market, investors may start to use more quantitative models to evaluate its potential. Some common models used at this stage include the net present value (NPV) model, the internal rate of return (IRR) model, and the discounted cash flow (DCF) model. These models can help investors to estimate the value of the startup based on its expected future cash flows and the required rate of return.
- Late stage: At the late stage, startups are typically well-established and have a proven track record of generating revenue. Investors may use more advanced statistical models to evaluate the potential of the startup, such as multivariate regression analysis or Monte Carlo simulations. These models can help to identify patterns and trends in the startup's financial performance and to forecast its future performance under different scenarios.

It is important to note that no single model is likely to be the "best" model for evaluating startups at all stages of development. Investors will often use a combination of different models and approaches to make a more informed decision about whether to invest in a startup.