Friday, June 3, 2011

Valuation of startups with the Monte Carlo simulation model

The issue of the valuation of internet companies at the seed stage is quite controversial. Companies of this category are considered to be quiet risky from the point of view of the investor, but the risk is not only the probability of loss, but big capital gains as well.

If you are the person, who wants to measure the value of the company of this sort with the discounted cash flow approach, I’d recommend you the following sources:

My goal in this post is to describe my model of valuation with Monte Carlo simulation instruments. In my opinion it’s an optimal choice for those who want to measure the value of the Internet Company and take contingency factors into consideration. After all this method can be easily modified for the real options approach implementation, which allows considering specific risks of the company as well.

Let me go straight to the point. The model was built for the valuation of companies in ecommerce. For this reason my approach is based on the assumption that the customers of the company in the time period are calculated according to the number of unique visitors and the conversion of this people into the customers:

It’s important to note that if we deal with startups there is a very high volatility in the flow of visitors.

The daily reach of visitors for Mixpanel and Zemanta are good examples:

Conversion rate of visitors into customers is volatile as well. Traditionally it varies from 5% to 7%. Let’s make an assumption that it’s like that, but of course there are cases of a higher one or lower. It fully depends on the business model of the company, the way how sales are organized, but it’s not actually the issue of this post.

Almost undetermined behavior of future visitors can be described with the differential equation of geometric Brownian motion:

As far as I know this differential equation can’t be solved and the only way to get the information on the most possible answer is to generate a big number of scenarios. And that is the basic idea of Monte Carlo simulation approach. The number of unique visitors in the period t can be described in the following way:

μ is the expected growth and σ is the volatility. The parameters are estimated on the historical data.

Z is the random variable with a normal distribution.

Almost the same is for the conversion rate:

Thanks to the conversion rate and the number of unique visitors we get the number of costumers. Let call this variable ‘TotalCastumers’.

The customers of the company are the sum of customers in each product category i, with the total number of product categories N.

Let’s consider that there are two categories of services provided by the company, then i=2.

The calculation of %Cast allows us to operate with the portfolio structure, which can be permanent or changing exponentially or even stochastically. I recommend you to make your choice according to the historical information of the company you want to evaluate.

After that we can start calculating sales revenue:

arpu_ is average revenue per user. The formula for the GrossMargin in the period t can be calculated according to the following equation:

Where COGS is the cost of goods sold.

After that we calculate OperatingProfit which is the GrossMargin minus FixedCosts:

We can also calculate Income after taxes which is calculated according to the value of OperatingProfit:

I decided to express depreciation and investments exponentially, but any other functional form also possible.

Free cash flow is calculated in the following way:

The value of the firm can be calculated according to the formula:

r is the cost of acquired capital, which is identified according to the ROI of the venture capitalist, who gives the money. g – is the future growth, which varies from 5% to 15% and depends on the industry.

The idea is that we generate a big number of scenarious for the flow of website visitors. Conversion can be taken as a mean of one's distribution.

That’s the theoretical model I wanted to share with you. The practical implementation of the model will be in the further post.

1 comment:

  1. I'd like to take the power of thanking you for that specialized guidance I've constantly enjoyed viewing your blog.Mr. Hugh