In the first article we looked at the required paid user conversion rate that would cover the costs of free users as well as fixed costs, and make the firm profitable. In order to keep the example simple, we looked at a single snapshot in time using some rough calculations. In this article I'd like to take a more dynamic and rigorous approach and look the numbers over a span of time with the help of a financial model. To help you follow along and to let you experiment with your own numbers, the Excel model can be downloaded here (xls, xlsx).

**Some Freemium Basics**

Before we delve into the actual numbers for Dropbox, I should explain the rationale behind the calculations and a concept that I call convergence. With any freemium model we have a set of free users that result in a pure cost to the firm, as well as a set of paid users that bring in revenue. Since user conversions typically lag new free user signups, and the fact that there are far more free users than paid users, there's often (but not always) a long period during which the firm encounters losses. A good way to represent this is with 2 lines on a graph (as shown below), one of which is the cost of free users plus fixed costs (in blue), while the other is profitability of a paid user (in red).

Above we can see two scenarios, one where the line's diverge, and another where they converge. If the two lines are diverging then clearly they will never cross and the company will never make a profit. At the point where the lines converge, and the paid user profit line exceeds the cost line, the firm begins to make money and the freemium model starts paying off. To put it another way, if the slope of the free user cost line is smaller than the paid user profit line then the firm will be profitable at some point.

In the above graphs I use a linear relationship but it's more likely that user growth will be exponential due to network effects and referrals (as shown below). The model provided uses an exponential growth rate that can be modified to evaluate different scenarios.

In order to yield a desirable profit scenario, the are several levers that the company has available to them. The main ones, and also the ones used in our model are as follows:

- The paid user conversion rate which is effected by the level of functionality provided to free users vs. paid users, as well as the value of your service overall
- Maximum storage limit for free users, a lower space limit results in a lower cost
- The price of a paid account
- The cost of storage, transfer or any other variable or fixed costs

**The Model Applied to Dropbox**

So without further ado, let's dive into a more detailed look at how Dropbox is doing using our newly constructed model. I've made a few adjustments to my assumptions based on reader feedback to the previous article so they are as follows:

- I assumed that Dropbox officially launched in September of 2008 at TechCrunch 50 so when looking at the spreadsheet, note that the current date is at about week 140.
- Several users felt that an average upload size of ~1.6M was too large and suggested that about 50% of that was more realistic. In this case we calculate that the average user uploads 8MB per day (10 files * 0.8MB) and downloads the same amount. The model factors in the storage cap of 2GB for free users and 50GB for paid users.
- Since the new model is no longer static, I've assumed a starting fixed cost of $8000 per month with a growth of $2400 per month. This growth rate gives us the $367,000 per month rate that Dropbox is at now (as per the previous article). This fixed cost primarily includes employee salaries and was calculated in the previous post.
- Our cost of storage, transfer, EC2 instances, and requests are all based on Amazon's published rates and have not changed from the previous post.
- I've chosen an initial signup rate of 1,000 users per week with an exponential growth rate of 1.2. This gives us a good approximation of user growth as it lines up with the 3M users in the GigaOM in 2009, and the 25M user mark today.
- It's assumed that free users store an additional 40MB every month until they reach their 2GB cap, while paid users store 12.5x this much (note 1). This figure gets us to our 433MB/user average that we calculated in the previous post, based on the GigaOM article.
- Projections are made over an 8 year period as some interesting results show up in later years
- Paid user drop-off is ignored for reasons explained in Note 3

Note that all assumptions are shown in the Excel model (note 2) and can be modified to your liking to see how scenarios change. Below I provide a few of the more interesting scenarios I've found. Please note that the figures presented are on a weekly basis.

__Scenario 1__Under this scenario we assume a paid user

**conversion rate of 3%**and that a paid user does about 12.5x more downloading and uploading than a free user (note 1). This produces the following graph:What we see from the above graph is that Dropbox is currently (at week 140) profitable, earning about $1.8M per month on costs of $3.7M. However; an important thing to note is that as free users gradually consume more of their space, they will cease to be profitable in week 295 as costs will rise more rapidly than paid user revenue. Two possible solutions to this would be to cap accounts at 1GB, or improve conversions, as we'll see next.

__Scenario 2__Under this scenario we assume a paid user

**conversion rate of 5%**and that a paid user does about 12.5x more downloading and uploading than a free one (note 1). This produces the following graph:At a 5% paid user conversion we see that DropBox is a runaway hit, currently (week 140) earning about $5.4M per month. This time the profitability will continue as the slope of the tangent for the paid user line at the end of year 8 exceeds that of the free user cost line. It turns out that at a 4.6% conversion rate, the slope of both tangents will be more or less equal and Dropbox can sustain profitability over the long term. If Dropbox were to cap free user storage at 1GB then a 4% conversion would suffice for sustained profitability.

__Scenario 3__Under our third scenario we introduce

**deduplication**. It was suggested by some readers that a deduplication gain of 20% is unlikely so let's reduce this to a more conservative 10%. In doing so we result in the following graph at a**3% conversion rate**(as in Scenario 1).We see that at 3%, even with deduplication we still get an undesirable convergance by the end of year 8 so we'll need a higher conversion rate. Despite this fact, deduplication has resulted in a profit today of $3.1M per month, a $1.3M increase over not using deduplication. It is easy to see now why they chose to use it.

__Scenario 4__In our final scenario we revisit the

**5% conversion**rate from scenario 2 but with a**deduplication**of 10% factored in.It is clear that at 5% with deduplication, Dropbox is making money hand over fist. Profitability today is $6.8M per month, and over $40M per month by the end of year 8. It turns out that thanks to deduplication, Dropbox needs a conversion rate of about 3.7% to be sustainably profitable.

**Summary**

There are several takeaways that we can infer from the model and above scenarios:

- Dropbox has tremendous potential provided it can achieve the necessary conversion rate of 3.5-4%
- Dropbox could easily have been profitable at a very early stage and likely is today
- Freemium models need to be studied over an extended period of time rather than as snapshot in time
- Our back of the envelope estimates in part 1 were not too far off but they also didn't show the full picture
- With some discounted cash flow analysis it's easy to see that under a 5% conversion rate, with deduplication, Dropbox could be worth well north of $1B, but this is a discussion for another post.

If you've not already done so, I suggest you download the Excel model (note 2) that I used for these calculations and play with the numbers on the assumptions sheet. Feel free to tweak it as needed it or use it as a starting point for formulating your own freemium models.

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**Note 1**- This is based on our average case from the previous article. A paid user has 25x more space than a free user, hence the midway point of 12.5x.

**Note 2**- The spreadsheet is available in both .xls and .xlsx formats. The model includes several sheets but focus your attention on the "Assumptions" and "Financials" sheets. Since it took a fair bit of time to create this spreadsheet I ask that you please note the original author if you reference it.

**Note 3**- Paid user drop-off was not explicitly incorporated as it exists for both paid and free users. Since both types of users drop-off it would be factored in by the user growth rate and the conversion rate. Drop-off can easily be incorporated into the model if you have specific numbers.