Your Business Goal Determines Your Best Course of Action

App in the Air is a mobile phone app for frequent fliers that includes flight information updates, airport maps from around the world, local weather conditions and currency exchange rates. It works on a freemium monthly subscription model: a basic version of the product is available for free, while access to a version with more features can be purchased for a monthly fee.

Businesses based on apps like these often share many of the same problems: With thousands of popular apps available for free (or low cost), it can be difficult to get potential users to hear about and download your product. Many people download an app and try it a few times, but then quickly lose interest and never use it again. Other people become regular users of the free version of the product, but never upgrade to the paid version. And many people who are paying customers let their subscriptions lapse after just a few months or a year.


Description of the Model

App in the Air’s CEO, Bayram Annakov, built a simulation model to capture much of this process. The diagram below is a simplified version of his work. There are two main portions: the main chain that tracks Potential Users becoming New Users, Retained Users and finally Paying Users. The second portion tracks Cash, income and expenses.

The stock-and-flow structure of the ‘App in the Air’ business, including some important parameter values.


‘Potential Users’ (near the upper-left corner of the diagram) download the app, making them New Users. Only about 20% of these new users retain using the app after the first month, becoming ‘Retained Users’. The other 80% leave the system, never to download or use the app again. Each month, some portion of the retained users who have the free version choose to upgrade to the monthly payment plan, making them ‘Paying Users’ and some portion of the Paying Users each month cancel their subscription.

It is Paying Users who generate the company’s income, by paying a monthly subscription price. One of the business’s main expenses is advertising, which raises awareness of the product and therefore helps to drive downloads. In advertising parlance, the amount of money spent to acquire a new customer is the ‘cost per acquisition’, or ‘CPA’. If it currently costs $50 on average to acquire a new customer, then we can find the number of downloads driven by advertising by dividing the ‘monthly advertising spending’ ($20,000) by the CPA. As the pool of potential users dries up, the cost per acquisition (CPA) of a new user should tend to go up. In this model, we simply divide the initial number of potential users by the current number. So, when the number of potential users falls to half of its original value, the CPA rises to $100. When the number of potential users remaining falls to one-quarter of its original value, the CPA doubles again.

The second means for acquiring new users is from referrals by existing users (both the ‘Retained Users’ who have the free version of the product and the ‘Paying Users’). We represent the rate of ‘downloads from referrals’ is by analogy to the rate of infection of a disease. The combined number of retained and paying users essentially ‘infect’ the remaining potential users. The rate of this is: 0.4 (Retained User + Paying Users) (Potential Users / INIT(Potential Users))


Identifying Leverage Points

What can we do to have the best impact on the company’s business? With our model, we can simply test these changes and compare the results.

First, let us consider the ‘base case’:

(A) 80% ‘churn rate’ for New Users, 2% of Retained Users become Paying Users each month, and 5% of Paying Users cancel their subscription.

Maybe with some effort we can do one of the following:

(B) reduce the ‘churn rate’ (the fraction of new users who stop using the app within the first month) from 80% to 76%.

(C) decrease the ‘subscription cancel ratio’ (the fraction of Paying Users who give up their subscription each month) from 5% to 4%.

(D) increase the fraction of Retained Users who become Paid Users each month from 0.02 to 0.04.

Which of these four things would have the best impact on the business?

The figure below shows the amount of Cash the business would have over time for each of these four cases. (For each graph, we have stopped drawing at the point of maximum cash on hand. After that point, expenses are always greater than income and the business begins permanently losing money.) In the base case, in the first months the company would lose money, since initially there are no Paying Users. The company’s expenses would exceed its income and it would see its initial pile of $500,000 in cash dwindle to just under $67,000 before the company became profitable. The amount of Cash on hand would peak at about $5.7 million at month 189.

The figure also shows the effect of (B) reducing the churn rate from 80% to 76%, (C) decreasing the subscription cancel ratio from 5% per month to 4% per month, and (D) increasing the fraction of Retained Users who become Paid Users from 2% per month to 4% per month.

Which of these is the best option for the company? Surprisingly, they all are.

For case C, decreasing the subscription cancellation ratio (the fraction of Paying Users who stop their paid plan) from 5% to 4% has obvious economic benefits. It is the equivalent of increasing the average lifetime of a customer from 20 months to 25 months. At a subscription price of $25 per month, this increases the lifetime value of a customer (LTV) by $125. The result is that the maximum amount of cash the company holds would now reach a peak of over $7.8 million around 200 months after the product launch. This is an increase of more than $2 million over the life of the company compared to the base case.

If our only goal is to maximize the total profit the company makes, then it looks like reducing the subscription cancel ratio is the best place to focus our efforts. However, both the base case and case C result in the company early in its life reaching a cash position of less than $80,000. If any of our estimates from the model – the initial pool of Potential Users, the churn ratio, the  rate of downloading the app – are wrong, or if there are any large unexpected expenses in the first few years of the company’s operation, then the company’s cash position could reasonably drop to zero and it would go bankrupt.

To minimize the chance of the company going bust, we should want the company’s minimum cash position to be as large as possible. For the cases we are considering here case D, increasing the fraction of Retained Users who become Paid Users each month from 2% to 4%, results in the company reaching profitability without the cash position ever going below $165,000. The maximum cash position for this case would be $6.55 million in month 158. So, increasing the ‘conversion to paid’ fraction results in less total profit overall, but with a lower chance of going bankrupt. If our goal is to minimize the chance of going bankrupt, case D, focusing on increasing the rate at which Retained Users become Paying Users, is our best option.

But if our goal is to maximize the rate at which we earn profit, then we are better off with case B, reducing the churn rate from 80% to 76%. At month 125, the cash position will be $6.35 million, for a net profit of $5.85 million in only 125 months, or $46,800 per month. We could quit (or sell) the business at that point and move on to the next venture, leaving someone else to squeeze the last profit out of a declining business over its last five or six profitable years.

So, depending on whether our goal is to maximize the company’s total profit, minimize the chance of going bankrupt, or maximize the rate per month at which we earn profit, we should focus our efforts on improving three separate aspects of the company’s business.


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