# Where is your business headed?

# Metrics and long-term profitability

*Morten Elk, www.simplesite.com*

## Introduction

One of the great questions when building a startup is how to measure progress or success. What should I measure and optimize? What are good or even excellent metrics? How do I convince myself and possibly investors that although numbers are small, I have an engine of growth that will eventually lead to a very profitable business?

Eric Ries persuasively argues in The Lean Startup that we should avoid focusing on “vanity metrics” and drop the “success theater” and instead zoom in on the “engine of growth” and the essential parameters that characterize that engine. Depending on the specific growth model, these are, among others, the viral coefficient, retention, lifetime value (LTV) etc. The main point is that unless you identify these parameters and monitor and improve them, you are not really building a sustainable success. On the other hand, if you get the underlying parameters right and manage to consistently improve them, you have the making of a successful business and although numbers might be small yet, although you might actually still be burning cash, your business is on the long-term growth and profitability track.

We present a model that we are using in SimpleSite to analyze the connection between key metrics in our service and the long-term profitability of the business. It is based on modeling the subscriber base as the water level in a leaky bathtub and allows us to make very specific predictions about our business. The model looks as follows and we'll get back to how to turn this picture into very useful predictions and insights.

## The setup

SimpleSite (and related European services) is a website builder that focuses on simplicity and user-friendliness, and is sold on a premium subscription model. We acquire new subscribers through advertising (e.g. AdWords) and viral effects. In this sense, we are a very traditional subscription business.

We have found it crucial to find a way to relate the right fundamental metrics to very precise predictions about the long-term consequences for our business. We need to be able to answer questions like “are we acquiring enough new subscribers for long-term profitability”, “are we acquiring customers at an acceptable cost” etc. A subscription business is something you build over time. You invest in customers in the short term and get long-term recurring revenues from those customers in the long term. It is vital be able to look ahead and make sure, you are making the right decisions today, building your business of tomorrow.

We have developed a prediction model that allows us to continuously make analytic predictions about the future of the business. To be able to turn basic metrics into very specific predictions has been a tremendous decision making support while developing the business – e.g. on assessing sales channels, deciding whether to open new markets etc.

We wish to share the methods, since we believe that the methods and specific formulae could be of similar use to any business that is based on a premium subscription model – which in fact represents a large class of on-line and (off-line) businesses.

In the following, I will outline our model of growth and then move on to showing how we can infer very specific predictions from the model - like customer lifetime value, long-term revenues, critical numbers for a profitable business. I have also made an example spreadsheet for download that allows for experimenting with the model with numbers for other businesses that have a similar underlying growth engine.

## The model - qualitatively

Simplesite.com is a website building and hosting service. It is run as a premium service. Users get to try the service for 30 days and then decide whether to have their website close or to continue as paying subscribers.

The main parameters of the business model are straightforward: Customers are acquired through paid advertising and viral effects (people visiting SimpleSite websites might make one, too). Customers pay a fixed subscription fee while subscribing and a certain percentage of subscribers stop subscribing in a given period of time (churn). We have a variable cost associated with a subscription (bandwidth, storage, domain fees).

The simplest way to picture the subscriber base is a bathtub. The water level represents the number of subscribers. New subscribers are continually “poured in” through paid acquisitions with a viral boost factor. Viral effects further grow the subscriber number at a rate proportional to the number of existing subscribers. Finally, subscribers are lost at a rate proportional to the number of subscribers.

An interesting observation that is intuitively clear from the picture is that as the water level grows, the loss grows with it. At some point the loss exactly balances the inflow and the water cannot rise further. This maximum water level or maximum subscriber number is the long-term stable state of the business. Given unchanged parameters, there is no way to get more subscribers than this. Unless churn is somehow lowered or inflow is somehow raised (buy more advertising, increase the viral effects), there really is a maximum or finite steady state for this business. That is what we call the long-term scenario.

## The model - analytically

Given the above picture, it is fairly straightforward to write down how the subscriber base evolves form one month to the next. Let us first define the parameters:

\( S \) | Number of paying subscribers |

\( \Delta S \) | Change in number of paying subscribers from one month to the next |

\( P \) | New subscribers acquired per month through paid channels (Google AdWords, partners, 1-1 permission emails etc.) |

\( V \) | New subscribers acquired per month through viral effects |

\( v \) | Viral factor. How many new viral subscribers do we get per month for each existing subscriber with an open website? This viral factor means that all paying subscribers cause a stream of new viral subscribers all the time. |

\( b \) | Sales boost factor. Another form of short-term viral effect. As new subscriber starts, she will be especially enthusiastic and communicative about her new website in the first few weeks. The factor b tells us how many extra subscribers this causes in the very short term. |

\( l \) | Churn or loss factor per month. Percentage of existing subscribers that started the month as subscribers, but are not subscribers anymore by the end of the month. |

\( r \) | Revenue per month per subscriber |

\( {LTV}^+ \) | Lifetime value from one paid acquisition of a subscriber. Here, we are taking the revenue caused by a customer purchase, not the net profit. The + indicates that we also include the revenue from the viral effects (short and long-term) of this paid subscriber acquisition. |

\( a \) | Acquisition cost per subscriber. |

\( c \) | Variable costs per subscriber per month. |

\( F \) | Fixed costs for the entire business and independent of number of subscribers. |

The viral acquisition of customers per month is straightforwardly given as

\[ V=bP+vS \]The complete change in the subscriber base from one month to the next is thus

\[ \Delta S=P-lS+bP+vS \]This can be entered directly in a spreadsheet – given the parameters, one can predict the subscriber base month by month. The spreadsheet linked at the end of this post shows such a month-by-month evolution.

## Long-term predictions

We are more ambitious, though, and want to have an actual formula that predicts how this business will behave in the long run. SimpleSite is a typical subscription business in which churn is larger than the viral effects and therefore, we must constantly feed new subscribers into the subscriber base by paid acquisitions of new subscribers. The maximum - or long-term - size of the subscriber base is a balance between acquisition, churn and viral effects. To us, it is vitally important to know this long-term situation, since it tells us what our long-term profitability (or lack thereof…) is.

In order to have a healthy long-term business, the revenues coming from the long-term subscriber base must be sufficient to yield a profitable business after fixed costs, sales costs and variable costs are paid.

To get the long-term prediction, we set \( \Delta S=0 \), representing that a steady situation has evolved. That can be solved for \( S \) and yields

\[ S_{const}= \frac{1+b}{l-v} P \]So, given acquisition, churn and viral effects, we have a simple formula for predicting the maximum and final number of subscribers \( S_{const} \) that this business will evolve towards in the long run.

Note, that this becomes arbitrarily large, if the viral coefficient \( v \) balances the loss factor \( l \) . In that case, the subscriber base will just keep growing and there is no steady state. This also means that decreasing the gap between the viral coefficient and the loss factor has dramatic effects on the obtainable size of the business.

The average lifetime of a single subscriber (paid or viral) is

\[ T= \frac{1}{l} \]Much more important for the sustainability of business, though, is the net lifetime revenue obtained as a consequence of one paid acquisition and all viral after-effects of that acquisition. That is calculated to be

\[ {LTV}^+ = \frac{1+b}{l-v} r \]Finally, we can do the complete long-term business case. If we are able stick to these parameters, where is our business headed? The predicted long-term earnings are

Earnings = revenue – acquisition costs – variable costs – fixed costs

or

\[ E= ( \frac{1+b}{l-v} (r-c)-a)P-F \]This brings everything together. We have to acquire customers at a rate high enough that the revenues minus acquisition costs and variable costs outweigh the fixed costs. All the important parameters in the engine of growth combine here to make a prediction about the long-term profitability; acquisition rate and cost, viral effects and churn. With these results in hand, it is actually very simple to see if a given set of underlying parameters will sustain a profitable business. From parameters that are readily measurable in only weeks or months, it is possible to make very long-term predictions about the health of the business - to assess whether the business is on the track of long-term profitability or not.

From this equation, it is also possible in a completely straightforward way to ask and answer important question such as

- Would it be profitable to acquire twice as many customers at a 50% higher price per customer?
- How many paid customer acquisitions do we need per month have break-even in the long-term perspective?
- What would be the effect on long-term earnings (and thus our company value) if we could increase the viral effect by 20%?
- Are we dead in the water if the price per acquisition increases by 20%?
- And many more…

The profitability per paid subscriber is easily calculated as well. Each paid subscriber incurs a sales cost, some variable costs and a revenue over her total lifetime.

Including also the effects of the viral customers caused by this paid customer, the net profit contribution resulting from one extra paid subscriber is

\[ d= \frac{1+b}{l-v} (r-c)-a \]The contribution must be positive or you are losing money acquiring customers, which sets a limit to your acquisition cost per customer:

\[ a \lt \frac{1+b}{l-v} (r-c) \]And you need as well to acquire enough customers that the contribution from all of them can cover your fixed costs and yield some profits in the long perspective.

## Other interesting observations

One can calculate the net viral effect per acquired customer, \( n \). This tells us how many additional customers we get in the long run for every customer we acquire through paid channels:

\[ n=b+ \frac{1+b}{l-v} v \]One can also approximate the repayment time, \( t \) (in months). That is the time it takes before all the revenues coming from a paid acquisition and the associated viral effects have balanced the acquisition cost and the variable costs incurred. It tells you the time it takes to reach break-even for one paid acquisition:

\[ t= \frac { ln ( a \frac{v-l}{(1+b)(r-c)}+1)}{v-l} \]## Example

Assume that you have the following underlying metrics:

\( P \) | 5.000 | New subscribers acquired per month through paid channels (Google AdWords, partners, 1-1 permission emails etc.) |

\( v \) | 0.5% | Every paying subscriber causes 0.005 new paying subscribers per month through viral effects. |

\( b \) | 30% | Viral sales boost. Every new sale (conversion) causes 0.3 more conversions on a short time-scale. |

\( l \) | 5% | 5% of all subscribers are lost due to churn every month. (Bandwidth costs, customer service salaries, ...) |

\( r \) | $5 | Average revenue per month per subscriber. |

\( a \) | $50 | Customers acquired through paid channels have an average cost of $50. |

\( c \) | $0.50 | Variable costs per subscriber per month. |

\( F \) | $200,000 | The cost of general salaries, rent etc per month. But not variable costs that scale with the subscriber number - they should be calculated per customer and included in \( c \). |

In this case, the long-term subscriber number is \( S_{const}= 144.000 \) subscribers - not a result which would be entirely obvious from the basic metrics above, if we did not have the aid of the formulae. The revenue generated as a consequence of one customer purchase is \( {LTV}^+ = \$ 144 \), or roughly three times the acquisiton cost of \( \ $50 \). The repayment time is \( n = \$ 11 \) months, which is not really that long. Finally - and most importantly - we find that the business is long-term profitable, having yearly long-term profits of \( \$ 2,400,000 \). Without some aid of modeling and analytics, this prediction would be rather hard to get at from the basic metrics.

The Excel model mentioned below uses these parameters and one can freely play around with different parameters to see, what the effect is of changing for instance churn, viral effects, customer acquisition rates etc. It is particularly enlightning to play with churn and viral effects as they have significant effects on the profitability. In our business, such knowledge has provided very strong incentives to perform A/B experiments to improve viral effects and lower churn. It is quite amazing to see what a 10% lowered churn can mean to the long-term business.

## Excel model

I have created an Excel spreadsheet here that implements all the formulas and allows for quick investigations with parameters pertaining to your own business.

The spreadsheet can be found here.

## References

Eric Ries, The Lean Startup

Dave McClure, Startup Metrics for Pirates, AARRR

More Startup Metrics for Pirates

More Startup Metrics for Pirates

Andrew Chen, Is Your Website a Leaky Bucket

For entrepeneurs