## LTV Methods - the LTV Equation

The "LTV Equation" is one of the most widespread means of calculating LTV. It is both relatively simple to use, and highly illustrative of the factors that affect LTV, and this makes it a great first step in calculating LTV.

The LTV equation is particularly suited to estimating LTV at SaaS subscription companies, where Users pay consistent, pre-defined amounts on a periodic basis, and where churn can be easily estimated. However it has a number of limitations and makes a number of implicit assumptions about the nature of Users, Revenue, and User Churn that make it unsuitable for use by all companies.

This post is the third in our CAC-LTV series, and explores how to use the LTV Equation, when it works well, and when it should be used with caution. The preceding articles are "An Intro to Startup Operations" and "A Lighthearted Intro to CAC-LTV".

## LTV Equation

The LTV equation is simply: -

It's important to bear in mind the following points:

- Periodic Revenue / User can be monthly revenue, annual, daily etc.
- Periodic Churn Rate can also be monthly, annual, daily etc. - but it must be the
*same periodic basis*as the revenue - Gross Margin needs to include all
*direct costs*associated with producing the good or service. For example, customer support overhead should be included. - SaaS software companies often operate with Gross Margins on 85-100% - and so this factor in the equation is frequently overlooked - but be careful of making this assumption if you have significant direct costs.

We can immediately see which factors are important if you want to increase LTV: -

*User Spend*- LTV will be higher if your Users spend more*Operational Efficiency*- LTV is higher if your direct costs are lower*Retention*- LTV is higher when your Retention is higher (ie Churn is lower)

## When *to* Use the LTV Equation

The LTV equation is most accurate when applied to businesses with the following circumstances: -

- Users pay fixed amounts on a regular periodic basis
- Revenue amounts don't vary by User, subscription level, upgrade or downgrade packages
- Churn is a consistent proportion of Users irrespective of how long Users have been using the product
- Users are free to unsubscribe whenever

It is best applied to SaaS subscription companies with simple products, charged monthly, with few upgrade or downgrade options. For example, it would be ideal to use the LTV Equation to calculate the LTV of a user of QuickBooks, or someone subscribing to Dollar Shave Club.

## When *NOT to* Use the LTV Equation

However, the LTV equation becomes increasingly *inaccurate* if any of the following situations occur: -

- Revenue occurs on an irregular basis
- Revenue amounts vary significantly (either through upgrade / downgrade packages, or because the amount depends upon another factor - e.g. distance travelled by Uber)
- Churn tends towards 0%
- Revenue expansion is present
- Expected User life on platform exceeds 5-10 years

Unfortunately this means that the LTV equation is inaccurate for the majority of modern startups or modern business models. For example, it is completely inappropriate to use the LTV Equation to estimate the LTV of a Rider on Uber (irregular revenue, low churn, revenue expansion), a User of Facebook (long life of User on platform) or AirBnB (irregular timing and amount of revenues).

## Deriving the LTV Equation

The LTV equation was originally developed to model Users at SaaS subscription companies (hence it is most accurate at modelling these Users) and can be derived in the following way.

Our objective is to determine the likely future profit stream from an average User of a service. If we start by assuming that the User pays a simple, fixed amount on a periodic basis, then the graph of revenue from that User over time looks like this: -

Clearly that User will stop using the product at some point in time, and so will churn. Some Users will churn almost immediately, others will churn signficantly later. If we assume that the probability of any given User churning is consistent (for example, 5% of Users churn each Month), then the graph of the % of Users in any given cohort still being active is an exponential decay curve: -

The likely future revenue from any given User is consequently the spend of that average User over time, multiplied by the likelihood of that User being active - ie the multiple of the 2 graphs show above, which yields: -

This looks like the present value of a Perpetuity (a financial bond which pays a set amount each month perpetually), where the discount rate is now equal to the User churn rate. So we can use the perpetuity valuation formula to calculate the present value of this stream of revenues.

One minor adjustment is required though - we've been talking about Revenues, when in fact we're interested in the Value of a User to the Startup in question, and so we need to adjust this equation to a Profit basis by multiplying by the Gross Margin.

We simply replace the Dividend per Period with the Revenue per period per User multiplied by the Gross Margin, and we replace the discount rate with the periodic Churn rate, and we have derived the LTV Equation: -

## Assumptions Inherent in the LTV Equation

In order to derive the LTV Equation above, we've had to make a number of simplifying assumptions about the User, Revenues, and User Churn. Specifically: -

#### Constant, perodic, recurring Revenue

This assumption falls apart if there is any variability in either the timing or the amount of Revenue

#### Constant Churn - Exponential Decay of Users

This assumption is at odds with the concept of Product-Market-Fit. By definition of PMF, we'd expect the User retention curve to initially drop and then flatten off (due to losing initial non-fitting users, and then strongly retaining the remainder). Therefore a Startup with strong indications of PMF cannot be modelled using exponential churn.

#### No Revenue Expansion

Revenue expansion cannot easily be factored into this model - in particular, situations in which Revenue expansion exceed User Churn result in a negative denominator which leads to meaningless figures.

## Summary

The LTV Equation is a simple and powerful way of understanding LTV. It is highly indicative of the functions that improve LTV - that is, Spend per User, Operational Efficiency (Gross Margin) and User Retention (low Churn) - and therefore is means of understanding what a Startup needs to focus on in order to improve LTV.

However, the equation itself is derived by making a number of specific assumptions. This means that it is most accurate when applied to SaaS subscription business model, but becomes increasingly inaccurate when applied to other business models - particularly marketplace companies.

Therefore we recommend that the LTV Equation be used with caution, and with a clear understanding of its limitations

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