← Blog

The Math Behind CLTV for a SaaS Business

Jan 20, 2021  ·  6 min read  · 

Anyone working in the marketing and finance business function is introduced to CLTV (Customer Lifetime Value) early in their academic and professional life. Few, however, get to calculate this very important metric from scratch. In all fairness, it is not mandatory to know the math behind calculating the value as long as one understands the concept behind it.

I am glad you have decided to learn the math behind Customer Lifetime Value. Take a comfortable seat, a pen, a notebook, and your favorite drink. We will be spending a few hours with CLTV, the most important metric in SaaS business, specifically in marketing investment. I will share a step-by-step derivation of LTV for a SaaS business model.

Customer Lifetime Value (CLTV) is an estimate of how much, on average, a customer will spend during their lifetime. Lifetime is defined as the duration between the first and last cycle of their subscription. Although LTV can be calculated for all types of business, it is particularly useful for a subscription business. It is an essential metric for assessing the financial health of a subscription business and adjusting customer acquisition cost (CAC). Prioritizing marketing channels based on LTV may help increase conversion, while minimizing churn in a market segment with higher LTV can help maintain MRR growth. A good rule of thumb is to maintain an LTV:CAC of 3 or higher.

Elements of LTV

There are a few elements considered for LTV calculation:

Subscription Models

In B2B as well as B2C domains, there are a few subscription models:

I will focus on LTV calculations for two types: Basic LTV for Fixed-Rate/Tier-Based subscriptions and Advanced LTV for Per-User/Per-Feature subscriptions where the latter involves contraction/expansion revenue.

Basic LTV

This method takes a simplistic approach and only works for businesses with a Fixed-Rate Subscription and constant monthly retention rate. Say a company has a churn rate of 1% from the first to second billing cycle, and so on.

The formula for basic LTV is:

LTV = ARPA × Average Customer Lifespan

LTV = ARPA / Customer Churn Rate

Where ARPA is average revenue per account/user, and Customer Lifespan is the average number of days between the first and last order date. These two formulas show that Average Customer Lifespan is the reciprocal of Customer Churn Rate. For example, if a business has a monthly churn rate of 1% (0.01), the estimated average customer lifespan is 1/0.01 = 100 months (approximately 8 years).

To get an accurate picture of LTV, it is important to take Gross Margin into consideration:

LTV = (ARPA × Gross Margin %) / Customer Churn Rate

Example: A company offers a subscription at $10 per user per month with a gross profit margin of 40% and a monthly retention rate of 97% (churn rate = 3%). The average customer lifespan is 1/0.03 = 33.33 months.

LTV = ($10 × 0.40) × 33.33 = $133.33

LTV = ($10 × 0.40) / 0.03 = $133.33

Since we are calculating customer acquisition cost in terms of present value, we also need to account for the discount rate (interest rate) applied to the present value of future cash flows. The value of $10 spent today acquiring a customer is higher than the $10 received from that customer after 3 years.

Advanced LTV

The single most important distinction between Basic LTV and Advanced LTV is expansion/contraction revenue — additional revenue generated due to upgrades (features or users) or deductions due to downgrades or cancellations.

The formula proposed by Stan Reiss in David Skok's post on LTV assumes a consistent revenue expansion/contraction or steady ARPA growth in amount (not growth rate). For scenarios with variable retention rate and ARPA, the equations can be generalized accordingly.

An example with constant ARPA and retention rate is available in HBR. For variable ARPA and retention rates, the calculation requires building cohort models with interest rates varying between 7%–12%. The payback period approach is recommended for early and growth-stage startups where LTV may not yet be accurate due to limited data.

Payback Period

The payback period is generally defined as the time it takes to recover the cost of marketing spend through revenue. It involves predicting revenue over time based on historical retention rates across cohorts, typically calculated for 12 to 18 months.

Fixed MRR — step by step:

  1. Get the number of active users over a 12, 18, or 24-month cycle for each cohort.
  2. Calculate the retention rate for each month compared to the first month for each cohort.
  3. Calculate the average retention rate over billing cycles across all cohorts.
  4. Multiply the monthly fixed subscription price with the retention rate.
  5. Sum the values to get the LTV.

Variable Retention Rate — step by step:

  1. Get the number of active users over a 12, 18, or 24-month cycle for each cohort.
  2. Sum total revenue of active users over each billing cycle for each cohort.
  3. Calculate ARPA by dividing total revenue by active users over the billing cycle for each cohort.
  4. Sum the values to get the LTV for each cohort.
  5. Calculate mean, median, and confidence interval to estimate LTV.

I hope this covers some of the most common use cases for calculating LTV. If you have any questions or need clarification, feel free to reach out.