Customer Lifetime Value Calculation

Solution & Explanation

Understanding Customer Lifetime Value (LTV): Customer Lifetime Value (LTV) is a metric that estimates the total revenue a business can expect from a customer over the duration of their relationship. It considers both the revenue generated and the retention of customers over time.

Given Data:

• Monthly Subscription Price: $100
• Monthly Churn Rate: 10% (0.1)
• Average Customer Tenure: 3.5 months

Key Points:

1. Churn Rate vs. Average Tenure:

   • The average tenure of 3.5 months might not be representative due to the company's short operational period.
   • The churn rate provides a more stable metric for predicting future customer behavior.

2. Formula for LTV Using Churn Rate:

   • The formula for LTV in a subscription model is:

     $\text{LTV} = \frac{\text{ARPU}}{\text{Churn Rate}}$

   • ARPU (Average Revenue Per User) is the monthly subscription price, $100.

   • Churn Rate is 0.1 (10%).

3. Calculation:

   $\text{LTV} = \frac{100}{0.1} = 1000$

   • Thus, the Lifetime Value of a customer is $1000.

Explanation of the Calculation:

• Revenue Stream:

  • Each month, a customer pays $100.
  • With a churn rate of 10%, the retention rate is 90% (0.9).

• Expected Revenue Over Time:

  • Month 1: All customers pay $100.
  • Month 2: 90% of customers remain, so expected revenue is $100 * 0.9.
  • Month 3: 81% remain (0.9 * 0.9), so revenue is $100 * 0.9^2.

• Infinite Series Sum:

  • The expected revenue can be expressed as an infinite geometric series:

    $\text{LTV} = 100 \times (1 + 0.9 + 0.9^2 + 0.9^3 + \ldots)$

  • The sum of this infinite series is:

    $\text{Sum} = \frac{1}{1 - 0.9} = 10$

  • Therefore, the LTV is:

    $\text{LTV} = 100 \times 10 = 1000$

Conclusion:

• The calculation using the churn rate provides a more reliable estimate of LTV, especially given the company's short operational history.
• This method accounts for the continual decline in customer base due to churn, providing a realistic forecast of the revenue from a single customer over their lifetime.