Scenario: Your company sells a smart HVAC control platform to commercial buildings. You need to calculate the 5-year customer lifetime value to justify a high customer acquisition cost.
Given metrics:
- ARPU: $450/month (includes $350 platform fee + $100 average add-on modules)
- Gross margin: 72% (platform is SaaS, low COGS)
- Monthly churn: 1.8% (98.2% retention)
- Initial setup fee: $8,000 (one-time, year 1 only)
Step 1: Calculate monthly LTV contribution with churn
Month 1: $450 × 0.72 × 1.000 = $324.00 Month 2: $450 × 0.72 × 0.982 = $318.17 Month 3: $450 × 0.72 × (0.982)² = $312.44 … Month 60: $450 × 0.72 × (0.982)^59 = $112.08
Step 2: Sum 60 months of recurring revenue
Using geometric series formula: LTV_recurring = ARPU × Margin × Σ(retention^month) from m=0 to 59
With Excel: =4500.72SUMPRODUCT((0.982^ROW(A1:A60))) = $16,847
Step 3: Add one-time setup revenue
Setup LTV = $8,000 × 0.72 = $5,760
Total 5-year LTV = $16,847 + $5,760 = $22,607
Business decision: With this $22,607 LTV, the company can justify spending up to $7,500 CAC (3:1 ratio) or $4,500 CAC (5:1 target ratio) on sales and marketing. At current CAC of $6,200, the business has healthy 3.6:1 unit economics, suitable for moderate growth investment.
Key insight: The 1.8% monthly churn (vs hypothetical 3% churn) adds $5,200 to LTV – a massive difference justifying significant investment in customer success to maintain low churn.