📐 Mathematical Formula & Derivation
\text{LTV} = \frac{\text{ARPU}_{month} \times \text{GM}_{\%}}{\text{Churn}_{month}}, \quad \text{Payback}_{months} = \frac{\text{CAC}}{\text{ARPU}_{month} \times \text{GM}_{\%}} 🔬 Engineering Methodology & Benchmark Analysis
A common mistake among early-stage founders is calculating LTV using gross revenue (ARPU ÷ Churn) while ignoring Cost of Goods Sold (COGS)—especially in AI-powered SaaS where LLM inference and GPU costs reduce gross margins from 85% down to 60%–70%.
Institutional investors require Gross-Margin Adjusted LTV. A healthy venture-scale SaaS business maintains an LTV:CAC ratio of at least 3.0x to 5.0x and recovers its CAC in under 12 months.
🛠️ Step-by-Step Engineering Calculation Guide
- Average Monthly Revenue per Account (ARPU / ARPA): Configure "Average Monthly Revenue per Account (ARPU / ARPA)" (default benchmark: 149) or select an industry preset.
- Gross Margin % (After Hosting, LLM APIs & Support): Configure "Gross Margin % (After Hosting, LLM APIs & Support)" (default benchmark: 78) or select an industry preset.
- Monthly Net Revenue / Logo Churn Rate (%): Configure "Monthly Net Revenue / Logo Churn Rate (%)" (default benchmark: 3.2) or select an industry preset.
- Fully Loaded Customer Acquisition Cost (CAC): Configure "Fully Loaded Customer Acquisition Cost (CAC)" (default benchmark: 850) or select an industry preset.