Customer Unit Economics Sensitivity and Payback Report

Role: Senior Growth Marketing Analyst & Unit Economics Specialist

Context

• Commercial Model Architecture: {{business_model}}
• Evaluated Traffic Streams: {{acquisition_channels}}
• Historic Churn & Retention Vectors: {{historical_churn_rate}}
• Monetization Baseline: {{average_order_value}}
• Contribution Profitability: {{gross_margin_pct}}
• Payback Horizon Target: {{target_payback_months}}

Task

Author a customer acquisition unit economics sensitivity report that decomposes Customer Lifetime Value (LTV), establishes maximum allowable Customer Acquisition Cost (CAC) thresholds, and identifies payback velocities across {{acquisition_channels}}.

Method

1. Model customer cohort survival functions using {{historical_churn_rate}} across 12, 24, and 36-month horizons.
2. Compute discounted Lifetime Value (LTV) incorporating {{average_order_value}} and {{gross_margin_pct}}.
3. Calculate maximum allowable CAC per channel that guarantees cost recovery within {{target_payback_months}}.
4. Build a multi-variable sensitivity matrix displaying LTV:CAC ratios under +/- 15% variances in churn, margin, and conversion rate.
5. Benchmark current channel performance in {{acquisition_channels}} against the theoretical unit-economic efficiency frontiers.
6. Identify capital drag where payback periods exceed {{target_payback_months}} and isolate high-velocity compounding segments.
7. Formulate capital allocation constraints and bidding bounds to maintain healthy unit economics across all channels.

Constraints

• MUST explicitly present all formulas and financial mechanics used to derive LTV and CAC limits.
• MUST NOT assume linear churn behavior unless justified by {{historical_churn_rate}} cohort patterns.
• All margin calculations must factor in {{gross_margin_pct}} rather than raw top-line revenue.
• Projections must account for cash-flow lag and discount rate impacts over the payback window.

Output format

Deliver an analytical unit economics report formatted as follows:

1. Unit Economics Overview (summary of baseline LTV, target CAC thresholds, and current efficiency index)
2. Cohort Decay & Payback Horizon Analysis (mathematical evaluation of break-even velocity against {{target_payback_months}})
3. Sensitivity Matrix (markdown table showing LTV:CAC fluctuations under churn and margin stress scenarios)
4. Channel Acquisition Guidance (specific spending ceilings, target CAC ranges, and reallocation mandates per channel) Total report length must be between 650 and 900 words.

Self-review

• Is every channel listed in {{acquisition_channels}} assigned an explicit CAC threshold?
• Does the payback calculation adhere strictly to {{target_payback_months}} using {{gross_margin_pct}}?
• Are the sensitivity scenarios mathematically consistent across both expansion and contraction iterations?