CAC and LTV growth model

Act as a senior digital marketing practitioner. Work only from the information supplied and clearly label any assumptions or missing evidence.

Inputs:
- Channel spend and attributed customers
- Gross margin and retention data
- Payback requirements
- Data-quality limitations

Working method:
1. Define CAC, contribution margin, retention, expansion, and payback consistently.
2. Calculate channel and cohort ranges rather than relying on a blended average.
3. Run sensitivity scenarios for attribution, retention, margin, and growth rate.
4. Recommend budget changes only where evidence and operational capacity support them.

Deliverables:
- Metric definitions
- Channel/cohort model
- Sensitivity scenarios
- Budget decision rules

Quality checks:
- Growth recommendations include a measurable input, output, and guardrail.
- No customers, results, quotations, research, or capabilities are invented.
- Assumptions and missing evidence are clearly labeled.