Customer lifetime value and CAC numerical

Formulas

• Customer lifetime = 1 / churn rate
• LTV = monthly revenue per customer x gross margin x lifetime
• CAC = sales and marketing spend / new customers
• Payback = CAC / (monthly gross profit per customer)

(a) Lifetime

$$\text{Lifetime} = \frac{1}{0.05} = 20\ \text{months}$$

(b) LTV

Monthly gross profit per customer:

$$500 \times 0.60 = \text{Rs } 300$$ $$\text{LTV} = 300 \times 20 = \text{Rs } 6{,}000$$

(c) CAC

$$\text{CAC} = \frac{3{,}00{,}000}{150} = \text{Rs } 2{,}000$$

(d) Ratio and payback

$$\frac{\text{LTV}}{\text{CAC}} = \frac{6{,}000}{2{,}000} = 3$$ $$\text{Payback} = \frac{2{,}000}{300} = 6.67\ \text{months}$$

Comment

A common rule of thumb is LTV:CAC of at least 3 and a payback under 12 months. The startup meets both, so its acquisition spend is healthy and it can scale marketing, provided churn does not rise (at 8% churn the lifetime falls to 12.5 months and LTV to Rs 3,750, giving a ratio of only 1.9).

Answer: Lifetime = 20 months; LTV = Rs 6,000; CAC = Rs 2,000; LTV:CAC = 3; payback = 6.7 months.