---
title: "Customer lifetime value and CAC numerical"
subject: "Entrepreneurship Development"
chapter: 4
key: "semester_7/entrepreneurship_development:ltv-cac-unit-economics"
source: https://www.bctengineer.com/q/semester_7/entrepreneurship_development/ltv-cac-unit-economics
site: BCT Engineering
---

# Customer lifetime value and CAC numerical

Entrepreneurship Development · Chapter 4: Business Model

- Asked in: year not given, 6 marks
- Video: [How to Calculate Customer Lifetime Value | The #1 Most Important Metric for Startups](https://www.youtube.com/watch?v=eHi875QuVcA) — Eric Andrews
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/entrepreneurship_development/ltv-cac-unit-economics
- Whole chapter: https://www.bctengineer.com/md/semester_7/entrepreneurship_development/chapter-4

## Question

A subscription startup charges Rs 500 per customer per month. Gross margin is 60% and monthly churn is 5%. It spent Rs 3,00,000 on marketing and sales in a month and gained 150 new customers. Calculate (a) average customer lifetime, (b) customer lifetime value (LTV), (c) customer acquisition cost (CAC), (d) the LTV:CAC ratio and the CAC payback period. Comment on the result.

## Short answer

Lifetime = 20 months. LTV = (500 x 0.60) x 20 = Rs 6,000. CAC = 3,00,000 / 150 = Rs 2,000. LTV:CAC = 3, payback = 2,000 / 300 = 6.67 months. The ratios (≥3 and <12 months) indicate healthy unit economics.

## Answer

#### 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. With 5% monthly churn, the customer lifetime is:
   A. 20 months
   B. 5 months
   C. 12 months
   D. 50 months
   Answer: A. 1/0.05 = 20 months. (Key point: Lifetime)

2. LTV is:
   A. Rs 10,000
   B. Rs 6,000
   C. Rs 300
   D. Rs 2,000
   Answer: B. Monthly gross profit 500 x 0.6 = 300; x 20 = 6,000. (Key point: LTV)

3. CAC is:
   A. Rs 3,000
   B. Rs 500
   C. Rs 2,000
   D. Rs 200
   Answer: C. 3,00,000 / 150 = Rs 2,000. (Key point: CAC)

4. LTV:CAC and payback are:
   A. 3 and 20 months
   B. 6 and 3.3 months
   C. 1.5 and 6.67 months
   D. 3 and 6.67 months
   Answer: D. 6,000/2,000 = 3; payback = 2,000/300 = 6.67 months, meeting the rule of thumb. (Key point: Ratio and payback)

## Related in Entrepreneurship Development

- [Break-even analysis for a startup](https://www.bctengineer.com/question.md?key=semester_7%2Fentrepreneurship_development%3Abreak-even-analysis-numerical) — Entrepreneurship Development, chapter 5
- [Marketing strategies, pricing and credit policy](https://www.bctengineer.com/question.md?key=semester_7%2Fentrepreneurship_development%3Amarketing-strategy-price-credit) — Entrepreneurship Development, chapter 5
- [NPV and payback of a startup project](https://www.bctengineer.com/question.md?key=semester_7%2Fentrepreneurship_development%3Anpv-payback-startup-project) — Entrepreneurship Development, chapter 5
- [Cost-plus pricing numerical](https://www.bctengineer.com/question.md?key=semester_7%2Fentrepreneurship_development%3Apricing-cost-plus-numerical) — Entrepreneurship Development, chapter 3
- [Market study and customer feedback](https://www.bctengineer.com/question.md?key=semester_7%2Fentrepreneurship_development%3Amarket-study-feedback) — Entrepreneurship Development, chapter 2
- [Customer segmentation and target segment](https://www.bctengineer.com/question.md?key=semester_7%2Fentrepreneurship_development%3Acustomer-segmentation-bases) — Entrepreneurship Development, chapter 4

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