# Discounted LTV and CAC payback in cash

> What a customer is worth in today's money and when their acquisition cost comes back.

- Course: [Finance for Product People: From Unit Economics to Business Cases](https://productovi.com/courses/finance-for-product.md)
- Module: Does growth pay for itself?
- Lesson 18/32, ~29 min
- Source: https://productovi.com/courses/finance-for-product/ltv-and-cac-payback-in-cash

## Leo's LTV slide

**Alex Tutor:** Back at Klasna's product team: Leo is building an investor deck and is proud of one slide.

**Leo:** For the investor deck: a family pays us about 28,000 UAH in its first year, and winning it costs 4,000. LTV is seven times CAC!

**Hanna:** 28,000 is what the family pays. Most of it leaves the same month, to the tutor. An investor will ask what stays with us.

**Sofia:** So LTV should be counted on contribution margin, not on sales?

**Alex Tutor:** Yes: **LTV** is what a customer leaves us over their life, so contribution margin, never sales or GMV. Here is one cohort: the 60 families who first paid in October 2025, after 240,000 UAH of ads that month.

**Alex Tutor:** So **CAC**, the cost of acquiring one family, is 240,000 / 60 = 4,000 UAH. They take English 16-packs, so every lesson leaves 184.50.

**Dataset (CSV):** [October 2025 cohort: 60 families, twelve months](https://productovi.com/datasets/finance-for-product/ltv-and-cac-payback-in-cash/klasna-cohort-oct-2025.csv)

One row per month since the families first paid. Contribution margin is lessons × 184.50 UAH (English 16-pack).

- `month`: Calendar month
- `months_since_start`: Months since the first payment: 0 = October 2025
- `active_families`: Families from the cohort who took lessons that month
- `lessons`: Lessons the cohort took that month
- `contribution_uah`: Contribution margin of those lessons, UAH

**Alex Tutor:** Add up the contribution column and divide by the 60 families who started, including those who left. That is the 12-month LTV per family.

> **Exercise:** Use the cohort table: 60 families first paid in October 2025, and `contribution_uah` is the cohort's contribution margin each month. What is the **12-month contribution margin per family** (divide by all 60 families who started)?

## A hryvnia in September is worth less

**Sofia:** 8,330 is still more than twice the CAC. But the September contribution arrives a whole year after we paid for the ads.

**Alex Tutor:** Right, and money that comes later is worth less today: Klasna could have used it meanwhile, and later money is less certain. So we **discount** each month's contribution back to October.

**Hanna:** For growth spending I use 2% a month, about 26.8% a year. Month k is divided by 1.02 to the power k; the October month stays as it is.

$$
LTV_{disc} = \sum_{k=0}^{11} \frac{CM_k}{(1 + r)^k} \qquad \text{payback: first } k \text{ with } \sum_{j=0}^{k} CM_j \ge CAC
$$

*CMₖ: contribution margin per family who started, in month k after the first payment; r: discount rate per month (2%).*

**Alex Tutor:** Done for all twelve months, the 8,330.18 becomes a **discounted LTV** of 7,683.74 UAH: 646 less. LTV to CAC is 7,683.74 / 4,000 = 1.92.

**Leo:** 1.92? Everyone says you need three.

**Alex Tutor:** That's a rough rule, not a law. And we stopped at twelve months: families still with us in September keep paying. What matters more is how soon the 4,000 comes back and whether we can fund the wait.

> **Exercise:** In September 2026 (month 11) the cohort leaves 26,937 UAH of contribution margin, 448.95 per family who started. What is that worth **in October 2025 money** at 2% a month?

**Alex Tutor:** Leo's "everyone says three" deserves an answer of its own.

> **Exercise:** The October cohort's discounted 12-month LTV is 7,683.74 UAH and CAC is 4,000: LTV/CAC = 1.92, below the "LTV should be three times CAC" rule Leo has heard. What should Klasna conclude?

## When the 4,000 comes back

**Sofia:** Payback, then: when does the cumulative contribution per family reach 4,000?

**Alex Tutor:** Find the month yourself first, then I'll walk the table.

> **Exercise:** Use the cohort table. CAC is 4,000 UAH per family. In which **months_since_start** (0 = October 2025) does the cumulative contribution margin per family who started first reach 4,000?

**Alex Tutor:** Walk down the table. October leaves 1,199.25 per family. By the end of January the total is 3,896.03, still short. February adds 802.58: 4,698.60. CAC is paid back in the fifth month.

**Hanna:** Discounted, the total by February is 4,537.09: same month. Over five months, waiting costs little. It is the long tail of the LTV where discounting bites.

**Alex Tutor:** And mind the cash dates. The 240,000 left Klasna in October, all at once. Only 71,955 came back that month. The gap until February is paid from Klasna's own bank account.

**Alex Tutor:** Put a number on that gap.

> **Exercise:** Klasna paid 240,000 UAH for the October cohort's ads, all in October 2025. The families pay as they go, so their contribution arrives as cash in the month of the lessons. Using the cohort table, how much of Klasna's own cash is still tied up in the cohort at the end of **January 2026** (months 0–3)?

> **Exercise:** Match each number about the October cohort to what it is.

## Same LTV, different cash

**Hanna:** For these families contribution and cash move together: they pay for packages, we pay tutors twice a month. Klasna for Teams is different.

**Sofia:** Because companies pay their invoices 30 to 60 days late?

**Alex Tutor:** Exactly. A Teams client can have the same LTV, yet its cash comes two months behind the lessons, while the tutors are paid on time. So its **CAC payback in cash** comes later than its payback on paper.

**Alex Tutor:** The opposite also happens: a family that prepays a 32-pack hands us cash before the lessons happen. Count payback on the dates money actually moves.

> **Exercise:** **True or false:** for a Teams client who pays each invoice 60 days after the lessons, the CAC payback month in cash comes **later** than the payback month counted on contribution margin.

## What makes payback shorter

**Leo:** If payback is what we have to fund, how do I make it shorter?

**Alex Tutor:** Three levers: a lower CAC, more contribution in the first months, and fewer families leaving early. Each one either lowers the bar or makes the line climb faster.

**Hanna:** Our cohort loses 9 of its 60 families after the first month. Keeping them is worth more than any discount, which only lowers what each lesson leaves.

**Alex Tutor:** And timing: being paid earlier, as with a prepaid package, brings payback in cash forward without changing the LTV at all.

> **Exercise:** Which changes would bring the CAC payback **in cash** of a cohort like October's earlier?

## Your turn: fix the slide

**Leo:** So what goes on my slide instead of "LTV is 7× CAC"?

**Alex Tutor:** One honest line plus the numbers behind it. Investors trust a smaller number they can check more than a big one they can't.

**Alex Tutor:** If you want the cohort mechanics in more depth, the product analytics course covers [CAC, payback and ROI](/courses/product-analytics/cac-payback-roi). Here we keep the finance view.

**Sofia:** Contribution, discounted, and payback on cash dates. Got it.

> **Exercise:** Leo's slide says a family pays about 28,000 UAH in its first year and costs 4,000 to win (240,000 UAH of ads for the 60 October families), so "LTV is 7× CAC". Rewrite that claim for the October cohort (3–5 sentences). Say what LTV should be based on, give the discounted LTV, the LTV/CAC ratio and the payback month, and name one limitation of the numbers.

> **Key ideas**
>
> - **LTV** is the contribution margin a customer leaves over their life, never sales or GMV. October cohort: 8,330.18 UAH per family in 12 months, not 27,993.
> - **CAC** = acquisition spend ÷ customers it brought: 240,000 / 60 = 4,000 UAH.
> - **Discount** later months: month k is divided by (1 + r)ᵏ. At 2% a month the LTV is 7,683.74 UAH, LTV/CAC 1.92.
> - **Payback** is the first month where cumulative contribution per customer reaches CAC: February, the fifth month (4,698.60). Discounting barely moves a short payback; it shrinks the long tail.
> - Count payback on **cash dates**: late B2B payers push it out, prepaid packages pull it in. The gap until payback is cash the company must have.

**Alex Tutor:** Next time we scale this up: what happens to the bank account when Klasna acquires more families every month.

- Previous lesson: [Price vs volume: how many customers can a discount lose?](https://productovi.com/courses/finance-for-product/price-vs-volume.md)
- Next lesson: [Overtrading: why fast growth eats cash](https://productovi.com/courses/finance-for-product/growth-eats-cash.md)

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