# Price vs volume: how many customers can a discount lose?

> The price vs volume trade-off: how much volume a price cut must win, or a price rise may lose, before contribution moves.

- 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 17/32, ~27 min
- Source: https://productovi.com/courses/finance-for-product/price-vs-volume

## Leo's September discount

**Alex Tutor:** Autumn planning at Klasna: you're still on the product team, and Leo has a pricing idea. It's the classic price vs volume question.

**Leo:** September is coming, and I want 10% off every English 16-pack. Last autumn we tested it for a month: 520 packages sold instead of the usual 400. That's 30% more!

**Hanna:** 30% more packages. How much more contribution?

**Sofia:** The price per lesson drops from 620 to 558 UAH. Do the costs drop too?

**Alex Tutor:** Only one of them. The payment fee is 2.5% of the price, so it goes from 15.50 to 13.95. The tutor still gets 390, video and AI still cost 30. So one lesson now leaves 558 − 390 − 13.95 − 30 = **124.05 UAH**.

**Alex Tutor:** Before, it left 184.50. The price fell by 62 hryvnias, and 60.45 of them came straight out of contribution margin. A 10% cut in price is a 33% cut in what each lesson earns.

**Alex Tutor:** Quick check before the next number: which costs actually move with the price?

> **Exercise:** Klasna cuts the price of an English lesson by 10%. Which of these costs **per lesson** change as a result? Select all that apply.

**Alex Tutor:** Try the same on maths, where the margin is a little thicker.

> **Exercise:** A maths lesson in the 16-lesson package costs 670 UAH; the tutor gets 420, video + AI cost 30, the fee is 2.5% of the price. What **contribution margin per lesson** is left after a 10% discount?

## How much volume a price cut needs to stand still

**Sofia:** So how many more lessons do we need to earn the same as before?

**Alex Tutor:** Total contribution is lessons × contribution per lesson. Keep the total and the lessons must grow by the ratio of the two margins: 184.50 / 124.05 = 1.487. That is **48.73% more lessons** just to stand still.

$$
\frac{Q_1}{Q_0} = \frac{CM_0}{CM_1} \qquad \Delta Q\% = \left(\frac{CM_0}{CM_1} - 1\right) \times 100
$$

*Q₀, Q₁: lessons before and after the price change; CM₀, CM₁: contribution margin per lesson before and after.*

**Alex Tutor:** Now apply it to last autumn's test, before Hanna shows her numbers.

> **Exercise:** In a usual month Klasna sells 400 English 16-packs at full price, leaving 184.50 UAH of contribution per lesson. In last autumn's test month it sold 520 packages at 10% off, leaving 124.05 per lesson. By how much did the month's **total contribution** change? (Negative if it fell.)

**Hanna:** Now last autumn's test. A usual month: 400 packages × 16 × 184.50 = 1,180,800 UAH. The test month: 520 × 16 × 124.05 = 1,032,096. We sold more and kept **148,704 less**.

**Leo:** But sales went up! 4,642,560 against 3,968,000.

**Alex Tutor:** By 17%, while contribution fell by 12.59%. Sales rose because families paid more in total; the tutors got paid for every extra lesson too. To match a usual month, the test needed 400 × 1.487 ≈ 595 packages, not 520.

> **Exercise:** Leo now considers **15% off** the English 16-pack (620 UAH a lesson, tutor 390, video + AI 30, fee 2.5%). By what percentage must lessons grow to keep the same total contribution margin?

## Why thin margins hurt most

**Sofia:** 5% needs about 20% more, 10% needs 49%, 15% almost 97%. It grows much faster than the discount.

**Extra lessons needed to keep the same contribution, English 16-pack**

| Discount | Extra lessons needed, % |
| --- | --- |
| 5% | 19.59 |
| 10% | 48.73 |
| 15% | 96.64 |
| 20% | 190.09 |

*Each discount comes almost entirely out of the 184.50 UAH a lesson leaves; the extra volume needed is CM₀ / CM₁ − 1.*

**Alex Tutor:** Each extra point of discount eats into a smaller and smaller margin. At 20% off a lesson leaves 63.60 UAH, so you need almost three times the lessons.

**Alex Tutor:** The thinner the margin to start with, the steeper the climb. What matters is the contribution margin ratio: the share of the price a lesson keeps.

**Hanna:** Programming lessons leave more hryvnias than English but a smaller share of their price. Guess which one a 10% discount hurts most.

> **Exercise:** A 10% discount on which package needs the **biggest** increase in lessons to keep the same contribution margin? (Per lesson: English 8-pack 650 UAH, CM 213.75; English 16-pack 620, CM 184.50; maths 16-pack 670, CM 203.25; programming 16-pack 720, CM 206.)

## Price increase: how many customers can you lose?

**Sofia:** Does the same logic work for a price rise? How many families could we lose?

**Alex Tutor:** Same formula, other direction. +5% makes the lesson 651, the fee 16.28, and contribution 214.73. The same total now needs only 184.50 / 214.73 = 0.859 of the lessons.

**Alex Tutor:** So Klasna could lose up to **14.08%** of its lessons after a 5% rise and still earn the same. A 5% discount needs 19.59% more; a 5% rise can afford to lose 14.08%.

**Hanna:** I'd still check who leaves. If it's the families who buy the most, the 14% shrinks fast.

**Leo:** And how strongly people react to a price, we never know in advance.

**Alex Tutor:** That reaction is called **[price elasticity](/glossary/fin-price-elasticity)**, and you rarely know it upfront. So don't start from a guess about demand: compute the volume the change needs, then ask whether that number is believable.

> **Exercise:** Klasna raises the English 16-pack price by **10%** (620 → 682 UAH a lesson; tutor 390, video + AI 30, fee 2.5%). Up to what share of lessons can it lose and still keep the same total contribution margin?

## Who got the discount

**Sofia:** Back to the test. The 120 extra packages still earned something. So where did the 148,704 go?

**Alex Tutor:** Split the buyers. The 120 new packages each left 16 × 124.05 = 1,984.80, so 238,176 UAH in all. Real money.

**Alex Tutor:** But the 400 families who buy every month anyway got the discount too: 400 × 16 × 60.45 = 386,880 UAH they would have paid us at full price. 238,176 − 386,880 = −148,704.

**Leo:** So the discount worked on new families and was a gift to the loyal ones.

**Hanna:** A gift worth 386,880 UAH a month. If it reaches only new families, it's a different decision.

> **Exercise:** **True or false:** last autumn's test lost contribution because the 120 extra packages were sold below their variable costs.

**Alex Tutor:** If you do give a discount, design it so the gift doesn't go to the wrong people.

> **Exercise:** Last autumn 10% off for everyone won 120 new packages (+238,176 UAH) but gave 386,880 UAH away to 400 families who buy every month anyway. Which September offer keeps the gain and drops the gift?

## Your turn: answer Leo

**Leo:** Fine, I get the maths. So: 10% off for everyone in September, yes or no?

**Sofia:** Not for everyone. It needs almost half as many lessons again, and last time it got 30%.

**Hanna:** And September has its own crowd: families coming back after the summer. They'd buy at full price.

**Alex Tutor:** Then say it to Leo in a few sentences: the margin numbers, what the test showed, and what you would do instead.

> **Exercise:** Leo asks: "10% off every English 16-pack in September, yes or no?" An English 16-pack lesson (620 UAH) leaves 184.50 UAH of contribution margin; after 10% off it leaves 124.05. Last autumn's month-long test sold 520 packages at 10% off instead of the usual 400. Write him a short reply (3–5 sentences) with the contribution numbers, the volume the discount needs, what last autumn's test showed, and what you'd do instead.

> **Key ideas**
>
> - A discount comes almost entirely out of contribution margin: 10% off the English 16-pack takes it from 184.50 to 124.05 UAH, a 33% drop.
> - Volume needed to keep the same contribution: CM₀ / CM₁ − 1. For 10% off: **+48.73%**; for 15%: +96.64%; for 20%: +190.09%.
> - The lower the contribution margin ratio, the more volume a discount needs (programming +51.69% vs English 8-pack +42.14%).
> - A price rise works the other way: +5% can lose up to 14.08% of lessons, +10% up to 24.68%.
> - Check who gets the discount: in last autumn's test the extra buyers added 238,176 UAH, the usual buyers took 386,880, net −148,704.
> - Compute the volume a price change needs, then judge whether it's believable.

**Alex Tutor:** Next time: what a family is worth over its whole life with Klasna, and when its acquisition cost comes back in cash.

- Previous lesson: [Case: can Klasna grow Teams without a loan?](https://productovi.com/courses/finance-for-product/teams-growth-case.md)
- Next lesson: [Discounted LTV and CAC payback in cash](https://productovi.com/courses/finance-for-product/ltv-and-cac-payback-in-cash.md)

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