Break-even point and margin of safety: a worked example

Leo

Good news: September to August closed with about 744 thousand UAH of operating profit. Summer is always quiet, and we still end in the black. So summer doesn't matter, right?

Hanna

July alone lost 391 thousand. I want one number per month: how many lessons just cover the fixed costs. And how far each month is from that line.

You

So the question is which months pay for themselves, not whether the year did.

Alex Tutor

That line is the break-even point: the number of lessons whose contribution exactly covers total fixed costs. Below it, the month loses money; above it, each extra lesson adds its contribution to profit.

Alex Tutor

c = \frac{S - V}{Q} \qquad Q_{BE} = \left\lceil \frac{F}{c} \right\rceil

c: contribution per lesson; S: lesson sales for the month; V: variable costs (tutor payouts, payment fees, video and AI); Q: lessons delivered; F: total fixed costs (coordinators, team, office and tools, marketing). Round up: there's no such thing as part of a lesson.

Alex Tutor

Dataset · 12 rows

Klasna by month, September 2025 – August 2026

Lessons, lesson sales and every cost line for 12 months. Amounts in UAH.

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Columns
month: Month (YYYY-MM)
active_learners: Learners with at least one lesson that month
lessons_delivered: 1:1 lessons delivered
lesson_sales_uah: What families paid for the lessons delivered, UAH
tutor_payouts_uah: Tutor payouts, UAH (variable)
payment_fees_uah: Payment-provider fees, UAH (variable)
video_ai_uah: Video minutes and AI, UAH (variable)
support_coordinators_uah: Support coordinators, UAH (fixed, steps up with learners)
team_salaries_uah: In-house team salaries, UAH (fixed)
office_tools_uah: Office and tools, UAH (fixed)
marketing_uah: Marketing, UAH (fixed: set each month, doesn't grow per lesson)

Data

month	active_learners	lessons_delivered	lesson_sales_uah	tutor_payouts_uah	payment_fees_uah	video_ai_uah	support_coordinators_uah	team_salaries_uah	office_tools_uah	marketing_uah
2025-09	820	5002	3056222	1980792	76405.55	155062	114000	540000	84000	190000
2025-10	900	5850	3591900	2322450	89797.5	181350	114000	540000	84000	240000
2025-11	950	6270	3862320	2495460	96558	194370	114000	540000	84000	240000
2025-12	880	5192	3203464	2066416	80086.6	160952	114000	540000	84000	200000
2026-01	930	5952	3678336	2374848	91958.4	184512	114000	540000	84000	240000

Show 7 more rows

2026-02	1010	6767	4188773	2700033	104719.33	209777	114000	540000	84000	260000
2026-03	1120	7840	4868640	3136000	121716	243040	114000	540000	84000	300000
2026-04	1260	9198	5721156	3688398	143028.9	285138	152000	540000	84000	320000
2026-05	1300	9620	6002880	3867240	150072	298220	152000	540000	84000	320000
2026-06	760	4256	2655744	1710912	66393.6	131936	76000	540000	84000	180000
2026-07	520	2600	1627600	1047800	40690	80600	76000	540000	84000	150000
2026-08	580	3016	1888016	1215448	47200.4	93496	76000	540000	84000	210000

Take March. Lesson sales: 4,868,640 UAH. Variable costs: 3,136,000 + 121,716 + 243,040 = 3,500,756. That leaves a contribution of 1,367,884 over 7,840 lessons: 174.48 UAH per lesson.

That's below the 184.50 UAH of an English lesson in a 16-lesson package: March mixes subjects and package sizes, and 32-lesson packages earn less per lesson.

Now the fixed side: coordinators, the team, office and tools, and marketing. We set marketing each month, but it doesn't grow per lesson, so it's fixed here too.

Alex Tutor

Question 1

Use the March 2026 row. Contribution per lesson is 174.48 UAH. How many lessons did Klasna need in March to break even? Add up the four fixed-cost lines and round up to a whole lesson.

Your answer

Units: lessons

Hanna

March delivered 7,840 lessons. How do I show in one number how safe that is?

Alex Tutor

With the margin of safety: how far lessons can fall before you reach break-even, as a share of actual lessons. For March: (7,840 − 5,950) ÷ 7,840 = 24.11%.

March could have lost almost a quarter of its lessons and still covered every fixed cost. Beyond that, each lost lesson is a loss.

You

And May, the exam peak? Same steps?

Alex Tutor

Same steps. Watch the fixed side: a fourth coordinator started in April, and marketing went up. Try it.

Alex Tutor

Question 2

Use the May 2026 row. What was Klasna's margin of safety in May? Round the break-even point up to a whole lesson, then give the margin of safety in percent to two decimals.

Your answer

Units: % (e.g. 12.34)

Leo

If March had brought 10% more lessons, would we have made 10% more profit?

Alex Tutor

More than that. March operating profit is 1,367,884 − 1,038,000 = 329,884 UAH. Operating leverage is contribution ÷ operating profit: 1,367,884 ÷ 329,884 = 4.15.

Ten percent more lessons add about 136,788 UAH of contribution while fixed costs stay put. Profit grows by 136,788 ÷ 329,884 ≈ 41%.

Hanna

And it cuts both ways. Ten percent fewer lessons, and March profit drops by the same 41%.

Alex Tutor

Right. Leverage is roughly 1 ÷ margin of safety: 1 ÷ 0.2411 ≈ 4.15. The closer a month is to break-even, the harder its profit swings.

Alex Tutor

Question 3

Klasna's operating leverage in March was 4.15. What does that tell Leo?

Choose one answerEach lesson earns 4.15 times what it costs in tutor payouts, fees and videoMarch covered its fixed costs 4.15 times overA 10% change in lessons, up or down, moves operating profit by about 41% in the same direction10% more lessons would add about 41% to profit, but 10% fewer would cut it by only about 10%

Hanna

Now July. Only two coordinators and 150,000 on marketing, so fixed costs are 850,000 UAH, and break-even drops to 4,820 lessons.

Alex Tutor

A lower line, but July delivered 2,600 lessons, just over half of it. Contribution of 458,510 minus 850,000 of fixed costs: an operating loss of 391,490 UAH.

Five months sit below their line: September, December, June, July and August. Together they lose 1,029,144.15 UAH. Spring's profit covers that, and the year ends at +744,174.72 UAH.

Leo

So the year is fine. That's my point.

You

The year is fine because spring was strong. With 20% fewer lessons from February to May, the same summer would wipe out the whole profit.

Alex Tutor

Question 4

July's break-even point (4,820 lessons) is lower than March's (5,950), so July was closer to covering its fixed costs than March.

TrueFalse

Alex Tutor

Break-even moves only when total fixed costs or contribution per lesson change. Selling more lessons doesn't move the line; it moves you along it.

Coordinators are a step cost: one per 400 active learners. A fourth in March would add 38,000 UAH, about 218 more lessons a month (38,000 ÷ 174.48 ≈ 217.8).

Leo

And if I add 20,000 UAH of ads in March?

Alex Tutor

The line moves from 5,950 to 6,064 lessons: 1,058,000 ÷ 174.48 = 6,063.8, rounded up. Every fixed-cost decision has a price in lessons a month.

Hanna

Price works from the other side: it changes contribution per lesson, so the same fixed costs need more lessons or fewer.

Alex Tutor

Question 5

Which of these would move Klasna's monthly break-even point? Select all that apply.

Choose all that applyLeo raises the monthly marketing spendA new English tutor joins at the usual payout of 390 UAH per lessonActive learners pass 1,600, so Klasna hires a fifth coordinatorFamilies book 500 more lessons than plannedKlasna raises the price of 16-lesson packagesThe payment provider cuts its fee from 2.5% to 2%

Alex Tutor

Leo

Fine, but one weak season is no reason to panic. Convince me in a few sentences.

Alex Tutor

Use what you have: each month's line, the distance from it, and what the yearly total hides.

Hanna

And give him something to do about it, not just a warning.

You

Got it: numbers first, then a proposal.

Alex Tutor

Question 6Short answer · AI-checked task

Leo says: “We made a profit for the year, so summer doesn't matter.” Reply to him in 3–5 sentences, using Klasna's numbers, and suggest what to do about summer.

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When someone quotes a yearly profit, ask for each month's line. That's where summer shows up.

Alex Tutor

That’s the lesson. You answered every task — nicely done.

Next lesson: Case: should Klasna launch group lessons?