Break-even point in units and margin of safety

The break-even point in units is the number of lessons whose contribution exactly covers all fixed costs of the month. Below it the month loses money; above it every extra lesson adds its contribution to profit.

Two inputs:

• Contribution per lesson = (lesson sales − variable costs) ÷ lessons. March 2026: 4,868,640 − (3,136,000 + 121,716 + 243,040) = 1,367,884 UAH over 7,840 lessons = 174.48 UAH.
• Total fixed costs = coordinators + team + office and tools + marketing. March: 114,000 + 540,000 + 84,000 + 300,000 = 1,038,000 UAH.

Break-even = 1,038,000 ÷ 174.48 = 5,949.1, rounded up to 5,950 lessons, because a part of a lesson earns nothing. At 5,949 lessons March would still be slightly short.

The monthly mix matters: March's 174.48 is below the 184.50 of an English 16-pack lesson, because the month mixes subjects and package sizes, and 32-lesson packages earn less per lesson.

The margin of safety says how far lessons can fall before a month reaches break-even:

margin of safety = (lessons delivered − break-even) ÷ lessons delivered

March 2026: (7,840 − 5,950) ÷ 7,840 = 24.11%. March could have lost almost a quarter of its lessons and still covered every fixed cost.

May, the exam peak, step by step:

1. Variable costs: 3,867,240 + 150,072 + 298,220 = 4,315,532 UAH.
2. Contribution: 6,002,880 − 4,315,532 = 1,687,348, or 175.40 UAH per lesson.
3. Fixed costs: 152,000 + 540,000 + 84,000 + 320,000 = 1,096,000 (a fourth coordinator since April, a bigger marketing budget).
4. Break-even: 1,096,000 ÷ 175.40 = 6,248.6 → 6,249 lessons.
5. Margin of safety: (9,620 − 6,249) ÷ 9,620 = 35.04%.

May's line is higher than March's, but lessons grew faster, so May is safer. Always divide by actual lessons, not by break-even.

The same five steps work for any month: variable costs, contribution, contribution per lesson, fixed costs, then break-even and the distance from it.

February 2026:

1. Variable costs: 2,700,033 + 104,719.33 + 209,777 = 3,014,529.33 UAH.
2. Contribution: 4,188,773 − 3,014,529.33 = 1,174,243.67 UAH.
3. Per lesson: 1,174,243.67 ÷ 6,767 = 173.53 UAH.
4. Fixed costs: 114,000 + 540,000 + 84,000 + 260,000 = 998,000.
5. Break-even: 998,000 ÷ 173.53 = 5,751.2 → 5,752. Margin of safety: (6,767 − 5,752) ÷ 6,767 = 15.00%.

Set next to other months, the margin of safety reads like a weather report: February 15.00%, March 24.11%, May 35.04%, and July −85.38%. A positive number is how far lessons can fall before a loss; a negative one is how far the month already is below the line. Keep the rounding order: round break-even up first, then compute the percentage.

Operating leverage explains why profit moves faster than lessons. Fixed costs stay put when volume changes, so every extra lesson's contribution goes straight to profit.

degree of operating leverage = contribution ÷ operating profit

March 2026: operating profit = 1,367,884 − 1,038,000 = 329,884 UAH. Leverage = 1,367,884 ÷ 329,884 = 4.15.

What it means: a 10% change in lessons moves operating profit by about 4.15 × 10% ≈ 41% in the same direction. Ten percent more lessons add about 136,788 UAH of contribution, which is 41% of 329,884. Ten percent fewer lessons remove the same 136,788.

Leverage is roughly 1 ÷ margin of safety: 1 ÷ 0.2411 ≈ 4.15. The closer a month sits to its break-even line, the smaller its profit and the harder that profit swings. May, with a 35.04% margin of safety, has a leverage of about 2.85; it is calmer.

Klasna's year, September 2025 to August 2026, closed with +744,174.72 UAH of operating profit. True, and not the whole story.

Five months sat below their break-even line: September, December, June, July and August. Together they lost 1,029,144.15 UAH; July alone lost 391,490. The other seven months earned 1,773,318.87, and that is what the year adds up to.

So the yearly profit depends on a strong spring. From February to May Klasna earned 5,834,066.77 UAH of contribution. With 20% fewer lessons in those months, about 1.17 million of contribution would disappear, more than the whole year's profit, and the same summer would turn the year into a loss.

The habit to build: when someone quotes a yearly profit, ask for each month's line and margin of safety. Then propose something concrete for the weak months, such as lower summer fixed costs or a summer product, instead of only a warning.

Break-even points differ from month to month, because fixed costs and contribution per lesson differ. In July Klasna had only two coordinators and 150,000 UAH of marketing, so fixed costs fell to 850,000 and the line dropped to 4,820 lessons, well below March's 5,950.

That does not make July safer. Safety is the distance between actual lessons and the line:

• March: 7,840 lessons against a line of 5,950, margin of safety +24.11%, operating profit 329,884 UAH.
• July: 2,600 lessons against a line of 4,820, margin of safety (2,600 − 4,820) ÷ 2,600 = −85.38%, operating loss 391,490 UAH.

A negative margin of safety means the month sits below its line: contribution of 458,510 could not cover 850,000 of fixed costs.

So never compare lines alone. Compare each month's lessons with its own line, and read the sign of the margin of safety first.

Break-even = total fixed costs ÷ contribution per lesson. So only two things move the line:

• Total fixed costs change: more marketing, a fifth coordinator once learners pass 1,600 (a step cost), a new hire on the team. Higher fixed costs raise the line.
• Contribution per lesson changes: a price rise or a lower payment fee raises contribution and lowers the line; a higher tutor payout or a bigger discount does the opposite.

What does not move it:

• Selling more lessons. 500 extra bookings move Klasna along the line, not the line itself; they raise the margin of safety.
• A new tutor on the usual payout. Tutors are paid per lesson delivered, so a new one adds no fixed cost and leaves contribution per lesson unchanged.

Every fixed-cost decision has a price in lessons a month. A fourth coordinator in March would have cost 38,000 ÷ 174.48 ≈ 218 more lessons; 20,000 UAH of extra ads would have moved the line from 5,950 to 6,064.

Any change in fixed costs can be translated into lessons a month: extra fixed cost ÷ contribution per lesson. It is the clearest way to show a manager what a decision really asks of the business.

March 2026 as the base: fixed costs 1,038,000 UAH, contribution 174.48 UAH per lesson, break-even 5,950 lessons.

• +20,000 UAH of ads: 1,058,000 ÷ 174.48 = 6,063.8 → 6,064 lessons, 114 more.
• +38,000 UAH for a fourth coordinator: about 218 more lessons.
• +40,000 UAH of marketing: 1,078,000 ÷ 174.48 = 6,178.36 → 6,179 lessons, 229 more.

Recompute the whole line (new fixed costs ÷ contribution, rounded up) rather than adding a rounded increment to the old line; the two can differ by a lesson.

The same view works the other way: price changes contribution per lesson, so a price rise means the same fixed costs need fewer lessons. Either way, the question is not "can we afford 40,000?" but "can we sell 229 more lessons a month?"