# Break-even point in units and margin of safety > Break-even point in units: how many lessons a month cover the fixed costs, and how far sales can fall before a loss. - Course: [Finance for Product People: From Unit Economics to Business Cases](https://productovi.com/courses/finance-for-product.md) - Module: What does one lesson earn us? - Lesson 3/32, ~29 min - Source: https://productovi.com/courses/finance-for-product/break-even ## A profitable year with a losing July **Alex Tutor:** Back at Klasna's product team: the year's results are in, and Leo is in a good mood. **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. **Sofia:** So the question is which months pay for themselves, not whether the year did. **Alex Tutor:** That line is the **break-even point in units**: 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. $$ c = \frac{S - V}{Q} \qquad Q_{BE} = \left\lceil \frac{F}{c} \right\rceil $$ *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.* **Dataset (CSV):** [Klasna by month, September 2025 – August 2026](https://productovi.com/datasets/finance-for-product/break-even/klasna-monthly-costs.csv) Lessons, lesson sales and every cost line for 12 months. Amounts in UAH. - `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) **Alex Tutor:** 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**. **Alex Tutor:** 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. **Alex Tutor:** 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. > **Exercise:** 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. ## Margin of safety: how far from the line **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. For March that's 7,840 − 5,950 = 1,890 lessons, or as a share of actual lessons, (7,840 − 5,950) ÷ 7,840 = **24.11%**. **Alex Tutor:** March could have lost almost a quarter of its lessons and still covered every fixed cost. Beyond that, each lost lesson is a loss. **Sofia:** 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. > **Exercise:** 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. **Alex Tutor:** One more month to make the steps automatic: February, the last month before spring. > **Exercise:** Use the February 2026 row. What was Klasna's **margin of safety** in February? Round the break-even point up to a whole lesson, then give the margin of safety in percent to two decimals. ## Degree of operating leverage: why profit moves faster **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. The **degree of operating leverage** is contribution ÷ operating profit: 1,367,884 ÷ 329,884 = **4.15**. **Alex Tutor:** 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. > **Exercise:** Klasna's operating leverage in March was 4.15. What does that tell Leo? ## July and the whole year **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**. **Alex Tutor:** 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. **Sofia:** 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:** Two replies Leo could hear. Which one uses the numbers honestly? > **Exercise:** Klasna's year (September 2025 – August 2026) closed with +744,174.72 UAH of operating profit. Five months were below their break-even point. Leo says: "We made a profit, so summer doesn't matter." Which reply is better? > **Exercise:** 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. ## What moves the line **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. The formula for any online business: [break-even point](/blog/break-even-point). **Alex Tutor:** 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. > **Exercise:** Which of these would move Klasna's monthly break-even point? Select all that apply. **Alex Tutor:** Now put a price in lessons on one of Leo's ideas. > **Exercise:** In March 2026 Klasna's fixed costs were 1,038,000 UAH and each lesson contributed 174.48 UAH. If Leo had spent **40,000 UAH more** on marketing that month, what would the break-even point have been? Round up to a whole lesson. ## An answer for Leo > **Three numbers for every month** > > - **Break-even point:** total fixed costs ÷ contribution per lesson, rounded up. > - **Margin of safety:** (lessons delivered − break-even) ÷ lessons delivered. > - **Operating leverage:** contribution ÷ operating profit; roughly 1 ÷ margin of safety. > > A yearly total can hide months below the line. **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. **Sofia:** Got it: numbers first, then a proposal. > **Exercise:** Leo says: “We made a profit for the year, so summer doesn't matter.” The year closed at +744,174.72 UAH of operating profit, but five months (September, December, June, July and August) lost 1,029,144.15 UAH together. Reply to him in 3–5 sentences, using Klasna's numbers, and suggest what to do about summer. **Alex Tutor:** When someone quotes a yearly profit, ask for each month's line. That's where summer shows up. - Previous lesson: [Cost behavior: fixed, variable and step costs](https://productovi.com/courses/finance-for-product/fixed-variable-and-step-costs.md) - Next lesson: [Case: should Klasna launch group lessons?](https://productovi.com/courses/finance-for-product/group-lessons-case.md) --- Productovi Learning. Free, no sign-up needed to read.