C02 · Lesson 2 of 22 · 14 min · 5 hands-on tasks
Cost-Volume-Profit Analysis
How much must Trailhead sell to stop losing money, and does it matter which bikes? Work out the contribution margin ratio, break-even revenue and the sales needed for a profit target, then discover why selling more of the 'exciting' e-bike pushes break-even further away.
🎥 Watch it (3 min)
🎬 Situation
Theo has sorted Trailhead's costs: $32.3M variable, $21.7M fixed, on $50M of sales. That leaves $17.7M of contribution, $4M short of the fixed costs.
The board asks one question: how much do we need to sell to break even? The answer turns out to depend on which bikes.
| Bike | Price | Variable cost | Contribution | CM ratio | Revenue |
|---|---|---|---|---|---|
| City | $600 | $380 | $220 | 36.7% | $18M (30,000 bikes) |
| Trail | $1,200 | $700 | $500 | 41.7% | $18M (15,000) |
| E-Cargo | $3,500 | $2,600 | $900 | 25.7% | $14M (4,000) |
🎮 Play
Profit vs sales, with a mix. Slide total revenue and the share each bike takes. The profit line crosses zero at break-even.
Hold revenue at $50M and drag E-Cargo's share up. The marker (break-even) runs away from you.
Build the CVP sheet. Theo's one-page answer for the board.
| A | B | |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| 9 | ||
| 10 |
- B5: CM ratio = contribution ÷ revenue, =B4/B2
- B8: break-even = fixed costs ÷ CM ratio
- B9: (fixed costs + 3) ÷ CM ratio
- B10: margin of safety = (revenue − break-even) ÷ revenue
🏷️ Name it
| Term | Formula | Trailhead |
|---|---|---|
| Contribution margin | Revenue − variable costs | $17.7M |
| CM ratio | Contribution ÷ revenue | 35.4% |
| Break-even revenue | Fixed costs ÷ CM ratio | $61.3M |
| Target-profit revenue | (Fixed costs + target profit) ÷ CM ratio | $69.8M for a $3M profit |
| Margin of safety | (Revenue − break-even) ÷ revenue | −22.6% |
| Operating leverage | Contribution ÷ operating profit | Very high near break-even |
| Sales mix | Each product's share of sales | 36% / 36% / 28% |
With one product you can break even in units: fixed costs ÷ contribution per unit. With several, use the mix-weighted CM ratio and break even in revenue, or use a weighted contribution per "bundle" of bikes.
🖍️ Like you're five: a lemonade stand that keeps 40 cents of every dollar needs $50 of sales to pay a $20 table rental. If it starts selling cookies that keep only 20 cents a dollar, it needs more sales to pay the same table.
Real life: CVP assumes prices, variable cost per unit, fixed costs and mix all stay put. Real life moves all four. Use CVP for fast, rough answers ("we need about $61M"), then test the assumptions with scenarios.
🔨 Do it: 5 tasks
0 / 5 doneTask 1 of 5 · The Trail bike's ratio
A Trail bike sells for $1,200 and has $700 of variable costs. What's its contribution margin ratio? Round to one decimal.
Task 2 of 5 · Break-even revenue
Trailhead's fixed costs are $21.7M and its overall CM ratio is 35.4%. What revenue breaks even? Answer in $ millions, one decimal.
Task 3 of 5 · Ten percent more sales
Contribution is $17.7M and fixed costs $21.7M. If sales rise 10% (same mix, same fixed costs), what's the new operating profit? Answer in $ millions.
Task 4 of 5 · A mix shift
CM ratios: City 36.7% ($220 ÷ $600), Trail 41.7%, E-Cargo 25.7% ($900 ÷ $3,500). If revenue becomes 30% City, 30% Trail, 40% E-Cargo, what's the overall CM ratio? One decimal.
Task 5 of 5 · What lowers break-even?
Which change lowers Trailhead's break-even revenue?
🧩 Case: "E-Cargo is our way out"
⭐ VIPTrailhead's CEO has a plan: "E-cargo is the fastest-growing part of the bike market. We'll put all our marketing behind it and sell $10M more E-Cargo bikes next year. That fixes the loss." Extra marketing: $1M.
Theo runs the numbers: $10M more revenue at E-Cargo's 25.7% CM ratio. What's the effect on profit?
What would you do? VIP members make the call, see what happens next across 2 decisions, and get the expert debrief.
🔁 Remember it
A company has a 40% CM ratio and $2M of fixed costs. Break-even revenue is...
Margin of safety measures...
Contribution $10M, operating profit $1M: operating leverage is 10×. A 5% drop in sales cuts profit by...
Contribution margin ratio = contribution ÷ revenue. Break-even revenue = fixed costs ÷ CM ratio; revenue for a target profit = (fixed costs + target) ÷ CM ratio. With several products, the sales mix sets the CM ratio, so a mix shift toward low-margin products raises break-even. Operating leverage (contribution ÷ operating profit) shows how hard profit swings when sales move.
📅 Use it Monday
For your product or team, find three numbers: revenue, variable costs, fixed costs. Work out the CM ratio and break-even. Then ask: if our mix shifted to our cheapest product, how far would break-even move?
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