02 // Visual Math & Finance SolversQ* = Fixed Cost / (Price − Variable Cost), Profit = (P − VC)·Q − FC
Visual Break-Even Point & Cost-Volume-Profit (CVP) Crossover Chart
Break-even analysis finds the critical unit volume $Q^* = \frac{\text{Fixed Costs}}{\text{Unit Price} - \text{Variable Cost}}$ where Total Revenue equals Total Cost ($\text{Operating Profit} = 0$), with each unit sold beyond $Q^*$ generating pure Contribution Margin $CM = P - VC$.
Q* = Fixed Cost / (Price − Variable Cost), Profit = (P − VC)·Q − FCInputs & Parameters (4)
$
1000$±1000200000$
$
5$±5500$
$
1$±2400$
u
100u±505000u
Break-Even Units (Q*)
800 units
Break-Even Revenue = $64,000
Operating Profit @ Q=1400
$30,000
Net profitable zone
Unit Contribution Margin
$50.00 / unit
CM Ratio = 62.5% of revenue
Operating Leverage (DOL)
2.33×
Margin of Safety = 42.9%
20-Row Comparison Table
Compare across:
| # | Fixed Overhead Costs (FC) ($) | Break-Even Volume (Q*) | Profit @ Q=1400 | CM Ratio |
|---|---|---|---|---|
| 01 | 1,000 $ | 20 u | $69,000 | 62.5% |
| 02 | 11,000 $ | 220 u | $59,000 | 62.5% |
| 03 | 22,000 $ | 440 u | $48,000 | 62.5% |
| 04 | 32,000 $ | 640 u | $38,000 | 62.5% |
| 05 | 43,000 $ | 860 u | $27,000 | 62.5% |
| 06 | 53,000 $ | 1,060 u | $17,000 | 62.5% |
| 07 | 64,000 $ | 1,280 u | $6,000 | 62.5% |
| 08 | 74,000 $ | 1,480 u | -$4,000 | 62.5% |
| 09 | 85,000 $ | 1,700 u | -$15,000 | 62.5% |
| 10 | 95,000 $ | 1,900 u | -$25,000 | 62.5% |
| 11 | 106,000 $ | 2,120 u | -$36,000 | 62.5% |
| 12 | 116,000 $ | 2,320 u | -$46,000 | 62.5% |
| 13 | 127,000 $ | 2,540 u | -$57,000 | 62.5% |
| 14 | 137,000 $ | 2,740 u | -$67,000 | 62.5% |
| 15 | 148,000 $ | 2,960 u | -$78,000 | 62.5% |
| 16 | 158,000 $ | 3,160 u | -$88,000 | 62.5% |
| 17 | 169,000 $ | 3,380 u | -$99,000 | 62.5% |
| 18 | 179,000 $ | 3,580 u | -$109,000 | 62.5% |
| 19 | 190,000 $ | 3,800 u | -$120,000 | 62.5% |
| 20 | 200,000 $ | 4,000 u | -$130,000 | 62.5% |
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Key Analytical Takeaways
- 01Unit Contribution Margin ($CM = P - VC$) determines the vertical wedge angle between the Revenue line and the Total Cost line.
- 02To the left of the Break-Even Crossover ($Q < Q^*$), the crimson wedge represents net operating loss; to the right ($Q > Q^*$), the teal wedge represents net operating profit.
- 03Margin of Safety measures how far current sales $Q$ can drop before hitting break-even: $(Q - Q^*) / Q$.
Frequently Asked Questions
What happens if Variable Cost per unit is greater than or equal to Selling Price?+
Contribution margin becomes zero or negative (CM ≤ 0), meaning the business loses money on every additional unit sold and the revenue line never crosses the cost line.
How do I calculate the units needed for a specific Target Profit?+
Add Target Profit to the numerator: Q_target = (Fixed Costs + Target Profit) / (Price − Variable Cost).
What is the contribution margin ratio?+
Contribution Margin Ratio = (Unit Price − Unit Variable Cost) / Unit Price, measuring the fraction of each revenue dollar available to cover fixed overhead and generate operating profit.