Break-even point analysis, target income, margin of safety and operating leverage.
Prince Sultan University · Reference: CMA Excel Learning System, Exam Review Part 1 and Part 2
How costs and volume move profit.
Important in profit planning, and a critical factor in decisions such as setting selling prices, choosing the product mix and making the best use of production facilities.
Level of activity.
What each unit sells for.
Raw materials, variable labor.
Utilities, taxes, depreciation.
The proportion of each product sold.
| Line | Total | Per unit |
|---|---|---|
| Sales | ✓ | ✓ |
| Less: Variable costs | ✓ | ✓ |
| = Contribution margin | ✓ | ✓ |
| Less: Fixed costs | ✓ | |
| Net income | ✓ |
The revenue left after deducting variable costs.
A maker of high-definition digital camcorders. Data for June 2026:
| Unit selling price | 500 |
| Unit variable costs | 300 |
| Total monthly fixed costs | 200,000 |
| Units sold | 1,600 |
| Sales (1,600 camcorders) | 800,000 |
| Variable costs | 480,000 |
| Contribution margin | 320,000 |
| Fixed costs | 200,000 |
| Net income | 120,000 |
A cell phone-operated thermostat. September 2026: price 85, variable cost 32 per unit, fixed costs 190,000 a month, 4,000 units sold.
| Total | Per unit | |
|---|---|---|
| Sales | 340,000 | 85 |
| Variable costs | 128,000 | 32 |
| Contribution margin | 212,000 | 53 |
| Fixed costs | 190,000 | |
| Net income | 22,000 |
What is left to cover fixed costs and earn a profit.
Contribution margin is available to cover fixed costs and to contribute to income. It can be computed in total and per unit.
| 1,000 units · zero net income | 1,001 units | Per unit | |
|---|---|---|---|
| Sales | 500,000 | 500,500 | 500 |
| Variable costs | 300,000 | 300,300 | 300 |
| Contribution margin | 200,000 | 200,200 | 200 |
| Fixed costs | 200,000 | 200,000 | |
| Net income | 0 | 200 |
Once fixed costs are covered, every extra unit adds its full contribution margin to net income.
Shows the percentage of each sales riyal available to apply toward fixed costs and profits.
Total CM ÷ Total sales = CM ratio %
Unit CM ÷ Unit selling price = CM ratio %
AbdulAziz: 200 ÷ 500. Every sales riyal adds 40 halalas to fixed costs and profit.
Current sales are 500,000. What does a 100,000 (200-unit) increase do?
| No change | With change | % of sales | |
|---|---|---|---|
| Sales | 500,000 | 600,000 | 100% |
| Variable costs | 300,000 | 360,000 | 60% |
| Contribution margin | 200,000 | 240,000 | 40% |
| Fixed costs | 200,000 | 200,000 | |
| Net income | 0 | 40,000 |
100,000 increase × 40% CM ratio = 40,000 more net income
Where total revenues equal total costs.
The level of activity at which total revenues equal total costs, fixed and variable.
Sales = Variable costs + Fixed costs + Net income.
Uses CM per unit or the CM ratio.
Where the total revenue and total cost lines cross.
Contribution margin equals total fixed costs. Total sales = total variable costs + total fixed costs. Expressed in units (use CM per unit) or in riyals (use the CM ratio).
Fixed costs ÷ CM per unit
200,000 ÷ 200
Fixed costs ÷ CM ratio
200,000 ÷ 40%
Check: 1,000 units × 500 = 500,000.
The level of sales needed to earn a specified income. Same three approaches as break-even: equation, contribution margin or CVP graph.
(Fixed costs + Target NI) ÷ CM per unit
( 200,000 + 120,000) ÷ 200
(Fixed costs + Target NI) ÷ CM ratio
( 200,000 + 120,000) ÷ 40%
The difference between actual or expected sales and break-even sales. The higher the riyals or percentage, the greater the margin of safety.
Actual sales − Break-even sales
750,000 − 500,000
Margin of safety ÷ Actual sales
250,000 ÷ 750,000
AbdulAziz Company, with actual or expected sales of 750,000.
Travel bags sell for 56. Fixed costs 320,000, variable costs 42 per unit.
CM ratio = ( 56 − 42) ÷ 56 = 25%
320,000 ÷ 25% = 1,280,000
1,382,400 − 1,280,000 = 102,400
102,400 ÷ 1,382,400 = 7.4%
( 320,000 + 410,000) ÷ 25%
= 2,920,000
How price, contribution margin and fixed costs move profit.
Today: 1,600 units × 75 unit CM = 120,000 CM − 45,000 fixed costs = 75,000 profit. Price is 400.
Sales rise from 1,600 to 1,725 units.
125 units × 75 = 9,375 more CM, less 8,000 fixed costs
Profit 76,375 · + 1,375
Sales rise from 1,600 to 1,900 units.
Unit CM falls to 50: 1,900 × 50 = 95,000 CM
Profit 50,000 · − 25,000
Sales rise from 1,600 to 2,600 units.
2,600 × 50 = 130,000 CM − 53,000 fixed costs
Profit 77,000 · + 2,000
| Today | A · Advertising | B · Price cut | C · Both | |
|---|---|---|---|---|
| Units sold | 1,600 | 1,725 | 1,900 | 2,600 |
| Unit CM | 75 | 75 | 50 | 50 |
| Total CM | 120,000 | 129,375 | 95,000 | 130,000 |
| Fixed costs | 45,000 | 53,000 | 45,000 | 53,000 |
| Profit | 75,000 | 76,375 | 50,000 | 77,000 |
| Change | · | + 1,375 | − 25,000 | + 2,000 |
Option C needs 1,000 more units for a 2,000 gain. Is the extra volume worth the risk?
What happens to profit when the assumptions move.
The probability distribution of the variables is known.
The probability distribution of the variables is not known.
Sensitivity analysis examines how an amount, such as the break-even point, changes when the factors behind it change. Three common methods for CVP:
If CM is 40 per unit and the CM ratio is 0.40, each unit change in volume moves profit by 40, and each riyal of sales moves profit by 0.40.
Forecast sales minus break-even sales. As a ratio, margin of safety ÷ planned sales: a useful measure for assessing risk.
DOL = Contribution margin ÷ Operating profit
Automation means higher fixed costs but a lower unit variable cost.
| Automated | Manual | |
|---|---|---|
| Sales | 1,000,000 | 1,000,000 |
| Variable costs | 500,000 | 800,000 |
| Contribution margin | 500,000 | 200,000 |
| Fixed costs | 375,000 | 100,000 |
| Operating profit | 125,000 | 100,000 |
| Price · variable cost · CM per unit | 100 · 50 · 50 | 100 · 80 · 20 |
500,000 ÷ 125,000
200,000 ÷ 100,000
Predict first: % change in profit = DOL × % change in sales.
| Automated | Manual | |
|---|---|---|
| Sales | 1,400,000 | 1,400,000 |
| Variable costs | 700,000 | 1,120,000 |
| Contribution margin | 700,000 | 280,000 |
| Fixed costs | 375,000 | 100,000 |
| Operating profit | 325,000 | 180,000 |
4.0 × 40%: 125,000 → 325,000
2.0 × 40%: 100,000 → 180,000
One break-even point for a whole sales mix.
| Calm | Windy | Gale | Total | |
|---|---|---|---|---|
| Last period's sales | 750,000 | 600,000 | 150,000 | 1,500,000 |
| Percent of sales | 50% | 40% | 10% | 100% |
| Price | 30 | 32 | 40 | |
| Unit variable cost | 24 | 24 | 36 | |
| CM per unit | 6 | 8 | 4 | |
| CM ratio | 20% | 25% | 10% |
0.5(0.20) + 0.4(0.25) + 0.1(0.10) = 0.21
168,000 ÷ 0.21 = 800,000
Calm 50% · 400,000
Windy 40% · 320,000
Gale 10% · 80,000
Score: 0 / 5
| Measure | Formula |
|---|---|
| Unit contribution margin | Unit selling price − Unit variable costs |
| CM ratio | Unit CM ÷ Unit selling price |
| Break-even units | Fixed costs ÷ Unit CM |
| Break-even riyals | Fixed costs ÷ CM ratio |
| Required sales in units | (Fixed costs + Target NI) ÷ Unit CM |
| Required sales in riyals | (Fixed costs + Target NI) ÷ CM ratio |
| Margin of safety | Actual sales − Break-even sales |
| Margin of safety ratio | Margin of safety ÷ Actual sales |
| Degree of operating leverage | Contribution margin ÷ Operating profit |
| Multi-product break-even | Fixed costs ÷ Weighted-average CM ratio |