One of the helpful uses of CVP analysis is the determination of the sales required to generate a target profit (or desired income).
The target sales volume required to achieve a specific level of income can be computed using the this formula:
| Target sales | = | Total fixed costs + Target income |
| CM per unit |
If the target income is on an after-tax basis, the formula to compute for the target sales would be:
| Total fixed costs + [Target income / (1-Tax rate)] |
| CM per unit |
If the target income is expressed in terms of percentage of sales (example, 20% of sales), the formula would be:
| Total fixed costs |
| CM per unit - (Percentage x Selling price) |
To illustrate the concepts above, consider the following data.
| Per Unit | Total | ||
| Sales (3,000 units) | $15 | $45,000 | |
| Less: Variable Costs | 5 | 15,000 | |
| Contribution Margin | $10 | $30,000 | |
| Less: Fixed Costs | 20,000 | ||
| Operating Income | $10,000 |
Compute for the sales volume required to attain the following:
1. A target income of $60,000 before taxes
| Target sales | = | Total fixed costs + Target income |
| CM per unit | ||
| = | $20,000 + $60,000 | |
| 10 per unit | ||
| Target sales | = | 8,000 units |
Analysis: Selling 8,000 units will result in an operating income of $60,000. To prove, let us compute for the net income at 8,000 units.
| Per Unit | Total | ||
| Sales (8,000 units) | $15 | $120,000 | |
| Less: Variable Costs | 5 | 40,000 | |
| Contribution Margin | $10 | $ 80,000 | |
| Less: Fixed Costs | 20,000 | ||
| Operating Income | $ 60,000 |
2. A target income of $60,000 after 40% tax
| Total fixed costs + [Target income /(1-Tax rate)] | ||
| CM per unit | ||
| 20,000 + [60,000/(1-40%)] | = | 20,000 + 100,000 |
| 10 | 10 | |
| Target sales = 12,000 units | ||
To prove, let us compute for the income after tax at 12,000 units.
| Per Unit | Total | ||
| Sales (12,000 units) | $15 | $180,000 | |
| Less: Variable Costs | 5 | 60,000 | |
| Contribution Margin | $10 | $120,000 | |
| Less: Fixed Costs | 20,000 | ||
| Operating Income | $100,000 | ||
| Less: Income Tax (40%) | 40,000 | ||
| Net Income | $ 60,000 |
3. A target income of 40% of sales
| Total fixed costs | ||
| CM per unit - (Percentage x Selling price) | ||
| 20,000 | = | 20,000 |
| 10 - (40% x 15) | 4 | |
| Target sales = 5,000 units | ||
To prove, let us compute for the operating income at 5,000 units. Notice that the resulting income of $30,000 is 40% of the $75,000 sales.
| Per Unit | Total | ||
| Sales (5,000 units) | $15 | $75,000 | |
| Less: Variable Costs | 5 | 25,000 | |
| Contribution Margin | $10 | $50,000 | |
| Less: Fixed Costs | 20,000 | ||
| Operating Income | $30,000 |
Aside from the determination of the break-even point, the CVP analysis can determine the level of sales required to generate a specific level of income. The target income could be expressed on a before-tax basis or after-tax basis. It can also be expressed as a percentage of sales. In all those cases, nonetheless, the CVP analysis can compute for the required sales volume.
The target sales volume can be derived by tweaking the break-even formulae to incorporate the desired income.
| Target sales | = | Total fixed costs + [Target income / (1-Tax rate)] |
| CM per unit |
If desired income is expressed in percentage:
| Target sales | = | Total fixed costs |
| CM per unit - (Percentage x Selling price) |
