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Target profit (desired income)
  • Formula for target sales volume
  • Example and conclusion
  • Key takeaways
 

Target profit

Target Sales Volume Formula

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)

Example

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.
  2. A target income of $60,000 after taxes (40% tax rate).
  3. A target income equal to 40% of sales.

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

Conclusion

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.

Key Takeaways

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)
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