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Target Profit

Introduction

One of the helpful uses of CVP analysis is the determination of the sales required to generate a target profit (income).

What's in Here

In this lesson, we will learn how to calculate the number of units to sell in order to generate a desired level of profit. This can be achieved by tweaking the break-even formula and incorporating the desired profit.

Target Sales Volume Formula

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.

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