CVP - Target Profit Analysis

Target Profit Analysis

Definition of Target Profit

• Target profit analysis is the examination to identify the required sales to achieve a specified level of operating profit.

Relationship to Breakeven Analysis

• Similar to breakeven point analysis, target profit can be expressed in terms of units or revenues.

• The methodology employs the same original formula used for calculating breakeven, with a key difference in setting the operating profit to the desired target rather than zero.

Formulas Used in Target Profit Analysis

Target Profit in Units

• The formula for determining the target profit level in terms of units sold is:
  $ext{Units Sold} = rac{ ext{Total Fixed Costs} + ext{Target Operating Income}}{ ext{Contribution Margin per Unit}}$

Target Profit in Revenues

• The formula for determining the target profit level in terms of revenues is:
  $ext{Revenue} = rac{ ext{Total Fixed Costs} + ext{Target Operating Income}}{ ext{Contribution Margin Percentage}}$

Example: Face Mask Business Analysis

• Previous calculations indicated the following:

  • Breakeven point guess had an estimated value of 22,000 masks, yielding an operating income of -$27,000.

  • A subsequent guess of 30,000 masks indicated an operating income of $45,000.

• Analysis goal is to confirm these values using the formulas.

Calculating Target Units for Guess One

• For the first guess (operating income of -$27,000):

  • Total Fixed Costs = $225,000

  • Target Operating Income = -$27,000

  • Contribution Margin per Unit = $9

• The calculation is: $X = rac{225,000 + (-27,000)}{9}$

  • Therefore, $X = rac{198,000}{9} = 22,000 ext{ units}$

Calculating Target Revenue for Guess Two

• For the second guess (operating income of $45,000):

  • Total Fixed Costs = $225,000

  • Target Operating Income = $45,000

  • Contribution Margin Percentage = 60% or 0.6

• The calculation is: $X = rac{225,000 + 45,000}{0.6}$

  • Therefore, $X = rac{270,000}{0.6} = 450,000 ext{ dollars}$

Target After Tax Profit Analysis

• Objective: To compute a target after-tax profit, understanding that entrepreneurs often look to realize a specific net profit after taxes.

Relationship Between Operating Income, Taxes, and After-tax Income

• The formula relating them is:

  • After-tax income = Operating income - Taxes

• Expressed in percentage terms:

  • If tax rate is represented as $t$, then:

  • $ext{After-tax Income} = ext{Operating Income} imes (1 - t)$

• Example with a tax rate of 30%:

  • After-tax income represents 70% of pretax income.

Formula for Determining Target After-tax Profit in Units

• The reformulated equation accounting for taxes is:
  $ext{Units} = rac{ ext{Total Fixed Costs} + rac{ ext{Target After-tax Profit}}{(1 - t)}}{ ext{Contribution Margin per Unit}}$

Formula for Determining Target After-tax Profit in Revenues

• The revenue calculation similarly adapts:
  $ext{Revenue} = rac{ ext{Total Fixed Costs} + rac{ ext{Target After-tax Profit}}{(1 - t)}}{ ext{Contribution Margin Percentage}}$

Numerical Example for Target After-tax Profit

• Given:

  • Total Fixed Costs: $225,000

  • Target After-tax Income: Convert to pretax:

  • For example, if desired after-tax profit is $90,000 with a tax rate of 30%:
    $ext{Pretax Income} = rac{90,000}{(1 - 0.3)} = rac{90,000}{0.7} = 128,571.43$

• Using this pretax income in the units formula:

  • Calculating the target revenue:
    $ext{Revenue} = rac{225,000 + 128,571.43}{0.6} <br>ightarrow ext{Revenue} = rac{353,571.43}{0.6} = 589,285.72$