A firm has $671,000 in fixed costs, a unit selling price of $11, and variable costs of $7. What...

Question:

A firm has $671,000 in fixed costs, a unit selling price of $11, and variable costs of $7. What are the number of sales, in units, necessary to earn a target profit of $144,000?

Target Profit and Breakeven Analysis:

Target profit is an extension of breakeven analysis. With breakeven analysis, a company calculates how much sales revenue must be earned or units must be sold in order to cover its costs but make zero in profit or loss. Breakeven analysis is target profit analysis where the target profit is zero.

Answer and Explanation: 1

The firm has to sell 203,750 units to earn a target profit of $144,000.

In order to calculate how many units must be sold to earn a target profit, we can use the following formula.

  • Sales in units = (Fixed cost + Target profit) / Contribution margin per unit

The contribution margin is the amount leftover over after variable costs are deducted from sales to contribute, or put towards, fixed costs. It can be expressed in three ways: as a dollar amount, as a percentage, or per unit. For this problem, we need the contribution margin per unit. It can be calculated as follows:

  • Contribution margin per unit = Selling price per unit - Variable cost per unit
  • Contribution margin per unit = $11 per unit - $7 per unit
  • Contribution margin per unit = $4 per unit

We are given the other values needed for this formula.

  • Sales in units = ($671,000 + $144,000) / $4 per unit
  • Sales in units = $815,000 / $4 per unit
  • Sales in units = 203,750 units

The firm has to sell 203,750 units to earn a target profit of $144,000. We can see this illustrated if we look at a contribution margin income statement.

Contribution Margin Income Statement
Sales ($11 per unit * 203,750 units) $2,241,250
Less: Variable costs ($7 per unit * 203,750 units) $1,426,250
Contribution margin $815,000
Less: Fixed costs $671,000
Operating income $144,000


Learn more about this topic:

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Target-Profit & Break-Even Analysis

from

Chapter 3 / Lesson 5
9K

Total costs are compared to total revenue and are either lower (profit), higher (loss), or equal (break-even point). Learn to calculate this and identify target profit, as well as establish a margin of safety to accommodate unanticipated risks.


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