Question

Mastery Problem: Target Income and Margin of Safety

Target Income and Margin of Safety

At the break-even point, sales and costs are exactly equal. However, the goal of most companies is to make a profit. When a company decides that it wants to earn more than the break-even point of income, it must define the amount it thinks it will realistically make. By modifying the break-even equation, the sales required to earn a target or desired amount of profit may be computed.

Complete the following:
If a company makes $3 off of each unit it sells and has a target operating income of $1,200, then it must sell  units. Similarly, if a company has a target operating income of $75,000 and knows that total expenses for the period will be $75,000, how much revenue must it earn to reach its target operating income? $

Units sold or revenue earned above and beyond the break-even point contributes to the margin of safety for a company. Margin of safety is a crude measure of risk, in that it serves as the padding between profit and the break-even point.

Complete the following:
Expressed in terms of units, if a company hits its break-even point in units (say, 100 units) and actually sells 400 units, then the margin of safety is  units. Similarly, if the break-even point in sales revenue is $200,000, and it actually has sales revenue of $400,000, then its margin of safety is $.

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APPLY THE CONCEPTS: Target income (number of units sold)

Suppose a business has pricing and cost information as follows::

Price and Cost Information	Amount
Selling Price per Unit	$10.00
Variable Cost per Unit	$2.50
Total Fixed Cost	$600

For the upcoming period, the company wishes to generate operating income of $900. Given the cost and pricing structure for the company’s product, how many units must the company sell to attain its target income?

Remember that the basic equation for calculating operating income is as follows:

Operating Income

=

(Unit Price x Units Sold)

-

(Variable Cost per Unit x Units Sold)

-

Fixed Cost

Step 1: Replace the operating income in the equation with your company’s target income, and insert your cost and pricing information into the equation, as well:

$

=

($ x Units Sold)

-

($ x Units Sold)

-

$

Step 2: Rearrange the equation to isolate units to one side of the equation:

Number of Units to Earn Target Income =	Fixed Cost + Target Income
	Unit selling price - Variable Cost per Unit

Number of Units to Earn Target Income =	$ + 900
	$ - $

Number of Units to Earn Target Income =  units

Step 3: Create a contribution margin income statement to check your previous work. Enter all amounts as positive numbers.

Sales		$
Total variable expense
	Total contribution margin	$
Total fixed expense
	Operating income	$

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APPLY THE CONCEPTS: Target income (sales revenue)

Another useful method for figuring out the type of performance your company will need to reach a target income is by using sales revenue. Rather than using the number of units, this method uses total sales revenue. In companies for which the total set of goods produced and sold is more varied, this would be the preferred method, as opposed to a business in which only one product is sold. Assume a company has pricing and cost information as follows:

Price and Cost Information	Amount
Selling Price per Unit	$20
Variable Cost per Unit	$10
Total Fixed Cost	$12,000

For the upcoming period, the company wishes to generate operating income of $75,000. Given the cost and pricing structure for the company’s product, how much sales revenue must it generate to attain its target income?

Step 1: Calculate the contribution margin ratio:

The contribution margin ratio is the contribution margin in proportion to the selling price on a per-unit basis.

Contribution Margin Ratio =	(Selling Price – Variable Cost)
	Selling Price

Note: The contribution margin ratio is calculated to one decimal place.)

Contribution Margin Ratio =	($ – $10)	=
	$

Step 2: Calculate the sales revenue required to attain the target income:

Sales Dollars =	(Target Income + Fixed Cost)
	Contribution Margin Ratio

Sales Dollars =	( $ + $12,000)	=	$

Step 3: Create a contribution margin income statement, to check your previous work. Enter all amounts as positive numbers.

Sales		$
Total variable expense
	Total contribution margin
Total fixed expense
	Operating income

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APPLY THE CONCEPTS: Margin of Safety
Margin of safety can allow you to see how much padding there is for your company between profit and loss. If this number is great, it may indicate that your company is performing very well. If this number is small, it may be worth looking into possible remediation. Consider the following pricing and cost information:

Price and Cost Information	Amount
Selling Price per Unit	$450
Variable Cost per Unit	$400
Total Fixed Cost	$70,000

For the upcoming period, the company projects that it will sell 2,000 units. Considering that the company has a unit break-even point of 1,400 units, what is the margin of safety in terms of both units and sales revenue? Round your answers to two decimal places, if necessary.

Margin of Safety in Units =  -  =

Margin of Safety in Sales Revenue = $ - $ = $

Answer 1

Answer 1:

If a company makes $3 off of each unit it sells and has a target operating income of $1,200, then it must sell 400 units. Similarly, if a company has a target operating income of $75,000 and knows that total expenses for the period will be $75,000, how much revenue must it earn to reach its target operating income? $150,000

Answer 2:

Expressed in terms of units, if a company hits its break-even point in units (say, 100 units) and actually sells 400 units, then the margin of safety is 300 units. Similarly, if the break-even point in sales revenue is $200,000, and it actually has sales revenue of $400,000, then its margin of safety is $200,000

Answer 3:

Operating Income

=

(Unit Price x Units Sold)

-

(Variable Cost per Unit x Units Sold)

-

Fixed Cost

Step 1:

$900

=

($10 x Units Sold)

-

($2.50 x Units Sold)

-

$600

Step 2:

Number of Units to Earn Target Income =	Fixed Cost + Target Income
	Unit selling price - Variable Cost per Unit

Number of Units to Earn Target Income =	$600 +$ 900
	$ 10 - $2.50

Number of Units to Earn Target Income = 200 units

Step 3:

Sales		$2,000
Total variable expense		$500
	Total contribution margin	$1,500
Total fixed expense		$600
	Operating income	$900

Answer 4:

Step 1: Contribution margin ratio:

The contribution margin ratio is the contribution margin in proportion to the selling price on a per-unit basis.

Contribution Margin Ratio =	(Selling Price – Variable Cost)
	Selling Price

Contribution Margin Ratio =	($20 – $10)	=50.0%
	$20

Step 2:

Sales Dollars =	(Target Income + Fixed Cost)
	Contribution Margin Ratio

Sales Dollars =	($75,000 + $12,000)	=	$174,000
	50.0%

Step 3:

Sales		$174,000
Total variable expense		$87,000
	Total contribution margin	$87,000
Total fixed expense		$12,000
	Operating income	$75,000

Answer 5:

Price and Cost Information	Amount
Selling Price per Unit	$450
Variable Cost per Unit	$400
Total Fixed Cost	$70,000

Company projects that it will sell 2,000 units.

Break-even point = 1,400 units,

Margin of Safety in Units = 2,000 -1,400 = 600

Margin of Safety in Sales Revenue = $900,000 - $630,000 = $270,000

Workings:

Sales revenue = 2000 * $450 =$900,000

Break-even in sales revenue = 1400 * 450 = $630,000