Question

Mastery Problem: CVP and the Contribution Margin Income Statement

For planning and control purposes, managers have a powerful tool known as cost-volume-profit (CVP) analysis. CVP shows how revenues, expenses, and profits behave as volume changes. In CVP analysis, costs are classified according to behavior: variable or fixed. Costs are classified by behavior on the income statement in CVP analysis to arrive at operating income. This format is known as the contribution margin income statement. Complete the following table to illustrate the format.

Contribution Margin Income Statement
Sales	$ XXX
Less: Variable costs	(XXX)
Contribution margin	$ XXX
Less: Fixed costs	(XXX)
Operating income	$ XXX

Contribution margin is calculated first. It is the difference between sales and variable costs. Contribution margin is the amount that is available to pay fixed costs. After those costs are paid, anything remaining from contribution margin becomes profit .

CVP and the Break-Even Point

Review the following concepts about CVP analysis and break-even point and then complete the related statements.

Concept	Statement
It is important to understand contribution margin because it is used to determine the break-even point, which can help predict the success of a new venture or product. The CVP formula can be used to determine the break-even point.	At the break-even point, operating income is $0 .
Contribution margin is the amount available to cover fixed costs. The CVP formula can be restated to reflect this.	At the break-even point, contribution margin is equal to fixed costs .
Managers analyze how changes in costs and selling prices will affect contribution margin and, therefore, the break-even point. An increase in selling price or a decrease in variable costs will cause contribution margin to increase, providing more than enough to cover fixed costs.	When contribution margin increases, the break-even point will decrease .
Likewise, if selling price decreases or variable costs increase, contribution margin will decrease and be less than fixed costs.	When contribution margin decreases, the break-even point will increase .
Any changes to fixed costs will affect the amount of contribution margin needed to cover fixed costs.	If fixed costs increase, the break-even point will increase . If fixed costs decrease, the break-even point will decrease .

APPLY THE CONCEPTS: Break-Even Point in Units

The break-even point can be expressed in terms of sales dollars or number of units. The break-even units tells us how many units must be sold so that operating income is $0.

Assume that you are part of the accounting team for Strunk Hardware. The company currently expects to sell 628 units for total revenue of $21,800 each month. Strunk Hardware estimates direct materials costs of $3,150, direct labor costs of $4,200, variable overhead costs of $2,100, and variable selling and administrative costs of $1,050. Fixed costs of $9,900 are also expected, which includes fixed overhead and selling and administrative costs. Using this information, complete the contribution margin income statement shown below.

Strunk Hardware
Contribution Margin Income Statement
Sales	$
Less: Variable costs
Contribution margin	$
Less: Fixed costs
Operating income	$

Strunk Hardware is examining cost behavior patterns. Your recommendation is to first determine the break-even point in units. First, calculate the contribution margin (CM) per unit (rounded to the nearest dollar). $

Next, complete the formula below to determine the break-even units.
Total Fixed Costs / Contribution Margin per Unit = Units
$/     $        =   units

APPLY THE CONCEPTS: The Profit-Volume Graph

A profit-volume graph helps managers to visualize the relationship between profits and units sold. The data for Strunk Hardware has been used to construct the profit-volume graph below. The purple points (diamond symbols) plot the profit line. The operating loss is the shaded area bordered by the red points (cross symbols). The operating profit is the area bounded by the green points (triangle symbols).

Choose the correct profit-volume graph for Strunk Hardware A

A.

B.

C.

D.

APPLY THE CONCEPTS: Effect of Changes to Sales Price, Variable Costs and Fixed Costs

Now consider each of the following scenarios for Strunk Hardware. Calculate the contribution margin (CM) per unit, rounded to nearest dollar, and the new break-even point in units, rounded to the nearest whole unit, for each scenario separately.

Scenario 1	Scenario 2	Scenario 3
Strunk will dispose of a machine in the factory. The depreciation on that equipment is $500 per month.	After some extensive market research, Strunk has determined that a sales price increase of $2 per unit will not affect the sales volume and will be effective immediately.	Strunk has been experiencing quality problems with a materials supplier. Changing suppliers will improve the quality of the product but will cause direct materials costs to increase by $1 per unit.
CM per unit: $	CM per unit: $	CM per unit: $
Break-even units:  units	Break-even units:  units	Break-even units:  units

Answer 1

Strunk Hardware
Contribution Margin Income Statement
Sales	21800
Less: Variable costs	9450
Contribution margin	12350
Less: Fixed costs	9900
Operating income	2450

Contribution margin per unit = $12350/628 units = $19.67 = $20

Total Fixed Costs/Contribution Margin per Unit = Units

$9900/$20 = $495 units

Note: The profit-volume graphs have not been given with the question.

Scenario 1	Scenario 2	Scenario 3
CM per unit: $20	CM per unit: $22	CM per unit: $19
	$20 + $2 = $22	$20 - $1 = $19
Break-even units: 470 units	Break-even units: 450 units	Break-even units: 521 units
($9900 - $500)/$20 = 470	$9900/$22 = 450	$9900/$19 = 521