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.

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Sales	$ XXX
Less: Fixed costsLess: Variable costs	(XXX)
Contribution marginGross margin	$ XXX
Less: Fixed costsLess: Variable costs	(XXX)
Operating income	$ XXX

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Contribution margin is calculated first. It is the difference between sales and variable costs. Contribution margin is the amount that is available to pay

directfixedmanufacturing

costs. After those costs are paid, anything remaining from contribution margin becomes

gross marginprofitrevenue

.

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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 $0equal to contribution marginequal to fixed costs .
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 $0equal to fixed costsequal to gross margin .
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 decreaseincreasenot change .
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 decreaseincreasenot change .
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 decreaseincreasenot change . If fixed costs decrease, the break-even point will decreaseincreasenot change .

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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 Koller Hardware. The company currently expects to sell 689 units for total revenue of $20,150 each month. Koller 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 $6,650 are also expected, which includes fixed overhead and selling and administrative costs. Using this information, complete the contribution margin income statement shown below.

Sales	$fill in the blank 6cdf8ff6000f017_1
Less: Fixed costsLess: Variable costs	- Select -
Contribution marginGross margin	$- Select -
Less: Fixed costsLess: Variable costs	- Select -
Operating income	$fill in the blank 6cdf8ff6000f017_8

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Koller 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). $fill in the blank 4128fe03006505d_1

Next, complete the formula below to determine the break-even units.
Total Fixed Costs / Contribution Margin per Unit = Units
$fill in the blank 4128fe03006505d_2/ $fill in the blank 4128fe03006505d_3 = fill in the blank 4128fe03006505d_4units

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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 Koller 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 Koller Hardware

ABCD

A.

B.

C.

D.

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

Now consider each of the following scenarios for Koller 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
Koller 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.	Koller will dispose of a machine in the factory. The depreciation on that equipment is $500 per month.	After some extensive market research, Koller has determined that a sales price increase of $2 per unit will not affect the sales volume and will be effective immediately.
CM per unit: $fill in the blank 2c9a53fe6ffb030_1	CM per unit: $fill in the blank 2c9a53fe6ffb030_2	CM per unit: $fill in the blank 2c9a53fe6ffb030_3
Break-even units: fill in the blank 2c9a53fe6ffb030_4 units	Break-even units: fill in the blank 2c9a53fe6ffb030_5units	Break-even units: fill in the blank 2c9a53fe6ffb030_6 units

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