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:variableorfixed. Costs are classified by behavior on the income statement in CVP analysis to arrive atoperating income. This format is known as the contribution margin income statement. Complete the following table to illustrate the format.

Contribution Margin Income StatementSales$ XXXLess: Variable costs

(XXX)Contribution margin

$ XXXLess: Fixed costs

(XXX)Operating income$ XXX

Feedback

Review the components of the Contribution Margin Income Statement and the underlined definitions above to determine their relationships in this statement.

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

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

.

Feedback

Rework the formula from the contribution margin income statement to solve for Fixed Costs:

Fixed Costs = Sales - Variable Costs - Operating Income

CVP and the Break-Even Point

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

ConceptStatementIt is important to understand contribution margin because it is used to determine thebreak-even point, which can help predict the success of a new venture or product. TheCVP formulacan 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 berestatedto reflect this.At the break-even point, contribution margin isequal 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 willdecrease

.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 willincrease

.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 willincrease

.

If fixed costs decrease, the break-even point willdecrease

.

Feedback

Rework the formula above to solve for Fixed Costs:

Fixed Costs = Sales - Variable Costs - Operating Income

Now consider what happens to this formula when Operating Income is equal to zero.

APPLY THE CONCEPTS: Break-Even Point in Units

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

Assume that you are part of the accounting team for Stewart Products. The company currently expects to sell 650 units for total revenue of $20,250 each month. Stewart Products 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 $6,750 are also expected, which includes fixed overhead and selling and administrative costs. Using this information, complete the contribution margin income statement shown below.

Stewart ProductsContribution Margin Income StatementSales$Less: Variable costs

Contribution margin

$Less: Fixed costs

Operating income$

Feedback

Review the formula and structure of this statement from the first two steps above, and apply these values.

Recall that direct labor and direct materials are included with variable costs.

Stewart Products is examining cost behavior patterns. Your recommendation is to first determine the break-even point in units. First, calculate thecontribution 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

Feedback

Use the information from the prior step to calculate these values. The contribution margin per unit is simply the contribution margin from the statement above divided by the number of units sold.

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 Stewart Products has been used to construct the profit-volume graph below. The purple points (diamond symbols) plot theprofit 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 Stewart Products

A.B.C.D.

Feedback

Look for a chart that reflects the breakeven point you computed in the step above.

To figure out the "Y intercept" value (where X=0), look back at the Contribution Margin Income Statement in the prior step and figure out what Operating Income would be if both sales and variable costs were zero.

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

Now consider each of the following scenarios for Stewart Products. 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 1Scenario 2Scenario 3Stewart 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.Stewart will dispose of a machine in the factory. The depreciation on that equipment is $500 per month.After some extensive market research, Stewart 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: $CM per unit: $CM per unit: $Break-even units:unitsBreak-even units:unitsBreak-even units:units