Mastery Problem: CVP Analysis - Constructing a Cost-Volume-Profit Chart

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CVP Analysis and the Contribution Margin Income Statement

For planning and control purposes, managers have a powerful tool known as cost-volume-profit (CVP) analysis. CVP analysis shows how revenues, expenses, and profits behave as volume changes, which helps identify problems and create solutions. In CVP analysis,costsare classified according to behavior:variableorfixed,rather than by category: product (which includes both variable and fixed) or period (which includes both variable and fixed). When variable costs are subtracted from sales, the contribution margin is obtained, representing the amount of dollars available to cover fixed costs after the costs related to sales are recovered. Fixed costs are deducted from the contribution margin to arrive atoperating income. This format is known as the contribution margin income statement. Complete the following table to illustrate the format.

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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APPLY THE CONCEPTS:

Prepare contribution margin income statement

Assume that you are part of the accounting team for Harrison Digital. The company has only one product that sells for $40 per unit. Harrison estimates total fixed costs to be $9,000. Harrison estimates direct materials cost of $8.00 per unit, direct labor costs of $10.00 per unit, and variable overhead costs of $2.00 per unit. The CEO would like to see what the gross margin and operating income will be if 700 units are sold in the next period. Prepare contribution margin income statement.

Sales	$fill in the blank 3d6797f9b059ff2_1
Less: Fixed costsLess: Variable costs	- Select -
Contribution marginGross margin	$- Select -
Less: Fixed costsLess: Variable costs	- Select -
Operating income	$fill in the blank 3d6797f9b059ff2_8

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CVP Analysis and the Break-Even Point in Sales Dollars

CVP analysis focuses on selling price, units sold, variable cost per unit, and total fixed costs. Managers can use the contribution margin format to understand the effects of changes in any of these areas. Contribution margin is the amount that is available to pay

directfixedmanufacturing

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

gross marginoperating incomerevenue

. A business can determine the level of sales needed to cover all costs by knowing the break-even point. The break-even point is where

operating income is zerothe contribution margin is equal to variable costsvariable costs exceed fixed costs

. This point can be expressed as thebreak-even point in unitsor thebreak-even point in sales dollars. The following formulas are used to calculate the break-even point in sales dollars:

1. Calculate thecontribution margin per unit: Selling Price - Variable Cost per Unit

2. Determine thecontribution margin ratio:	Contribution Margin per Unit
Selling Price

3. Compute the break-even point in sales dollars:	Total Fixed Costs
Contribution Margin Ratio

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APPLY THE CONCEPTS: Calculate the break-even point in sales dollars for Harrison Digital

Further analysis of Harrison Digital's fixed costs revealed that the company actually faces annual fixed overhead costs of $9,800 and annual fixed selling and administrative costs of $4,200. Variable cost estimates are correct: direct materials cost, $8.00 per unit; direct labor costs, $10.00 per unit; and variable overhead costs, $2.00 per unit. At this time, the selling price of $40 will not change. Complete the following formulas for the revised fixed costs. Enter the ratio as a percentage.

Contribution Margin per Unit

=

$fill in the blank 0abeb9fb0fe2fbc_1

-

$fill in the blank 0abeb9fb0fe2fbc_2

=

$fill in the blank 0abeb9fb0fe2fbc_3

Contribution Margin Ratio	=	$fill in the blank 0abeb9fb0fe2fbc_4	=	fill in the blank 0abeb9fb0fe2fbc_5 %
	$fill in the blank 0abeb9fb0fe2fbc_6

Now complete the formulas for (1) the break-even point in sales dollars and (2) the units sold at the break-even point. To calculate this, divide the break-even point in sales dollars by the unit selling price.

Break-Even Point in Sales Dollars	=	$fill in the blank 0abeb9fb0fe2fbc_7	=	$fill in the blank 0abeb9fb0fe2fbc_8
	fill in the blank 0abeb9fb0fe2fbc_9 %

Units Sold at Break-Even Point

=

fill in the blank 0abeb9fb0fe2fbc_10 units

Assume that the number of units that Harrison sold exceeded the break-even point by one (1).

How much would operating income be? $fill in the blank 0abeb9fb0fe2fbc_11

What would operating income be if the units sold exceeded the break-even point by five (5) units? $fill in the blank 0abeb9fb0fe2fbc_12

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The Cost-Volume-Profit Graph

The CVP graph shows the relationships among cost, volume, and profits. The X- (horizontal) axis is the total units, and the Y- (vertical) axis is the dollars (sales or costs). The intersection of these two axes, the origin, is where both units and dollars are zero. There are two lines to be plotted on the graph: the sales line and the total costs line. Thesales linecrosses the Y-axis where sales dollars are

equal to total revenuezero (0)

. Theslopeof any line is the variable rate. The slope of the sales line is equal to the

total fixed costunit selling priceunit variable cost

. Recall that total fixed costs

decreasedo not changeincrease

regardless of the number of units sold, even if zero units are sold. Therefore, thetotal costs linewill cross the Y-axis at

total fixed coststotal salestotal variable costszero (0)

dollars. As each additional unit is sold, the total costs will increase by

the unit selling pricethe unit variable costzero (0)

. Therefore, the slope of the total costs line is equal to the

total fixed costunit selling priceunit variable cost

. The break-even point exists at the point where

sales crosses the Y-axisthe two lines intersecttotal costs cross the X-axis

.

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APPLY THE CONCEPTS: Create the CVP graph for Harrison Digital

Review the information and previous calculations for the break-even point in sales dollars for Harrison Digital. Choose the graph that correctly represents the CVP graph for Harrison Digital.

a.
b.
c.

Select your choice.

abc

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APPLY THE CONCEPTS: Use the CVP graph to analyze the effects of changes in price and costs

Graph the following on your own paper. At the original position, the break-even point in sales dollars is $24,000 at 500 units. The fixed costs are $8,000.

Assume the slope of the sales line is equal to the selling price. When the two points of the sales line are at the origin and the break-even point, you see that the slope of the line is $48, which means that the selling price is $fill in the blank 8ae6ea047febfb2_1.

When the two points of the total costs line are at the origin and the break-even point, you see that the slope of the line is $32.00, which means that the variable cost per unit is $fill in the blank 8ae6ea047febfb2_2.

Leave the break-even point (x) at its original position. Use it as a reference point to answer the following questions. Analyze the scenarios by sliding the points on the lines to get the slope desired. Recall that the new break-even point for each scenario exists where the sales and total costs lines intersect. Compare it to the original break-even point (x). (You may want to put the lines back to their original position for each scenario.) Each scenario should be considered independently.

1. The company purchases a fixed asset and increases fixed costs by $2,000. Variable costs remain the same, which means that the slope does not change. This will cause the break-even point to

move to the leftmove to the right

, which means that break-even point in sales dollars

decreasesincreases

.

2. A new supplier can provide a product of equal quality at $4.00 per unit less than the current direct materials cost. If the new supplier is used, the slope of the total costs line will be $fill in the blank 8ae6ea047febfb2_5, and the break-even point in sales dollars

decreasesincreases

.

3. Market research shows that a price increase will decrease the number of units sold. A price increase will cause the slope of the sales line to

decreaseincrease

. But internal analysis shows that this price increase will cause the break-even point in sales to shift to the

leftright

, which means that

fewermore

units will need to be sold to break even.