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

Question Content Area

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, costs are classified according to behavior: variable or fixed, 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 at operating income. This format is known as the contribution margin income statement. Complete the following table to illustrate the format.

blank Contribution Margin Income Statement blank

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

Question Content Area

APPLY THE CONCEPTS:

Prepare a contribution margin income statement

Assume that you are part of the accounting team for Sutcliffe Computing. The company has only one product that sells for $80 per unit. Sutcliffe estimates total fixed costs to be $3,800. Sutcliffe estimates direct materials cost of $24.00 per unit, direct labor costs of $30.00 per unit, and variable overhead costs of $6.00 per unit. The CEO would like to see what the gross margin and operating income will be if 300 units are sold in the next period. Prepare a contribution margin income statement.

Sutcliffe Computing Contribution Margin Income Statement blank

Sales	$fill in the blank e3f2ad014fea03e_1
Less: Fixed costsLess: Variable costsLess: Variable costs	Less: Variable costs
Contribution marginGross marginContribution margin	$Contribution margin
Less: Fixed costsLess: Variable costsLess: Fixed costs	Less: Fixed costs
Operating income	$fill in the blank e3f2ad014fea03e_8

Question Content Area

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 the break-even point in units or the break-even point in sales dollars. The following formulas are used to calculate the break-even point in sales dollars:

1. Calculate the contribution margin per unit: Selling Price Variable Cost per Unit

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

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

Question Content Area

APPLY THE CONCEPTS: Calculate the break-even point in sales dollars for Sutcliffe Computing

Further analysis of Sutcliffe Computings fixed costs revealed that the company actually faces annual fixed overhead costs of $4,200 and annual fixed selling and administrative costs of $1,800. Variable cost estimates are correct: direct materials cost, $24.00 per unit; direct labor costs, $30.00 per unit; and variable overhead costs, $6.00 per unit. At this time, the selling price of $80 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 b694fcff6071008_1

$fill in the blank b694fcff6071008_2

=

$fill in the blank b694fcff6071008_3

Contribution Margin Ratio	=	$fill in the blank b694fcff6071008_4	=	fill in the blank b694fcff6071008_5 %
		$fill in the blank b694fcff6071008_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 b694fcff6071008_7	=	$fill in the blank b694fcff6071008_8
		fill in the blank b694fcff6071008_9 %

Units Sold at Break-Even Point

=

fill in the blank b694fcff6071008_10 units

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

How much would operating income be? $fill in the blank b694fcff6071008_11

What would operating income be if the units sold exceeded the break-even point by five (5) units? $fill in the blank b694fcff6071008_12

Question Content Area

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. The sales line crosses the Y-axis where sales dollars are

equal to total revenuezero (0)

. The slope of 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, the total costs line will 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

.

Question Content Area

APPLY THE CONCEPTS: Create the CVP graph for Sutcliffe Computing

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

a.
b.
c.

Select your choice.

abc

Question Content Area

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 0d1bf5f22fba021_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 0d1bf5f22fba021_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 sells a fixed asset and reduces 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 higher-quality product, but direct materials will increase by $4.00 per unit. If the new supplier is used, the slope of the total costs line will be $fill in the blank 0d1bf5f22fba021_5, and the break-even point in sales dollars

decreasesincreases

.

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

decreaseincrease

. But internal analysis shows that this price decrease 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.