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 Feedback $ XXX

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

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.

Concept Statement

It is important to understand contribution margin because it is used to determine the break-

At the break-even point, even point, which can help predict the success of a new venture or product. The CVP operating income is $0 . formula can be used to determine the break-even point.

At the break-even point,

Contribution margin is the amount available to cover fixed costs. The CVP formula can be contribution margin is equal restated to reflect this. to fixed costs .

Managers analyze how changes in costs and selling prices will affect contribution margin

When contribution margin and, therefore, the break-even point. An increase in selling price or a decrease in variable increases, the break-even costs will cause contribution margin to increase, providing more than enough to cover fixed point will decrease . costs.

When contribution margin

Likewise, if selling price decreases or variable costs increase, contribution margin will decreases, the break-even decrease and be less than fixed costs. point will increase . If fixed costs increase, the break-even point will Any changes to fixed costs will affect the amount of contribution margin needed to cover increase .

fixed costs. If fixed costs decrease, the

break-even point will decrease .

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. 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 Schallheim Products. The company currently expects to sell 533 units for total revenue of $16,900 each month. Schallheim 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 $4,800 are also expected, which includes fixed overhead and selling and administrative costs. Using this information, complete the contribution margin income statement shown below.

Schallheim Products

Contribution Margin Income Statement

16900

Sales $fill in the blank 5bd3fe088fbbfe4_1

10500

Less: Variable costs

6400

Contribution margin

4800

Less: Fixed costs

fill in the blank 5bd3fe088fbbfe4_3 $fill in the blank 5bd3fe088fbbfe4_5 fill in the blank 5bd3fe088fbbfe4_7

1600

Operating income $fill in the blank 5bd3fe088fbbfe4_8

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.

Schallheim Products 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 03b29506706c05a_1

12.00

Next, complete the formula below to determine the break-even units.

Total Fixed Costs / Contribution Margin per Unit = Units

4800

  $fill in the blank 03b29506706c05a\_2/       $fill in the blank 03b29506706c05a\_3

12 400

= fill in the blank 03b29506706c05a_4 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 Schallheim Products 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 Schallheim Products A

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

Scenario 1 Scenario 2 Scenario 3

Schallheim will dispose of a machine in the factory. The depreciation on that equipment is $500 per month. After some extensive market research, Schallheim has determined that a sales price increase of $2 per unit will not affect the sales volume and will be effective immediately. Schallheim 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: $fill in the blank CM per unit: $fill in the blank CM per unit: $fill in the blank f7551c072023062_3

12 14

Now consider each of the following scenarios for Schallheim 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. f7551c072023062_1 f7551c072023062_2 11

Break-even units: fill in the blank

Break-even units: fill in the blank Break-even units: fill in the blank

358

343

436

f7551c072023062_4 f7551c072023062_5 units f7551c072023062_6 units units

Feedback

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

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.

Contribution Margin Income Statement

Sales $ XXX

Less: Variable costs XXX

Contribution margin $ XXX

Less: Fixed costs XXX

Operating income Feedback $ XXX

Roll your mouse over the underlined definitions to review the cost concepts. The purpose of this statement format is to separate out the effects of variable costs from fixed costs.

APPLY THE CONCEPTS:

Prepare a contribution margin income statement

Assume that you are part of the accounting team for Starr Productions. The company has only one product that sells for $40 per unit. Starr estimates total fixed costs to be $3,700. Starr estimates direct materials cost of $12.00 per unit, direct labor costs of $15.00 per unit, and variable overhead costs of $3.00 per unit. The CEO would like to see what the gross margin and operating income will be if 600 units are sold in the next period. Prepare a contribution margin income statement.

Starr Productions

Contribution Margin Income Statement

24000

Sales $fill in the blank 6f474cf84008fc2_1

18000

Less: Variable costs

6000

Contribution margin

3700

Less: Fixed costs

fill in the blank 6f474cf84008fc2_3 $fill in the blank 6f474cf84008fc2_5 fill in the blank 6f474cf84008fc2_7

2300

Operating income $fill in the blank 6f474cf84008fc2_8

Feedback

Apply the numbers given in this section to the format determined in the section above.

Total revenues will be equal to the unit sales price times the number of units sold. The total variable cost will be equal to the total of all variable unit costs times the number of units sold.

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 fixed costs. After those costs are paid, anything remaining from contribution margin becomes operating income . 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 zero . 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

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

Selling Price

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

Contribution Margin Ratio

Feedback

Review the statement format and the example from the sections above. What happens as the contribution margin approaches zero?

APPLY THE CONCEPTS: Calculate the break-even point in sales dollars for Starr Productions

Further analysis of Starr Productions’s 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, $12.00 per unit; direct labor costs, $15.00 per unit; and variable overhead costs, $3.00 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 = $fill in the blank – $fill in the blank = $fill in the blank

Margin per 08d563f46f8cfe9_1 08d563f46f8cfe9_2 08d563f46f8cfe9_3

40 30 10

Unit

$fill in the blank fill in the blank

Contribution 08d563f46f8cfe9_4 = 08d563f46f8cfe9_5

=

10

25

Margin Ratio

%

$fill in the blank

08d563f46f8cfe9\_6	 

40

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 $fill in the blank $fill in the blank

Point in Sales = 08d563f46f8cfe9_7 = 08d563f46f8cfe9_8

6000 24000

Dollars

fill in the blank

08d563f46f8cfe9\_9	 

25

%

Units Sold at fill in the blank 08d563f46f8cfe9_10

600

=

Break-Even Point units

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

How much would operating income be?

10

$fill in the blank 08d563f46f8cfe9_11

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

50

$fill in the blank 08d563f46f8cfe9_12

Feedback

Use the data along with the formulas introduced in the previous section to compute Contribution Margin per Unit and Contribution Margin Ratio.

The change in Contribution Margin with sales volume will then be equal to the Contribution Margin per Unit times the unit change.

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 zero (0) . The slope of any line is the variable rate. The slope of the sales line is equal to the unit selling price . Recall that total fixed costs do not change 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 costs dollars. As each additional unit is sold, the total costs will increase by the unit variable cost . Therefore, the slope of the total costs line is equal to the unit variable cost . The break-even point exists at the point where the two lines intersect .

Feedback

Try drawing the lines described on a piece of paper in order to get a visual handle on the concept. Start with a blank X-Y axis grid:

Y (dollars)

|

|

|

|

|

|

|

|

-—————————— X (units)

APPLY THE CONCEPTS: Create the CVP graph for Starr Productions

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

b.

c.

Select your choice. a

Feedback

Try drawing the lines described on a piece of paper in order to get a visual handle on the concept. Start with a blank X-Y axis grid:

Y (dollars)

|

|

|

|

|

|

|

|

-—————————— X (units)

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 breakeven point, you see that the slope of the line is $48, which means that the selling price is $fill in the blank 71640af92fae04f_1

48

.

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

32

means that the variable cost per unit is $fill in the blank 71640af92fae04f_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 right , which means that break-even point in sales dollars increases .

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

28

supplier is used, the slope of the total costs line will be $fill in the blank 71640af92fae04f_5 , and the break-even point in sales dollars decreases .

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 increase . But internal analysis shows that this price increase will cause the break-even point in sales to shift to the left , which means that fewer units will need to be sold to break even.

Feedback

Mastery Problem: Target Income and Margin of Safety

Target Income and Margin of Safety

At the break-even point, sales and costs are exactly equal. However, the goal of most companies is to make a profit. When a company decides that it wants to earn more than the break-even point of income, it must define the amount it thinks it will realistically make. By modifying the break-even equation, the sales required to earn a target or desired amount of profit may be computed.

Complete the following:

If a company makes $3 off of each unit it sells and has a target operating income of $1,200, then it must sell fill in the blank

400

edc2bf010fa9ff8_1 units. Similarly, if a company has a target operating income of $75,000 and knows that total expenses for the period will be $75,000, how much revenue must it earn to reach its target operating income? $fill in the blank

150000

edc2bf010fa9ff8_2

Units sold or revenue earned above and beyond the break-even point contributes to the margin of safety for a company. Margin of safety is a crude measure of risk, in that it serves as the padding between profit and the break-even point.

Complete the following:

Expressed in terms of units, if a company hits its break-even point in units (say, 100 units) and actually sells 400 units, then the margin

300

of safety is fill in the blank edc2bf010fa9ff8_3 units. Similarly, if the break-even point in sales revenue is $200,000,

200000

and it actually has sales revenue of $400,000, then its margin of safety is $fill in the blank edc2bf010fa9ff8_4 .

Feedback

The target units will be the target income divided by the profit per unit.

The margin of safety in terms of units is the difference between projected units sold and the breakeven level of units.

The margin of safety in terms of revenue is the difference between projected units sold times their price, and the breakeven level of units times their price.

APPLY THE CONCEPTS: Target income (number of units sold) Suppose a business has pricing and cost information as follows::

Price and Cost Information Amount

Selling Price per Unit $10.00

Variable Cost per Unit $2.00

Total Fixed Cost $400

For the upcoming period, the company wishes to generate operating income of $720. Given the cost and pricing structure for the company’s product, how many units must the company sell to attain its target income?

Remember that the basic equation for calculating operating income is as follows:

Operating Income = (Unit Price x Units Sold) - (Variable Cost per Unit x Units Sold) - Fixed Cost

Step 1: Replace the operating income in the equation with your company’s target income, and insert your cost and pricing information into the equation, as well:

($fill in the blank ($fill in the blank

$fill in the blank 62359afcf034077_2 62359afcf034077_3 $fill in the blank

62359afcf034077_1 = 10 - 2.00 - 62359afcf034077_4

720 x Units x Units 400 Sold) Sold)

Step 2: Rearrange the equation to isolate units to one side of the equation:

Fixed Cost + Target Income

Number of Units to Earn Target Income =

Unit selling price - Variable Cost per Unit

400

Number of Units to $fill in the blank 62359afcf034077_5 +

Earn Target Income = 720

10

$fill in the blank 62359afcf034077_6 -

2.00

$fill in the blank 62359afcf034077_7

140

Number of Units to Earn Target Income = fill in the blank 62359afcf034077_8 units

Step 3: Create a contribution margin income statement to check your previous work. Enter all amounts as positive numbers.

$fill in the blank

Sales 62359afcf034077_9

1400

Total variable fill in the blank 62359afcf034077_10

expense 280

Total contribution $fill in the blank

62359afcf034077_11

margin 1120

Total fixed fill in the blank

expense 62359afcf034077_12

400

$fill in the blank

Operating 62359afcf034077_13

income 720

Feedback

Carry each value shown into each equation and compute the result.

APPLY THE CONCEPTS: Target income (sales revenue)

Another useful method for figuring out the type of performance your company will need to reach a target income is by using sales revenue. Rather than using the number of units, this method uses total sales revenue. In companies for which the total set of goods produced and sold is more varied, this would be the preferred method, as opposed to a business in which only one product is sold. Assume a company has pricing and cost information as follows:

Price and Cost Information Amount

Selling Price per Unit $30

Variable Cost per Unit $15

Total Fixed Cost $15,000

For the upcoming period, the company wishes to generate operating income of $40,000. Given the cost and pricing structure for the company’s product, how much sales revenue must it generate to attain its target income?

Step 1: Calculate the contribution margin ratio:

The contribution margin ratio is the contribution margin in proportion to the selling price on a per-unit basis.

(Selling Price – Variable Cost)

Contribution Margin Ratio =

Selling Price

Note: The contribution margin ratio is calculated to one decimal place.)

($fill in the blank

44662c025f9f02d_1 fill in the blank

30

0.5

Contribution – $15) = 44662c025f9f02d_2

Margin Ratio =

$fill in the blank

44662c025f9f02d_3

30

Step 2: Calculate the sales revenue required to attain the target income:

(Target Income + Fixed Cost)

Sales Dollars =

Contribution Margin Ratio

( $fill in the blank

44662c025f9f02d_4 $fill in the blank

40000

110000

Sales + $15,000) = 44662c025f9f02d_5

Dollars =

fill in the blank

44662c025f9f02d_6

0.50

Step 3: Create a contribution margin income statement, to check your previous work. Enter all amounts as positive numbers.

Sales $fill in the blank

44662c025f9f02d_7

110000

Total variable expense fill in the blank

44662c025f9f02d_8

55000

Total contribution fill in the blank

44662c025f9f02d_9

margin 55000

Total fixed fill in the blank

44662c025f9f02d_10

expense 15000

Operating

fill in the blank

44662c025f9f02d_11

income 40000

Feedback

Carry each value shown into each equation and compute the result.

To complete the income statement, carry down your calculated target sales dollars and use the contribution margin ratio to calculate total contribution margin. The total variable expense will be the difference between these two values.

APPLY THE CONCEPTS: Margin of Safety

Margin of safety can allow you to see how much padding there is for your company between profit and loss. If this number is great, it may indicate that your company is performing very well. If this number is small, it may be worth looking into possible remediation. Consider the following pricing and cost information:

Price and Cost Information Amount

Selling Price per Unit $450

Variable Cost per Unit $400

Total Fixed Cost $70,000

For the upcoming period, the company projects that it will sell 2,000 units. Considering that the company has a unit break-even point of 1,400 units, what is the margin of safety in terms of both units and sales revenue? Round your answers to two decimal places, if necessary.

Mastery Problem: Contribution Margin, Cost-Volume-Profit Analysis and Break-Even Point (Overview) Fixed, Variable and Mixed Costs

An appreciation of cost behavior is needed in order for management to understand and predict profitability as the costs of material, labor and other operating expenses and levels of production and sales change. It’s important to review the cost behavior of fixed, variable and mixed costs before contribution margins, cost-volume-profit analysis, and break-even points.

1. In the table below, Have-A-Seat Inc. has outlined many of the costs associated with producing office chairs. With respect to the production and sale of office chairs, classify each cost as fixed, mixed, or variable.

Variable Cost

a. Pressure-molded plastic for chair frames

Variable Cost

b. Pension cost: $0.50 per employee hour on the job

Mixed Cost

c. Insurance premiums for inventory: $2,100 per month plus $0.01 for each dollar of inventory over $2 million

Fixed Cost

d. Property taxes: $120,000 per year for the factory building and land

2. Variable costs per unit stay the same with changes in the level of activity, while fixed costs per unit decrease as the number of units increases and increase as the number of units decreases.

Feedback

Refer to the rollovers to fixed, variable and mixed costs for help with this part.

Contribution Margin Income Statement

A contribution margin income statement organizes costs by behavior (variable or fixed), rather than by function (operating, selling, or administrative). The contribution margin is the difference between sales and variable expenses .

Byron Manufacturing has one product that sells for $24.00 per unit. The company estimates fixed costs at $6,000, direct materials at $4.00 per unit, direct labor at $5.00 per unit, and variable overhead costs at $3.00 per unit.

Fill in the contribution margin income statement when 730 units are sold:

Byron Manufacturing

Contribution Margin Income Statement

17520

Sales $fill in the blank 3e1e04058fda065_2

8760

Less: Variable costs fill in the blank 3e1e04058fda065_4

8760

Contribution margin $fill in the blank 3e1e04058fda065_5

6000

Less: Fixed costs fill in the blank 3e1e04058fda065_7

2760

Operating income $fill in the blank 3e1e04058fda065_8

12

Calculate Byron Manufacturing’s per unit contribution margin : $fill in the blank 3e1e04058fda065_9 .

The contribution margin ratio is 50% .

Calculating the Break-even Point:

12000

The break-even point in sales dollars is $fill in the blank 3e1e04058fda065_11 which is a break-even point in units of

500

fill in the blank 3e1e04058fda065_12 units.

Feedback

Use the sell price and the number of units sold to calculate sales. Use the variable costs and the number of units sold to calculate variable costs. Fixed costs are provided. Refer to the rollovers for help with the calculations for per-unit contribution margin, contribution margin ratio, and break-even point.

CVP Analysis using a chart:

The cost-volume-profit chart for Byron Manufacturing is shown. Use the graph to complete the sentences given below.

Byron Manufacturing reaches its break-even level of activity when it sells 500 units and generates $12,000 in revenue, because at this level of activity the firm’s revenue equals its total cost. In addition, you can determine from the chart that Byron Manufacturing’s fixed costs are $6,000 and its price per unit is $24.00 and variable cost per unit is $12.00 .

If fixed costs increase, what will happen to the break-even point?

The break-even point will increase.

If the price per unit decreases, what will happen to the break-even point?

The break-even point will increase. Feedback

The CVP chart illustrates the calculations done in the preceding part. The results are the same.

CVP analysis is used to analyze the effects of changes in selling prices, costs and volume on profits. It is also used to determine target profit, the margin of safety, operating leverage, product mix and choosing among marketing strategies and others.

Suppose Byron management has a target operating income of $3,000. Assume the same costs as above and the sell price remains at $24 per unit. How many units does Byron need to sell to meet this goal?

750

fill in the blank 9e459e00cfbcfd3_1 units

What is Byron’s margin of safety in sales and in units when Byron sells 730 units?

5520

Margin of safety in sales $fill in the blank 9e459e00cfbcfd3_2 Margin of safety in units fill in the blank

230

9e459e00cfbcfd3_3 units

What is the degree of operating leverage when 730 units are sold? If required, round your answer to two decimal places.

3.17

fill in the blank 9e459e00cfbcfd3_4

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