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 | $ XXX |
APPLY THE CONCEPTS:
Prepare a contribution margin income statement
Assume that you are part of the accounting team for Starr Manufacturing. The company has only one product that sells for $20 per unit. Starr estimates total fixed costs to be $9,800. Starr estimates direct materials cost of $4.00 per unit, direct labor costs of $5.00 per unit, and variable overhead costs of $1.00 per unit. The CEO would like to see what the gross margin and operating income will be if 1400 units are sold in the next period. Prepare a contribution margin income statement.
Starr Manufacturing | |
Contribution Margin Income Statement | |
Sales | $ |
Less: Variable costs | |
Contribution margin | $ |
Less: Fixed costs | |
Operating income | $ |
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 costs. After those costs are paid, anything remaining from contribution margin becomes . 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 . 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 |
APPLY THE CONCEPTS: Calculate the break-even point in sales dollars for Starr Manufacturing
Further analysis of Starr Manufacturing’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, $4.00 per unit; direct labor costs, $5.00 per unit; and variable overhead costs, $1.00 per unit. At this time, the selling price of $20 will not change. Complete the following formulas for the revised fixed costs. Enter the ratio as a percentage.
Contribution Margin per Unit | = | $ | – | $ | = | $ |
Contribution Margin Ratio | = | $ | = | % |
$ |
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 | = | $ | = | $ |
% |
Units Sold at 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?
$
What would operating
income be if the units sold exceeded the break-even point by five
(5) units?
$
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 . The slope of any line is the variable rate. The slope of the sales line is equal to the . Recall that total fixed costs regardless of the number of units sold, even if zero units are sold. Therefore, the total costs line will cross the Y-axis at dollars. As each additional unit is sold, the total costs will increase by . Therefore, the slope of the total costs line is equal to the . The break-even point exists at the point where .
APPLY THE CONCEPTS: Create the CVP graph for Starr Manufacturing
Review the information and previous calculations for the break-even point in sales dollars for Starr Manufacturing. Choose the graph that correctly represents the CVP graph for Starr Manufacturing.
a. | |
b. | |
c. |
Select your
choice.
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 $.
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 $.
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 , which means that break-even point in sales dollars .
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 $, and the break-even point in sales dollars .
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 . But internal analysis shows that this price decrease will cause the break-even point in sales to shift to the , which means that units will need to be sold to break even.
Check My Work
Starr Manufacturing | |
Contribution Margin Income Statement | |
Sales (1400*20) | $28,000 |
Less: Variable costs (1400*(4+5+1)) | $14,000 |
Contribution margin | $14,000 |
Less: Fixed costs | $ 9,800 |
Operating income | $ 4,200 |
Contribution Margin per Unit (14000/1400) | 10 |
Contribution margin ratio (10/20) | 50% |
Break-even point in sales dollar (9800/50%) | $19,600 |
Contribution Margin per Unit | $ 10 |
Contribution margin ratio | 50% |
Break-even point in sales dollar ((9800+4200)/50%) | $28,000 |
Units Sold at Break-Even Point ((9800+4200)/10) | 1400 |
Operating income (1) | $ 10 |
Operating income (5) (5*10) | $ 50 |
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