4: Chapter CostVolumeProfit Analysis: A Managerial Planning Tool
Cornerstones of Managerial Accounting, 4e
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Learning Objectives
1. Determine the break-even point in number of units and in total sales dollars. 2. Determine the number of units that must be sold, and the amount of revenue required, to earn a targeted profit. 3. Prepare a profit-volume graph and a cost-volume-profit graph, and explain the meaning of each. 4. Apply cost-volume-profit analysis in a multiple-product setting. 5. Explain the impact of risk, uncertainty, and changing variables on cost-volume-profit analysis.
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Cost-volume-profit (CVP) analysis estimates how changes in the following three factors affect a company's profit. Costs (both variable and fixed) Sales volume Price
Profi t
BreakEven Point in Units and Sales Dollars
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BreakEven Point in Units and in Sales Dollars
(continued)
Companies use CVP analysis to help them reach important benchmarks, like breakeven point. The break-even point is the point where total revenue equals total cost (i.e., the point of zero profit). Put another way, the break-even point is the level of sales at which contribution margin just covers fixed costs and consequently operating income is equal to zero. Since new companies typically experience losses (negative operating income) initially, they view their first break-even period as a significant milestone.
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$$$$$$$$
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BreakEven Point in Units and in Sales Dollars
(continued)
Besides breakeven point, CVP analysis can address many other issues as well, including: 1 the number of units that must be sold to break even the impact of a given reduction 2 in fixed costs on the break-even point 3 the impact of an increase in price on profit
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Using Operating Income in CostVolumeProfit Analysis
Direct materials Direct labor Variable selling and administrative costs Fixed selling and administrative costs
Variable overhead Fixed overhead
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Using Operating Income in CostVolumeProfit Analysis
(continued)
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Cornerstone 41 Preparing a Contribution Margin Income Statement
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Cornerstone 41 Preparing a Contribution Margin Income Statement (continued)
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BreakEven Point in Units
If the contribution margin income statement is recast as an equation, it becomes more useful for solving CVP problems.
Basic CVP Equation
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Cornerstone 42 Calculating the BreakEven Point in Units
Information: Recall in Cornerstone 4-1 that Whittaker sells mowers for $400 each and variable cost per mower is $325. Total fixed cost equals $45,000. Required: 1. Calculate the number of mowers that Whittier must sell to break even. 2. Check your answer by preparing a contribution margin income statement based on the breakeven point.
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Cornerstone 42 Calculating the BreakEven Point in Units
(continued)
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BreakEven Point in Units
To recap, the break-even units are equal to the fixed cost divided by the contribution margin per unit.
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Sometimes, managers using CVP analysis may prefer to use sales revenue as the measure of sales activity instead of units sold. A units sold measure can be converted to a sales revenue measure by multiplying the unit selling price by the units sold:
BreakEven Point in Sales Dollars
For example, the break-even point for Whittier is 600 mowers; the selling cost is $400 per mower. So, Breakeven in Sales $'s = 600 x $400 =
$240,000
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Variable Cost Ratio and Contribution Margin Ratio
Any answer expressed in units sold can be easily converted to one expressed in sales revenues.
Alternatively:
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Cornerstone 43 Calculating the Variable Cost Ratio and the Contribution Margin Ratio
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Cornerstone 43 1 Calculating the Variable Cost Ratio and the Contribution Margin Ratio (continued)
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Since the total contribution margin is the revenue remaining after total variable costs are covered, it must be the revenue available to cover fixed costs and contribute to profit. How does the relationship of fixed cost to contribution margin affect operating income? There are three possibilities:
Fixed Cost's Relationship with the Variable Cost Ratio and the Contribution Margin Ratio
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Fixed cost equals contribution margin; operating income is zero; the company breaks even. Fixed cost is less than contribution margin; operating income is greater than zero; the company makes a profit. Fixed cost is greater than contribution margin; operating income is less than zero; the company makes a loss.
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Calculating BreakEven in Sales Dollars
The equation to figure the break-even sales dollars is:
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Cornerstone 44 Calculating the BreakEven Point in Sales Dollars
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Cornerstone 44 Calculating the BreakEven Point in Sales Dollars (continued)
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Cornerstone 44 Calculating the BreakEven Point in Sales Dollars (continued)
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Units to Be Sold to Achieve a Target Income
While the break-even point is useful information and an important benchmark for relatively young companies, most companies would like to earn operating income greater than $0. CVP allows us to do this by adding the target income amount to the fixed cost. First, let's look in terms of the units that must be sold to earn a desired income.
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Cornerstone 45 2 Calculating the Number of Units to Be Sold to Earn A Target Operating Information: Income
Whittier Company sells mowers at $400 each. Variable cost per unit is $325, and total fixed cost is $45,000. Required: 1. Calculate the number of units that Whittier must sell to earn operating income of $37,500. 2. Check your answer by preparing a contribution margin income statement based on the number of units calculated.
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Cornerstone 45 Calculating the Number of Units to Be Sold to Earn A Target Operating Income (continued)
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Sales Revenue to Achieve a Target Income
How much sales revenue must Whittier generate to earn an operating income of $37,500? This question is similar to the one we asked earlier in terms of units but phrases the question directly in terms of sales revenue. To answer the question, add the targeted operating income of $37,500 to the $45,000 of fixed cost and divide by the contribution margin ratio. This equation is:
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Information: Whittier Company sells mowers at $400 each. Variable cost per unit is $325, and total fixed is cost $45,000. Required: 1. Calculate the contribution margin ratio. 2. Calculate the sales that Whittier must make to earn an operating income of $37,500. 3. Check your answer by preparing a contribution margin income statement based on the sales dollars calculated.
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Cornerstone 46 Calculating Sales Needed to Earn a Target Operating Income
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Cornerstone 46 Calculating Sales Needed to Earn A Target Operating Income (continued)
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Impact of Change in Revenue on Change in Profit
Assuming that fixed costs remain unchanged, the contribution margin ratio can be used to find the profit impact of a change in sales revenue. To obtain the total change in profits from a change in revenues, multiply the contribution margin ratio times the change in sales:
Change in Profits
Contribution Change = Margin in x Ratio Sales
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Graphs of CostVolumeProfit Relationships: The ProfitVolume Graph
3
A profit-volume graph visually portrays the relationship between profits (operating income) and units sold.
The profit-volume graph is the graph of the operating income equation:
Operating income = (Price x Units) - (Unit variable cost x Units) - Total fixed cost
In this graph, operating income is the dependent variable, and units is the independent variable.
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Graphs of CostVolumeProfit 3 Relationships: The CostVolumeProfit Graph The cost-volume-profit graph depicts the relationships among cost,
volume, and profits (operating income).
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CVP Analysis Assumptions
Major assumptions of CVP analysis include:
Linear revenue and cost functions remain constant over the relevant range.
1
2
Selling prices and costs are known with certainty.
3
All units produced are sold; no finished goods inventories remain.
4
Sales mix is known with certainty for multipleproduct break-even settings.
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4
MultipleProduct Analysis
Cost-volume-profit analysis is fairly simple in the singleproduct setting. However, most firms produce and sell a number of products or services. How do we adapt the formulas used in a singleproduct setting to a multiple-product setting? One important distinction is to separate direct fixed expenses from common fixed expenses. Direct fixed expenses are those fixed costs that can be traced to each segment and would be avoided if the segment did not exist. Common fixed expenses are the fixed costs that are not traceable to the segments and would remain even if one of the segments was eliminated.
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Break-Even Calculations for Multiple Products
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4
Cornerstone 47 Calculating The BreakEven Units for a MultipleProduct Firm
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Cornerstone 47 Calculating The BreakEven Units for a MultipleProduct Firm (continued)
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4
Cornerstone 47 Calculating The BreakEven Units for a MultipleProduct Firm (continued)
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Cornerstone 48 4 Calculating The BreakEven Sales Dollars for A MultipleProduct Firm Information:
Recall that Whittier Company sells two products that are expected to produce total revenue next year of $1,120,000 and total variable cost of $870,000. Total fixed cost is expected to equal $96,250. Required: 1. Calculate the break-even point in sales dollars for Whittier. 2. Check your answer by preparing a contribution margin income statement.
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Cornerstone 48 Calculating The BreakEven Sales Dollars for A MultipleProduct Firm (continued)
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4
Finding the BreakEven Point for a New Business
You Decide
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5
CostVolumeProfit Analysis and Risk and Uncertainty
Managers must be aware of so many factors in our dynamic world. CVP analysis is a tool that managers use to handle risk and uncertainty.
in ges n Cha es?? pric
? y? nt ai
? Risks? Fixed ? costs?
t er c Un
Variable costs??
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Introducing Risk and Uncertainty
An important assumption of CVP analysis is that prices and costs are known with certainty.
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However, risk and uncertainty are a part of business decision making and must be dealt with somehow.
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Methods to Deal with Uncertainty and Risk
Management must realize the uncertain nature of future prices, costs, and quantities. Management must assume a breakeven "band" rather than a breakeven point.
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5
Margin of Safety and Operating Leverage
HELP WANTED: Managers to consider measures of risk, like margin of safety and operating leverage. MUST HAVE knowledge of Fixed and Variable costs.
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Margin of Safety
The margin of safety is the units sold or the revenue earned above the break-even volume. For example, if the break-even volume for a company is 200 units and the company is currently selling 500 units, the margin of safety in units is: Sales - Break-even units = 500 200 = 300 units If the break-even volume for a company is $200,000 and the current revenues are $500,000, the margin of safety in sales revenue is: Revenue - Break-even volume = $500,000 200,000 = $300,000 The margin of safety as a percentage of total sales dollars can then be expressed as: Margin of safety Revenues = $300,000 $500,000 =
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Cornerstone 49 Computing the Margin of Safety
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Operating Leverage
Operating leverage is use of fixed costs to extract higher percentage changes in profits as sales activity changes. Operating leverage is the measure of the proportion of fixed costs in a company's cost structure. It is used as an indicator of how sensitive profit is to changes in sales volume.
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5
Operating Leverage
(continued)
The degree of operating leverage (DOL) can be measured for a given level of sales by taking the ratio of contribution margin to operating income or:
Contribution margin Operating income
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5
Cornerstone 410 Computing the Degree of Operating Leverage
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Summary of Operating Leverage
Operatin Leverage g HIGH LOW
% profit increase with sales increase % loss increase with sales decrease
Large Large
Small Small
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5
Cornerstone 411 Calculating the Impact of Increased Sales on Operating Income Using the Degree of Operating Leverage
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5
Sensitivity Analysis
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5
Using Contribution Margin Income Statements To Consider Varying Scenarios
You Decide
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