Cost Volume Profit Analysis  Explained
What is Cost Volume Analysis?
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What is CostVolumeProfit Analysis for SingleProduct Company?
The profit equation shows that profit equals total revenues minus total variable costs and total fixed costs.
Profit = Revenue  Total Variable Costs  Total Fixed Costs
This profit equation is used extensively in costvolumeprofit (CVP) analysis, and the information in the profit equation is typically presented in the form of a contribution margin income statement.
Recall that the contribution margin income statement starts with sales, deducts variable costs to determine the contribution margin, and deducts fixed costs to arrive at profit.
We use the term “variable cost” because it describes a cost that varies in total with changes in volume of activity.
We use the term “fixed cost” because it describes a cost that is fixed (does not change) in total with changes in volume of activity.
To allow for a mathematical approach to performing CVP analysis, the contribution margin income statement is converted to an equation using the following variables:
Key Equation
S = Selling price per unit
V = Variable cost per unit
F = Total fixed costs
Q = Quantity of units produced and sold
Thus Profit = Total sales − Total variable costs − Total fixed costs = (S×Q) − (V×Q)−F
Recall that when identifying cost behavior patterns, we assume that management is using the cost information to make shortterm decisions.
Variable and fixed cost concepts are useful for shortterm decision making.
The shortterm period varies, depending on a company’s current production capacity and the time required to change capacity. In the long term, all cost behavior patterns are likely to change.
Measuring Output and Relevant Range
Determining the BreakEven Point and Target Point
Companies often want to know the sales required to break even, which is called the breakeven point.
The breakeven point can be described either in units or in sales dollars.
The break even point in units is the number of units that must be sold to achieve zero profit.
The break even point in sales dollars is the total sales measured in dollars required to achieve zero profit.
If a company sells products or services easily measured in units (e.g., cars, computers, or mountain bikes), then the formula for breakeven point in units is used.
If a company sells products or services not easily measured in units (e.g., restaurants, law firms, or electricians), then the formula for breakeven point in sales dollars is used.
How to Determine the BreakEven Point in Units?
The breakeven point in units is found by setting profit to zero using the profit equation.
Profit = 0 = (S×Q) − (V×Q)−F
Once profit is set to zero, fill in the appropriate information for selling price per unit (S), variable cost per unit (V), and total fixed costs (F), and solve for the quantity of units produced and sold (Q).
How to Determine the Target Profit in Units
Finding a target profit in units simply means that a company would like to know how many units of product must be sold to achieve a certain profit.
Finding the target profit in units is similar to finding the breakeven point in units except that profit is no longer set to zero.
Instead, set the profit to the target profit the company would like to achieve. Then fill in the information for selling price per unit (S), variable cost per unit (V), and total fixed costs (F), and solve for the quantity of units produced and sold (Q):
Profit in $ = (S×Q)−(V×Q)−F
You can confirm the finding by following contribution margin income statement.
BreakEven Point in Sales Dollars
Often, break even cannot easily measure sales in units?
For these types of companies, the breakeven point is measured in sales dollars.
That is, we determine the total revenue (total sales dollars) required to achieve zero profit for companies that cannot easily measure sales in units.
Finding the breakeven point in sales dollars requires the introduction of two new terms: contribution margin per unit and contribution margin ratio.
The shortcut formula is as follows:
Q = (F + Target Profit) ÷ (S − V)
Contribution Margin per Unit
The contribution margin per unit is the amount each unit sold contributes to (1) covering fixed costs and (2) increasing profit.
We calculate it by subtracting variable costs per unit (V) from the selling price per unit (S).
Key Equation:
Contribution margin per unit = S − V
Contribution Margin Ratio (Margin of Safety)
The contribution margin ratio (often called contribution margin percent) is the contribution margin as a percentage of sales. It measures the amount each sales dollar contributes to (1) covering fixed costs and (2) increasing profit.
The contribution margin ratio is the contribution margin per unit divided by the selling price per unit.
(Note that the contribution margin ratio can also be calculated using the total contribution margin and total sales; the result is the same.)
With an understanding of the contribution margin and contribution margin ratio, we can now calculate the breakeven point in sales dollars.
Key Equation:
Contribution margin ratio = (S − V) ÷ S
The formula to find the breakeven point in sales dollars is as follows.
Breakeven point in sales dollars=Total fixed costs + Target profitContribution margin ratio
Target Profit in Sales Dollars
Finding a target profit in sales dollars simply means that a company would like to know total sales measured in dollars required to achieve a certain profit.
Finding the target profit in sales dollars is similar to finding the breakeven point in sales dollars except that “target profit” is no longer set to zero. Instead, target profit is set to the profit the company would like to achieve.
Key Equation:
Target profit in sales dollars = (Total fixed costs + Target profit) / Contribution margin ratio
Instead of setting the target profit to $0, set it to a target dollar profit.
This results in an answer of the amount of monthly sales needed to achieve this profit.
Cost Volume Profit Relationships
CostVolumeProfit Analysis for MultipleProduct and Service Companies
The following information is required to find the breakeven point for companies with more than one product:
Monthly fixed costs total .
Percent of total sales volume that each product represents
The unit selling price and variable cost information for the products.
Finding the BreakEven Point and Target Profit in Units for MultipleProduct Companies
First, we must expand the profit equation presented earlier to include multiple products.
The following terms are used once again.
However, subscript r identifies one product, and subscript s identifies the second product.
(Note: Sr stands for the 1st model’s selling price per unit.)
CM is new to this section and represents the contribution margin.
Key Equation:
S = Selling price per unit
V = Variable cost per unit
F = Total fixed costs
Q = Quantity of units produced and sold
CM = Contribution margin
Thus,
Profit = Total sales − Total variable costs − Total fixed costs [(Sr×Qr)+(Ss×Qs)] −[(Vr×Qr )+ (Vs × Qs)] − F
Without going through a detailed derivation, this equation can be restated in a simplified manner, as follows:
Profit = (Unit CM for r × Quantity of r) + (Unit CM for s × Quantity of s) − F
There actually are many different breakeven points, because the profit equation has two unknown variables, Qr and Qs.
BreakEven Point in Units and the Weighted Average Contribution Margin per Unit
Because most companies sell multiple products that have different selling prices and different variable costs, the breakeven or target profit point depends on the sales mix.
The sales mix is the proportion of one product’s sales to total sales.
In calculating the breakeven point, we must assume the sales mix for the r and s models will remain consistent with historical sales, respectively, at all different sales levels.
The formula used to solve for the breakeven point in units for multipleproduct companies is similar to the one used for a singleproduct company, with one change.
Instead of using the contribution margin per unit in the denominator, multipleproduct companies use a weighted average contribution margin per unit.
The formula to find the breakeven point in units is as follows.
Weighted Average Contribution margin = (Unit CM for r × Sales Mix % of r) + (Unit CM for s × Sales Mix % of s)
Break Even in Units = Fixed Costs / Weighted Average Contribution Margin
When a company assumes a constant sales mix, a weighted average contribution margin per unit can be calculated by multiplying each product’s unit contribution margin by its proportion of total sales.
Target Profit in Units
We now know how to calculate the breakeven point in units for a company with multiple products.
Finding the target profit in units for a company with multiple products is similar to finding the breakeven point in units except that profit is no longer set to zero.
Instead, profit is set to the target profit the company would like to achieve.
BreakEven Point in Sales Dollars and the Weighted Average Contribution Margin Ratio
For companies that have unique products not easily measured in units, it requires extra steps to find the breakeven point.
Rather than measuring the breakeven point in units, a more practical approach for these types of companies is to find the breakeven point in sales dollars.
We can use the formula that follows to find the breakeven point in sales dollars for organizations with multiple products or services.
Note that this formula is similar to the one used to find the breakeven point in sales dollars for an organization with one product, except that the contribution margin ratio now becomes the weighted average contribution margin ratio.
Key Equation:
Breakeven point in sales dollars = (Total fixed costs + Target profit) / Weighted average contribution margin ratio
The contribution margin ratio differs for each department:
If we have the contribution margin ratio for each department, we will need it for the company as a whole.
The contribution margin ratio for the company as a whole is the weighted average contribution margin ratio.
We calculate it by dividing the total contribution margin by total sales.
WeightedAverage Contribution Margin Ratio = Total Contribution Margin / Total Sales
This assumes that the sales mix remains the same at all levels of sales. (The sales mix here is measured in sales dollars for each department as a proportion of total sales dollars.)
Now that you know the weighted average contribution margin ratio, it is possible to calculate the breakeven point in sales dollars.
Target Profit in Sales Dollars
Finding the target profit in sales dollars for a company with multiple products or services is similar to finding the breakeven point in sales dollars except that profit is no longer set to zero.
Instead, profit is set to the target profit the company would like to achieve.
Break even point in sales dollars = (Total fixed costs + Target profit) / Weighted average contribution margin ratio
Important Assumptions
Several assumptions are required to perform breakeven and target profit calculations for companies with multiple products or services.
These assumptions are as follows:
 Costs can be separated into fixed and variable components.
 Contribution margin ratio remains constant for each product, segment, or department.
 Sales mix remains constant with changes in total sales.
However, these assumptions may not be realistic, particularly if significant changes are made to the organization’s operations.
When performing CVP analysis, it is important to consider the accuracy of these simplifying assumptions.
Cost Volume and Operating Income
Cost Volume Profit Analysis and Operating Leverage
Income Taxes and CostVolumeProfit Analysis
Some organizations, such as notforprofit entities and governmental agencies, are not required to pay income taxes.
How do we find the target profit in units or sales dollars for organizations that pay income taxes?
Three steps are required:
Step 1. Determine the desired target profit after taxes.
Step 2. Convert the desired target profit after taxes to the target profit before taxes. The formula used to solve for target profit before taxes is as follows.
Target profit before taxes = Target profit after taxes ÷ (1 − tax rate)
Step 3. Use the target profit before taxes in the appropriate formula to calculate the target profit in units or sales dollars.
The formula used to solve for target profit in units is
(Total fixed costs + Target profit) / (Selling price per unit − Variable cost per unit)
Using CostVolumeProfit Models for Sensitivity Analysis
We can use the costvolumeprofit (CVP) financial model described in this chapter for singleproduct, multipleproduct, and service organizations to perform sensitivity analysis, also called whatif analysis.
Sensitivity analysis shows how the CVP model will change with changes in any of its variables (e.g., changes in fixed costs, variable costs, sales price, or sales mix).
The focus is typically on how changes in variables will alter profit.
Management makes a best guess of units in monthly sales. This is called the “base case.”
A sensitivity analysis can answer the following questions for management
1. How will profit change if the sales price increases by $___ per unit?
2. How will profit change if sales volume decreases by ___ units?
3. How will profit change if fixed costs decrease by $_______ and variable cost increases $______ per unit (10 percent)?
The CVP model answers these questions.
The best approach is to create a table representing the various scenarios (generally in Excel).
Each column represents a different scenario, with the first column showing the base case and the remaining columns providing answers to the three questions posed by management.
The top part shows the value of each variable based on the scenarios presented previously, and the bottom part presents the results in contribution margin income statement format.
Although the focus of sensitivity analysis is typically on how changes in variables will affect profit, accountants also use sensitivity analysis to determine the impact of changes in variables on the breakeven point and target profit.
Impact of Cost Structure on CostVolumeProfit Analysis
Cost structure is the term used to describe the proportion of fixed and variable costs to total costs.
Operating leverage refers to the level of fixed costs within an organization.
Companies with a relatively high proportion of fixed costs have high operating leverage.
Businesses that rely on direct labor and direct materials tend to have higher variable costs than fixed costs.
Operating leverage is an important concept because it affects how sensitive profits are to changes in sales volume.
This is best illustrated by comparing two companies with identical sales and profits but with different cost structures.
High Operating Leverage Company (HOLC) has relatively high fixed costs, and Low Operating Leverage Company (LOLC) has relatively low fixed costs.
One way to observe the importance of operating leverage is to compare the breakeven point in sales dollars for each company.
Higher operating leverage can lead to higher profit. However, high operating leverage companies that encounter declining sales tend to feel the negative impact more than companies with low operating leverage.
Variance in Cost Volume Profit Analysis
Cost Volume Profit Analysis  Risk and Uncertainty
Related Topics
 Job Costing vs Process Costing
 Assign Direct Material and Direct Labor to Job
 Assign Manufacturing Overhead Costs to Job
 Assign Overhead Costs to Products
 Plantwide Cost Allocation
 Department Cost Allocation
 ActivityBased Costing
 WeightedAverage Cost of Products
 Production Cost Report
 Fixed, Variable, and Mixed Cost Estimations
 Contribution Margin Income Statement
 CostVolumeProfit Analysis
 Margin of Safety
 Contribution Margin per Unit of Constraint
 Absorption Costing vs Variable Costing
 Differential Analysis and Decisions
 Cost Decisions for Joint Products
 Capital Budgeting
 Life Cycle Costing
 The Master Budget
 ActivityBased Budgeting
 Standard Costs
 Imputed Value
 Variance Analysis for Product Costs
 Absorption Pricing
 Price Variance
 Absorption Variance
 Responsibility Centers
 Comparing Segmented Income
 Using ROI to Evaluate Performance
 Using Residual Income to Evaluate Performance
 Use Economic Value Added to Evaluate Performance
 Transfer Pricing