– Introduction to CVP analysis Show
– Calculations for a CVP analysis – Using a CVP to target a desired profit – Break-even point explained – Computing the break-even point
Introduction:CVP analysis looks at the effect of sales volume variations on costs and operating profit. The analysis is based on the classification of expenses as variable (expenses that vary in direct proportion to sales volume) or fixed (expenses that remain unchanged over the long term, irrespective of the sales volume). Accordingly, operating income is defined as follows: Operating Income = Sales – Variable Costs – Fixed Costs A CVP analysis is used to determine the sales volume required to achieve a specified profit level. Therefore, the analysis reveals the break-even point where the sales volume yields a net operating income of zero and the sales cutoff amount that generates the first dollar of profit. Cost-volume
profit analysis is an essential tool used to guide managerial, financial and investment decisions. Cost-Volume Profit AnalysisContribution Margin and Contribution Margin PercentageThe first step required to perform a CVP analysis is to display the revenue and expense line items in a Contribution Margin Income Statement and compute the Contribution Margin Ratio. A simplified Contribution Margin Income Statement classifies the line items and ratios as follows: Contribution Margin Income StatementTable 15.1 Contribution Margin Income Statement
Table 15.1 Contribution Margin Income Statement. The table shows the percent of income for sales, contribution margin, and operating income are observed as totals, after variable and fixed cost deductions. * Contribution Margin Percentage The method relies on the following assumptions:
The equation: Operating Income = Sales – Variable Costs – Fixed Costs Sales = units sold X price per unit Variable Costs = units sold X cost per unit The first equation above can be expanded to highlight the components of each line item: Operating Income = (units sold X price per unit) – (units sold X cost per unit) – Fixed Cost The contribution margin is defined as Sales – Variable Costs. Therefore, Contribution Margin ($) = (units sold X price per unit) – (units sold X cost per unit) And the Contribution Margin Percentage (CM%) is computed as follows: CM% = Contribution Margin ($) / Sales ($) Accordingly, the following is another way to express the relationship between contribution margin, CM percentage, and sales: Contribution Margin $ = Sales $ X Contribution Margin % The contribution margin percentage indicates the portion each dollar of sales generates to pay for fixed expenses (in our example, each dollar of sales generates $.40 that is available to cover the fixed costs). As variable costs change in direct proportion (i.e. in %) of revenue, the contribution margin also changes in direct proportion to revenues, However, the contribution margin percentage remains the same. Example: Revenues $100 – (20 units X $5) Var. Costs $60 – 60% (20 units X 60%) CM $40 – 40% The equation above demonstrates 100 percent of income ($100) minus $60 from variable costs equals $40 contribution margin. the equation below demonstrates revenues doubling to $200 and deducting fixed costs of $120, that results in $80 contribution margin. If revenues double: Revenues $200 – (40 units X $5) Fixed Costs $120 – 60% (40 units X 60%) CM $80 – 40% Targeted Profit CVP analysis is conducted to determine a revenue level required to achieve a specified profit. The revenue may be expressed in number of units sold or in dollar amounts. Income StatementTable 15.2 Income Statement
Table 15.2 Income Statement. The table shows an income statement that observes total income from sales, contribution margin total after variable cost deduction, and operating income total after fixed cost deduction. How much sales is required to achieve a $20 profit?
CVP formulas to be remembered:
Required number of units sold For Targeted Profit = [latex]\huge{\frac{(\text{Fixed Costs Dollar + Targeted Profit Dollar})}{\text{Contribution Margin Dollar Per Unit}}}[/latex] The previous equation reads: Required number of units sold for targeted profit equals fixed costs dollar plus targeted profit dollar, divided by Contribution Margin dollar per unit.
Required Dollar Sales For Targeted Profit = [latex]\huge{\frac{(\text{Fixed Costs Dollar + Targeted Profit Dollar})}{\text{Contribution Margin Percentage}}}[/latex] The previos equation reads: Required dollar sales for targeted profit equals fixed costs dollar plus targeted profit dollar, divided by Contribution Margin percentage. Break-even Point The break-even point is reached when total costs and total revenues are equal, generating no gain or loss (Operating Income of $0). Business operators use the calculation to determine how many product units they need to sell at a given price point to break even or to produce the first dollar of profit. Break-even analysis is also used in cost/profit analyses to verify how much incremental sales (or revenue) is needed to justify new investments. The following graph illustrates the break-even point based on the number of covers sold in a restaurant Figure 15.1 Break-even point based on the number of covers sold in a restaurantLong description:
Computing the Break-Even Point Computing the break-even point is equivalent to finding the sales that yield a targeted profit of zero. Example The average check (selling price per cover) for the Roadside Exotic BBQ Restaurant is $16. The restaurant averages 85 covers sold a day or 2,250 covers per month. The restaurant currently loses money as indicated in the following statement: Roadside Exotic BBQ
Restaurant
Table 15.4 Income Statement for an Exotic Barbecue Restaurant |
Statement Item | Dollar Amount | Percent of Income |
---|---|---|
Sales (2,250 Covers x $16) | $40,800 | 100% |
(Deduction) Variable Costs | ($29,376) | (72%) |
(Total) Contribution Margin | $11,424 | 28% |
(Deduction) Fixed Costs | ($13,464) | (30%) |
(Total) Operating Income | ($2,040) | (5%) |
Table 15.4 Income Statement for an Exotic Barbecue Restaurant.
The owner wants to know the sales volume required in terms of both dollars ($) and the number of covers for the restaurant to break even considering its current expense structure.
- Required number of covers sold
Required number of covers sold = [latex]\huge{\frac{(\text{Fixed Costs Dollar + Targeted Profit Dollar})}{\text{Contribution Margin Dollar Per Unit}}}[/latex]
The equation just shown is meant to be read as: fixed costs dollar plus targeted profit dollar, divided by contribution margin dollar per unit
In this case,
- Targeted Profit = zero (definition of Break-even)
- Contribution Margin per unit: $16 X 28% (CM%) = $4.48
[latex]\huge{\frac{\text{Fixed Cost Dollar}}{\text{Contribution Margin Dollar /unit}} = \frac{\$ 13,464}{\$ 4.48}}[/latex] = 3,005.36 (3,006) covers or
100.18 (101) covers per day.
Verification
Roadside Exotic BBQ Restaurant
Income StatementTable 15.5 Income Statement of an Exotic Barbecue Restaurant
Statement Item Dollar Ammount Percent of Income Sales (3,005.36 Covers x$16)
$48,086
100%
(Deduction) Variable Costs
($34,622)
(72%)
(Total) Contribution Margin
$13,464
28%
(Deduction) Fixed Costs
($13,464)
(28%)
(Total) Operating Income
($0)
(0%)
Table 15.5 Income Statement of an Exotic Barbecue Restaurant
- Required Sales
Sales $ = Targeted Profit $ + Fixed Expense $
Contribution Margin %Since targeted profit is zero, the formula for the Break-Even Sales is:
Fixed Expense $ = $13,464 = $48,086
Contribution Margin % 28%Break-Even formulas to be remembered:
- Break-Even number of Units sold
Break-Even number of units sold =
(Fixed Costs Dollar / Contribution Margin Dollar per unit)
- Break-Even Sales
Break-Even Sales $ =
(Fixed Costs Dollar / Contribution Margin Percentage)
Summary
The break-even point calculation allows food service operators to calculate the number of covers (or units sold) or total sales needed to cover all costs of the operation given the level of business generated. Once the break-even point is met, additional revenue (or sales) starts to generate a profit, which is typically at least one purpose of running a business. Cost volume profit analysis allows the food service operator to calculate similar figures but with a targeted profit in mind. This CVP analysis is an essential tool in guiding managerial, financial and investment decisions for current operations or future business ideas or plans.
Review Questions
Short Answer
- How would conducting a cost volume profit analysis help a food service operator make decisions about future business ideas?
- What sort of assumptions need to be made about a food service operation in order to complete a cost volume profit analysis
- How might calculating a break-even point be useful to a food service manager?