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: Show
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 StatementStatement Item Amount Percent of Income Sales $100 100% (Deduction) Variable Costs $60 60% (Total) Contribution Margin $40 40%* (Deduction) Fixed Costs $30 30% (Total) Operating Income $10 10% Table 15.1 Contribution Margin Income Statement. The table shows the percent of income for sales, contribution margin, and operating income are observed as totals, after variable and fixed cost deductions. * Contribution Margin Percentage The method relies on the following assumptions:
The equation: Operating Income = Sales – Variable Costs – Fixed Costs Sales = units sold X price per unit Variable Costs = units sold X cost per unit The first equation above can be expanded to highlight the components of each line item: Operating Income = (units sold X price per unit) – (units sold X cost per unit) – Fixed Cost The contribution margin is defined as Sales – Variable Costs. Therefore, Contribution Margin ($) = (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 StatementStatement ItemAmountPercent of IncomeSales (20 units X $5) $100 100% (Deduction) Variable Costs (20 units X $3) ($60) (60%) (Total) Contribution Margin $40 40% (Deduction) Fixed Costs ($30) (30%) (Total) Operating Income $10 10% 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 RestaurantTable 15.4 Income Statement for an Exotic Barbecue RestaurantStatement ItemDollar AmountPercent of Income |