1. Based on amount of profit contributed: This approach is based on the concept of the contribution margin, or the amount that each unit contributes toward covering fixed expenses and generating profit. Mathematically, the contribution margin per unit is calculated as follows:

Contribution Margin = Selling Price — Variable Expenses Per Unit

2. Break-even is where fixed expenses are covered: If the contribution margin is the amount that each unit contributes toward covering the fixed expenses, the break-even point in units, or the point where the fixed expenses are covered can be found in the following manner:

Break-even Sales (in units) = Fixed Expenses

Contribution Margin per unit

3. Break-even in dollars: To find the break-even point in dollars simply multiply the break-even point in units by the selling price. Alternatively, one can use the contribution margin ratio, which is the contribution margin expressed as a percentage of the selling price. Thus:

Break-even Sales (in dollars) = Fixed Expenses

Contribution Margin Ratio

1. The Equation Approach

Sales - Total Variable Expenses – Total Fixed Expenses = Profit

Break-even Sales (in dollars) = Total Variable Expenses + Total Fixed Expenses

 

Sales (in units) = (Fixed Expenses + Target Net Income)

Contribution Margin Per Unit

Sales (in units) = (Fixed Expenses + Target Net Income)

Contribution Margin Per Unit

Sales (in dollars) = Total Variable Exp. + Total Fixed Exp. + Target Net Profit

2. Applying CVP Analysis

1. Safety margin: The safety margin of an organization is computed as follows:

Safety Margin = Budgeted Sales — Break-even Sales

This measure shows the amount that sales can fall before a firm starts to lose money.

2. Useful for "what if" questions: The impact of changes in fixed expenses, variable expenses, selling prices, and volume on profit can be analyzed by using CVP analysis. Therefore, CVP is a useful tool in answering "what if" questions (i.e. sevsitivity analysis).

1. Multiple products require weighting sale mix: Most firms have more than one product line, and CVP analysis may be adapted for these firms. The same basic equations are used; however, the contribution margin must be weighted by the sales mix. The sales mix is the number of units sold of a given product relative to the total units sold by the firm.

1. Example: If a company sells 8,000 units of product A and 2,000 units of product B, the sales mix is 80% A and 20% B.

1. Weighted-average contribution really a market basket: A weighted-average unit contribution margin is calculated by multiplying a product’s contribution margin by its sales mix percentage, and then summing the results for individual products. The result is often divided into fixed expenses (as before) to arrive at the break-even point in units. In this case, however, the units are really a market basket of the various goods in the sales-mix percentage.
2. Final step: As a final step, the sale-mix percentage are multiplied by the number of "units" to calculate the individual product sales to break even. It should be evident that a change in a firm’s sales mix will alter the company’s break-even point.

1. The CPV model is based on a number of underlying assumptions listed below.

1. Linear behavior of total revenue: The behavior of the total revenue is linear within the relevant range.
2. Linear behavior of total expenses: The behavior of total expenses is linear with the relevant range. This assumption dictates that (a) expenses can be categorized as fixed, variable, or semivariable and (b) efficiency and productivity remain as predicted.
3. Sales mix constant: The sales mix remains constant over the relevant range.
4. Inventory levels constant: Inventory levels remain constant throughout the period (i.e. sales = production).

1. Traditional includes cost-of-goods sold: The traditional income statement for a manufacturer includes a cost-of-goods-sold figure that combines variable costs and fixed manufacturing overhead. The statement’s format does not group costs by behavior but rather by function, thus making CVP analysis difficult.
2. Contribution highlights cost behavior: The contribution income statement is presented in a format that highlights cost behavior. Variable expenses are subtracted from sales to produce a total contribution margin. Next fixed expenses are subtracted to yield the period’s net income. This format is used for variable costing.

1. Highly automated, high fixed costs: The cost structure of an organization is the relative proportion of fixed and variable costs. An automated manufacturing plant has a high proportion of fixed costs while a a labor intensive plant has a high proportion of variable costs. Many advanced manufacturing facilities therefore have relatively high break-even points, which could be troublesome during periods of economic recession.
2. Structure affects profit fluctuation: An organization’s cost structure has a significant effect on the way that profits fluctuate in response to changes in sales volume. The greater the proportion of fixed costs in a firm’s structure, the greater the impact on profit from a given percentage change in sales revenue.
3. Operating leverage determines extent an organization uses fixed costs: The extent to which an orgaization uses fixed costs in its cost structure is called operating leverage. A firm with a high proportion of fixed costs and a low proportion of variable costs has high operating leverage and the ability to greatly increase net income from an increase in sales revenue. In other words, after the break-even point is not reached, losses will be larger in a high leverage situation.
4. Measuring degree of operating leverage: The degree of operating leverage can be measured as follows:

Operating leverage Factor = Contribution margin

Net income

1. CVP Analysis, Activity-Based Costing, and Advanced Manufacturing Systems

1. Cost behavior may change: Cost behavior may change with a shift from a traditional-costing system to an ABC system. The traditional CVP analysis requires a single, volume-based cost driver, namely, sales volume. With the multiple drivers of ABC, some traditional fixed costs are now considered variable (with respect to the appropriate drivers).
2. ABC offers improved understanding: With the improved accuracy of ABC, a company receives a richer understanding of cost behavior and CVP relationships.

1. Target income generally before taxes: The target net income figure, unless specifically stated as after tax, usually means net income before taxes.
2. Minor adjustment converts to after tax: A minor adjustment is made to the after-tax income to convert it to a before-tax figure, and the before-tax figure is plugged into the CVP formulas shown earlier.

Before tax income = After tax income

1- Tax Rate