Cornerstones of Managerial Accounting 2e Chapter Four Cost-Volume-Profit Analysis: A Managerial Planning Tool Mowen/Hansen Copyright © 2008 Thomson South-Western, a part of the Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license.

Cost-Volume-Profit Analysis A powerful tool for planning and decision making. It can be used to calculate: The number of units that must be sold to break-even The impact of an increase in price on profit. The impact of a given reduction in fixed costs on the break-even point.

Or to put it another way: Break-Even Point Total Revenue = Total Cost Or to put it another way: Total Revenue – Total Cost Zero Profit

Using Operating Income in Cost-Volume-Profit Analysis Contribution Margin Variable Expense Contribution Margin Sales - = Contribution Margin is then used to cover Fixed Costs and Operating Income.

Contribution Margin Income Statement Divides costs based on behavior Costs are divided into variable and fixed components Important subtotal is contribution margin Sales revenue minus variable expenses

Break-even point is when Operating Income is zero. Contribution Margin Variable Expense Contribution Margin Sales - = Contribution Margin Fixed Costs Operating Income - = Break-even point is when Operating Income is zero.

Units to Be Sold to Achieve a Target Income Two ways: Using Operating Income equation Using the Basic Break-even equation Cornerstone 4-5 will walk us through these computations

Units to Be Sold to Achieve a Target Income Number of units to earn target income Fixed Cost + Target Income = Price – Variable Cost per unit Number of units to earn target income $45,000 + $37,500 = $400 - $325 Number of units to earn target income 1,100 =

Sales Revenue to Achieve a Target Income Sales dollars to earn target income Fixed Cost + Target Income = Contribution margin ratio Sales dollars to earn target income $45,000 + $37,500 = 0.1875 Sales dollars to earn target income $440,000 =

Profit-Volume Graph Visually portrays the relationship between profits and units sold Operating Income is the dependent variable Units sold is the independent variable

Cost-Volume-Profit Graph Depicts the relationship among cost, volume, and profits To obtain the more detailed relationships, it is necessary to graph two separate lines: Total revenue Total cost The vertical axis is measured in dollars The horizontal axis is measured in units sold

Assumptions of Cost-Volume-Profit Analysis Revenue and cost functions are linear Price, total fixed costs, and unit variable costs can be identified and remain constant over relevant range All units produced are sold-there are no change in inventory levels Sales mix is constant Selling prices and costs are known with certainty

Linear Cost and Revenue Functions Cost-Volume-Profit assumes that cost and revenue functions are linear. In other words they are straight lines.

Production Equal to Sales Cost-Volume-Profit assumes that what is produced is actually sold Inventory levels do not change over the period CVP focuses on current costs by excluding inventory costs of previous periods

Constant Sales Mix Multiple product break-even analysis requires a constant sales mix. Relative combination of products being sold by a firm Sales mix is difficult to predict with certainty

Certainty of Prices and Costs In actuality, firms seldom know prices, variable costs, and fixed costs with certainty. There are formal ways of explicitly building uncertainty into the Cost-Volume-Profit model.

Multiple-Product Analysis Cost-Volume-Profit analysis becomes more complex with multiple products. We need to adapt the single-product formulas.

Direct Fixed Expenses Those fixed costs that can be traced to each segment and would be avoided if the segment did not exist.

Common Fixed Expenses The fixed costs that are not traceable to the segments and would remain even if one of the segments was eliminated.

Multiple-Product Analysis Break-even point in units Key is to identify the expected sales mix. Sales mix is the relative combination of products being sold by a firm.

Sales Mix Measured in units sold Reduced to the smallest possible whole numbers Required in order to determine break even point in units

CVP Analysis: Risk and Uncertainty The break-even point can be affected by changes in: Price Unit contribution margin Fixed cost Changes in any of the above will affect the sales mix.

Risk and Uncertainty Effects on Managers Management must realize the uncertain nature of future prices, costs, and quantities. Managers move from consideration of a break-even point to what might be called a “break-even band”. Managers may engage in sensitivity or what-if analysis.

Margin of Safety The units sold or the revenue earned above the break-even volume. Can be viewed as a crude measure of risk. When there is a downturn in sales, the risk of suffering losses will be less if the firm’s margin of safety is large than if the margin of safety is small.

Margin of Safety 400 1,000 600 Margin of Safety in units Sales in units Break-even units = - Margin of Safety in units = 1,000 - 600 Margin of Safety in units 400 =

Margin of Safety $160,000 Margin of Safety in sales revenue Break-even sales = Sales - Margin of Safety in sales revenue = $400(1,000) - $400(600) Margin of Safety in sales revenue $160,000 =

Degree of Operating Leverage The relative mix of fixed costs to variable costs in a company Higher proportions of fixed costs to the amount of variable costs create higher operating leverage The greater the degree of operating leverage, the larger the effect on operating income when sales change Degree of Operating Leverage Contribution Margin = Operating Income

Operating Leverage The degree of operating leverage (DOL) can be measured for a given level of sales. Degree of operating leverage Contribution Margin = Operating Income Degree of operating leverage ($400 – $325)(1,000 units) = $30,000 Degree of operating leverage 2.5 =

Percentage Change in Operating Leverage = DOL x % change in sales % change in operating leverage 2.5 20% = x % change in operating leverage 50% =

Expected Operating Income Original operating income = (% change x Orig. operating income) + Expected Operating Income = $30,000 + (0.50 x $30,000) Expected Operating Income $45,000 =