Mastery Problem: CVP Analysis - Constructing a Cost-Volume-Profit Chart CVP Analysis and the Contribution Margin Income Statement For planning and control purposes, managers have a powerful tool known as cost-volume-profit (CVP) analysis. CVP analysis shows how revenues, expenses, and profits behave as volume changes, which helps identify problems and create solutions. In CVP analysis, costs are classified according to behavior: variable or fixed, rather than by category: product (which includes both variable and fixed) or period (which includes both variable and fixed). When variable costs are subtracted from sales, the contribution margin is obtained, representing the amount of dollars available to cover fixed costs after the costs related to sales are recovered. Fixed costs are deducted from the contribution margin to arrive at operating income. This format is known as the contribution margin income statement. Complete the following table to illustrate the format. Contribution Margin Income Statement Sales $ XXX Less: Variable costs XXX Contribution $ margin XXX Less: Fixed costs XXX Operating income $ XXX Feedback Roll your mouse over the underlined definitions to review the cost concepts. The purpose of this statement format is to separate out the effects of variable costs from fixed costs. APPLY THE CONCEPTS: Prepare a contribution margin income statement Assume that you are part of the accounting team for Epstein Hardware. The company has only one product that sells for $20 per unit. Epstein estimates total fixed costs to be $9,800. Epstein estimates direct materials cost of $4.00 per unit, direct labor costs of $5.00 per unit, and variable overhead costs of $1.00 per unit. The CEO would like to see what the gross margin and operating income will be if 1400 units are sold in the next period. Prepare a contribution margin income statement. Epstein Hardware Contribution Margin Income Statement Sales $ Less: Variable costs Contribution $ margin Less: Fixed costs Operating income $ CVP Analysis and the Break-Even Point in Sales Dollars CVP analysis focuses on selling price, units sold, variable cost per unit, and total fixed costs. Managers can use the contribution margin format to understand the effects of changes in any of these areas. Contribution margin is the amount that is available to pay fixed costs. After those costs are paid, anything remaining from contribution margin becomes operating income . A business can determine the level of sales needed to cover all costs by knowing the break-even point. The break-even point is where operating income is zero . This point can be expressed as the break-even point in units or the break-even point in sales dollars. The following formulas are used to calculate the break-even point in sales dollars: 1. Calculate the contribution margin per unit: Selling Price - Variable Cost per Unit Contribution Margin per Unit 2. Determine the contribution margin ratio: Selling Price Total Fixed Costs 3. Compute the break-even point in sales dollars: Contribution Margin Ratio Feedback Review the statement format and the example from the sections above. What happens as the contribution margin approaches zero? APPLY THE CONCEPTS: Calculate the break-even point in sales dollars for Epstein Hardware Further analysis of Epstein Hardware's fixed costs revealed that the company actually faces annual fixed overhead costs of $9,800 and annual fixed selling and administrative costs of $4,200. Variable cost estimates are correct: direct materials cost, $4.00 per unit; direct labor costs, $5.00 per unit; and variable overhead costs, $1.00 per unit. At this time, the selling price of $20 will not change. Complete the following formulas for the revised fixed costs. Enter the ratio as a percentage. Contribution Margin per Unit Contribution Margin Ratio = $ = $ - $ = $ = % $ Now complete the formulas for (1) the break-even point in sales dollars and (2) the units sold at the break-even point. To calculate this, divide the break-even point in sales dollars by the unit selling price. Break-Even Point in Sales Dollars = $ = $ % Units Sold at Break-Even Point = units Assume that the number of units that Epstein sold exceeded the break-even point by one (1). How much would operating income be? $ What would operating income be if the units sold exceeded the break-even point by five (5) units? $ The Cost-Volume-Profit Graph The CVP graph shows the relationships among cost, volume, and profits. The X- (horizontal) axis is the total units, and the Y- (vertical) axis is the dollars (sales or costs). The intersection of these two axes, the origin, is where both units and dollars are zero. There are two lines to be plotted on the graph: the sales line and the total costs line. The sales line crosses the Y-axis where sales dollars are zero (0) . The slope of any line is the variable rate. The slope of the sales line is equal to the unit selling price . Recall that total fixed costs do not change regardless of the number of units sold, even if zero units are sold. Therefore, the total costs line will cross the Y-axis at total fixed costs dollars. As each additional unit is sold, the total costs will increase by the unit variable cost . Therefore, the slope of the total costs line is equal to the unit variable cost . The break-even point exists at the point where the two lines intersect . Feedback Try drawing the lines described on a piece of paper in order to get a visual handle on the concept. Start with a blank X-Y axis grid: Y (dollars) | | | | | | | | ------------------------------- X (units) APPLY THE CONCEPTS: Create the CVP graph for Epstein Hardware Review the information and previous calculations for the break-even point in sales dollars for Epstein Hardware. Choose the graph that correctly represents the CVP graph for Epstein Hardware. a. b. c. Select your choice. Feedback Try drawing the lines described on a piece of paper in order to get a visual handle on the concept. Start with a blank X-Y axis grid: Y (dollars) | | | | | | | | ------------------------------- X (units) APPLY THE CONCEPTS: Use the CVP graph to analyze the effects of changes in price and costs Graph the following on your own paper. At the original position, the break-even point in sales dollars is $24,000 at 500 units. The fixed costs are $8,000. Assume the slope of the sales line is equal to the selling price. When the two points of the sales line are at the origin and the break-even point, you see that the slope of the line is $48, which means that the selling price is $ . When the two points of the total costs line are at the origin and the break-even point, you see that the slope of the line is $32.00, which means that the variable cost per unit is $ . Leave the break-even point (x) at its original position. Use it as a reference point to answer the following questions. Analyze the scenarios by sliding the points on the lines to get the slope desired. Recall that the new break-even point for each scenario exists where the sales and total costs lines intersect. Compare it to the original break-even point (x). (You may want to put the lines back to their original position for each scenario.) Each scenario should be considered independently. 1. The company purchases a fixed asset and increases fixed costs by $2,000. Variable costs remain the same, which means that the slope does not change. This will cause the break-even point to move to the right , which means that break-even point in sales dollars increases . 2. A new supplier can provide a product of equal quality at $4.00 per unit less than the current direct materials cost. If the new supplier is used, the slope of the total costs line will be $ break-even point in sales dollars decreases . , and the 3. Market research shows that a price increase will decrease the number of units sold. A price increase will cause the slope of the sales line to increase . But internal analysis shows that this price increase will cause the break-even point in sales to shift to the lef , which means that fewer units will need to be sold to break even. Feedback Changes in fixed cost will move the Total Cost Line straight up and down. Changes to variable cost will cause the Total Cost Line to pivot around its starting point. Changes to sales price will cause the Sales Line to pivot around its starting point