Fundamentals of Cost-Volume-Profit Analysis Chapter 3 Fundamentals of Cost-Volume-Profit Analysis In order to be a well prepared leader and manager, one must have a systematic method of analyzing the ever changing environment. Chapter 3 focuses on how decision-makers analyze changes in the volume of sales. McGraw-Hill/Irwin Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. 3 - 1

Cost-Volume-Profit Analysis L.O. 1 Use cost-volume-profit (CVP) analysis to analyze decisions. What is CVP? CVP analysis explores the relationship between revenue, cost, and volume and their effect on profits. Managers must make decisions about volume, pricing and costs and are concerned about the impact of their decisions on profit. Therefore, they need to understand the relations among revenues, costs, volume and profit. Cost-volume-profit, or CVP, analysis provides managers with information for decision making. 3 - 2

Profit Equation The Income Statement Total revenues – Total costs LO1 Profit Equation The Income Statement Total revenues – Total costs = Operating profit The Income Statement written horizontally Operating profit Profit = Total revenues – TC Total costs TR In studying CVP we will start with the profit equation. The profit equation is: Operating profit = Total revenues – Total costs. Don’t let the profit equation confuse you. It is nothing more than the income statement written horizontally. 3 - 3

LO1 Contribution Margin This is the difference between price and variable cost. It is what is leftover to cover fixed costs and then add to operating profit. Contribution margin = Price per unit – Variable cost per unit P – V Let’s review the contribution margin from Chapter 2. The unit contribution margin is the difference between the sales price per unit and variable costs per unit. That is (P-V). 3 - 4

CVP Summary: Break-Even LO1 CVP Summary: Break-Even Break-even volume (units) = Fixed costs Unit contribution margin Break-even volume (sales dollars) = Fixed costs Contribution margin ratio In summary, at break-even target profit is zero. Therefore, break-even sales volume in units equals fixed costs divided by unit contribution margin and break-even sales volume in dollars equals fixed costs divided by contribution margin ratio. 3 - 5

CVP Summary: Target Volume LO1 CVP Summary: Target Volume Target volume (units) = Fixed costs + Target profit Unit contribution margin Target volume (sales dollars) = Fixed costs + Target profit Contribution margin ratio Now we will review the contribution margin ratio. The contribution margin ratio is the contribution margin as a percentage of sales revenue. The total contribution margin ratio equals total contribution margin as a percent of total sales revenue. The unit contribution margin ratio equals the contribution margin per unit as a percent of sales price per unit. Recall our discussion in Chapter 2 of relevant range? A relevant range is a range of activity where our cost structure remains constant. Therefore, as long as we are in the relevant range, the total contribution margin ratio and the unit contribution margin ratio will be the same. Again let’s look at U-Develop. 3 - 6

Use of CVP to Analyze the Effect of Different Cost Structures L.O. 2 Understand the effect of cost structure on decisions. Cost structure: The proportion of fixed and variable costs to total costs. Operating leverage: The extent to which the cost structure is comprised of fixed costs. Let’s talk about cost structure. Cost structure is the proportion of fixed and variable costs to total costs. An organization’s cost structure has a significant effect on the sensitivity of its profits to changes in volume. You are probably starting to see just how important cost behavior is in decision making. Fixed costs remain the same in total regardless of the activity level. This means that even if there is no activity fixed costs remain the same. However, variable costs vary with the activity level and, remember, no activity means no variable costs. Operating leverage describes the extent to which an organization’s cost structure is made up of fixed costs, those costs that do not change when the level of activity changes. 3 - 7

Margin of Safety or The excess of projected or actual sales LO2 Margin of Safety The excess of projected or actual sales volume over break-even volume or The excess of projected or actual sales revenue over break-even revenue Suppose U-Develop sells 8,000 prints. Margin of safety is the excess of projected or actual sales volume over break-even volume or the excess of projected or actual sales revenue over break-even revenue. In other words, the margin of safety indicates the risk of losing money that a company faces. How much can sales decrease in either volume or revenue before the company experiences a net loss? Suppose U-Develop sells 8,000 prints. Recall that U-Develop’s break-even was 6,250 prints. The margin of safety is 1,750 prints (8,000-6,250), or in dollars $1,050 ($4,800 -$3,750). At a break-even volume of 6,250, its margin of safety is: Sales – Break-even = 8,000 – 6,250 = 1,750 prints 3 - 8

CVP Analysis with Spreadsheets L.O. 3 Use Microsoft Excel to perform CVP analysis. A spreadsheet program is ideally suited to performing CPV routinely. 1. Choose “Tools: Goal Seek…” from the menu bar. $0.60 $0.36 $1,500 ($300) 5,000 U-Develop Price Variable cost Fixed cost Profit Volume $0.00 6,250 2. In the “Set cell” edit field, enter the cell address for the target profit calculation. 3. In the “To value” edit field, enter the target profit. It is important to be able to do CVP analysis and understand the relations and it is important to work examples and do problems by hand at first. However, a spreadsheet program is ideally suited to doing CVP routinely. 4. In the “By changing cell” edit field, enter the cell address of the volume variable. 5. Click “OK” and the program will find the break-even volume. 3 - 9

Extensions of the CVP Model: Income Taxes L.O. 4 Incorporate taxes, multiple products, and alternative cost structures into the CVP analysis. The owners of U-Develop want to generate after-tax operating profits of $1,800. The tax rate is 25%. What is the target operating profit? So far we have ignored taxes. What if U-Develop is in a 25% tax bracket and wants a profit of $1,800 after paying income taxes? Now what needs to be covered by the contribution margin per unit? Fixed cost and the before-tax profit required to earn an after-tax profit of $1,800. Dividing the after-tax profit of $1,800 by one minus the tax rate results in the before-tax profit required for an after-tax profit of $2,400. Target operating profit = TOP ÷ (1 – Tax rate) TOP = $1,800 ÷ (1 – 0.25) = $2,400 3 - 10

Extensions of the CVP Model: Multiproduct Analysis LO4 Extensions of the CVP Model: Multiproduct Analysis Management expects to sell 9 prints at $.60 each for every enlargement it sells at $1.00. Selling price Less: Variable cost Contribution margin $0.60 .36 $0.24 $1.00 .56 $0.44 Prints Enlargements What happens when a company has multiple products? Suppose U-Develop sells both prints and enlargements. Prints have a contribution margin of $0.24 per unit. Notice that enlargements have a contribution margin of $0.44 per unit. Assume total fixed costs are $1,820. To calculate break-even divide total fixed costs by the contribution margin per unit. In order to use the single product mix method, managers must define a package or bundle of products and compute break-even or target volume for the package or bundle. And, because prints have a contribution margin per unit of $0.24 and enlargements have a contribution margin per unit of $0.44 we need a weighted average contribution margin. Total fixed costs = $1,820 3 - 11

Extensions of the CVP Model: Multiproduct Analysis LO4 Extensions of the CVP Model: Multiproduct Analysis What is the contribution margin of the mix? (9 × $0.24) + (1 × $0.44) = $2.16 + $0.44 = $2.60 What is the weighted-average contribution margin of the mix? (.90 × $0.24) + (.10 × $0.44) = $0.26 If for every nine prints sold U-Develop sells one enlargement, the package or bundle is ten. Nine of the bundle of ten are prints and one of the bundle of ten is an enlargement. To calculate the weighted average contribution margin multiply the $0.24 contribution margin per unit of prints by 9/10 and the contribution margin of $0.44 per unit of enlargements by 1/10. The weighted average contribution margin of the package or bundle is $0.26 per unit. What is the breakeven of the mix? 3 - 12

Extensions of the CVP Model: Multiproduct Analysis LO4 Extensions of the CVP Model: Multiproduct Analysis 7000 × 90% = 6,300 prints 7000 × 10% = 700 enlargements Total units = 7,000 $1,820 fixed costs ÷ $0.26 = 7,000 units Now divide fixed costs of $1,820 by the weighted average contribution margin per unit of $0.26 and you find that 7,000 units must be sold to break-even. Of the 7,000 units 6,300 (or 9/10) are prints and 700 (or 1/10) are enlargements. 3 - 13

Extensions of the CVP Model: Alternative Cost Structures LO4 Extensions of the CVP Model: Alternative Cost Structures Given: Fixed costs of $1,500 are sufficient for monthly volumes less than or equal to 5,000 prints. For every additional 5,000 prints U-Develop must rent a machine for $480 per month. Original break-even was 6,250 units. That’s a lot of information! But we are not finished yet. Sometimes firms need to rent more equipment and therefore their fixed costs change. Let’s assume that U-Develop can make 5,000 prints a month with their existing equipment. This would mean that they could not breakeven using only their equipment since breakeven was 6,250 units. If U-Develop can rent a machine for $480 and increase their production by 5,000 prints per machine rented, then their breakeven calculation would change. ($0.24 x 6,250) – ($1,500 + $480) = ($480) 3 - 14

Extensions of the CVP Model: Alternative Cost Structures LO4 Extensions of the CVP Model: Alternative Cost Structures What is the break-even using new fixed cost containing the rental of the additional machine? Break-even units = ($1,500 + $480) ÷ $0.24 = 8,250 New fixed costs are now ($1,500 + 480) or $1,980. Sales price and variable costs are not changing, so the CM per unit remains at $0.24. The new breakeven is: $1,980 /$0.24 = 8,250! 3 - 15

Assumptions and Limitations of CVP Analysis L.O. 5 Understand the assumptions and limitations of CVP analysis. Although the CVP model is a very strong tool, the output is dependent upon the assumptions made by cost analysts. These assumptions include which costs are fixed and which are variable. As with all models, there are assumptions and limitations. CVP is a very powerful tool, yet it is only as strong as the assumptions made by the analyst. The analyst must make assumptions with respect to which costs are fixed and which are variable. 3 - 16

End of Chapter 3 McGraw-Hill/Irwin Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.