Fundamentals of Cost Analysis for Decision Making Chapter 3

Learning Objectives Use cost-volume-profit (CVP) analysis to analyze decisions. 2. Understand the effect of cost structure on decisions. 3. Use differential analysis to analyze decisions. Understand how to apply differential analysis to pricing decisions. Understand several approaches for establishing prices based on costs for long-run pricing decisions. Understand how to apply differential analysis to production decisions. 7. Understand the theory of constraints (Appendix).

V ? C P Cost-Volume-Profit Analysis What is Cost Volume Profit L.O. 1 Use cost-volume-profit (CVP) analysis to analyze decisions. V ? C P What is Cost Volume Profit CVP studies the relations among revenue, cost, and volume and their effect on profit.

The Profit Equation The Income Statement Operating profit equals total revenue less total costs. Operating profit Total revenues Total costs The Profit Equation It’s the income statement written horizontally. Operating profit Total revenues Total costs p TR TC

Profit Equation Continued TR Price Units of output produced and sold P X TR PX TC Variable costs per unit Units of output Fixed costs X F V VX F TC

Profit Equation Continued TR TC p PX VX F p P F V X [ ]

Developed 12,000 prints in March U-Develop; an Example U-Develop Income Statement Month of March 200X Total Per Unit Sales $7,200 $0.60 Less Variable cost of goods sold 3,600 0.30 720 Less Variable selling cost 0.06 2,880 Contribution margin 0.24 Less Fixed costs 1,500 Developed 12,000 prints in March Operating profit $1,380

Profit Equation Example U-Develop p P V F X $1,380 $.60 $.36 $1,500 12,000 units [ ] $.30 + $.06 $1,380 $2,880 $1,500 $1,380 p

Contribution Margin Total contribution margin The difference between total revenue and total variable costs. P V X P V X Unit contribution margin CM unit The difference between sales price and variable costs per unit. CM unit P V

Contribution Margin Example CVP studies the relations among revenue, cost, and volume and their effect on profit. U-Develop CM P V X Total CM $.60 $.36 12,000 units CM CM $2,880 $.30 + $.06 CM Unit CM unit P V $.60 $.36 CM unit $.24 CM unit

Contribution Margin Continued U-Develop ? $.24 CM unit Why do I care? For every $1.00 in sales, U-Develop has $.24 available to first cover fixed costs and then to increase profits.

[ ] Target Volume in Units P V F X Target Profit Target Volume (Units) Fixed costs Target profit Unit contribution margin F p X P V

Target Volume Units Example U-Develop Target Profit of $1,800 p F X CM unit $1,800 $1,500 X $.24 X 13,750 units

Contribution Margin Ratio Contribution margin as a percentage of sales revenue. Total contribution margin ratio Total contribution margin as a percent of total sales revenue. P X V Unit contribution margin ratio P V Contribution margin per unit as a percent of sales price per unit. CMR unit

CMR Example U-Develop CMR P V X $.60 $.36 12,000 .60 CMR $2,880 $7,200 .40 CMR unit $.24 $.60 .40

Target Volume in Sales Dollars = Fixed costs + Target profit Contribution margin ratio Target volume sales dollars TR F TR p + CMR =

Target Sales Dollars Example U-Develop F TR p + CMR = TR .40 $1,800 $1,500 TR $8,250 13,750 x $.60 = $8,250

Break-Even The sales volume level at which profits equal zero. Total revenues = Total costs Use the target volume formulas to find the break-even point. Set target profit to zero (p = 0) F X p + CM unit = p = 0 Break-even volume (units) = Fixed costs CMunit

Break-Even Units Example U-Develop F X p CM unit X $.24 1,500 X 6,250 prints

Total revenues = Total costs Break-Even in Sales Dollars The total sales dollars at which profits equal zero. p = 0 Total revenues = Total costs F TR CMR TR F CMR

Break-Even Sales Dollars Example U-Develop F TR p CMR TR .40 $1500 TR $3,750 6,250 prints X $.60 = $3,750

CVP Summary Summary of Target Volume and Break-Even Formulas Target volume (units) = Fixed costs + Target profit Unit contribution margin Target volume sales dollars = Fixed costs + Target profit Contribution margin ratio

CVP Summary Continued Summary of Target Volume and Break-Even Formulas Break-even volume (units) = Fixed costs Unit contribution margin Break-even volume (sales dollars) = Fixed costs Contribution margin ratio

Graphic Presentation U-Develop Break-Even $3,750 6,250 prints Total revenue Total cost $3,750 6,250 prints

CVP and the Effect of Different Cost Structures L.O. 2 Understand the effect of cost structure on decisions. Cost structure Operating leverage The proportion of fixed and variable costs to total costs. The extent to which the cost structure is made up of fixed costs. Contribution margin Net income The higher the organization’s operating leverage, the higher the break-even point.

Comparison of Cost Structures Lo-Lev Company Hi-Lev Company (1,000,000 units) Amount Percentage Sales $1,000,000 100% Variable Costs $750,000 75% $250,000 25% Contribution margin $250,000 25% $750,000 75% Fixed costs $50,000 5% $550,000 55% Operating profit $200,000 20% Break-even point 200,000 units 733,334 units Contribution margin per unit $0.25 $0.75 Degree of Operating Leverage 1.25 3.75

Operating Leverage Example Suppose Lo-Lev & Hi-Lev both increase sales 10% or $100,000. Why do I care? Lo-Lev Hi-Lev Sales CMR Increase in Profit Prior NI NI with sales increase of 10% $100,000 .25 $25,000 $200,000 $225,000 $100,000 .75 $75,000 $200,000 $275,000

Operating Leverage Continued Lo-Lev Hi-Lev Percent Increase in sales Degree of Operating Leverage Percent increase in NI Prior NI NI with sales increase of 10% 10% 1.25 12.5% $200,000 $225,000 10% 1.75 17.5% $200,000 $275,000

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 8,000 6,250 1,750 prints $4,800 $3,750 $1,050 1750 x $.60 = $1,050

Extending CVP: Taxes p Profit of $3,000 But this means taxes. What if U-Develop is in the 15% tax bracket and wants profit after taxes of $3,000? CM unit F 1 - t p Target Volume .85 X $1,500 $3,000 $.24 X 20,956 units

CVP and Taxes Continued Check it out 20,956 $.60 $12,574 Sales VC 20,956 $.36 7,544 CM $5,030 FC 1,500 NIBT $3,530 Taxes 530 3,530 15% Net Income $3,000

Extending CVP: Multiple Products What if: U-Develop does prints and enlargements? Prints Enlargements Selling price $.60 $1.00 Variable cost .36 .56 Contribution margin $. 24 $. 44 Total Fixed Costs $1,820

Product Mix For every 9 prints sold U-Develop sells 1 enlargement. Weighted Average Contribution Margin 9/10 $.24 1/10 $.44 $ .26 6,300 prints 9/10 Breakeven $1,820 $.26 7,000 700 enlargements 1/10

Differential Analysis L.O. 3 Use differential analysis to analyze decisions. Differential Analysis The process of estimating revenues and costs of alternative actions available to decision makers and of comparing these estimates to the status quo. Short Run The period of time over which capacity will be unchanged, usually one year.

Differential Costs Alternative A Alternative B Costs that change in response to an alternative course of action. Differential costs differ between actions. Alternative A Alternative B

Sunk Costs IT’S GONE TOO BAD SO SAD Costs incurred in the past that cannot be changed by present or future decisions. IT’S GONE TOO BAD SO SAD A sunk cost is NOT relevant.

Differential Analysis and Pricing Decisions L.O. 4 Understand how to apply differential analysis to pricing decisions. Variable costs Must always be covered. Cost ($) Activity level Fixed costs Must be covered in the long run. Costs ($) Activity level

Full Cost and Pricing Decisions Full cost of manufacturing and selling a product. Variable costs Necessary to manufacture and sell the product. and Fixed costs Share of organization’s fixed costs. Ultimately full costs must be recovered.

Short-run vs Long-run Variable costs Must always be covered. Short-run Pricing Decisions Fixed costs Must be covered in the long run. Long-run Pricing Decisions

Short-run vs Long-run Pricing Decisions Year 1 Short-run Pricing Decision Long-run Pricing Decision Shorter than one year Longer than one year Pricing a one-time special order. Pricing a new product. How much material is required? Do I need a new plant?

Short-run Pricing Decisions: Special Orders An order that will not affect other sales and is usually a one-time occurrence. Value of Option 1 Accept Special Order? Is Option 1 > Option 2? Status Quo: Reject special offer Alternative: Accept special offer Value of Option 2 Option 1 Option 2

Special Order Example Analysis of Special Order U-Develop Status Quo: Alternative: Reject Special Order Accept Special Order Difference Comparison of Totals Variable costs (1,000) (1,100) (100) Fixed costs (1,200) Operating profit $300 $400 $100 Sales revenue $2,500 $2,700 $200 Total contribution 1,500 1,600 100 Alternative Presentation: Differential Analysis Differential operating profit (before taxes) $100 Differential sales, 500 at 40¢ $200 Less differential costs, 500 at 20¢ 100

Long-run Pricing Decisions L.O. 5 Understand several approaches for establishing prices based on costs for long-run pricing decisions. In the long run an organization must cover variable and fixed costs. Life-cycle product costing and pricing Target costing for Target pricing

Life-cycle Product Costing and Pricing Product life-cycle The time from initial research and development to the time that support to the customer ends. R&D Design Manufacturing Marketing Distribution & Customer Service (Disposal) Take Back Cradle Grave To Life-cycle Costing Concerned with covering costs in all categories of the life cycle.

Target Costing from Target Pricing Target price The price based on customers’ perceived value for the product and the price that competitors charge. What would a customer pay? Desired profit How much profit do I need? Target cost The maximum amount of cost allowed. Can I make it at this cost?

Differential Analysis for Production Decisions L.O. 6 Understand how to apply differential analysis to production decisions. Decision to make goods or services internally or purchase them externally. Make or buy? Decision to add or drop a product line or close a business unit. Add or drop a segment? Decision on what products or services to offer. Product Mix

Make or Buy Example Make or buy? Decision to make goods or services internally or externally. 100,000 prints Per Unit 100,000 prints Cost directly traceable Direct materials $0.05 $5,000 Direct labor 0.12 12,000 Variable manufacturing overhead 0.03 3,000 Fixed manufacturing overhead 4,000 Common costs allocated to this product line 10,000 $34,000

Make or Buy Continued Make or Buy Analysis, U-Develop Status Quo: Alternative: Process Prints Outsource Processing Difference 100,000 prints Direct costs 5,000 $25,000 a 20,000 Direct materials higher Labor 12,000 lower Variable overhead 3,000 lower Fixed overhead 4,000 lower Common costs 10,000 b Total costs $34,000 $35,000 $1,000 higher Differential costs increase by $1,000, so reject alternative to buy. a 100,000 units purchased at $.25 = $25,000. b These common costs remain unchanged for these volumes. Because they do not change, they could be omitted from the analysis.

Make or Buy Continued Make or Buy Analysis, U-Develop Status Quo: Alternative: Process Prints Outsource Processing Difference 50,000 prints Direct costs 2,500 c $12,500 d 10,000 Direct materials higher Labor 6,000 lower Variable overhead 1,500 lower Fixed overhead 4,000 lower Common costs 10,000 b Total costs $24,000 $22,500 $1,500 lower Differential costs decrease by $1,500, so accept alternative to buy. b These common costs remain unchanged for these volumes. Because they do not change, they could be omitted from the analysis. c Total variable costs reduced by half because volume was reduced by half. d 50,000 units purchased at $.25 =$12,500.

Opportunity Costs of Making Make-or-Buy Analysis with Opportunity Cost of U-Develop Status Quo Alternative Process Prints Outsource Processing Difference Total cost of 100,000 prints $34,000 $35,000 1,000 Higher a Opportunity cost of using facilities to make covers 2,000 Lower a Total costs, including opportunity costs $36,000 $35,000 1,000 Lower a Differential costs decrease by $1,000 so accept the alternative. a These indicate whether the alternative is higher or lower than the status quo.

Add or Drop Example Add or drop a segment? Decision to add or drop a product line or close a business unit. Fourth Quarter Product Line Income Statement, U-Develop Less fixed costs: Total Prints Cameras Frames Sales revenue $80,000 $10,000 $50,000 $20,000 Cost of sales (all variables) 53,000 _ 8,000 30,000 15,000 Contribution margin $27,000 $2,000 $5,000 Rent 4,000 1,000 2,000 Salaries 5,000 2,500 1,500 Marketing and administrative _3,000 __500 _1,500 _1,000 Operating profit (loss) $15,000 $(500) $14,000 $1,500

Add or Drop Continued Differential Analysis U-Develop Status Quo: Alternative: Keep Prints Drop Prints Difference Less fixed costs: Sales revenue $80,000 $70,000 $10,000 decrease Cost of sales (all variables) 53,000 45,000 _8,000 Contribution margin $27,000 $25,000 $2,000 Salaries 5,000 4,000 1,000 Marketing and administrative _3,000 _2,750 __250 Operating profit (loss) $15,000 $14,250 $750 Rent Profits decrease $750 so keep prints.

Product Choice Decisions Constraints Activities, resources, or policies that limit the attainment of an objective. Contribution margin per unit of scarce resource Contribution margin per unit of a particular input with limited availability.

Product Choice Decisions Example Revenue and Cost Information, U-Develop Metal Frames Wood Frames Price $50 $80 Less variable costs per unit Material 8 22 Labor 8 24 Overhead 4 Contribution margin per unit $30 Fixed manufacturing costs: $3,000 per month Fixed marketing and administrative costs: $1,500 per month

Product Choice Decisions Example Revenue and Cost Information, U-Develop Per Unit Metal Frames Wood Frames Contribution margin $30 Machine hours required .5 1 Contribution margin per machine hour $60 $30 Metal Frames have a higher contribution margin per machine hour.

Product Choice Decisions Example Suppose U-Develop has 200 machine hours per month available. Capacity 400 200 Contribution margin per unit $30 Total contribution margin $12,000 $6,000 Metal Frames Wood Frames Less fixed manufacturing costs 3,000 Less fixed M&A costs 1,500 Operating profit $7,500 $1,500 Selling metal frames results in higher profits than selling wooden frames.

Theory of Constraints Theory of Constraints L.O. 7 Understand the theory of constraints (Appendix). Theory of Constraints Focuses on revenue and cost management when faced with bottlenecks. Bottleneck Operation where the work required limits production. The bottleneck is a constraining resource.

Chapter 3 The End