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Chapter 5

Chapter 5. Cost-Volume-Profit Analysis. Classifies all revenue and cost into volume-related and non-volume related groups Measure of volume depends on the business Fixed cost stay the same Revisit some definitions. CVP Foundations. LO1: Understand the Cost-Volume-Profit relation. .

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Chapter 5

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  1. Chapter 5 Cost-Volume-Profit Analysis

  2. Classifies all revenue and cost into volume-related and non-volume related groups Measure of volume depends on the business Fixed cost stay the same Revisit some definitions CVP Foundations LO1: Understand the Cost-Volume-Profit relation.

  3. Pre-tax profit = Revenue – cost = Revenue – variable cost – fixed cost = Contribution margin – fixed cost = Unit contribution margin × sales volume – fixed cost As a formula:Profit = ( P – VC )  Q - FC CVP Model LO1: Understand the Cost-Volume-Profit relation.

  4. Using the CVP Relation

  5. Estimate profit at various sales levels Effect of taxes Calculate volume required for target profit Break even analysis (Zero profit) CVP and Profit Planning LO2: Use the CVP relation to plan profit.

  6. Cost-Volume-Profit (CVP) Model LO2: Use the CVP relation to plan profit.

  7. Profit Graph LO2: Use the CVP relation to plan profit.

  8. Test Your Knowledge! Which one of the following correctly indicates how to calculate breakeven volume? • Variable costs divided by unit contribution margin • Profit divided by sales volume • Fixed costs divided by unit contribution margin • Variable costs divided by fixed costs

  9. Test Your Knowledge! Which one of the following correctly indicates how to calculate breakeven volume? • Variable costs divided by unit contribution margin • Profit divided by sales volume • Fixed costs divided by unit contribution margin • Variable costs divided by fixed costs Fixed costs divided by unit contribution margin indicates the breakeven volume where profit will be zero.

  10. ($50 - $30) ($150,000/$20) ($75,000 X $50) ($50 - $30)/$50 ($1,500,000/0.40) ($3,750,000/$50) $20 $75,000 $3,750,000 0.40 $3,750,000 $75,000

  11. Can calculate profit at any volume Breakeven analysis Volume with zero profit Target Profit LO2: Use the CVP relation to plan profit.

  12. Target Profit: Examples • Data Table • Breakeven volume for Sierra 0 = breakeven volume × $15 – 1,200,000 Breakeven volume = 80,000 pounds LO2: Use the CVP relation to plan profit.

  13. Alternate Formulation • Can work with revenues instead of units • Contribution margin ratio = Unit Contribution Margin / Price • This is the contribution per sales $ • We have: Multiply & divide the first term by price to get… • Work with percent and $ directly

  14. Can calculate profit at any volume Breakeven analysis Revenue for zero profit Target Profit with CMR LO2: Use the CVP relation to plan profit.

  15. Profit at sales of 100,000 units = $300,000 Contribution margin ratio = $15/$25 = 60% Revenue at 100,000 units = $2,500,000 Profit = $2,500,000 × 0.6 - $1,200,000 = $300,000! We also know breakeven = 80,000 pounds Associated revenue = $2,000,000 Profit = $2,000,000 × 0.6 - $1,200,000 = $0! The Methods are Equivalent LO2: Use the CVP relation to plan profit.

  16. Taxes are an unavoidable cost of doing business Single tax rate on income Profit after tax (PAT) = Profit before tax (PBT) – taxes paid Taxes paid = tax rate  Profit before tax Profit after tax =(1- tax rate)  Profit before tax Profit after tax = (1- tax rate)  [Contribution margin – fixed cost] Taxes LO2: Use the CVP relation to plan profit.

  17. Taxes Change Slope of Profit Line LO2: Use the CVP relation to plan profit.

  18. In CVP model, profit is proportional to volume Profit could be limited by: Demand for product Supply of product (capacity limitations) Planning operations involves making short term decisions that identify the factor limiting profit and seek to relax that constraint Operational Planning LO3: Make short-term decisions using CVP analysis.

  19. Change the parameters to increase profit If demand is the constraint Increase prices - Expand product line If capacity is the constraint Change pricing - Rationalize product line Add capacity (long-term decision considered later) Manage risk Change cost structure Expand product portfolio Evaluating Decisions LO3: Make short-term decisions using CVP analysis.

  20. Changing Prices LO3: Make short-term decisions using CVP analysis.

  21. At a given volume, how much “cushion” does firm have before it starts making a loss? Margin of safety formula: Margin of safety is Often expressed as a percentage Can be calculated in units Can be calculated using sales revenue % change in profit = % change in sales × (1/ MOS) Evaluating Operating Risk LO4: Measure risk using the CVP relation.

  22. At sales of 100,000 pounds Profit Multiplier at 100K = (1 / MOS) = 5 Current profit 100K × $15 – 1.2MM = $300K 10% increase => sales = 110K pounds Profit = 110K × $15 – 1.2MM = $450K 50% increase = 10% × 5! Margin of Safety: Example LO4: Measure risk using the CVP relation.

  23. Breakeven volume = $1,500,000 / $20 = 75,000 • Breakeven revenues = $1,500,000 / 0.40 = $3,750,000 • If sales were to increase by 20%, then the percent change in profit before taxes = 0.20 x (1/0.0625) = $100,000 • Profit would increase by $100,000 x 3.2 = $320,000 • In turn, $100,000 + $320,000 = $420,000

  24. Can change cost structure Automation substitutes FC for VC Outsourcing substitutes VC for FC Operating Leverage Increasing the amount of fixed cost increases business risk, for given volume Operating Leverage = Fixed Cost / Total Cost Change Cost Structure LO4: Measure risk using the CVP relation.

  25. Alternate Cost Structures LO4: Measure risk using the CVP relation.

  26. As demand increases, OL decreases For given demand, decisions that increase FC and lower VC increase OL Profit is more sensitive to volume changes when OL is high At lower demand levels, a cost structure with lower OL is typically preferred to a cost structure with higher OL Points to note LO4: Measure risk using the CVP relation.

  27. Multi-Product CVP • With two products, CVP model becomes • No appealing way to allocate joint cost and revenue • Multi-product CVP model is only valid for the specified mix. • Cannot determine “best” product mix LO5: Perform CVP analysis with multiple products.

  28. With the new technology… • Total costs = $1,240,000 + ($9 x Sales volume in units) • Without the new technology… • Total costs = $1,200,000 + ($10 x Sales volume in units) • Setting the two equations equal to each other, we have: • $1,240,000 + ($9 x Sales volume in units) = $1,200,000 + ($10 x Sales volume in units) • Solving, we find Sales volume in units = 40,000 pounds

  29. There are two equivalent approaches for applying the multi-product model Weighted Average Contribution Margin Approach Weighted Average CMR (WACMR) approach Can use with aggregate financial data Mechanics: Multi-Product CVP LO5: Perform CVP analysis with multiple products.

  30. Sales mix 5/8 of sales from E, 3/8 from S Weighted Average Contribution Margin (5/8) × $6 + (3/8) × $15 = $9.375 per average pound Breakeven volume = $1,275,000 / $9.375 = 136,000 lbs. Applying sales mix, we have 85,000 E & 51,000 S Weighted UCM Approach LO5: Perform CVP analysis with multiple products.

  31. Revenue mix 50% from E and 50% from S Weighted Average Contribution Margin Ratio 0.5 × 40% + .5 × 60% = 50% Breakeven revenue = $1,275,000 / 0.500 = $2,550,000 Applying revenue mix, we have $1.275 MM for E => 85,000 lbs. $1.275 MM from S => 51,000 lbs. Weighted CMR Approach LO5: Perform CVP analysis with multiple products.

  32. $8.5714 (rounded) 1 175,000 pounds 2 125,000 50,000 3 (5/7 x $6) = (2/7 x $15) = $60/7 = $8.5714 (rounded) 1 ($1,275,000 + $225,000) / $8.5714 = 175,000 pounds 2 3 175,000 pounds x 5/7 = 125,000 pounds of Economy; 175,000 x 2/7 = 50,000 pounds of Standard

  33. Linearity of revenue Linearity of variable cost Fixed costs cannot be changed No uncertainty Single period analysis Valid only for given product mix Profit maximization is not the criterion Used to answer “what if” questions Assumes that capacity is always available Limitations of CVP Analysis LO6: List the assumptions underlying CVP analysis.

  34. Test Your Knowledge! Which of the following is not a key assumption using CVP analysis? • Capacity is available with no limitations on the supply of raw materials. • Selling prices, unit variable costs, and fixed costs are known with certainty. • Variable costs and revenue increase proportionately with sales volume. • CVP will always provide the best answer for short-term decisions.

  35. Test Your Knowledge! Which of the following is not a key assumption using CVP analysis? • Capacity is available with no limitations on the supply of raw materials. • Selling prices, unit variable costs, and fixed costs are known with certainty. • Variable costs and revenue increase proportionately with sales volume. • CVP will always provide the best answer for short-term decisions. CVP cannot predict the best decisions for all situations. For example, it is effective when revenues and variable costs increase proportionally with sales, sales prices and costs are known with certainty, and product mix stays the same.

  36. 0.50 1 $2,550,000 2 $1,275,000 $1,275,000 3 85,000 51,000 4 (0.50 x 0.40) + (0.50 x 0.60) 1 $1,275,000 / 0.50 2 $2,550,000 x 0.50 (Economy); $2,550,000 x 0.50 (Standard) 3 $1,275,000 / $15 (Economy); $1,275,000 x $25 (Standard) 4

  37. Exercise 5.30 CVP relation and profit planning, unit contribution margin approach (LO1, LO2). Ajay Singh plans to offer gift-wrapping services at the local mall during the month of December. Ajay will wrap each package, regardless of size, in the customer’s choice of wrapping paper and bow for a price of $3. Ajay estimates that his variable costs will total $1 per package wrapped and that his fixed costs will total $600 for the month. • Required: • Express Ajay’s profit before taxes in terms of the number of packages sold. • How many packages does Ajay need to wrap to break even? • How many packages must Ajay wrap to earn a profit of $1,400?

  38. Exercise 5.30 (Continued) • Express Ajay’s profit before taxes in terms of the number of packages sold. • Recall that: • Profit before taxes = (unit contribution margin x sales volume in units) – fixed costs. • Additionally, Unit contribution margin = Unit selling price – Unit variable cost. = $3.00 – $1.00 = $2.00 per package. • The problem also informs us that Ajay’s fixed costs for the month = $600. • Thus, Ajay’s profit is: • Profit before taxes = ($2.00 x number of packages sold) – $600.

  39. Exercise 5.30 (Continued) • How many packages does Ajay need to wrap to break even? • Breaking even implies a profit of zero. Thus, we have: • $0 = ($2,00 x Breakeven volume) - $600 • Or…

  40. Exercise 5.30 (Concluded) • How many packages must Ajay wrap to earn a profit of $1,400? • Substituting Ajay’s target profit of $1,400 into the expression for profit we developed in part [a], we have: • $1,400 = ($2,00 x Required # of packages) - $600 • Or…

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