Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis Cost-Volume-Profit (CVP) Analysis - the study of the interrelationships between costs and volume and how they impact profit. I can’t make a good marketing decision without understanding the CVP relationships.

Cost-Volume-Profit Analysis CVP aids management in . . . setting prices for products and services. introducing a new product or service. replacing a piece of equipment. deciding whether a given product or service should be made within the firm or purchased outside the firm. performing strategic “what if?” analyses.

Cost-Volume-Profit Analysis Profit = Revenues - Total Costs or Revenues = Fixed Costs + Variable Costs + Profits or (Units sold × Price) = Fixed Cost + (Units sold × Unit Variable Cost) + Profit

Cost-Volume-Profit Analysis Q = units sold v = unit variable cost f = total fixed cost p = unit selling price N = operating profit The CVP Model: (p × Q) = f + (v × Q) + N

The Contribution Margin and Contribution Income Statement The unit contribution margin is the difference between unit sales price and unit variable cost, and is a measure of the increase in profit for a unit increase in sales. The total contribution margin is the unit contribution margin multiplied by the number of units sold. p – v = Unit contribution margin

The Contribution Margin and Contribution Income Statement Household Furnishings, Inc. Per Monthly Annual Unit Fixed cost $5,000 $60,000 Desired operating profit $4,000 $48,000 Price $37,500 $450,000 $75 Variable cost $17,500 $210,000 $35 Planned production 250 units 3,000 units Planned Sales 250 units 3,000 units

The Contribution Margin and Contribution Income Statement Household Furnishings, Inc. 2,400 units × $75 = $180,000

The Contribution Margin and Contribution Income Statement Household Furnishings, Inc. $15,000 × 53.33% = $8,000

Strategic Role of CVP Analysis What if the expected level of profit at a give sales volume? What additional amount of sales is needed to achieve a desired level of profit? What will be the effect on profits of a given increase in sales? What is the required funding level for a governmental agency, given desired service level? Is the forecast for sales consistent with forecasted profits? What additional profit would be obtained from a given percentage of reduction in unit variable costs?

CVP Analysis for Breakeven Planning The Equation Method: Break-Even in Units $75 × Q = $5,000 + ($35 × Q) Selling price per unit Total fixed cost Variable cost per unit

CVP Analysis for Breakeven Planning The Equation Method: Break-Even in Units $75 × Q = $5,000 + ($35 × Q) ($75 - $35) × Q = $5,000 Q = $5,000 ÷ $40 Q = 125 units per month

CVP Analysis for Breakeven Planning The Equation Method: Break-Even in Dollars Y = (v ÷ p) × Y + f + N

CVP Analysis for Breakeven Planning The Equation Method: Break-Even in Dollars Y = (.4667) × Y + f + N $210,000 ÷ $450,000

CVP Analysis for Breakeven Planning The Equation Method: Break-Even in Dollars Y = (.4667) × Y + f + N Y = .4467 × Y + $5,000 + 0 Y = $9,375 per month

CVP Analysis for Breakeven Planning Contribution Margin Method f p -v Q = $5,000 $75 - $35 Q = Q = 125 units per month

The CVP Graph (5,000) Q = 125 Breakeven Point Total Revenue Total Cost Cost or Revenue Total Cost (5,000) Output Volume Q = 125 Breakeven Point

Profit-Volume Graph Profits Q = 125 Profits Total Cost Output Volume Output Volume Q = 125 Losses 25,000 50,000 75,000

CVP Analysis for Breakeven Planning Contribution Margin Method f (p - v) ÷ p p × Q = $5,000 ($75 - $35) ÷ $75 p × Q = p × Q = $9,375 per month

f + N (p – v) f + N (p – v) ÷ p Revenue Planning Breakeven in units = Management wants to know the sales volume necessary to achieve $48,000 in annual profit. f + N (p – v) Breakeven in units = f + N (p – v) ÷ p Breakeven in dollars =

Revenue Planning f + N (p – v) $60,000 + $48,000 $75 – $35 Management wants to know the sales volume necessary to achieve $48,000 in annual profit. f + N (p – v) Breakeven in units = Breakeven in units = $60,000 + $48,000 $75 – $35 Breakeven in units = 2,700 units per year

Trade-offs Between Fixed and Variable Costs Management is considering a new piece of equipment that will reduce variable costs but also increase fixed costs by $2,500 per month. Annual sales are currently 2,700 units. How much will unit variable cost have to fall to maintain the current level of profit, assuming sales volume and other factors remain the same? Q = 2,700 units p = $75 v = unknown f = ($5,000 + $2,250)×12 = $87,000 N = $48,000

Trade-offs Between Fixed and Variable Costs Management is considering a new piece of equipment that will reduce variable costs but also increase fixed costs by $2,500 per month. Annual sales are currently 2,700 units. How much will unit variable cost have to fall to maintain the current level of profit, assuming sales volume and other factors remain the same? v = p – (f + N) Q v = $75 – ($87,000 + $48,000) 2,700 = $25

Sales Commissions and Salaries Management finds that $1,000 of the $5,000 monthly fixed costs is sales salaries, and that $7.50 of the $35 variable cost is sales commissions. If salaries are increased to $1,450, how much would sales commission rate need to be decreased to keep profits the same? v = r × $75 + $27.50 Original $35 - $7.50 (10% of $75)

Sales Commissions and Salaries Management finds that $1,000 of the $5,000 monthly fixed costs is sales salaries, and that $7.50 of the $35 variable cost is sales commissions. If salaries are increased to $1,450, how much would sales commission rate need to be decreased to keep profits the same? v = r × $75 + $27.50 Fixed costs will increase by $450 per month and variable costs will decrease. f = $5,000 + $450 = $5,450

Sales Commissions and Salaries Managers would have to reduce the commission rate from 10% to 7.33% to keep profits the same if the salespeople’s salaries are increased by $450. $65,400 - $48,000 2,700 r × $75 + $27.50 = $75 – r = .0733

Including Income Taxes in CVP Analysis f + p - v Q = N (1 - t ) t = tax rate If the company is subject to a 20% tax rate. $48,000/(1 - .2) $75 - $35 Q = $60,000 + Q = 3,000 units per year

Sensitivity Analysis of CVP Results What-if Sensitivity Analysis Management may look at changes in unit variable cost, total fixed costs or unit selling price on profits. Look at the analysis below:

Sensitivity Analysis of CVP Results Margin of Safety Margin of Safety = Planned Sales - Breakeven Sales 3,000 units - 1,500 units Margin of Safety = Margin of Safety = 1,500 units

CVP Graph for a Firm with Relatively High Fixed Costs $1.5 $.5 Total Revenue Losses @ 25,000 units = – 25,000 x $10 = – $250,000 Cost or Revenue (in millions) Total Cost Fixed cost/yr. $500,000 Variable cost/ unit $2 Price $12 Contribution margin $10 25,000 50,000 75,000 Output in Units

CVP Graph for a Firm with Relatively High Fixed Costs Profits @ 75,000 units = 25,000 x $10 = $250,000 $1.5 $.5 Total Revenue Cost or Revenue (in millions) Total Cost Fixed cost/yr. $500,000 Variable cost/ unit $2 Price $12 Contribution margin $10 25,000 50,000 75,000 Output in Units

CVP Graph of a Firm with Relatively Low Fixed Costs $1.5 $.5 Total Revenue Total Cost Losses @ 25,000 units = -25,000 x $3 = -$75,000 $1.0 Cost or Revenue (in millions) Fixed cost/yr. $150,000 Variable cost/ unit $9 Price $12 Contribution margin $3 $ .l5 Output in Units 25,000 50,000 75,000

CVP Graph of a Firm with Relatively Low Fixed Costs $1.5 $.5 Profits @ 75,000 units = 25,000 x 3 = $75,000 Total Revenue Total Cost $1.0 Cost or Revenue (in millions) Fixed cost/yr. $150,000 Variable cost/ unit $9 Price $12 Contribution margin $3 $ .l5 Output in Units 25,000 50,000 75,000

CVP Analysis with Multiple Products Here is information about two surfboard models manufactured:

CVP Analysis with Multiple Products Assume a Constant Sales Mix The product mix in units sold is 1.5 Pro : 1 Hang Ten

CVP Analysis with Multiple Products Assume a Constant Sales Mix Hang Ten 1.0 × $62.50 = $62.50 Pro 1.5 × $150.00 = 225.00 Total contribution $287.50 = 135 packages (rounded) X = $38,750.00 $287.50

CVP Analysis with Multiple Products Assume a Constant Sales Mix X = 135 packages (rounded) Nose-to-Toes uses a weighted-average product mix to calculate break-even.

CVP Analysis with Multiple Products Here is the calculation of Nose-to-Toes’ average contribution margin . . . 1.0 ÷ 2.5 = 40% 40% × $62.50 = $25.00

CVP Analysis with Multiple Products We find the break-even point as follows . . . X = $38,750 $115 = 337 boards (rounded)

CVP Analysis with Step Cost Behavior Revenues, Total Costs Total Revenue Total Cost $100,000 Losses Output in Units 10,000 20,000 25,000 30,000

CVP Analysis with Step Cost Behavior There is no breakeven below the 10,000 unit level of output. Revenues, Total Costs Total Revenue $100,000 Losses Output in Units 10,000 20,000 25,000 30,000

Assumptions and Limitations of CVP Analysis Linearity and the Relevant Range Identifying Fixed and Variable Cost for CVP Analysis

End of Chapter 8