4 Cost-Volume-Profit Analysis

The Theory

With cost-volume-profit (CVP) analysis, you can use the cost structure of a firm to calculate the volume (in units or dollars) required to break even or hit a target profit, to analyze how close the firm’s sales are to break-even sales by finding the margin of safety (MOS), and to analyze the effect of changes in cost structure on profit by finding the point of indifference. To use CVP analysis, you must understand the concepts of revenue, fixed costs (FC), variable costs (VC), and contribution margin (CM).

Contribution margin is the amount that sales contribute toward covering fixed costs and producing profit; in other words, contribution margin is the revenue produced by sales minus the variable costs associated with those sales. It can be expressed in total (CM), on a per-unit basis (unit contribution margin, or UCM) or as a percentage of revenues (contribution margin ratio, or CMR):

CM = Revenue – VC

UCM = Sales price – VC per unit

CMR = CM ÷ Revenue = UCM ÷ Sales Price

CVP analysis is based on the equation for before-tax profit:

Profit = Revenue – VC – FC

Or, because CM = Revenue – VC:

Profit = CM – Fixed costs

If information is on a per-unit basis, that equation can also be expressed on a per-unit basis:

Profit = UCM x Units – FC

And if information is expressed in terms of revenues, that equation can be expressed in terms of revenues as well:

Profit = CMR x Revenue – FC

 

The Method

To calculate before-tax profit:

To calculate volume required to break even (profit = $0) in terms of units or revenue:

To calculate volume required to hit a target before-tax profit in terms of units or revenue:

To calculate margin of safety in terms of units, revenue, or a ratio:

MOS = Units – Break-even units

MOS = Revenue – Break-even revenue

MOS Ratio = MOS in units ÷ Units = MOS in revenue ÷ revenue

To find the point of indifference, compare two cost structures by setting their before-tax profit equations equal to each other, using a variable for volume.

Illustrative Example

Jonesmith, Inc. incurs $30 per unit in variable costs and $500,000 in total fixed costs. Each unit sells for $80. Jonesmith is considering making an investment that would increase fixed costs by $50,000 but decrease variable costs by $2 per unit.

Calculate the following:

• Before-tax profit if Jonesmith sells 20,000 units
• Before-tax profit if Jonesmith earns revenue of $2,000,000
• The units Jonesmith needs to sell to break even
• The revenues Jonesmith needs to earn to break even
• The units Jonesmith needs to sell to achieve $200,000 in before-tax profit
• The revenues Jonesmith needs to earn to achieve $400,000 in before-tax profit
• Jonesmith’s margin of safety in units if Jonesmith sells 20,000 units
• Jonesmith’s margin of safety in dollars if Jonesmith earns revenue of $2,000,000
• Jonesmith’s margin of safety ratio if Jonesmith earns revenue of $2,000,000
• The unit sales at which Jonesmith would be indifferent between making and not making the new investment

Calculate the before-tax profit if Jonesmith sells 20,000 units:

• UCM = $80 – $30 = $50
• Profit = $50 × 20,000 – $500,000 = $500,000

Calculate the before-tax profit if Jonesmith earns revenue of $2,000,000:

• CMR = $50 ÷ $80 = 62.5%
• Profit = 62.5% × $2,000,000 – $500,000 = $750,000

Calculate the units Jonesmith needs to sell to break even:

• $500,000 ÷ $50 = 10,000

Calculate the revenues Jonesmith needs to earn to break even:

• $500,000 ÷ 62.5% = $800,000

Calculate the units Jonesmith needs to sell to achieve $200,000 in before-tax profit:

• ($200,000 + $500,000) ÷ $50 = 14,000

Calculate the revenues Jonesmith needs to sell to achieve $400,000 in before-tax profit:

• ($400,000 + $500,000) ÷ 62.5% = $1,440,000

Calculate Jonesmith’s margin of safety in units if Jonesmith sells 20,000 units:

• 20,000 – 10,000 = 10,000
• Calculate Jonesmith’s margin of safety in dollars if Jonesmith earns revenue of $2,000,000:
• $2,000,000 – $800,000 = $1,200,000

Calculate Jonesmith’s margin of safety ratio if Jonesmith earns revenue of $2,000,000:

• $1,200,000 ÷ $2,000,000 = 60%

Calculate the unit sales at which Jonesmith would be indifferent between making and not making the new investment:

• New UCM = $80 – 28 = $52; New FC = $500,000 + $50,000 = $550,000
• $50 × Units – $500,000 = $52 × Units – $550,000; Units = 25,000

Lecture Example

Information about your firm:

• Selling price per unit: $400
• Variable cost per unit: $250
• Annual fixed costs: $6,000,000
• Units the business will sell next year: 50,000

Calculate the following:

1. Unit contribution margin
2. Contribution margin ratio
3. Before-tax profit at expected unit sales level
4. Unit sales if the business wants to earn $1,800,000 in before-tax profit
5. Revenue if the business wants to earn $1,800,000 in before-tax profit
6. Breakeven point in units
7. Breakeven point in revenues
8. Margin of safety in units
9. Margin of safety in revenues
10. Margin of safety ratio

Your firm can purchase a new machine that will increase annual fixed costs by 18.75% but will decrease variable cost per unit by 10%. At what level of production would your firm be indifferent between purchasing and not purchasing the new machine?