Cost-Volume-Profit (CVP) Analysis

• Cost-Volume-Profit (CVP) analysis is also known as Break-Even analysis
• CVP analysis helps managers understand the interrelationships between cost, volume, and profit in an organization
• CVP analysis focuses on the following interactions:
  • The prices of products
  • The volume or level of activity
  • Per unit variable costs
  • Total fixed costs
  • Mix of products sold

Approaches to Break-Even/CVP Analysis

• Graphical Approach
• Contribution Approach
• Equation Approach

Break-Even Point Using Graphical Approach

• The break-even point occurs where total revenue and total costs are equal
• A firm must sell Q1 to generate sufficient revenue to cover its costs
• If a firm chooses to set a price higher than €2 (say €3), the Total Revenue curve would be steeper
• When the Total Revenue curve is steeper, the firm would not have to sell as many units to break even
• A higher price would lower the break-even point, and the margin of safety would widen
• With a higher price, more units could be sold before a loss would be made

Preparation of Break-Even Graph

• Plot the fixed cost line
• Plot the total cost line
• Plot the sales revenue line
• The graph should be labeled, indicating:
  • Break-Even Point (Units and Revenues)
  • Profit & Loss Zones
  • Margin of safety

Contribution Approach

• The contribution approach centers around the idea that each unit sold provides a certain amount of contribution margin to cover fixed costs
• Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted
• Contribution is calculated as selling price less variable cost
• Break-Even Point = Fixed Cost / Contribution per unit
• Contribution Ratio = Contribution per unit / Selling Price per unit

Wind Bicycle Co. Example

• Wind Bicycle Co. sells 500 bikes
• Sales are €250,000, or €500 per unit
• Variable expenses are €150,000, or €300 per unit
• Contribution margin is €100,000, or €200 per unit
• Fixed expenses are €80,000
• Net income is €20,000
• For each additional unit Wind sells, €200 more in contribution margin will help to cover fixed expenses and profit
• Wind must generate at least €80,000 in total CM to break even
• If Wind sells 400 units in a month, it will be operating at the break-even point
• Sales will be €200,000 or €500 per bike
• Variable expenses will be €120,000 or €300 per bike
• Contribution margin will be €80,000 or €200 per bike
• Fixed expenses will be €80,000
• Net profit will be zero
• If Wind sells one additional unit (401 bikes), net profit will increase by €200

Contribution Margin Ratio Example

• With 400 bikes sold, sales are €200,000
• Variable expenses are €120,000
• Contribution margin is €80,000
• Fixed expenses are €80,000
• Net profit is 0
• With 500 bikes sold, sales are €250,000
• Variable expenses are €150,000
• Contribution margin is €100,000
• Fixed expenses are €80,000
• Net profit is €20,000
• A €50,000 increase in sales revenue results in a €20,000 increase in CM
• (€50,000 × 40% = €20,000)

Changes in Fixed Costs and Sales Volume

• Wind is currently selling 500 bikes per month
• The company's sales manager believes that an increase of €10,000 in the monthly advertising budget would increase bike sales to 540 units
• Increased CM (40 units * €200) = €8,000
• Increase in advertising = €10,000
• Decrease in Profit = €2,000
• Current sales (500 bikes) are €250,000
• Variable expenses are €150,000
• Contribution margin is €100,000
• Fixed expenses are €80,000
• Net profit is €20,000
• Projected sales (540 bikes) are €270,000
• Variable expenses are €162,000
• Contribution margin is €108,000
• Fixed expenses are €90,000
• Net profit is €18,000

Equation Approach

• The equation method centers on the contribution approach to the Profit and Loss statement

Break-Even/CVP Equations

• Profit = Sales - (Variable Costs + Fixed Costs)
• Sales = Variable Cost + Fixed Costs + Profit

Equation Approach Example 1

• Sales = Variable Cost + Fixed Costs + Profit
• €500Q = €300Q + €80,000 + €0
• €200Q = €80,000
• Q = 400 bikes
  • Where:
    • Q = Number of bikes sold
    • €500 = Unit sales price
    • €300 = Unit variable expenses
    • €80,000 = Total fixed expenses

Equation Approach Example 2

• Sales = Variable Costs + Fixed Costs + Profits
• X = 0.60X + €80,000 + €0
  • Where:
    • X = Total sales
    • 0.60 = Variable expenses as a % of sales
    • €80,000 = Total fixed expenses
• X = €200,000

Break-Even Analysis: Determining Bikes to be Sold to Earn Profit

• Sales = Variable Cost + Fixed Costs + Profit
• €500Q = €300Q + €80,000 + €100,000
• €200Q = €180,000
• Q = 900 bikes

Margin of Safety

• Margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales
• It is the amount by which sales can drop before losses begin to be incurred
• Margin of Safety = (Actual/Budgeted Sales (Units or Volume) – BEP Sales (Units or Volume)) * 100 / Actual/Budgeted Sales (Units or Volume)

Key Business Indicators

• Break-even-point (BEP) in units and/or revenues
• Contribution (Selling price - Variable cost)
• Contribution/Sales ratio
• Margin of safety (%)

Break Even Arithmetic Equations

• Contribution Sales Ratio = Contribution Per Unit / Selling Price Per Unit
• Break Even Point in Units = Total Fixed Costs / Contribution Per Unit
• Break Even Point in Units = Sales = VC + FC + Profit
• Margin Of Safety = (Actual/Budgeted Sales (Units or Volume) – BEP Sales (Units or Volume)) * 100 / Actual/Budgeted Sales (Units or Volume)

Underlying Assumptions of Break-Even Analysis

• Fixed Costs remain constant throughout all relevant levels of activity
• Variable Cost per unit remains constant throughout all relevant levels of activity
• Selling Price per unit remains constant throughout all relevant levels of activity
• The relevant range of activity is the range within the above
• Linear assumptions are considered to be valid

Limitations of Break-Even Analysis

• Can only be applied to a single product or single mix of products
• The linear assumptions relating to fixed costs, variable costs and selling prices does not represent reality
• Assumes that sales and production are equal i.e. there is no change in inventory levels

Question 1 Variables

• Sales = Variable Cost + Fixed Cost
• 6x = 1.60x + 48,000
• 6x - 1.60x = 48,000
• 4.4x = 48,000
• X = 10,909; Break Even in Units
• Variable Cost + Selling Price increase by 10%
• 1.2 + 10% = 1.32 per unit
• 6 + 10% = 6.60 per unit
• Fixed Production increase by 25%
• 40,000 + 25% = 50,000

Equations for Question 1

• 6.6x = (1.32 + .40)x + 58,000
• 6.6 x - 1.72x = 58,000
• 4.88 = 58,000
• X = 11,885

Pop Question on Data from Last Month's Operations

• Selling Price €30 per unit
• Variable Production Cost €15 per unit
• Fixed Production Cost €80,000
• Variable selling and admin expenses €3 per unit
• Fixed selling and administration expenses €40,000
• The company's break even in terms of sales revenue is:
  • c. €200,000

Pop Q: Contribution Approach to the Income Statement

• The contribution approach to the income statement is useful to managers in planning and decision-making

Multi-Product CVP Analysis

• Sales mix is the relative proportions in which a company's products are sold
• Different products have different selling prices, cost structures, and contributions
• To breakeven:
  • Wind Co. sells helmets and shirts
  • Expects to sell 2 shirts for every helmet sold
  • Helmets: €SP = €70; CM = €28 per dress
  • Shirts: €SP = €20; CM = €11 per shirt
  • Total fixed costs are €84,000
  • To find the breakeven, use the following:
  • Fixed Costs / Contribution per mix = 84,000 / 50 = 1,680 mixes
  • 1,680 mixes = 1,680 helmets + 3,360 shirts
  • 1,680 (70) + 3,360 (20) = €184,800

Operating Leverage

• Operating Leverage is a measure of how sensitive net profit is to percentage changes in sales
• With high leverage, a small percentage increase in sales can produce a much larger percentage increase in net profit
• Degree of operating leverage = Contribution Margin / Net profit
  • Wind Co. Operating Leverage: € 100,000 / €20,000 = 5
  • With a measure of operating leverage of 5, if Wind increases its sales by 10%, net profit would increase by 50%

Operating Leverage example from €250,000 to €275,000

• This is a 10% increase in sales from €250,000 to €275,000 results in a 50% increase in profit from €20,000 to €30,000

Question Two

Profit earned last year:

• Total contr. (2500 units @ 32 each) € 80,000
• Less: Fixed Costs €(60,000)
• Profit € 20,000

Break-even point for the current year

• BEP (Units) = Fixed Costs / Contribution per Unit
  • 60,000 / 32 = 1,875 Units

MOS (Margin of Safety) is derived as:

• Sales – BEP X 100 / Sales
• (2500 – 1875) x 100 / 2500 = 25%

Second Set of Data for Question 2

• BEP = Fixed Cost / Unit Contribution
• 66,000 / 28.40 = 2,324 Units
• Target volume for 20,000 profit -Volume = (66,000 + 20,000) /28.40 = 3,028 Units
• Current C/M ratio= 32/80 = 40%
• Variable cost / selling price = 60%
• Revised variable costs= 51.60
• Revised selling price (51.60 / 60 x 100) = 86

Question Two: Table of Data

Units @ 90, 75 and 80 of sales, with the changes in variable costs, and outputs

Question Three Calculations:

• Total time required on assembling machine is: (2,500 * 0.5) + (3,400 * 1.0) + (5,100 * 0.5) = 7200Total time available on assembling machines is 8,000 hours
• Total time required on cutting machine is: (2,500 * 1.0) + (3,400 * 1.0) + (5,100 * 0.5) = 8,450 hoursTotal time available on cutting machines is 5,000 hours. Therefore,this is a limiting factor
• Therefore produce3,400 product B using 3,400 hours3,200 product c using 1,600 hours
• 5,000 hours
• Assuming that the business would make no saving in variable production costs by subcontracting, it would be worth paying up to the contribution per unit €5 for product C - Which would therefore be- €5 * (5,100-3200) = 9500 in total
• •Similarly it would be worthwhile paying up to €6 per unit for product A- That is €6 * 2,500 = €15,000 in total

Data table for Question Three