Chapter 5

Assumptions of CVP Analysis  Selling price is constant.  Costs are linear.  In multi-product companies, the sales mix is constant.  In manufacturing companies, inventories do not change (units produced = units sold).

The Basics of Cost-Volume- Profit (CVP) Analysis Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

The Contribution Approach For each additional unit Wind sells, $200 more in contribution margin will help to cover fixed expenses and profit.

The Variable Expense Ratio The variable expense ratio is the ratio of variable expenses to sales. It can be computed by dividing the total variable expenses by the total sales, or in a single product analysis, it can be computed by dividing the variable expenses per unit by the unit selling price.

Contribution Margin Ratio In terms of contibution margin per unit, the contribution margin ratio is: $200 $500 = 40% Unit CM Unit selling price CM Ratio = For Wind Bicycle Co. the ratio is:

Contribution Margin Ratio The contribution margin ratio using total dollars is: For Wind Bicycle Co. the ratio is: $100,000 $250,000 = 40% Total CM Total sales CM Ratio =

Break-Even Analysis Break-even analysis can be approached in three ways: 1.Graphical analysis. 2.Equation method. 3.Contribution margin method.

B/E Relationships in Graphic Form Viewing CVP relationships in a graph is often helpful. Consider the following information for Wind Co.:

Units Dollars B/E Graph Break-even point Profit Area Loss Area

Break-Even Analysis (cont’d) Here is information from Wind Bicycle Co.:

Equation Method We calculate the break-even point in units as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 400 bikes

Equation Method We can also use the following equation to compute the break-even point in sales dollars. X = 0.60X + $80,000 + $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000 Sales = Variable expenses + Fixed expenses + Profits

Contribution Margin Method The contribution margin method is a variation of the equation method. Fixed expenses Unit contribution margin = Break-even point in units sold Fixed expenses CM ratio = Break-even point in total sales dollars

Target Profit Analysis Suppose Wind Co. wants to know how many bikes must be sold to earn a profit of $100,000. We can use either the Equation or Contribution Margin approaches to determine the sales volume needed to achieve a target net profit.

Equation Method We calculate the target profit in units as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $100,000 $200Q = $180,000 Q = $180,000 ÷ $200 per bike Q = 900 bikes

Equation Method We can also use the following equation to compute the target profit in sales dollars. X = 0.60X + $80,000 + $100, X = $180,000 X = $180,000 ÷ 0.40 X = $450,000 Sales = Variable expenses + Fixed expenses + Profits

The Contribution Margin Method We can determine the number of bikes that must be sold to earn a target profit of $100,000 using the contribution margin approach. Fixed expenses + Target profit Unit contribution margin = Unit sales to attain the target profit $80,000 + $100,000 $200 per bike = 900 bikes

The Contribution Margin Method We can determine the sales needed to earn a target profit of $100,000 using the contribution margin approach. Fixed expenses + Target profit Contribution Margin Ratio = Sales to attain the target profit $80,000 + $100,000 40% = $450,000

The Margin of Safety The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. Margin of safety = Total sales - Break-even sales

Operating Leverage A measure of how sensitive net operating income is to percentage changes in sales. With high operating leverage, a small percentage increase in sales can produce a much larger percentage increase in net operating income. Contribution margin Net operating income Degree of operating leverage =

Operating Leverage 10% increase in sales from $250,000 to $275, % increase in sales from $250,000 to $275, results in a 50% increase in income from $20,000 to $30, results in a 50% increase in income from $20,000 to $30,000.

Operating Leverage With an operating leverage of 5, if Wind increases its sales by 10%, net operating income would increase by 50%. Here’s the verification!

The Concept of Sales Mix Sales mix is the relative proportion in which a company’s products are sold. Different products have different selling prices, cost structures, and contribution margins. When a company sells more than one product, break-even analysis becomes more complex as the following example illustrates.

Multi-Product Break-Even Analysis Bikes comprise 45% of RBC’s total sales revenue and carts comprise the remaining 55%. RBC provides the following information: $265,000 $550,000 = 48.2% (rounded)

Multi-Product Break-Even Analysis Fixed expenses CM ratio = Dollar sales to break even $170, % = = $352,697

End of Chapter 5