Chapter 6
Break-Even Analysis: Dollar Sales Using CM Ratio
Now, let's use the formula method to calculate the dollar sales at the break-even point Dollar Sales to break even = Fixed expenses / CM Ratio Dollar sales = $80,000/40% Dollar sales = $200,000
The Contribution Approach - Part 5
- We do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit. - If RBC sells 430 bikes, its net operating income will be $6,000 (30 units × $200 per unit).
Concept check 3 - Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. An average of 2,100 cups are sold each month. What is the break-even sales in units?
Break-even = Fixed expenses/CM per unit $1,300/$1.49/cup-$0.36/cup $1,300/$1.13/cup 1,150 cups
Concept Check 2 - Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. An average of 2,100 cups are sold each month. What is the break-even sales dollars?
Break-even sales = Fixed expenses/CM ratio $1,300.0/0.758 $1,715
Concept Check 1 - Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. An average of 2,100 cups are sold each month. What is the CM Ratio for Coffee Klatch?
CM Ratio = Unit Contribution Margin / Unit Selling Price $1.49-$0.36/$1.49 $1.13/$1.49 0.758
Basics of Cost-Volume-Profit Analysis - Part 2
Contribution Margin first to cover fixed expenses. Ny remaining Contribution Margin contributes to net operating income (profit)
The Contribution Approach - Part 2
Each month, RBC must generate at least $80,000 in total contribution margin to break even (which is the level of sales at which profit is zero)
Contribution Margin Ratio (CM Ratio) and the Variable Expense Ratio - Step 1 (2 of 2)
For RBC, the contribution margin ratio is calculated as follows: CM Ratio = $80,000/$200,000 = 40% For each $1.00 increase in sales results in a total contribution margin increase of 40 cents
The Contribution Approach - Part 3
If RBC sells 400 units in a month, it will be operating at the break-even point.
The Contribution Approach - Part 4
If RBC sells one more bike (401 bikes), net operating income will increase by $200
Break-Even Analysis: Equation Method Part 2
In a single product situation, the equation method for computing the unit sales at the break-even point is: Profit = Unit CM x Q - Fixed Expenses - $0 = $200 x Q - Fixed expenses - $200 x Q = $0 + $80,000 - Q = $80,000 / $200 - Q = 400 units
Basic of Cost-Volume-Profit Analysis - Part 1: Contribution Margin
Is the amount remaining from sales revenue after variable expenses have been deducted
CVP Relationships in Equation Form - Using Unit Contribution Margin
It is often useful to express the simple profit equation in terms of the unit contribution margin (Unit CM) as follows: ◦Unit CM = Selling price per unit − Variable expenses per unit ◦Unit CM = P − V ◦Profit = (P × Q − V × Q) − Fixed expenses ◦Profit = (P − V) × Q − Fixed expenses ◦Profit = Unit CM × Q − Fixed expenses
CVP Relationships in Equation Form - Example Using Unit CM
Profit = (P × Q − V × Q) − Fixed expenses Profit = (P − V) × Q − Fixed expenses Profit = Unit CM × Q − Fixed expenses Profit = ($500 − $300) × 401 − $80,000 Profit = $200 × 401 − $80,000 Profit = $80,200 − $80,000 Profit = $200 This equation can also be used to compute RBC's $200 profit if it sells 401 bikes.
The Contribution Approach - Part 1
Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If Racing sells an additional bicycle, $200 additional CM will be generated to cover fixed expenses and profit.
Contribution Margin Ratio (CM Ratio) and the Variable Expense Ratio - Step 2
The CM ratio can also be calculated by dividing the contribution margin per unit by selling price per unit CM Ratio = Contribution margin per unit/ Selling price per unit CM Ratio = $200/$500 = 40%
CVP Relationships in Equation Form
The contribution format income statement can be expressed in the following equation: Profit = (Sales - Variable expense) Fixed expenses
Basics of Cost-Volume-Profit Analysis - Part 1: Contribution Income Statement
The contribution income statement is helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. The emphasis is on cost behavior.
Contribution Margin Ratio (CM Ratio) and the Variable Expense Ratio - Step 1 (1 of 2)
The contribution margin as a percentage of sales is referred to as the contribution margin ratio (CM Ratio). This ratio is computed as follows: CM Ratio = Contribution margin / Sales
Break-Even Analysis
The equation and formula methods can be used to determine the unit sales and dollar sales needed to achieve a target profit of zero. Let's use the RBC information to complete the break-even analysis
Break-Even Analysis: Equation Method Part 1
The equation method relies on the basic profit equation introduced earlier in the chapter. Because Racing Bicycle has only one product, we'll use the contribution margin form of this equation to perform the break-even calculations. We calculate the break-even point by solving the equation below: ◦Profit = Unit CM × Q − Fixed expenses ◦$0 = $200 × Q − Fixed expenses
Applications of Contributions Ratio - Increase in Sales Volume
The relationship between profit and the CM ratio can be expressed using the following equation: - Profit = (CM ratio x Sales) - Fixed expenses - If RBC increased its sales volume to 500 bikes, what would management expect profit or net operating income to be? - Profit = (40% x $250,000) - $80,000 - Profit = $100,000 - $80,000 - Profit = $20,000
CVP Relationships in Equation Form - Example
This equation can be used to show the profit RBC earns if it sells 401. Notice, the answer of $200 mirrors our earlier solution. ◦Profit = (Sales − Variable expenses) − Fixed expenses ◦Sales: 401 units × $500 ◦Variable expenses: 401 units × $300 ◦Fixed expenses: $80,000 ◦Profit = ($200,500 − $120,300) − $80,000 ◦$200 = ($200,500 − $120,300) − $80,000
Cost-Volume-Profit Analysis: Key Assumptions
To simplify CVP Calculations, managers typically adopt the following assumptions with respect to these factors: 1. Selling price is constant. The price of a product or service will not change as volume changes. 2. Costs are linear and can be accurately divided into variable and fixed components. The variable costs are constant per unit and the fixed costs are constant in total over the entire relevant range.
