Chapter 6: Cost-Volume-Profit Relationships

The degree of operating leverage at a given level of sales is computed by the following formula:

Degree of Operating Leverage = Contribution Margin / Net operating income

Profit = (Contribution Margin Ratio x Sales) - Fixed Expenses

Ex. 72% (CMR) x $832,000 (S) - $265,000 (FE) = $334,040 (P)

Cost-volume-profit (CVP) graph

Illustrates the relationships among revenue, cost, profit, and volume over wide ranges of activity.

Net operating income equals

(unit sales - unit sales to break even) x unit contribution margin

The profit graph allows users to easily identify...

- the profit at any given sales volume - the sales volume required to reach the break-even point

The primary purpose of cost-volume-profit (CVP) analysis is to estimate how profits are affected by the following five factors:

1. Selling prices. 2. Sales volume. 3. Unit variable costs. 4. Total fixed costs. 5. Mix of products sold.

Variable expense ratio

A ratio computed by dividing variable expenses by sales (VC per unit / P per unit)

The Formula Method

A shortcut version of the Equation Method: Unit Sales to Break Even = Fixed Expenses / Unit CM

Concept Check 1: Which of the following statements is a common assumption underlying cost-volume-profit analysis? (You may select more than one answer.) a. The variable cost per unit remains constant b. The selling price per unit remains constant. c. The total fixed costs are constant within a relevant range. d. The total variable costs remain constant as the level of sales fluctuate.

A, B, and C. (The total variable costs will change as the level of sales fluctuates.)

Concept Check 8: Which of the following statements is true? (You may select more than one answer.) a. One minus the contribution margin ratio equals the variable expense ratio. b. Incremental analysis focuses only on costs and revenues that change as a result of a decision. c. Sales commissions based on sales dollars can lead to lower profits than commissions based on contribution margin. d. If a company's total sales remain constant, then its net operating income must remain constant even if the sales mix fluctuates.

A, B, and C. If a company's total sales remain constant, its net operating income may change if the sales mix fluctuates.

Concept Check 5: Assume a company produces one product that sells for $55, has a variable cost per unit of $35, and has fixed costs of $100,000. How many units must the company sell to earn a target profit of $50,000?

A. (100,000 + 50,000) / $20 contribution margin per unit = 7500 units

Concept Check 6: Given the same facts as in question 5 (Assume a company produces one product that sells for $55, has a variable cost per unit of $35, and has fixed costs of $100,000.), if the company exactly meets its target profit, what will be its margin of safety in sales dollars?

C. 2500 units x $55 per unit = $137,500

Concept Check 7: Which of the following statements is false with respect to the margin of safety? (You may select more than one answer.) a. The total budgeted (or actual) sales minus sales at the break-even point equals the margin of safety in dollars. b. The margin of safety in dollars divided by the total budgeted (or actual) sales in dollars equals the margin of safety percentage. c. In a single product company, the margin of safety in dollars divided by the variable cost per unit equals the margin of safety in units. d. The margin of safety in dollars can be a negative number.

C. The margin of safety in dollars divided by the selling price per unit equals the margin of safety in units.

Net operating income

CM - fixed expenses = net operating income (aka "profit") OR (Sales - Variable expenses) - fixed expenses = net operating income (aka "profit")

Concept Check 3: The contribution margin ratio always increases when (you may select more than one answer): a. Sales increase b. Fixed costs decrease c. Total variable costs decrease d. Variable costs as a percent of sales decrease.

D. (The contribution margin ratio equals 1.0 - variable costs as a percent of sales.)

The contribution format income statement can be expressed in equation form as follows:

Profit = (Sales - Variable Expenses) - Fixed Expenses Sales = Selling price per unit x Quantity sold = P x Q Variable Expenses = Variable expenses per unit x Quantity

Simple profit equation in terms of unit contribution margin:

Profit = Unit CM x Q - Fixed Expenses

Fixed costs / CMR =

Sales

Fixed cost / CM ratio =

Sales (to break-even)

Unit CM =

Selling price per unit (P) - Variable expenses per unit (V)

Contribution margin

The amount remaining from sales revenues after all variable expenses have been deducted. Used to cover fixed expenses; remainder is profit. CM = Sales - Variable Expenses

Selling price is constant. The price of a product or service will not change as volume changes.

To simplify CVP calculations, managers typically adopt the following assumptions with respect to these factors; Assumption 1

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.

To simplify CVP calculations, managers typically adopt the following assumptions with respect to these factors; Assumption 2

In multiproduct companies, the mix of products sold remains constant.

To simplify CVP calculations, managers typically adopt the following assumptions with respect to these factors; Assumption 3

To prepare a CVP graph, lines must be drawn representing:

Total revenue Total expense Total fixed expense

Operating leverage is

a measure of how sensitive net operating income is to a given percentage change in dollar sales. Acts as a multiplier.

If the total contribution margin is less than the total fixed expenses...

a net loss occurs

Incremental Analysis

an analytical approach that focuses only on those costs and revenues that change as a result of a decision

Which of the following items are found above the contribution margin on a contribution margin format income statement? a. Fixed expenses b. Variable expenses c. Sales d. Net operating income

b. Variable expenses c. Sales

To solve for net operating income at any sales volume above the break-even point requires knowledge of the: a. total variable expense b. contribution margin per unit c. projected unit sales d. total contribution margin e. number of units produced f. break-even unit sales

b. contribution margin per unit c. projected unit sales f. break-even unit sales

The contribution margin statement is primarily used for...

internal decision making

Cost-volume-profit (CVP) analysis helps

managers make many important decisions such as what products and services to offer, what prices to charge, what marketing strategy to use, and what cost structure to maintain.

The Equation Method

relies on the basic profit equation in order to calculate the break-even point. Profit = Unit CM x Q - Fixed expense

Equation that should be used when setting a target selling price for a special order bulk sale that does not affect a company's normal sales:

selling price per unit = variable cost per unit + desired profit per unit

The contribution margin ratio (CM ratio) is

the contribution margin as a percentage of sales. Computed as: CM ratio = (contribution margin)/sales

The margin of safety is

the excess of budgeted or actual sales dollars over the break-even volume of sales dollars. It is the amount by which sales can drop before losses are incurred. Margin of Safety (in dollars) / price per unit = units

The break-even point is

the level of sales at which profit is zero. Once the break-even point has been reached, the net operating income will increase by the amount of the unit contribution margin for each additional unit sold.

The margin of safety percentage is:

the margin of safety in dollars divided by total budgeted (or actual) sales in dollars

The term sales mix refers to

the relative proportions in which a company's products are sold.

In target profit analysis,

we estimate what sales volume is needed to achieve a specific target profit.

Concept Check 2: Once a company hits its break-even point, net operating income will...

Increase by an amount equal to the selling price per unit multiplied by the number of units sold above the break-even point.

The vertical distance between the total revenue line and the total expense line on a CVP graph represents the total:

profit or loss