Ch 21 - Cost-Volumne - Profit Anaylsis

Cost behavior

____ _____: the manner in which a cost changes as a related activity changes.

activity bases

_____ ______ (activity drivers): A common measure of activity related to each job, such as direct labor hours or machine hours, by which costs are allocated to jobs; measures of activity used in analyzing and classifying cost behavior. (any event or action that causes costs to go up or down) 

relevant range

_____ ______: The range of activity over which changes in cost are of interest to management.(is the specific volume of production or level of operations that management expects to maintain. Within this normal range, cost rules stay the same. Outside this range, the company might have to buy more machines or hire more staff, which changes the fixed and variable costs)

COST BEHAVIOR

• Understanding cost behavior helps managers predict profits (as sales and production volumes change) and estimate costs (affects a variety of decisions like weather to replace machine)

• Understanding cost behavior depends on:

  • Identifying the activities called activity bases (activity drivers) that cause costs to change

    • Example: calculating patient food eats → activity base is # of patients staying overnight

  • Specifying the range of activity called  relevant range over which the changes in the cost are of interest.

    • Example: relevant range is range of # of patients who normally stay in the hospital

[An activity base measures the specific events or tasks that cause a cost to go up or down. The relevant range is the specific level of activity where a business expects its cost predictions to remain valid.]

• Costs are normally classified as variable costs, fixed costs, or mixed costs.

Variable costs: costs that vary in proportion to changes in the activity base. 

Variable Costs- cost that very in proportion to changes an activity base.

• When the activity base is units produced, direct materials and direct labor are usually variable costs.

• Characteristics of variable cost:

  • Total cost changes proportionally as the activity base changes.

    • More units produced (activity base) = more cost (aka send more on materials to make units)

      • Activity base: Units produced

      • Direct materials cost per unit: $10

        • 5000 units, $10 per unit = $50,000

        • 10,000 unit, $10 per unit = $100,000

        • (As production increases, total variable costs increase proportionally, but the cost per unit remains the same.)

    • Total Variable Cost=Variable Cost per Unit×Activity Base

  • Cost per unit remains the same regardless of changes in activity base

Fixed Cost

Fixed cost: costs that remain the same in total dollar amount as the activity base changes.

• When the activity base is units produced, many factory overhead costs (such as straight-line depreciation) are fixed costs.

  • Example: supervisor salary 

• Characteristics

  • Total cost remains same regardless of changes in the activity base. (Salary os $70,000 no matter if 10,000 0r 30,000 items produced)

    • Formula Fixed Cost per Unit= Total Fixed Cost / Activity Base

  • cost per unit decreases as the activity level increases. (Wage cost per unit rises and falls per unit of item produced —> $75,000 becomes $.30 per bottle or 1.50 per bottle depending on bottles produced)

  • cost per unit increases as the activity level decreases.

Fixed cost: costs that remain the same in total dollar amount as the activity base changes.

Mixed costs (semivariable or semifixed costs): are costs that have characteristics of both a variable and a fixed cost. 

Mixed costs (semivariable or semifixed costs): are costs that have characteristics of both a variable and a fixed cost. 

• Characteristics

  • Part of the cost remains fixed regardless of activity.

  • Part of the cost changes with the activity level.

Mixed Cost Formula → Total Cost=(Variable Cost per Unit×Activity Level)+Fixed Cost

Example → Rental Charge=$15,000+($1×hours used over 10,000)

• For analysis purposes, mixed costs usually separated into their fixed and variable components. 

high-low method: Used to separate mixed cost into its fixed and variable components.

• Uses the highest and lowest activity levels and their related costs to estimate variable cost per unit and fixed cost. 

Step 1: Find the variable cost per unit

1. Find the activity base and relevant range and difference between the lowest and highest amounts for ACTIVITY and TOTAL COST

   1. Activity base is Unit produced —> High # of units - Lowest # of units = activity base difference

   2. Relevant Range is Total Cost —> Highest dose - Lowest cost = relevant range difference

2. Solve → Variable Cost per Unit= Difference in Total Cost/ Difference in Activity

Step 2: Find the fixed cost

1. Fixed Cost= Total Cost − (Variable Cost per Unit × Units Produced)

   1. Note: the TOTAL FIXED COST is the same at highest and lowest # from Step 1

Step 3: Write the cost equation

1. Total Cost= (Variable Cost per Unit(step1)  × Units Produced) + Fixed Cost(step2)

high-low method: A technique that uses the highest and lowest total costs as a basis for estimating the variable cost per unit and the fixed cost component of a mixed cost. 

Contribution margin: the excess of sales over variable costs.

Cost-volume-profit analysis: the examination of the relationships among selling prices, sales and production volume, costs, expenses, and profits. Cost-volume-profit

Cost-volume-profit analysis: the examination of the relationships among selling prices, sales and production volume, costs, expenses, and profits. Cost-volume-profit

• useful for managerial decision making because it is used to Analyzing the effects of changes in selling prices on profits, costs on profits, and volume on profits. Also for setting selling prices, selecting the mix of products to sell, and choosing among marketing strategies

Contribution margin: the excess of sales over variable costs.

Formula → Contribution Margin = Sales − Variable Costs

• Purpose → Shows the profit potential of a company.

• Contribution margin is used to see if amount earned will be enough to Cover fixed costs. The remaining money becomes operating income.

  • (Once fixed costs are covered, additional contribution margin increase income)

  • Contribution Margin > Fixed Costs → Income from operations.

  • Contribution Margin = Fixed Costs → Break-even.

  • Contribution Margin < Fixed Costs → Operating loss.

    • Sales price = What the customer pays.

    • Variable cost = What it costs to make/sell one more unit.

    • Contribution margin = What's left to pay fixed costs and earn profit.

Summary of Cost Behavior Concepts

Method for reporting VARIABLE and FIXED costs is variable costing (direct costing).

Variable Costing—> only variable manufacturing (DM, DL, and variable FoH) are included in product cost. Fixed FoH is treated as expense of the period in which it incurred.

	Total Amount	Per-Unit Amount	Costs for the activity base of units produced
Variable	Increases and decreases proportionately with activity level.	Remains the same regardless of activity level.	• Direct materials • Direct labor • Electricity expense • Supplies
Fixed	Remains the same regardless of activity level.	Increases and decreases  inversely with activity level.	• Straight-line depreciation • Property taxes • Production supervisor salaries • Insurance expense
Mixed	Contain fixed cost components that incurred even if nothing is produced. For analysis fixed and variable cost components are separated using high-low method		• Quality Control Department salaries • Purchasing Department salaries •Maintenance expenses •Warehouse expenses

The contribution margin ratio (profit-volume ratio): indicates the percentage of each sales dollar available to cover fixed costs and to provide income from operations. (the percentage of each sales dollar available to cover fixed costs and provide income from operations.)

Contribution margin ratio (profit-volume ratio): indicates the percentage of each sales dollar available to cover fixed costs and to provide income from operations.

• Formula → Contribution Margin Ratio = Contribution Margin ÷ Sales

• Most useful when changes in sales (increase/decrease) are measured in sales dollars.

• Measures the percentage of each sales dollar that contributes to:

  • Covering fixed costs.

  • Income from operations.

Change in Income from Operations = Change in Sales Dollars  X Contribution Margin Ratio

Step 1: Contribution Margin ratio = 400,000/1,000,000 = 40%

Step 2: Change in Income from Operation = 80,000 x 40% = 32,000 (operation increase) 

• Key Points

  • Variable Cost Ratio = 100% − Contribution Margin Ratio

  • Total Contribution Margin = Sales × Contribution Margin Ratio

    • 1,080,000 x (100%-40%=60%)= 648,000

  • Assumes sales price and variable cost per unit remain constant.

• Contribution margin ratio is also useful in developing business strategies.

  • High contribution margin ratio + production below 100% capacity:

    • An increase in sales volume can significantly increase income from operations.

    • The company may implement a sales campaign to increase sales.

  • Low contribution margin ratio: 

    • Small contribution margin ratio →  company should focus on reducing costs before attempting to promote sales.

  • Low contribution margin ratio: Reducing costs may be more effective than increasing sales.

unit contribution margin: The dollars available from each unit of sales to cover fixed costs and provide operating profits.

Unit Contribution Margin - The dollars available from each unit of sales to cover fixed costs and provide operating profits.

• Useful for analyzing profit potential of proposed decisions 

Unit Contribution Margin = Sales Price per Unit − Variable Cost per Unit

• Example: Selling price: $20, Variable cost per unit: $12, contribution margin: $8 

20 - 12 = $8 contribution margin

• Most useful when changes in sales (increase or decrease) are measured in sale units (quantities).

Change in Income from Operations = Change in Sales Units × Unit Contribution Margin

Example: increase from 50,000 units to 65,000 units → 15,000 units x  $8 = $120,000

• Key Points

  • Each additional unit sold contributes its unit contribution margin toward fixed costs and profit.

  • After fixed costs are covered, each additional unit contribution margin increases income from operations.

  • Managers use unit contribution margin to evaluate decisions such as advertising and sales promotions.

Mathematical Approach to Cost-Volume-Profit Analysis

• cost-volume-profit analysis uses equations to determine:

• Sales need to Break-even sales

• Sales needed to earn a target profit

BREAK-EVEN POINT: the level of operations at which a company’s revenues and expenses are equal (Revenues = Expenses). 

Break-even occurs when total contribution margin = total fixed costs.

• At break-even:

  • Revenue covers all variable costs and fixed costs.

  • The company reports neither income nor a loss from operations.

  • The break-even point is affected by changes in:

    • Fixed costs

    • Unit variable costs

    • Unit selling prices.

Break-Even Point in Sale units: 

Example:

Fixed costs→90,000

Unit Contribution margin→$10 (= ( unit selling price) 25 - (unit variable cost) 15)

Fixed cost → 90,000

STEP 1: Contribution Margin Ratio

Contribution Margin Ratio = Unit Contribution Margin ÷ Unit Selling Price

$10 / $15 = 40% Contribution Margin Ratio

STEP 2: Break-Even Sales (Dollars)

Break-Even Sales (dollars) = Fixed Costs ÷ Contribution Margin Ratio

90,000/40%= $225,000 Break-Even Sales (dollars)

EFFECT OF CHANGES IN FIXED COSTS:
Fixed costs (do not change with the level of activity) may change because of:

• Advertising campaigns

• Property tax rates

• Factory supervisors' salaries

Effect on Break-Even

• Increase in fixed costs → Increase in break-even point

• Decrease in fixed costs → Decrease in break-even point

Why?

• Higher fixed costs require more total contribution margin to break even.

• More contribution margin means more units must be sold.

EFFECT OF CHANGES IN UNITS VARIABLE COSTS:

• Unit variable costs (do not change with the level of activity)may be affected by changes in factors like:

  • Direct material costs per unit

  • Direct labor wage rates

  • Sales commissions paid to salespeople 

• Effect on Break-Even

  • If Increase in unit variable costs → Increase in break-even 

  • If Decrease in unit variable costs → Decrease in break-even 

• Why?

  • Higher unit variable costs reduce the unit contribution margin.

  • A lower unit contribution margin means more units must be sold to cover fixed costs.

  • Unit Contribution Margin = Unit Selling Price − Unit Variable Cost

EFFECT OF CHANGES IN UNIT SELLING PRICE:

• Changes in unit selling price affect Unit contribution margin which affects Break-even point

• Effect on Break-Even Point

  • If Increase in unit selling price → Decrease in break-even point

  • Decrease in unit selling price → Increase in break-even point

• Why?

  • Higher selling price increases unit contribution margin.

  • A higher unit contribution margin means fewer units are needed to cover fixed costs.

Summary of Effects of Changes on Break-even Point

• Break-even changes in the same direction as fixed costs and variable costs, but opposite direction of selling price.

• SAME:

  • Fixed Income ↑ = Break-Even sales  ↑

  • Fixed Income  ↓ = Break-Even sales   ↓

  • Unit Variable Cost ↑ = Break-Even sales  ↑

  • Unit Variable Cost ↓ = Break-Even sales ↓

• OPPOSITE:

  • Unit SELLING Price ↑ = Break-Even sales ↓

  • Unit SELLING Price  ↓ = Break-Even sales ↑

TARGET PROFIT

• Break-Even Point —> Sales & costs are Equal

• Company's goal is to earn a profit.

• The break-even equation can be modified to determine the sales needed to earn a target/desired profit.

SALES NEEDED (UNITS)

Sales (units) = (Fixed Costs + Target Profit) ÷ Unit Contribution Margin

Example: Fixed Costs-200,000, Target Profit 100,000, unit contribution margin 30 (= unit selling price 75 - unit variable cost 45) 

(200,000 + 100,000 / 30 = 10,000 units

• Sales need to earn target profit can be computed using contribution margin ratio:

SALES NEEDED (DOLLARS)

1. Contribution Margin Ratio = Unit Contribution MArgin / Unit Selling Price

   1. 30 / 75 = 40%

2. Sales (dollars) = (Fixed Costs + Target Profile) / Contribution MArgin Ratio

   1. (200,000 + 100,000 / 40% = $750,000 (sales) 

KEY

• Add target profit to fixed costs because the contribution margin must cover:

  1. Fixed costs

  2. Desired profit

• The result shows the number of units or sales dollars needed to achieve the target profit.

cost-volume-profit chart (break-even chart): graphically shows sales, costs, and the related profit or loss for various levels of units sold. A CVP chart shows sales, costs, and profit/loss at different levels of units sold.()

Graphic Approach to Cost-Volume-Profit (CVP) Analysis

• CVP analysis can be presented using a graph or equation.

• A graph is preferred by managers because operating profit and loss for different levels can be seen

cost-volume-profit chart (break-even chart): Assists in understanding relationship among sales, costs, and operating profit or loss

Steps to Prepare a CVP Chart

1. Identify axes

   • Horizontal axis = Units of sales

     • (x-axis) Relevant Range is the normal zone of sales volume where a company expects to operate and where its costs stay predictable.

   • Vertical axis = Operating profit and loss (in dollars)

2. LINES

   • TOTAL SALES LINE: 1st point is at (0,0) and slopes upward. 2nd point is determined by Max # of units in relevant range X unit SALE PRICE

   • TOTAL COST LINE: 1st point is at beginning of TOTAL FIXED COST on vertical axis. 2nd point determined by Max # of units in relevant range x unit VARIABLE COST

   • BREAK EVEN POINT: intersection point between total sale and total cost line. Dotted line from this point to horizontal axis indicates units of sale at breakeven pt and dotted lin to vertical axis indicates sale dollars and cost at break even point.

3. PROFITS. & LOSSES

• Right of break-even point = operating profit area

  • Operating profits are earned when sales levels are RIGHT of break even point )operating profit area)

• Left of break-even point  = operating loss area

  • Operating loss will incurred when sales levels are LEFT of break-even point (operating loss area)

Effect of Changes

• Decrease in fixed costs:

  • Lowers total cost line.

  • Decreases break-even point.

• Increase in fixed costs:

  • Raises total cost line.

  • Increases break-even point.

• Changes in Unit selling price, Fixed costs and Unit variable costs can be analyzed using a CVP chart.

  • If the manager reduced fixed costs the result will be TOTAL COST LINE will change NOT total sales line. Changes the placement of break-even point and reduce number of sales needed 

    • Reducing fixed costs changes the total cost line, not the total sales line.

    • The total sales line does not change because it depends on the selling price and number of units sold.

    • Lower fixed costs shift the total cost line downward.

    • The break-even point changes, reducing the number of sales needed to break even.

profit-volume chart A chart used to assist management in understanding the relationship between profit and volume. 

Key: Profit-volume charts focus only on the effect of sales volume on profit or loss.

Profit-Volume Chart

profit-volume chart A chart used to assist management in understanding the relationship between profit and volume. 

Key: Profit-volume charts focus only on the effect of sales volume on profit or loss.

• It ONLY plots the difference between Total sales and Total costs (profits)

• A profit-volume chart allows managers to determine the operating profit/loss for various levels of units sold (the relationship between sales volume and operating profit or loss. (It shows the relationship between sales volume and operating profit or loss.)

• The maximum operating loss = fixed costs 

Steps to Prepare a Profit-Volume Chart

• Step 1: Set the Horizontal Axis

  • Draws the bottom scale representing Units of Sales (spanning from 0 units to the maximum relevant range of 10,000 units).

• Step 2: Plot the Maximum Loss Point

  • Places a point at zero sales on the far left.

  • This point equals the company's Fixed Costs as a negative number (-$100,000), representing the automatic loss if nothing is sold.

• Step 3: Plot the Maximum Profit Point

  • Places a point at full capacity on the far right (10,000 units).

  • This represents the best-case Operating Profit scenario (+$100,000).

• Step 4: Draw the Profit Line

  • Connects the Maximum Loss Point (Step 2) and Maximum Profit Point (Step 3) with a single straight, diagonal line.

• Step 5: Identify the Break-Even Point & Zones

  • Locates where the profit line crosses the $0 horizontal baseline.

  • This intersection reveals the Break-Even Point (5,000 units) and divides the chart into two distinct visual areas:

    • Loss Area (Red): Everything to the left of the break-even point.

    
    

Key Vocabulary to Memorize

• Fixed Costs: Costs that do not change with production volume (e.g., rent). On this chart, they dictate your starting point below the $0 line.

• Variable Costs: Costs that climb with every unit made (e.g., materials). They determine how steeply your profit line climbs.

• Break-Even Point: The precise sales volume where total revenue perfectly matches total costs. Profit is exactly $0.

• Relevant Range: The specific operational limits of the business (in this case, up to 10,000 units). The math is only tested within these boundaries.

Effect of Changes

Effective changes in units selling price, total fixed cost, in unit variable costs on profit can be analyzed using the profit volume chart.

• Increase in fixed costs:

  • Increases maximum operating loss.

  • Decreases maximum operating profit.

  • Increases break-even point.

• Decrease in fixed costs:

  • Decreases maximum operating loss.

  • Increases maximum operating profit.

    • Decreases break-even point.

Use of Spreadsheets in Cost-Volume-Profit (CVP) Analysis

• Spreadsheets make both graphic and mathematical approaches to CVP analysis easier to use.

• Managers change assumptions about selling price, costs, and sales volume to see how these changes affect the break-even point and profit.

• This is called what-if analysis or sensitivity analysis.

What-if analysis (sensitivity analysis):

• An analysis that examines how changes in assumptions affect results.

Assumptions of Cost-Volume-Profit (CVP) Analysis

CVP analysis depends on these assumptions:

• Total sales and total costs are represented by straight lines.

• Operating efficiency remains constant within the relevant range of operating activity. 

• Costs can be separated into fixed and variable components.

• Sales mix is constant.

• Inventory quantities do not change during the period.

Key Point:
These assumptions simplify CVP analysis and make it useful for decision making within the relevant range.

Sales Mix: the relative distribution of sales among products sold by a company

SALE MIX CONSIDERATION

companies sell more than 1 product at different selling price and with different unit VARIABLE COSTS and different unit CONTRIBUTION MARGIN

• Companies that sell multiple products  must consider the sales mix when performing CVP analysis.

Sales Mix: the relative distribution of sales among products sold by a company

• Expressed as:

  • Percentage of total units sold (80%, 20%)

  • Ratio (example: 80:20)

Composite Unit (Overall Product)

• Treat multiple products as one combined product (Enterprise Product E).

• The selling price, variable cost, and contribution margin of E are calculated using each product’s amount multiplied by its sales mix percentage and then added together.

• Sales mix = the percentage of total sales made up by each product.

Break-Even Analysis for Multiple Products (Composite Unit)

Weighted-average unit selling price:

Selling Price of E=(Sale Price A × Sales Mix % A) +(Sale Price B × Sales Mix % B)

Weighted-average unit variable cost:

Variable Cost of E=(Variable cost A × Sales Mix % A) +(Variable cost B × Sales Mix % B)

Weighted-average unit contribution margin:

Contribution Margin of E=(Contribution margin × Sales Mix % A) +(Contribution margin B × Sales Mix % B)

Then use the normal break-even formula:

Break-even Sales (units) for E = Fixed Cost / Unit Contribution Margin ​

Key Points

• Break-even analysis with multiple products depends on a constant sales mix.

• A change in sales mix changes the overall contribution margin and break-even point. 

  • Change in sales mix % → Change in average contribution margin → Change in break-even point.

• After finding the break-even units for the composite product, allocate units based on the sales mix.

Operating leverage: A ratio that measures the relationship between a company’s contribution margin and income from operations, computed as contribution margin divided by income from operations.

Operating Leverage

Operating leverage measures the relationship between contribution margin and income from operations.

• Formula: Operating Leverage = Contribution Margin ÷ Income from Operations

• Difference between contribution margin and income from operations is fixed costs 

  • Companies with high fixed costs usually have high operating leverage.

    • Example: airline and automotive companies 

  • Companies with low fixed costs usually have low operating leverage.

    • NORMAL for LABOR-intensive companies (professional service companies) 

Effect of Sales Changes

• Operating leverage can be used to measure impact of changes in sales on income from operation 

Formula: Percent Change in Income from Operations = Percent Change in Sales × Operating Leverage

50% = 10% x 5 = 50%

Business Strategy

• High operating leverage:

  • A small increase in sales can create a large increase in income.

  • Companies may focus on increasing sales.

• Low operating leverage:

  • Income changes less with sales changes.

  • Companies may focus on reducing variable costs or increasing leverage.

margin of safety: A ratio that indicates the possible decrease in sales that may occur before an operating loss results, computed as sales less break-even sales divided by sales. 

Margin of Safety - indicates the amount sales can decrease before an operating loss occurs. 

Formula: Margin of Safety = (Sales − Sales at Break-Even Point) ÷ Sales

• Forms of Margin of Safety 

  • Dollars of sales

    • Margin of Safety (dollars) = Current Sales − Break-Even Sales

      • 250,000(sales) − 200,000(sale at breakeven pt) = $50,000

  • Units of sales

    • Margin of Safety (units) = Margin of Safety (dollars) ÷ Unit Selling Price

      • 50,000 (margin in $) ÷ 25 (unit selling price) = 20,000 units

  • Percentage of current sales

    • Margin of Safety (%) = (Current Sales − Break-Even Sales) ÷ Current Sales

      • (250,000  − 200,000) ÷ 25 = 20%

• CURRENT SALES may decline, $50,000, 2,000 units or 20% BEFORE operating loss occurs

Key Point

• A low margin of safety means a small decline in sales could result in an operating loss.

• A high margin of safety means the company can withstand a larger decrease in sales before a loss occurs.