Masters of Business Administration Accounting for Managers

Masters of Business Administration Accounting for Managers
Short Term Decision Making Cost-Volume-Profit Analysis By: Associate Professor Dr. GholamReza Zandi

Types of Cost Behavior Patterns
A variable cost is a cost whose total dollar amount varies in direct proportion to changes in the activity level.

A measure of what causes the incurrence of a variable cost.
The Activity Base Units produced Miles driven Labor hours Machine hours A measure of what causes the incurrence of a variable cost. An activity base (also called a cost driver) is a measure of what causes the incurrence of variable costs. As the level of the activity base increases, the variable cost increases proportionally. Units produced (or sold) is not the only activity base within companies. A cost can be considered variable if it varies with activity bases such as miles driven, machine hours, or labor hours.

True Variable Cost Example
A variable cost is a cost whose total dollar amount varies in direct proportion to changes in the activity level. Your total long distance telephone bill is based on how many minutes you talk. Total Long Distance Telephone Bill As an example of an activity base, consider your total long distance telephone bill. The activity base is the number of minutes that you talk. Minutes Talked

Recall the summary of our cost behavior discussion from Chapter 1. Variable costs remain constant if expressed on a per unit basis.

Variable Cost Per Unit Example
A variable cost remains constant if expressed on a per unit basis. The per minute cost of long distance calls is constant, for example, 10¢ per minute. Per Minute Telephone Charge Referring to the telephone example, the cost per minute talked is constant (e.g., 10 cents per minute) Minutes Talked

Extent of Variable Costs
The proportion of variable costs differs across organizations. For example . . . A public utility with large investments in equipment will tend to have fewer variable costs. A manufacturing company will often have many variable costs. The proportion of variable costs differs across organizations. For example: A public utility like Florida Power and Light, with large investments in equipment, will tend to have fewer variable costs. A manufacturing company like Black and Decker will often have many variable costs associated with the manufacture and distribution of its products to customers. A merchandising company like Wal-Mart will usually have a high proportion of variable costs such as the cost of merchandise purchased for resale. Some service companies, such as restaurants, have a high proportion of variable costs due to their raw material costs. Other service companies, such as an architectural firm, have a high proportion of fixed costs in the form of highly trained salaried employees. A merchandising company usually will have a high proportion of variable costs like cost of sales. A service company will normally have a high proportion of variable costs.

Examples of Variable Costs
Merchandising companies – cost of goods sold. Manufacturing companies – direct materials, direct labor, and variable overhead. Merchandising and manufacturing companies – commissions, shipping costs, and clerical costs such as invoicing. Service companies – supplies, travel, and clerical. Common examples of variable costs are: 1. Merchandising companies  cost of goods sold. Manufacturing companies  direct materials, direct labor, and variable overhead. Merchandising and manufacturing companies  commissions, shipping costs, and clerical costs such as invoicing. Service companies  supplies, travel, and clerical.

True Variable Cost Direct materials is a true or proportionately variable cost because the amount used during a period will vary in direct proportion to the level of production activity. A True variable cost is an amount used during the period that varies in direct proportion to the activity level. The long distance phone bill was one example of a true variable cost. Direct material is another example of a cost that behaves in a true variable pattern. Direct materials purchased but not used can be stored and carried forward to the next period as inventory. Cost Volume

Step-Variable Costs A resource that is obtainable only in large chunks (such as maintenance workers) and whose costs increase or decrease only in response to fairly wide changes in activity. Volume Cost A step variable cost is a resource that is obtainable only in large chunks and whose costs change only in response to fairly wide changes in activity. For example, maintenance workers are often considered to be a variable cost, but this labor cost does not behave as a true variable cost.

Step-Variable Costs Small changes in the level of production are not likely to have any effect on the number of maintenance workers employed. Volume Cost Small changes in the level of production are not likely to have any effect on the number of maintenance workers employed.

Step-Variable Costs Only fairly wide changes in the activity level will cause a change in the number of maintenance workers employed. Volume Cost Only fairly wide changes in the activity level will cause a change in the number of maintenance workers employed. Maintenance workers are obtainable only in large chunks of a whole person who is capable of working approximately 2,000 hours a year.

The Linearity Assumption and the Relevant Range
A straight line closely approximates a curvilinear variable cost line within the relevant range. Economist’s Curvilinear Cost Function Total Cost Part I Economists correctly point out that many costs that accountants classify as variable costs actually behave in a curvilinear fashion. Part II Nonetheless, within a narrow band of activity known as the relevant range, a curvilinear cost can be satisfactorily approximated by a straight line. Part III The relevant range is the range of activity within which the assumptions made about cost behavior are valid. Accountant’s Straight-Line Approximation (constant unit variable cost) Activity

Let’s turn our attention to fixed cost behavior. A fixed cost is a cost whose total dollar amount remains constant as the activity level changes.

Total Fixed Cost Example
A fixed cost is a cost whose total dollar amount remains constant as the activity level changes. Your monthly basic telephone bill is probably fixed and does not change when you make more local calls. Monthly Basic Telephone Bill For example, your monthly basic telephone bill is probably fixed and does not change when you make more local calls. Number of Local Calls

Recall the summary of our cost behavior discussion from Chapter 1. Average fixed costs per unit decrease as the activity level increases.

Fixed Cost Per Unit Example
Average fixed costs per unit decrease as the activity level increases. The fixed cost per local call decreases as more local calls are made. Monthly Basic Telephone Bill per Local Call For example, the fixed cost per local call decreases as more local calls are made. Number of Local Calls

Types of Fixed Costs Committed Discretionary Examples Examples
Long-term, cannot be significantly reduced in the short-term. Discretionary May be altered in the short-term by current managerial decisions Examples Depreciation on Buildings and Equipment and Real Estate Taxes Examples Advertising and Research and Development Part I Committed costs are long-term in nature (i.e., greater than one year). These costs cannot be significantly reduced even for short periods of time without seriously impairing the long-run goals of the organization. Examples of committed-fixed costs include depreciation on buildings and equipment and real estate taxes. Part II Discretionary costs usually arise from annual decisions by management to spend in certain fixed cost areas. These costs can be cut for short periods of time with minimal damage to the long-term goals of the organization. Examples of discretionary fixed costs include advertising and research and development. A cost may be discretionary or committed depending on management’s strategy. For example, some construction companies may layoff workers during months with minimal customer demand. However, other construction companies may opt to retain their workers all year.

The Trend Toward Fixed Costs
The trend in many industries is toward greater fixed costs relative to variable costs. As machines take over many mundane tasks previously performed by humans, “knowledge workers” are demanded for their minds rather than their muscles. Knowledge workers tend to be salaried, highly-trained and difficult to replace. The cost to compensate these valued employees is relatively fixed rather than variable. Part I The trend in many industries is toward greater fixed costs relative to variable costs. For example: H&R Block employees used to fill out tax returns for customers by hand. Now, computer software is used to complete tax returns. Safeway and Kroger employees used to key-in prices by hand on cash registers. Now, barcode readers enter price and other product information automatically. Part II As machines take over many mundane tasks previously performed by humans, “knowledge workers” are demanded for their minds rather than their muscles. Knowledge workers tend to be salaried, highly-trained and difficult to replace; consequently, the cost of compensating these valued employees is relatively fixed rather than variable.

Is Labor a Variable or a Fixed Cost?
The behavior of wage and salary costs can differ across countries, depending on labor regulations, labor contracts, and custom. In France, Germany, China, and Japan, management has little flexibility in adjusting the size of the labor force. Labor costs are more fixed in nature. The behavior of wage and salary costs can differ across countries, depending on labor regulations, labor contracts, and custom. For example: In France, Germany, China, and Japan management has little flexibility in adjusting the size of the labor force; hence, labor costs are more fixed in nature. Within countries managers can view labor costs differently depending on their strategy. Nonetheless, most companies in the United States continue to view direct labor as a variable cost. Most companies in the United States continue to view direct labor as a variable cost.

Fixed Costs and Relevant Range
90 Total cost doesn’t change for a wide range of activity, and then jumps to a new higher cost for the next higher range of activity. Relevant Range 60 Rent Cost in Thousands of Dollars 30 The relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat. , , , Rented Area (Square Feet)

The relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat. Example: Office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet. As the business grows, more space is rented, increasing the total cost. For example, assume office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet. Fixed costs would increase in a step fashion at a rate of $30,000 for each additional 1,000 square feet.

Step-variable costs can be adjusted more quickly and . . . The width of the activity steps is much wider for the fixed cost. How does this type of fixed cost differ from a step-variable cost? While this step-function pattern appears similar to the idea of step-variable costs, there are two important differences between step-variable costs and fixed costs: Step-variable costs can often be adjusted quickly as conditions change, whereas fixed costs cannot be changed easily. The width of the steps for fixed costs is wider than the width of the steps for step-variable costs. For example, a step-variable cost such as maintenance workers may have steps with a width of 40 hours a week. However, fixed costs may have steps that have a width of thousands or tens of thousands of hours of activity.

Which of the following statements about cost behavior are true?
Quick Check  Which of the following statements about cost behavior are true? Fixed costs per unit vary with the level of activity. Variable costs per unit are constant within the relevant range. Total fixed costs are constant within the relevant range. Total variable costs are constant within the relevant range. Take a minute to answer this question before we move on. There can be more than one correct answer. Be careful and take your time.

Which of the following statements about cost behavior are true?
Quick Check  Which of the following statements about cost behavior are true? Fixed costs per unit vary with the level of activity. Variable costs per unit are constant within the relevant range. Total fixed costs are constant within the relevant range. Total variable costs are constant within the relevant range. Number 4 is not correct because total variable costs increase as activity increases, within the relevant range and decrease as activity decreases, within the relevant range.

Fixed Monthly Utility Charge
Mixed Costs A mixed cost has both fixed and variable components. Consider your utility costs. X Y Total mixed cost Total Utility Cost A mixed cost contains both variable and fixed cost elements. For example, utility bills often contain fixed and variable cost components. The fixed portion of the utility bill is constant regardless of kilowatt hours consumed. This cost represents the minimum cost that is incurred to have the service ready and available for use. The variable portion of the bill varies in direct proportion to the consumption of kilowatt hours. Variable Cost per KW Fixed Monthly Utility Charge Activity (Kilowatt Hours)

Fixed Monthly Utility Charge
Mixed Costs X Y Total mixed cost Total Utility Cost An equation can be used to express the relationship between mixed costs and the level of the activity. This equation can be used to calculate what the total mixed cost would be for any level of activity. The equation is Y = a + bX Y = The total mixed cost. a = The total fixed cost (the vertical intercept of the line). b = The variable cost per unit of activity (the slope of the line). X = The level of activity. Variable Cost per KW Fixed Monthly Utility Charge Activity (Kilowatt Hours)

Mixed Costs Example Y = a + bX Y = $40 + ($0.03 × 2,000) Y = $100
If your fixed monthly utility charge is $40, your variable cost is $0.03 per kilowatt hour, and your monthly activity level is 2,000 kilowatt hours, the amount of your utility bill is: Y = a + bX Y = $40 + ($0.03 × 2,000) Y = $100 For example, if your fixed monthly utility charge is $40, your variable cost is 3 cents per kilowatt hour, and your monthly activity level was 2,000 kilowatt hours, this equation can be used to calculate your total utility cost of $100.

Analysis of Mixed Costs
Account analysis Each account is classified as either variable or fixed based on the analyst’s knowledge of how the account behaves. Engineering Approach Cost estimates are based on an evaluation of production methods, and material, labor and overhead requirements. In account analysis, each account under consideration is classified as variable or fixed based on the analyst’s prior knowledge about how costs behave. This approach is limited in value in the sense that it glosses over the fact that some accounts may have both fixed and variable components. The engineering approach classifies costs based on an industrial engineer’s evaluation of production methods, material specifications, labor requirements, equipment usage, power consumption, and so on. This approach is particularly useful when no past experience is available concerning activity and costs.

The Scattergraph Method
Plot the data points on a graph (total cost vs. activity). * Maintenance Cost 1,000’s of Dollars 10 20 Patient-days in 1,000’s X Y The scattergraph plot is also called the quick-and-dirty method. The first step when using this method to analyze a mixed cost is to plot the data on a scattergraph. The cost, which is known as the dependent variable, is plotted on the Y axis. The activity, which is known as the independent variable, is plotted on the X axis. The second step is to examine the dots on the scattergraph to see if they are linear, such that a straight line can be drawn that approximates the relation between cost and activity. If the dots are not linear, do not analyze the data any further. Instead, search for another independent variable that bears a stronger linear relationship with the dependent variable.

Draw a line through the data points with about an equal number of points above and below the line. * Maintenance Cost 1,000’s of Dollars 10 20 Patient-days in 1,000’s X Y The third step is to draw a straight line where, roughly speaking, an equal number of points reside above and below the line. Make sure that the straight line goes through at least one data point on the scattergraph.

Use one data point to estimate the total level of activity and the total cost. * Maintenance Cost 1,000’s of Dollars 10 20 Patient-days in 1,000’s X Y Total maintenance cost = $11,000 Patient days = 800 Intercept = Fixed cost: $10,000 Part I The fourth step is to identify the Y intercept. This intercept represents the estimated fixed cost portion of the mixed cost ($10,000 in this example). Part II The fifth step is to estimate the variable cost per unit of the activity by first selecting one point on the scattergraph that intersects the straight line and then determining the total cost and the total activity level at the chosen point.

Make a quick estimate of variable cost per unit and determine the cost equation. Variable cost per unit = $1, = $1.25/patient-day Step 5 (continued) Part I Subtract the fixed costs from the total costs to arrive at the total variable costs for the chosen activity level. Part II Divide the total variable costs by the activity level at the chosen point. This is the variable cost per unit of activity. Part II Construct an equation that can be used to estimate total costs at any activity level. Y = $10,000 + $1.25X Number of patient days Total maintenance cost

The High-Low Method Assume the following hours of maintenance work and the total maintenance costs for six months. This method can be used to analyze mixed costs if a scattergraph plot reveals a linear relationship between the X and Y variables. For illustrative purposes, assume the information as shown.

The High-Low Method The variable cost per hour of maintenance is equal to the change in cost divided by the change in hours. Part I The first step is to choose the data points pertaining to the highest and lowest activity levels (high = 800 units; low = 500 units). Notice, this method relies on two data points to estimate the fixed and variable portions of a mixed cost, as opposed to one data point with the scattergraph method. The second step is to determine the total costs associated with the two chosen points (high = $9,800; low = $7,400). Part II The third step is to calculate the change in cost between the two data points ($2,400) and divide it by the change in activity level between the two data points (300 units). The quotient represents an estimate of variable cost per unit of activity ($8.00 per unit). = $8.00/hour $2,

The High-Low Method Total Fixed Cost = Total Cost – Total Variable Cost The fourth step is to take the total cost at either activity level (in this case, $9,800) and deduct the variable cost component ($6,400). The residual represents the estimate of total fixed costs ($3,400). The variable cost component ($6,400) is determined by multiplying the level of activity (800 units) by the estimated variable cost per unit of the activity ($8.00 per unit). Total Fixed Cost = $9,800 – ($8/hour × 800 hours) Total Fixed Cost = $9,800 – $6,400 Total Fixed Cost = $3,400

The Cost Equation for Maintenance
The High-Low Method Y = $3,400 + $8.00X The Cost Equation for Maintenance The fifth step is to construct an equation that can be used to estimate the total cost at any activity level (Y = $3,400 + $8.00X).

Quick Check  Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission? a. $0.08 per unit b. $0.10 per unit c. $0.12 per unit d. $0.125 per unit Now, let’s apply what we have just discussed to determine the variable portion of sales salaries and commissions for this company.

Quick Check  Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission? a. $0.08 per unit b. $0.10 per unit c. $0.12 per unit d. $0.125 per unit $4,000 ÷ 40,000 units = $0.10 per unit The correct answer is 10 cents per unit.

Quick Check  Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 Using the same data, calculate the total fixed cost portion of sales salaries and commissions.

Quick Check  Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 The calculation for the answer is a bit more complex, but we see that total fixed cost equals $2,000.

The Contribution Format
The contribution margin format emphasizes cost behavior, by separating costs into fixed and variable categories. Contribution margin covers fixed costs and provides for income. This approach separates costs into fixed and variable categories. Sales minus variable costs equals contribution margin. The contribution margin minus fixed costs equals net operating income.

Uses of the Contribution Format
The contribution income statement format is used as an internal planning and decision making tool. We will use this approach for: Cost-volume-profit analysis. Budgeting. Special decisions such as pricing and make-or-buy analysis. This approach is used as an internal planning and decision making tool. For example, this approach is useful for: 1. Cost-volume-profit analysis (chapter 6). 2. Budgeting (chapter 7). 3. Special decisions such as pricing and make-or-buy analysis (chapter 11).

The Contribution Format
The contribution approach differs from the traditional approach illustrated in chapter 1. The traditional approach organizes costs in a functional format. Costs relating to production, administration, and sales are grouped together without regard to their cost behavior. The traditional approach is used primarily for external reporting purposes. Used primarily for external reporting. Used primarily by management.

Overview of Absorption and Variable Costing
Absorption Costing Variable Costing Product Costs Period Costs Direct Materials Direct Labor Variable Manufacturing Overhead Fixed Manufacturing Overhead Variable Selling and Administrative Expenses Fixed Selling and Administrative Expenses Product Costs Period Costs Absorption costing treats all manufacturing costs as product costs, regardless of whether they are variable or fixed. The cost of a unit of product consists of direct materials, direct labor, and both variable and fixed overhead. Variable and fixed selling and administrative expenses are treated as period costs and are deducted from revenue as incurred. Variable costing treats only those costs of production that vary with output as product costs. The cost of a unit of product consists of direct materials, direct labor, and variable overhead. Fixed manufacturing overhead, and both variable and fixed selling and administrative expenses are treated as period costs and deducted from revenue as incurred.

Quick Check  Which method will produce the highest values for work in process and finished goods inventories? a. Absorption costing. b. Variable costing. c. They produce the same values for these inventories. d. It depends. To answer this question correctly, recall which method includes more manufacturing costs in the unit product cost.

Quick Check  Which method will produce the highest values for work in process and finished goods inventories? a. Absorption costing. b. Variable costing. c. They produce the same values for these inventories. d. It depends. Unit product costs are in both work in process and finished goods inventories. Absorption costing results in the highest inventory values because it treats fixed manufacturing overhead as a product cost. Using variable costing, fixed manufacturing overhead is expensed as incurred and never becomes a part of the product cost.

Unit Cost Computations
Harvey Company produces a single product with the following information available: Assume Harvey Company produces a single product with available information as shown.

Unit product cost is determined as follows: The unit product costs under absorption and variable costing would be $16 and $10, respectively. Under absorption costing, all production costs, variable and fixed, are included when determining unit product cost. Under variable costing, only the variable production costs are included in product costs. Selling and administrative expenses are always treated as period expenses and deducted from revenue as incurred.

Income Comparison of Absorption and Variable Costing
Let’s assume the following additional information for Harvey Company. 20,000 units were sold during the year at a price of $30 each. There is no beginning inventory. The Harvey Company example continued (additional assumptions): 20,000 units were sold during the year. The selling price per unit is $30. There is no beginning inventory. Now, let’s compute net operating income using both absorption and variable costing.

Absorption Costing An income statement prepared using absorption costing shows that: The unit product cost is $16. The fixed manufacturing overhead cost deferred in inventory is $30,000 (5,000 units × $6 per unit). The net operating income is $120,000.

Variable Costing Variable manufacturing costs only.
All fixed manufacturing overhead is expensed. An income statement prepared using variable costing shows that: The unit product cost is $10. All $150,000 of fixed manufacturing cost is expensed in the current period. The net operating income is $90,000.

Comparing Absorption and Variable Costing
Let’s compare the methods. Under absorption costing, $120,000 of fixed manufacturing overhead is included in cost of goods sold and $30,000 is deferred in ending inventory as an asset on the balance sheet. Under variable costing, the entire $150,000 of fixed manufacturing overhead is treated as a period expense. The variable costing ending inventory is $30,000 less than absorption costing, thus explaining the difference in net operating income between the two methods.

We can reconcile the difference between absorption and variable net operating income as follows: The difference in net operating income between the two methods ($30,000) can also be reconciled by multiplying the number of units in ending inventory (5,000 units) by the fixed manufacturing overhead per unit ($6) that is deferred in ending inventory under absorption costing. Fixed mfg. overhead $150,000 Units produced ,000 units = = $6.00 per unit

Extended Comparison of Income Data
Here is information about the operation of Harvey Company for the second year. Let’s continue the Harvey Company example with these additional assumptions/facts: 30,000 units were sold in year 2. The selling price per unit, variable costs per unit, total fixed costs, and number of units produced remain unchanged. 5,000 units are in beginning inventory.

Since the variable costs per unit, total fixed costs, and the number of units produced remained unchanged, the unit cost computations also remain unchanged. Since there was no change in the variable costs per unit, total fixed costs, or the number of units produced, the unit costs remain unchanged.

produced in the current period.
Absorption Costing These are the 25,000 units produced in the current period. An income statement prepared using absorption costing for the second year shows that: The unit product cost is $16. The fixed manufacturing overhead cost released from inventory is $30,000. The net operating income is $230,000.

Variable Costing All fixed manufacturing overhead is expensed.
Variable manufacturing costs only. All fixed manufacturing overhead is expensed. An income statement prepared using absorption costing for the second year shows that: The unit product cost is $10. All $150,000 of fixed manufacturing overhead cost is expensed in the current period. The net operating income is $260,000.

We can reconcile the difference between absorption and variable net operating income as follows: The difference in net operating income between the two methods ($30,000) can be reconciled by multiplying the number of units in beginning inventory (5,000 units) by the fixed manufacturing overhead per unit ($6) that is released from beginning inventory under absorption costing. Fixed mfg. overhead $150,000 Units produced ,000 units = = $6.00 per unit

Across the two year time frame, both methods reported the same total net operating income ($350,000). This is because over an extended period of time sales cannot exceed production, nor can production much exceed sales. The shorter the time period, the more the net operating income figures will tend to differ.

Summary of Key Insights
We can summarize what we have observed over the two-year period for Harvey as follows: When production is greater than sales, as in year 1 for Harvey, absorption costing net operating income is greater than variable costing net operating income. When production is less than sales, as in year 2 for Harvey, absorption costing net operating income is less than variable costing net operating income. When production equals sales, the two methods report the same net operating income. NOI = net operating income

Basics of Cost-Volume-Profit Analysis
The contribution income statement is helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. For example, let's look at a hypothetical contribution income statement for Racing Bicycle Company (RBC). Notice that: The emphasis is on cost behavior. Variable costs are separate from fixed costs. The contribution margin is the amount remaining from sales revenue after variable expenses have been deducted. Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

Basics of Cost-Volume-Profit Analysis
Contribution margin is used first to cover fixed expenses. Any remaining contribution margin contributes to net operating income. CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.

The Contribution Approach
Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If RBC sells an additional bicycle, $200 more in contribution margin will be generated to cover fixed expenses and profit. Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. For each additional unit Racing Bicycle Company sells, $200 more in contribution margin will help to cover fixed expenses and provide a profit.

To breakeven, RBC must generate $80,000 in total CM each month to cover fixed costs. Each month, Racing Bicycle Company must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero).

If RBC sells 400 units a month, it will be operating at the break-even point. If Racing Bicycle Company sells 400 units a month, it will be operating at the break-even point.

If RBC sells one more bike (401 bikes), net operating income will increase by $200. If Racing Bicycle Company sells one more bike above the 400 bikes needed to breakeven (401 bikes total), net operating income will increase by $200.

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. 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. For example, if RBC sells 430 bikes, its net operating income will be $6,000.

CVP Relationships in Graphic Form
The relationship among revenue, cost, profit and volume can be expressed graphically by preparing a CVP graph. RBC developed contribution margin income statements at 300, 400, and 500 units sold. We will use this information to prepare the CVP graph. The relationship among revenue, cost, profit and volume can be expressed graphically by preparing a cost-volume-profit (CVP) graph. To illustrate, we will use contribution income statements for Racing Bicycle Company at 300, 400, and 500 units sold.

CVP Graph In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. Dollars In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. A CVP graph can be prepared in three steps. Units

CVP Graph Fixed Expenses Dollars Units
Draw a line parallel to the volume axis to represent total fixed expenses. Units

CVP Graph Total Expenses Fixed Expenses Dollars Units
Choose a sales volume (e.g., 500 units) and plot the point representing total expenses (e.g., fixed and variable) at that sales volume. Draw a line through the data point back to where the fixed expenses line intersects the dollar axis. Units

CVP Graph Total Sales Total Expenses Fixed Expenses Dollars Units
Choose a sales volume (e.g., 500 units) and plot the point representing total sales dollars at the chosen activity level. Draw a line through the data point back to the origin. Units

Break-even point (400 units or $200,000 in sales)
CVP Graph Break-even point (400 units or $200,000 in sales) Profit Area Dollars The break-even point is where the total revenue and total expenses lines intersect. In the case of Racing Bicycle Company, break-even is 400 bikes sold, or sales revenue of $200,000. The profit or loss at any given sales level is measured by the vertical distance between the total revenue and the total expenses lines. Loss Area Units

Contribution Margin Ratio
The contribution margin ratio is: For Racing Bicycle Company the ratio is: Total CM Total sales CM Ratio = = 40% $80,000 $200,000 The contribution margin ratio is calculated by dividing the total contribution margin by total sales. For RBC the contribution margin ratio is 40 percent. Thus, each $1.00 increase in sales results in a total contribution margin increase of 40 cents. Each $1.00 increase in sales results in a total contribution margin increase of 40¢.

Or, in terms of units, the contribution margin ratio is: For Racing Bicycle Company the ratio is: Unit CM Unit selling price CM Ratio = The contribution margin ratio can also be calculated by dividing the contribution margin per unit by the selling price per unit. For RBC, the contribution margin ratio is 40 percent. $200 $500 = 40%

A $50,000 increase in sales revenue results in a $20,000 increase in CM. ($50,000 × 40% = $20,000) If Racing Bicycle Company increases sales from 400 to 500 bikes, the increase in contribution margin ($20,000) can be calculated by multiplying the increase in sales ($50,000) by the CM ratio (40%).

Quick Check  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. On average, 2,100 cups are sold each month. What is the CM Ratio for Coffee Klatch? a b c d Can you calculate the contribution margin ratio for Coffee Klatch? The calculation may take a minute or so to complete.

Unit contribution margin
Quick Check  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. On average, 2,100 cups are sold each month. What is the CM Ratio for Coffee Klatch? a b c d Unit contribution margin Unit selling price CM Ratio = = ($1.49-$0.36) $1.49 $1.13 = 0.758 How did you do? The CM ratio is 75.8 percent.

Changes in Fixed Costs and Sales Volume
What is the profit impact if RBC can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000? What is the profit impact if Racing Bicycle Company can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000?

$80,000 + $10,000 advertising = $90,000 Preparing a contribution income statement reveals a $2,000 decrease in net operating income. Even though sales increase by $20,000, the $12,000 increase in variable costs and a $10,000 increase in fixed costs for the new advertising campaign will result in the $2,000 decline in net operating income. Sales increased by $20,000, but net operating income decreased by $2,000.

The Shortcut Solution A shortcut solution using incremental analysis also reveals a $2,000 decrease in net operating income.

Changes in Variable Costs and Sales Volume
What is the profit impact if RBC can use higher quality raw materials, thus, increasing variable costs per unit by $10, to generate an increase in unit sales from 500 to 580? What is the profit impact if Racing Bicycle Company can use higher quality raw materials, thus increasing variable costs per unit by $10, to generate an increase in unit sales from 500 to 580?

Changes in Variable Costs and Sales Volume
580 units × $310 variable cost/unit = $179,800 Part I Sales revenue will increase by $40,000 (80 bikes times $500 per bike) and variable costs will increase by $29,800. The result is a $10,200 increase in contribution margin, and with no change in fixed costs, net operating income will also increase by $10,200. Part II The shortcut solution also reveals a $10,200 increase in net operating income. Sales increase by $40,000, and net operating income increases by $10,200.

Change in Fixed Cost, Sales Price and Volume
What is the profit impact if RBC: (1) cuts its selling price $20 per unit, (2) increases its advertising budget by $15,000 per month, and (3) increases unit sales from 500 to 650 units per month? What is the profit impact if Racing Bicycle Company: (1) cuts its selling price $20 per unit, (2) increases its advertising budget by $15,000 per month, and (3) increases unit sales from 500 to 650 units per month?

Part I Even though contribution margin per bike decreases to $180, Racing Bicycle Company increases total contribution by $17,000 because it sells 150 more bikes. Since advertising, a fixed cost, has increased by $15,000, only $2,000 of the increased contribution margin adds to net operating income. Part II The shortcut solution also reveals a $2,000 increase in net operating income. Sales increase by $62,000, fixed costs increase by $15,000, and net operating income increases by $2,000.

What is the profit impact if RBC: (1) pays a $15 sales commission per bike sold, instead of paying salespersons flat salaries that currently total $6,000 per month, and (2) increases unit sales from 500 to 575 bikes? What is the profit impact if Racing Bicycle Company: (1) pays a $15 sales commission per bike sold instead of paying salespersons flat salaries that currently total $6,000 per month, and (2) increases unit sales from 500 to 575 bikes?

Part I Net operating income increases by $12,375. Notice that sales revenue and variable expenses increased, as well. Fixed expenses were decreased as a result of making sales commissions variable in nature. Part II The shortcut solution also reveals a $12,375 increase in net operating income. Sales increase by $37,500, variable costs increase by $31,125, but fixed expenses decrease by $6,000.

Change in Regular Sales Price
If RBC has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers or fixed expenses, what price would it quote to the wholesaler if it wants to increase monthly profits by $3,000? If Racing Bicycle Company has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers or fixed expenses, what price should it quote to the wholesaler if it wants to increase monthly profits by $3,000?

Change in Regular Sales Price
If we desire a profit of $3,000 on the sale of 150 bikes, we must have a profit of $20 per bike. The variable cost associated with each bike is $300, so we would quote a selling price of $320.

Break-Even Analysis Equation method Contribution margin method
Break-even analysis can be approached in two ways: Equation method Contribution margin method The breakeven point can be computed using either the equation method or the contribution margin method.

At the break-even point
Equation Method Profits = (Sales – Variable expenses) – Fixed expenses OR Sales = Variable expenses + Fixed expenses + Profits At the break-even point profits equal zero The equation can be stated in one of two ways: Profits = (Sales – Variable expenses) – Fixed Expenses or Sales = Variable expenses + Fixed expenses + Profits

Here is the information from RBC:
Break-Even Analysis Here is the information from RBC: The equation method can be illustrated using data from Racing Bicycle Company.

We calculate the break-even point as follows:
Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 Where: Q = Number of bikes sold $500 = Unit selling price $300 = Unit variable expense $80,000 = Total fixed expense The break-even point in units is determined by creating the equation as shown, where Q is the number of bikes sold, $500 is the unit selling price, $300 is the unit variable expense, and $80,000 is the total fixed expense.

We calculate the break-even point as follows:
Equation Method We calculate the break-even point 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 Solving this equation shows that the break-even point in units is 400 bikes.

Equation Method X = 0.60X + $80,000 + $0
The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80, $0 Where: X = Total sales dollars 0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses The equation can be modified as shown to calculate the break-even point in sales dollars. In this equation, X is total sales dollars, 0.60 is the variable expense as a percentage of sales, and $80,000 is the total fixed expense.

Equation Method 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000
The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80, $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000 Solving this equation shows that the break-even point in sales dollars is $200,000.

Contribution Margin Method
The contribution margin method has two key equations. Fixed expenses CM per unit = Break-even point in units sold The contribution margin method has two key equations: Break-even point in units sold equals fixed expenses divided by the unit contribution margin, and Break-even point in sales dollars equals fixed expenses divided by the contribution margin ratio. Fixed expenses CM ratio = Break-even point in total sales dollars

Contribution Margin Method
The contribution margin method can be illustrated using data from RBC. $80,000 40% = $200,000 break-even sales Fixed expenses CM ratio = Break-even point in total sales dollars CM per unit Break-even point in units sold $200 per bike = 400 bikes to breakeven Part I The contribution margin method can be illustrated using data from RBC. Part II The break-even point in unit sales (400 bikes) and sales dollars ($200,000) is the same as shown for the equation method.

Quick Check  872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups
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. On average 2,100 cups are sold each month. What is the break-even sales in units? 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups Now use the contribution margin approach to calculate the break-even point in cups of coffee sold.

Quick Check  872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups
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. On average 2,100 cups are sold each month. What is the break-even sales in units? 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups The contribution margin per cup of coffee is $1.13. The number of cups to sell to reach break-even is 1,150.

Quick Check  Fixed expenses Unit CM Break-even = $1,300 =
$1.49/cup - $0.36/cup $1.13/cup = 1,150 cups =

Quick Check  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. On average 2,100 cups are sold each month. What is the break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129 Let’s calculate the break-even in sales dollars for Coffee Klatch.

Quick Check  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. On average 2,100 cups are sold each month. What is the break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129 With a contribution margin ratio of 75.8% rounded, break-even sales revenue is $1,715. Fixed expenses CM Ratio Break-even sales $1,300 0.758 = $1,715 =

Target Profit Analysis
The equation and contribution margin methods can be used to determine the sales volume needed to achieve a target profit. Suppose Racing Bicycle Company wants to know how many bikes must be sold to earn a profit of $100,000. The equation and contribution margin methods can be used to determine the sales volume needed to achieve a target profit. For example: Suppose RBC wants to know how many bikes must be sold to earn a profit of $100,000.

The CVP Equation Method
Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80, $100,000 $200Q = $180,000 Q = 900 bikes The equation method can be used to determine that 900 bikes must be sold to earn the desired target profit. Instead of setting profit to zero, like we do in a break-even analysis, we set the profit level to $100,000. Solving for Q, we see that the company will have to sell 900 bikes to achieve the desired profit level.

The Contribution Margin Approach
The contribution margin method can be used to determine that 900 bikes must be sold to earn the target profit of $100,000. Fixed expenses + Target profit Unit contribution margin = Unit sales to attain the target profit Likewise, the contribution margin method can also be used to determine that 900 bikes must be sold to earn the $100,000 target profit. $80, $100,000 $200/bike = 900 bikes

Quick Check  a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups
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. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups The Coffee Klatch wants to earn a monthly profit of $2,500. How many cups of coffee must the company sell to reach this profit goal?

Quick Check  a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups
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. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups We add the desired profit to the fixed cost and divide by the unit contribution of $1.13. The company must sell 3,363 cups of coffee to reach its profit goal.

Fixed expenses + Target profit Unit sales to attain target profit
Quick Check  Fixed expenses + Target profit Unit CM Unit sales to attain target profit = 3,363 cups = $3,800 $1.13 $1,300 + $2,500 $ $0.36

Let’s look at RBC and determine 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 Let’s look at RBC and determine the margin of safety. The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. Let’s calculate the margin of safety for Racing Bicycle Company.

The Margin of Safety If we assume that RBC has actual sales of $250,000, given that we have already determined the break-even sales to be $200,000, the margin of safety is $50,000 as shown If we assume that Racing Bicycle Company has actual sales of $250,000, given that we have already determined the break-even sales to be $200,000, the margin of safety is $50,000.

The Margin of Safety The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000) The margin of safety can be expressed as a percent of sales. For example: Racing Bicycle Company’s margin of safety is 20% of sales ($50,000 divided by $250,000).

Margin of Safety in units
The Margin of Safety The margin of safety can be expressed in terms of the number of units sold. The margin of safety at RBC is $50,000, and each bike sells for $500. Margin of Safety in units = = 100 bikes $50,000 $500 The margin of safety can be expressed in terms of the number of units sold. For example: Racing Bicycle Company’s margin of safety is 100 bikes ($50,000 divided by $500 per bike).

Quick Check  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. On average 2,100 cups are sold each month. What is the margin of safety? a. 3,250 cups b cups c. 1,150 cups d. 2,100 cups Let’s calculate the margin of safety in cups of coffee for the Coffee Klatch.

Quick Check  a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups
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. On average 2,100 cups are sold each month. What is the margin of safety? a. 3,250 cups b cups c. 1,150 cups d. 2,100 cups The margin of safety is 950 cups, or we can calculate the margin of safety as 45 percent of sales.

Margin of safety percentage
Quick Check  Margin of safety = Total sales – Break-even sales = 950 cups = 2,100 cups – 1,150 cups or 950 cups 2,100 cups Margin of safety percentage = = 45%

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. Let’s assume RBC sells bikes and carts and that the sales mix between the two products remains the same. The term sales mix refers to the relative proportions in which a company’s products are sold. Since different products have different selling prices, variable costs, and contribution margins, when a company sells more than one product, breakeven analysis become more complex as the following example illustrates.

Multi-product Break-even Analysis
RBC provides the following information: $265,000 $550,000 = 48.2% (rounded) Assume RBC now sells carts in addition to bikes. The bikes comprise 45 percent of the company’s total sales revenue and the carts comprise the remaining 55 percent. The contribution margin ratio for both products combined is 48.2 percent.

Multi-product Break-even Analysis
Fixed expenses CM Ratio Break-even sales $170,000 48.2% = $352,697 = Rounding Error Part I The break-even point in sales would be $352, We calculate this amount in the normal way. We divide total fixed expenses of $170,000 by the combined contribution margin ratio of 48.2 percent. Part II We can verify the computation by preparing a contribution format income statement for the two products at the total breakeven revenue of $352,697. Bikes account for 45 percent of this amount, or $158,714, and carts account for 55% of the break-even sales, or $193,983. Notice a slight rounding error of $176.

Key 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). There are four key assumptions underlying cost-volume-profit analysis: Selling price is constant. Costs are linear and can be accurately divided into variable and fixed elements. The variable element is constant per unit, and the fixed element is constant in total over the entire relevant range. In multiproduct companies, the sales mix is constant. In manufacturing companies, inventories do not change. The number of units produced equals the number of units sold.

The End End of Chapter 1.

Masters of Business Administration Accounting for Managers

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