Chester & Wayne

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Learning Objectives

After studying Chapter 6, you will be able to:

Understand the signi�icance of cost behavior to decision making and control.

Identify the interacting elements of cost-volume-pro�it analysis.

Explain the break-even equation and its underlying assumptions.

Calculate the effect on pro�its of changes in selling prices, variable costs, or �ixed costs.

Calculate operating leverage, determine its effects on changes in pro�it, and understand how margin of safety relates to operating leverage.

Find break-even points and volumes that attain desired pro�it levels when multiple products are sold in combination.

Obtain cost functions by account analysis, the engineering approach, the scattergraph approach, and the high-low method.

6 Cost Estimation and Cost-Volume-Pro�itRelationships

Olga_Anourina/iStock/Thinkstock

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Estimate cost functions using regression analysis, construct control limits, and apply multiple regression.

“Can You Lose a Little on Each One, but Make It Up on Volume?”

David Scott, owner of Baker Cruise Lines, began his cruise business 15 years ago. During that time, he has enjoyed a number of upswings and weathered several downturns in the economy. Generally, the business has had pro�itable years and has provided a high standard of living for David and his family.

But times are changing. Personnel costs continue to rise, particularly fringe bene�its like medical insurance premiums. Other costs of operating the cruise ships continue to rise as well. At the same time, because of increased competition from new competitors, prices of cruises have fallen dramatically. David has begun to slash operating costs, but he still faces shrinking pro�it margins.

Because of high pro�itability in the past, David never analyzed how his costs change in relation to changes in activity levels, nor did he analyze the relationships among revenues, costs, and passenger volume to see how they relate to pro�it levels. Now, David is wondering how far revenues can drop before he sees the red ink in losses. With that information, he hopes to identify what changes will keep operations pro�itable. David sees many other businesses closing their doors and is fearful he will have to follow suit someday. He just doesn’t know what factors will in�luence his future costs and revenues.

Managers like David Scott of Baker Cruise Lines need to understand cost behavior and cost estimation to be in a better position to plan, make decisions, and control costs. As we discussed in Chapter 1, cost behavior describes the relationship between costs and an activity as the level of activity increases or decreases. Determining cost behavior is important to management’s understanding of overhead costs, marketing costs, and general and administrative expenses and for proper implementation of budgets and budgetary controls. With knowledge of cost behavior, managers can also estimate how costs are affected as future activity levels change, which can lead to better decisions. In addition, knowledge of cost behavior can assist managers in analyzing the interactions among revenues, costs, and volume for pro�it-planning purposes. These interactions are covered later in this chapter.

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6.1 Signi�icance of Cost Behavior to Decision Making and Control To understand more fully the signi�icance of a manager’s analysis of cost behavior, we look at three areas: decision making, planning and control, and trends in �ixed costs.

Decision Making

Cost behavior affects the decisions management makes. Variable costs are the incremental or differential costs in most decisions. Fixed costs change only if the speci�ic decision includes a change in the capacity requirement, such as more �loor space or adding another salaried employee.

Cost-based pricing requires a good understanding of cost behavior because �ixed costs pose conceptual problems when converted to per-unit amounts. Fixed costs per unit assume a given volume. If the volume turns out to be different from what was used in determining the cost-based price, the �ixed cost component of the total cost yields a misleading price. For instance, if �ixed costs total $2,000 and currently 2,000 units are being produced, then the �ixed cost per unit is $1. However, if production is cut in half, then the �ixed cost per unit increases to $2 ($2,000 / 1,000). Managers must know which costs are �ixed, as well as anticipated volume, to make good pricing decisions.

Planning and Control

A company plans and controls variable costs differently than it plans and controls �ixed costs. Variable costs are planned in terms of input/output relationships. For example, for each unit produced, the materials cost consists of a price per unit of materials times the number of units of materials; the labor cost consists of the labor rate times the number of labor hours. Once operations are underway, levels of activities may change. The input/output relationships identify changes in resources necessary to respond to the change in activity. If activity levels increase, this signals that more resources (materials, labor, or variable overhead) are needed. If activity levels decrease, the resources are not needed, and procedures can be triggered to stop purchases and reassign or lay off workers. In cases where more materials or labor time are used than are necessary in the input/output relationship, inef�iciencies and waste are in excess of the levels anticipated, and managers must investigate causes and eliminate or reduce the �inancial impact of the unfavorable variances.

Fixed costs, on the other hand, are planned on an annual basis, if not longer. Control of �ixed costs is exercised at two points in time. The �irst time is when the decision is made to incur a �ixed cost. Management evaluates the necessity of the cost and makes the decision to move forward or reject the proposal. Once �ixed costs are incurred, another point of control enters, that being the daily decision of how best to use the capacity provided by the cost. For example, a university makes a decision to build a new classroom and faculty of�ice building. That decision is the �irst point of control. After construction, control is implemented in using the building to its maximum capacity. This will occur if classes are scheduled throughout the day and evening.

Another difference in the planning and control of variable and �ixed costs is the level at which costs are controllable. Variable costs can be controlled at the lowest supervisory level. Fixed costs are often controllable only at higher managerial levels.

Trends in Fixed Costs

Organizations are �inding that an increasing portion of their total costs are �ixed costs. The following are a few of the more critical changes taking place.

Implementation of more automated equipment is replacing variable labor costs and a major share of the variable overhead costs. Many companies have laid off hourly employees, which is a variable cost, and replaced them with machinery that creates depreciation and other �ixed costs. Thus, �ixed costs are becoming a more signi�icant part of total costs. Costs associated with the additional automated equipment such as depreciation, taxes, insurance, and

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�ixed maintenance charges are substantially higher. Some industries, like steel and automobile, are becoming essentially �ixed cost industries, with variable costs playing a less important role than was once the case.

Another factor that has helped to increase �ixed costs signi�icantly is the movement in some industries toward a guaranteed annual wage for production workers. Employees who were once hourly wage earners are now becoming salaried. With the use of more automated equipment, the workers of a company may not represent “touch labor,” that is, work directly on the product. Instead, the production worker may merely observe that the equipment is operating as it should and is properly supplied with materials or may monitor production by means of a television screen. The production line employee is handling more of the functions normally associated with indirect labor, and the cost is a �ixed cost.

Contemporary Practice 6.1: Separating Variable and Fixed Costs

A survey of 148 German companies and 130 U.S. companies found that 46% of U.S. companies separate variable and �ixed costs for each cost center, as compared to 36% of German companies.

Source: Krumwiede, K., & Suessmair, A. (2007, June). Getting down to speci�ics on RCA. Strategic Finance, 51–55.

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6.2 Cost-Volume-Pro�it (CVP) Analysis The separation of �ixed costs from variable costs contributes to an understanding of how revenues, costs, and volume interact to generate pro�its. With this understanding, managers can perform any number of analyses that �it into a broad category called cost-volume-pro�it (CVP) analysis or, more commonly, break-even analysis. Examples of such analyses include �inding the:

1. Number of unit sales required to break even (i.e., total revenues equal total costs) 2. Dollars of sales needed to achieve a speci�ied pro�it level 3. Effect on pro�its if selling prices and variable costs increase or decrease by a speci�ic amount per unit 4. Increase in selling price needed to cover a projected �ixed cost increase

CVP analysis, as its name implies, examines the interaction of factors that in�luence the level of pro�its. Although the name gives the impression that only cost and volume determine pro�its, several important factors exist that determine whether we have pro�its or losses and whether pro�its increase or decrease over time. The key factors appear in the basic CVP equation:

(Unit selling price)(Sales volume) – (Unit variable cost)(Sales volume) – Total �ixed cost =

Pretax pro�it

The basic CVP equation is merely a condensed income statement, in equation form, where total variable costs (Unit variable cost × Sales volume in units) and total �ixed costs are deducted from total sales revenues (Unit selling price × Sales volume in units) to arrive at pretax pro�it. This equation, as well as other variations that will be discussed later, appears as Equation 1 in Figure 6.1.

Figure 6.1: Equations for CVP analysis

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The excess of total sales revenue over total variable cost is called the contribution margin or, more precisely, variable contribution margin. From the basic CVP equation, we see that the contribution margin contributes to covering �ixed costs as well as generating operating income. The contribution margin, as well as the contribution margin ratio, often plays an important role in CVP analysis. The latter measure is the ratio of the contribution margin to total sales revenue (or, equivalently, the ratio of the contribution margin per unit to the selling price).

Before proceeding, several fundamental assumptions are made to strengthen CVP analysis:

1. Relevant range—CVP analysis is limited to the company’s relevant range of activity (i.e., the normal range of expected activity).

2. Cost behavior identi�ication—�ixed and variable costs can be identi�ied separately. 3. Linearity—the selling price and variable cost per unit are constant across all sales levels within the

company’s relevant range of activity. 4. Equality of production and sales—all units are produced and sold and inventory changes are ignored. 5. Activity measure—the primary cost driver is volume of units. 6. Constant sales mix—the sales of each product in a multiproduct �irm is a constant percentage.

Assumptions 1, 2, and 3 are straightforward. Assumption 4 is required because if sales and production are not equal, some amount of variable and �ixed costs are treated as assets (inventories) rather than expenses. As long as

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inventories remain fairly stable between adjacent time periods, this assumption does not seriously limit the applicability of CVP analysis. Regarding assumption 5, factors other than volume may drive costs, as we have discussed earlier in this chapter, and as we will discuss further in later chapters. Costs that vary with cost drivers other than volume can be added to the �ixed-cost component. Assumption 6 is discussed in detail later in this chapter. In many cases, these assumptions are and must be violated in real-world situations, but the basic logic and analysis adds value. While our discussion may appear to presume that CVP analysis is applicable only to companies that sell physical products, these techniques are just as applicable to service organizations.

Basics of CVP Analysis

CVP analysis is often called break-even analysis because of the signi�icance of the break-even point, which is the volume where total revenue equals total costs. It indicates how many units of product must be sold or how much revenue is needed to at least cover all costs. All break-even analysis can be approached by using Equation 1 and by creating its derivations, as shown in Figure 6.1.

Each unit of product sold is expected to yield revenue in excess of its variable cost and thus contribute to the recovery of �ixed costs and provide a pro�it. The point at which pro�it is zero indicates that the contribution margin is equal to the �ixed costs. Sales volume must increase beyond the break-even point for a company to realize a pro�it.

Let’s look at CVP relationships in the context of Felsen Electronics, a wholesale distributor of calculators. Assume that price and costs for its calculators are as follows:

Dollars per Unit Percentage of Selling Price

Selling price $25 100%

Variable cost 15 60%

Contribution margin $10 40%

Total �ixed cost $100,000

Each calculator sold contributes $10 to covering �ixed costs and the creation of a pro�it. Hence, the company must sell 10,000 calculators to break even. The 10,000 calculators sold will result in a total contribution margin of $100,000, equaling total �ixed cost.

The break-even point can be calculated by using the basic CVP equations that appear as Equations 3 and 4 in Figure 6.1. For Felsen Electronics, the break-even point is determined as follows:

Break-even point in units = Total �ixed cost / Contribution margin per unit

= $100,000 / $10 per unit

= 10,000 units

A break-even point measured in sales dollars can be computed by directly using Equation 4 of Figure 6.1, as follows:

Total �ixed cost / Contribution margin ratio = Break-even point in sales dollars

$100,000 / 0.40 = $250,000

A Desired Pretax Pro�it

In business, only breaking even is not satisfactory, but the break-even relationships do serve as a base for pro�it planning. If we have a target pro�it level, we can insert that number into the basic CVP equation. This yields the

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following equations, which appear as Equations 5 and 6 in Figure 6.1:

(Total �ixed cost + Pretax pro�it) / Contribution margin ratio = Sales dollars required

(Total �ixed cost + Pretax pro�it) / Contribution margin per unit = Unit sales required

Continuing with the Felsen Electronics illustration, suppose that Enoch Goodfriend, the President, had set a pro�it objective of $200,000 before taxes. The units and revenues required to attain this objective are determined as follows:

($100,000 + $200,000) / $10 = 30,000 calculators

or

($100,000 + $200,000) / 0.40 = $750,000

A Desired Aftertax Pro�it

The pro�it objective may be stated as a net income after income taxes. Rather than changing with volume of units, income taxes vary with pro�its after the break-even point. When income taxes are to be considered, the basic CVP equation is altered using Equations 2, 7, and 8 in Figure 6.1. Equation 7 works as follows:

Target aftertax pro�it in units =

(Fixed costs + (Aftertax pro�it / (1 – Tax rate))) / Contribution margin per unit

Equation 8 yields the sales dollars needed to earn the desired aftertax pro�it.

Suppose Enoch Goodfriend had budgeted a $105,000 aftertax pro�it and that the income tax rate was 30%. We use the above equations to obtain the following volume and sales:

($100,000 + ($105,000 / (1 – 0.30))) / $10 = 25,000 calculators

or

($100,000 + ($105,000 / (1 – 0.30))) / 0.40 = $625,000

Contemporary Practice 6.2: Break-Even Attendance per Game for Hockey Team

“The Wheeling Nailers announced on Thursday the team again will play 10 of its home dates in Johnstown next season . . . Going over the lease, the ticket prices, our travel and our expenses we came out with 2,500 (attendance) to break even.”

Source: Mastovich, M. (2011, February 10). Nailers returning next year. The Tribune Democrat. Retrieved from http://tribune- democrat.com/sports/x62526069/Nailers-returning-next-year (http://tribune-democrat.com/sports/x62526069/Nailers-returning-next-year)

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6.3 Graphical Analysis Total sales dollars and total costs at different sales volumes can be estimated and plotted on a graph. The information shown on the graph can also be given in conventional reports, but it is often easier to grasp the fundamental facts when they are presented in graphic or pictorial form. Let’s look at two common forms of graphical analysis—the break-even chart and the pro�it-volume graph.

The Break-Even Chart

Dollars are shown on the vertical scale of the break-even chart, and the units of product to be sold are shown on the horizontal scale. The total costs are plotted for the various quantities to be sold and are connected by a line. This line is merely a combination of the �ixed and variable cost diagrams from Chapter 1. Total sales at various levels are similarly entered on the chart.

The break-even point lies at the intersection of the total revenue and total cost lines. Losses are measured to the left of the break-even point; the amount of the loss at any point is equal to the dollar difference between the total cost line and the total revenue line. Pro�it is measured to the right of the break-even point, and, at any point, is equal to the dollar difference between the total revenue line and the total cost line. This dollar difference equals the contribution margin per unit multiplied by the volume in excess of the break-even point.

In Figure 6.2, a break-even chart has been prepared for Felsen Electronics using the following data associated with sales levels between 5,000 and 30,000 calculators.

Number of Calculators Produced and Sold

5,000 10,000 15,000 20,000 25,000 30,000

Total revenue $125,000 $250,000 $375,000 $500,000 $625,000 $750,000

Cost:

Variable $ 75,000 $150,000 $225,000 $300,000 $375,000 $450,000

Fixed 100,000 100,000 100,000 100,000 100,000 100,000

Total cost $175,000 $250,000 $325,000 $400,000 $475,000 $550,000

Pro�it (loss) ($50,000) 0 $ 50,000 $100,000 $150,000 $200,000

Curvature of Revenue and Cost Lines

In some cases, revenues and costs cannot be represented by straight lines. If more units are to be sold, management may have to reduce selling prices. Under these conditions, the revenue function is a curve instead of a straight line. Costs may also be nonlinear depending on what changes take place as volume increases. The cost curve may rise slowly at the start, then more steeply as volume is expanded. This occurs if the variable cost per unit becomes higher as more units are manufactured. Also, �ixed costs might change as volume increases. For example, volume increases might cause a jump in supervision, equipment, and space costs. Therefore, it may be possible to have two break-even points, as shown in Figure 6.3.

Figure 6.2: Break-even chart

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Figure 6.3: Break-even chart with two break-even points

The Pro�it-Volume Graph

A pro�it-volume (P/V) graph is sometimes used in place of, or along with, a break-even chart. Data used in the earlier illustration of a break-even chart in Figure 6.2 have also been used in preparing the P/V graph shown in Figure 6.4. In general, pro�its and losses appear on the vertical scale; units of product, sales revenue, and/or percentages of capacity appear on the horizontal scale. A horizontal line is drawn on the graph to separate pro�its from losses. The pro�it or loss at each of various sales levels is plotted. These points are then connected to form a pro�it line. The slope of the pro�it line is the contribution margin per unit if the horizontal line is stated as units of product and is the contribution margin ratio if the horizontal line is stated as sales revenue.

The break-even point is the point where the pro�it line intersects the horizontal line. Dollars of pro�it are measured on the vertical scale above the line, and dollars of loss are measured below the line. The P/V graph may be preferred to the break-even chart because pro�it or loss at any point is shown speci�ically on the vertical scale. However, the P/V graph does not clearly show how cost varies with activity. Break-even charts and P/V graphs are often used together, thus obtaining the advantages of both.

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Figure 6.4: Pro�it-volume graph

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6.4 Analysis of Changes in CVP Variables Break-even charts and P/V graphs are convenient devices to show how pro�it is affected by changes in the factors that impact pro�it. For example, if unit selling price, unit variable cost, and total �ixed cost remain constant, how many more units must be sold to realize a greater pro�it? Or, if the unit variable cost can be reduced, what additional pro�it can be expected at any given volume of sales? The effects of changes in sales volume, unit variable cost, unit selling price, and total �ixed cost are discussed in the following paragraphs. In all these cases, the starting point for analysis is the CVP equations in Figure 6.1.

Sales Volume

For some companies, substantial pro�its depend on high sales volume. For example, if each unit of product is sold at a relatively low contribution margin, high pro�its are a function of selling in large quantities. This is more signi�icant when the �ixed cost is high.

For an illustration, consider Adrian Grant & Company, which handles a product with a selling price of $1 per unit. Assume a variable cost of $0.70 per unit and a �ixed cost of $180,000 per year. The contribution margin, therefore, is $0.30 per unit ($1 – $0.70). Before any pro�it is realized, the company must sell enough units for the total contribution margin to recover the �ixed cost. Therefore, 600,000 units must be sold just to break even:

$180,000 ÷ $.30 = 600,000 units

For every unit sold in excess of 600,000, a $0.30 pro�it before tax is earned. In such a situation, the company must be certain that it can sell substantially more than 600,000 units to earn a reasonable pro�it on its investment.

When products sell for relatively high contribution margins per unit, the �ixed cost is recaptured with the sale of fewer units, and a pro�it can be made on a relatively low sales volume. Suppose that each unit of product sells for $1,000 and that the variable cost per unit is $900. The �ixed cost for the year is $180,000. The contribution margin ratio is only 10%, but this is equal to $100 from each unit sold. The break-even point will be reached when 1,800 units are sold. The physical quantity handled is much lower than it was in the preceding example, but the same principle applies. More than 1,800 units must be sold if the company is to produce a pro�it.

A key relationship between changes in volume and pretax pro�it is the following:

Contribution margin per unit × Change in sales volume = Change in net income

This relationship presumes that the contribution margin per unit remains unchanged when the sales volume changes. It also presumes that �ixed costs have not been changed. Suppose that Enoch Goodfriend of Felsen Electronics wishes to know how the sale of an additional 500 calculators would impact pro�its. The above relationship reveals that net income would increase by $5,000 ($10 contribution margin per unit × 500 units).

Variable Costs

The relationship between the selling price of a product and its variable cost is important in any line of business. Even small savings in variable cost can add signi�icantly to pro�its. A reduction of a fraction of a dollar in the unit cost becomes a contribution to �ixed cost and pro�it. If 50,000 units are sold in a year, a $0.10 decrease in the unit cost becomes a $5,000 increase in pro�it. Conversely, a $0.10 increase in unit cost decreases pro�it by $5,000.

Management is continually searching for opportunities to make even small cost savings. What appears trivial may turn out to be the difference between pro�it or loss for the year. In manufacturing, it may be possible to save on materials cost by using cheaper materials that are just as satisfactory. Using materials more effectively can also result in savings. Improving methods of production may decrease labor and overhead costs per unit.

A small savings in unit cost can give a company a competitive advantage. If prices must be reduced, the low-cost producer will usually suffer less. At any given price and �ixed cost structure, the low-cost producer will become

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pro�itable faster as sales volume increases.

The following operating results of three companies show how pro�it is in�luenced by changes in the variable cost pattern. Each of the three companies sells 100,000 units of one product line at a price of $5 per unit. Each has an annual �ixed cost of $150,000. Company A can manufacture and sell each unit at a variable cost of $2.50. Company B has found ways to save costs and can produce each unit for a variable cost of $2, while Company C has allowed its unit variable cost to rise to $3.

Company A Company B Company C

Number of units sold 100,000 100,000 100,000

Unit selling price $5.00 $5.00 $5.00

Unit variable cost 2.50 2.00 3.00

Unit contribution margin 2.50 3.00 2.00

Contribution margin ratio 50% 60% 40%

Total sales revenue $500,000 $500,000 $500,000

Total variable cost 250,000 200,000 300,000

Total contribution margin $250,000 $300,000 $200,000

Fixed cost 150,000 150,000 150,000

Income before income tax $100,000 $150,000 $50,000

A difference of $0.50 in unit variable cost between Company A and Company B or between Company A and Company C adds up to a $50,000 difference in pro�it when 100,000 units are sold. The low-cost producer has a $1 per unit pro�it advantage over the high-cost producer. If sales volume should fall to 60,000 units per company, Company B would have a pro�it of $30,000, Company A would break even, and Company C would suffer a loss of $30,000. The same results are shown in the break-even chart in Figure 6.5.

Figure 6.5: Effects of variable cost changes

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The �ixed cost line for each company is drawn at $150,000, the amount of the �ixed cost. When 40,000 units are sold, a difference of $20,000 occurs between each total cost line. The lines diverge as greater quantities are sold. At the 100,000-unit level, the difference is $50,000 between each total cost line. Company B can make a pro�it by selling any quantity in excess of 50,000 units, but Company C must sell 75,000 units to break even. With its present cost structure, Company C will have to sell in greater volume if it is to earn a pro�it equal to pro�its earned by Company A or Company B. Company C is the inef�icient producer in the group and, as such, operates at a disadvantage. When there is enough business for everyone, Company C will earn a pro�it, but will most likely earn less than the others. When business conditions are poor, Company C will be more vulnerable to losses.

Price Policy

One of the ways to improve pro�it is to get more sales volume; to stimulate sales volume, management may decide to reduce prices. Bear in mind, however, that if demand for the product is inelastic (i.e., not affected by price changes) or if competitors also reduce prices, volume may not increase at all. Moreover, even if the price reduction results in an increase in sales volume, the increase may not be enough to overcome the handicap of selling at a lower price. This point is often overlooked by optimistic managers who believe that a small increase in volume can compensate for a slight decrease in price.

Price cuts or increases in variable costs will decrease the unit contribution margin. On a unit basis, price decreases may appear to be insigni�icant, but when the unit differential is multiplied by thousands of units, the total effect may be tremendous. Many more units may need to be sold to make up for the difference. Company A, for example, hopes to increase pro�it by stimulating sales volume; to do so, it plans to reduce the unit price by 10%. The following tabulation portrays its present and contemplated situations:

Present Situation Contemplated Situation

Selling price $5.00 $4.50

Variable cost 2.50 2.50

Contribution margin $2.50 $2.00

Contribution margin ratio 50% 44.4%

At present, one-half of each revenue dollar can be applied to �ixed cost and pro�it. When revenues are twice the �ixed cost, Company A will break even. Therefore, 60,000 units yielding revenues of $300,000 must be sold if �ixed cost is $150,000. But when the price is reduced, less than half of each dollar can be applied to �ixed cost and pro�it. To recover $150,000 in �ixed cost, unit sales must be 75,000 ($150,000 divided by the $2 contribution margin per unit). Thus, to overcome the effect of a 10% price cut, unit sales must increase by 25%:

(75,000 – 60,000) ÷ 60,000 = 25% increase

Similarly, revenue must increase to $337,500 (75,000 units × $4.50 per unit). This represents a 12.5% increase, as follows:

($337,500 – $300,000) ÷ $300,000 = 12.5% increase

Not only must total revenue be higher, but with a lower price, more units must be sold to obtain that revenue. A break-even chart showing these changes appears in Figure 6.6.

Figure 6.6: Effects of price reduction

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The present pretax income of $100,000 can still be earned if 125,000 units are sold. This is obtained using Equation 5 of Figure 6.1:

($150,000 + $100,000) ÷ $2 = 125,000 units

Fixed Costs

A change in �ixed cost has no effect on the contribution margin. Increases in �ixed cost are recovered when the contribution margin from additional units sold is equal to the increase in �ixed cost. Presuming that the contribution margin per unit remains unchanged, the following general relationship holds:

(Contribution margin per unit × Change in sales volume) – Change in �ixed cost =

Change in net income

Suppose Enoch Goodfriend estimates that, if he spends an additional $30,000 on advertising, he should be able to sell an additional 2,500 calculators. The above equation reveals that pro�its would decrease by $5,000 or [($10 × 2,500) – $30,000].

Because �ixed cost is not part of the contribution margin computation, the slope of the total cost line on a break- even chart is unaffected by changes in �ixed cost. The new total cost line is drawn parallel to the original line, and the vertical distance between the two lines, at any point, is equal to the increase or the decrease in �ixed cost.

The break-even chart in Figure 6.7 shows the results of an increase in �ixed cost from $100,000 to $130,000 at Felsen Electronics. Under the new �ixed cost structure, the total cost line shifts upward, and, at any point, the new line is $30,000 higher than it was originally. To break even or maintain the same pro�it as before, Felsen Electronics must sell 3,000 more calculators.

Figure 6.7: Effects of an increase in �ixed cost

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Decreases in �ixed cost would cause the total cost line to shift downward. The total contribution margin can decline by the amount of the decrease in �ixed cost without affecting pro�it. The lower sales volume now needed to maintain the same pro�it can be calculated by dividing the unit contribution margin into the decrease in �ixed cost.

Ethical Considerations When Changing CVP Variables

Managers are often under pressure to reduce costs—both variable and �ixed costs. Many companies have downsized in recent years by eliminating jobs and even closing plants. Managers must be careful not to cut costs in an unethical manner, such as the use of inferior quality materials in a product, which may risk injury to the product users. Changing a price can also involve ethical issues. For instance, immediately after a hurricane hit southern Florida several years ago, some sellers of building supplies were accused of “price gouging.”

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6.5 Measures of Relationship Between Operating Levels and Break-Even Points Companies want to know where they are with respect to the break-even point. If they are operating around the break-even point, management may be more conservative in its approach to implementing changes and mapping out new strategies. On the other hand, if they are operating well away from the break-even point, management will be more aggressive because the downside risk is not as great. Two measures that relate to this distance between a break-even point and the current or planned operating volume are operating leverage and margin of safety. These measures are the subject of the following sections.

Operating Leverage

Operating leverage measures the effect that a percentage change in sales revenue has on pretax pro�it. It is a principle by which management in a high �ixed cost industry with a relatively high contribution margin ratio (low variable costs relative to sales revenue) can increase pro�its substantially with a small increase in sales volume. We typically call this measure the operating leverage factor or the degree of operating leverage, and it is computed as follows:

(Contribution margin) / (Net income before taxes) = Operating leverage factor

As pro�it moves closer to zero, the closer the company is to the break-even point. This will yield a high operating leverage factor. As sales volume increases, the contribution margin and pretax pro�it both increase; consequently, the operating leverage factor becomes progressively smaller. Hence, the operating leverage factor is related to the distance between the break-even point and a current or expected sales volume. With an increase in sales volume, pro�its will increase by the percentage increase in sales volume multiplied by the operating leverage factor.

Suppose Felsen Electronics is currently selling 15,000 calculators. With its unit contribution margin of $10 and �ixed costs of $100,000, its operating leverage factor is 3, computed as follows:

At a sales volume of 15,000, if sales volume can be increased by an additional 10%, pro�it can be increased by 30%:

Increase in sales volume × Operating leverage factor = Increase in pretax pro�it

10% × 3 = 30%

A 10% increase in sales volume will increase sales from 15,000 units to 16,500 units. Operating leverage suggests that the pretax pro�it should be $65,000 ($50,000 × 1.3). Indeed, when we deduct the $100,000 �ixed cost from the new contribution margin of $165,000 (16,500 × $10), we obtain a pretax pro�it of $65,000.

A company with high �ixed costs will have to sell in large volume to recover the �ixed costs. However, if the company also has a high contribution margin ratio, it will move into higher pro�its very quickly after the break-even volume is attained. Hence, a fairly small percentage increase in sales volume (computed on a base that is already fairly large) will increase pro�its rapidly.

Margin of Safety

The margin of safety is the excess of actual (or expected) sales over sales at the break-even point. The excess may also be computed as a percentage of actual (or expected) sales. The margin of safety, expressed either in dollars or as a percentage, shows how much sales volume can be reduced without sustaining losses. The equations for calculating margin of safety are:

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Margin of safety in dollars = Actual (or expected) sales – Break-even sales

Margin of safety in percentage form = (Margin of safety in dollars) / (Actual (or expected) sales)

For our purposes, margin of safety is the percentage form. Therefore, unless otherwise speci�ied, a reference to margin of safety will mean a percentage.

Recall that the break-even sales level for Felsen Electronics was $250,000. At an actual sales level of 15,000 calculators, its safety margin is one-third, calculated as follows:

Note that one-third is the reciprocal of the operating leverage factor computed earlier for Felsen Electronics. The margin of safety will always be the reciprocal of the operating leverage factor.

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6.6 The Sales Mix When selling more than one product line, the relative proportion of each product line to the total sales is called the sales mix. With each product line having a different contribution margin, management will try to maximize the sales of the product lines with higher contribution margins. However, a sales mix results because limits on either sales or production of any given product line may exist.

When products have their own individual production facilities and �ixed costs are speci�ically identi�ied with the product line, cost-volume-pro�it analysis is performed for each product line. However, in many cases, product lines share facilities, and the �ixed costs relate to many products. For such a situation, cost-volume-pro�it analysis requires averaging of data by using the sales mix percentages as weights. Consequently, a break-even point can be computed for any assumed mix of sales, and a break-even chart or P/V graph can be constructed for any sales mix.

Let’s consider cost-volume-pro�it analysis with a sales mix. Suppose that Bijan’s Exotic Catering Service offers three basic dinners for events that it caters: duck, venison, and shark. Assume that the following budget is prepared for these three product lines. Fixed costs are budgeted at $500,000 for the period:

Product Lines Sales Volume (Meals) Price per Meal Unit Variable Cost

Contribution Margin

Dollars Ratio

Duck 20,000 $50 $20 $30 60%

Venison 10,000 50 30 20 40%

Shark 10,000 50 40 10 20%

Total 40,000

The break-even point in units (i.e., meals) is computed using a weighted average contribution margin as follows:

Product Lines Sales Mix Proportions

Contribution Margin per Meal

Weighted Contribution Margin

Duck 50% × $30 = $15.00

Venison 25% × 20 = 5.00

Shark 25% × 10 = 2.50

Weighted contribution margin

$22.50

(Fixed cost) / (Weighted contribution margin) = $500,000 / $22.50 = 22,222 total units

The detailed composition of this overall break-even point of 22,222 units (and contribution margins at this level) is as follows:

Product Lines Sales Mix Proportions

Total Units

No. of Meals

Margin per Meal

Contribution Margin

Duck 50% × 22,222 = 11,111 × $30 = $333,330

Venison 25% × 22,222 = 5,556 × 20 = 111,120

Shark 25% × 22,222 = 5,556 × 10 = 55,560

Break-even contribution margin*

$500,010

* Approximately equal to �ixed cost of $500,000. Difference is due to rounding.

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To obtain the sales revenue at the break-even point directly, we calculate it as we did earlier in the chapter. Simply divide the weighted contribution margin ratio into the �ixed costs. Individual product line revenues will be total revenues multiplied by individual sales mix proportions. Continuing with our illustration, we have:

Product Lines

Duck Venison Shark Total

Units (number of meals) 20,000 10,000 10,000 40,000

Revenues $1,000,000 $500,000 $500,000 $2,000,000

Variable cost 400 000 300,000 400,000 1,100,000

Contribution margin $600,000 $200,000 $100,000 $ 900,000

Less �ixed cost 500,000

Budgeted net income before taxes $ 400,000

As shown in the following calculations, the weighted contribution margin ratio is 45%, and revenue at the break- even point is $1,111,111.

(Total contribution margin) / (Total revenues) = $900,000 / $2,000,000 = 45%

(Fixed cost) / (Weighted contribution margin ratio) = 500,000 / (45%) = $1,111,111

Another way to obtain the number of meals needed to break even is by using an equation approach. Let “d” represent the number of duck meals, “v” represent the number of venison meals, and “s” represent the number of shark meals. The following equation is an extension of the basic CVP equation to this scenario with multiple products:

$30d + $20v + $10s = $500,000

Next, we need to write the equation in terms of one variable rather than three by using the information from the sales mix proportions. Since there are half as many venison and shark meals as duck meals, we can rewrite the equation as follows:

$30d + $20(.5d) + $10(.5d) = $500,000

Solving this equation, we obtain d = 11,111, and therefore, v = s = .5(11,111) = 5,556. These are the same numbers of meals we derived earlier.

If the actual sales mix changes from the budgeted sales mix, the break-even point and other factors of cost-volume- pro�it analysis may change. Suppose that Bijan’s Exotic Catering Service actually operated at the budgeted capacity with �ixed costs of $500,000. The unit selling prices and variable costs were also in agreement with the budget. Yet, with the same volume of 40,000 meals and total revenue of $2,000,000, the pretax pro�it was considerably lower than anticipated. The difference was due to a changed sales mix. Assume the following actual results:

Product Lines Sales Volume (Meals)

Unit Contribution Margin

Total Contribution Margin Revenue

Duck 5,000 $30 $150,000 $250,000

Venison 20,000 20 400,000 1,000,000

Shark 15,000 10 150,000 750,000

Total 40,000 $700,000 $2,000,000

Less �ixed cost 500,000

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Product Lines Sales Volume (Meals)

Unit Contribution Margin

Total Contribution Margin Revenue

Actual net income after taxes

$200,000

Instead of earning $400,000 before taxes, the company earned only $200,000. Sales of venison and shark, the less pro�itable products, were much better than expected. At the same time, sales of the best product line, duck, were less than expected. As a result, the total contribution margin was less than budgeted, so net income before taxes was also less than budgeted.

One way to encourage the sales force to sell more of the high contribution margin lines is to compute sales commissions on the contribution margin rather than on sales revenue. If sales commissions are based on sales revenue, a sales force may sell a high volume of less pro�itable product lines and still earn a satisfactory commission. But if sales commissions are related to contribution margin, the sales force is encouraged to strive for greater sales of more pro�itable products and, in doing so, will help to improve total company pro�its.

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6.7 Cost Estimation Cost estimation is the process of determining a cost relationship with activity for an individual cost item or grouping of costs. We typically express this relationship as an equation that re�lects the cost behavior within the relevant range. In Chapter 1, we referred to this equation as a cost function—a + b (X). The dependent variable (Y) of the equation is what we want to predict (i.e., costs, in our case). The independent variable (X) (i.e., the activity) is used to predict the dependent variable. The cost function can be written as follows:

Y = a + b (X)

This equation states that Y, the total cost, is equal to a value a plus a factor of variability applied to the activity level X. The value a represents the �ixed cost. The factor b represents the change in Y in relation to the change in X, i.e., the variable cost per unit of activity.

Although a number of techniques exist for estimating a cost-to-activity relationship, we will discuss �ive techniques: (1) account analysis, (2) engineering approach, (3) scattergraph and visual �it, (4) high-low method, and (5) regression analysis.

Account Analysis

In account analysis, accountants estimate variable and �ixed cost behaviors of a particular cost by evaluating information from two sources. First, the accountant reviews and interprets managerial policies with respect to the cost. Second, the accountant inspects the historical activity of the cost. All cost accounts are classi�ied as �ixed or variable. If a cost shows semi-variable or semi-�ixed cost behavior, the analyst either (1) makes a subjective estimate of the variable and �ixed portions of the cost or (2) classi�ies the account according to the preponderant cost behavior. Unit variable costs are estimated by dividing total variable costs by the quantity of the cost driver.

As an example, suppose for cost control purposes, the managing partner of Joe Carmela & Associates, a stock brokerage �irm, wishes to estimate the brokers’ automobile expenses as a function of miles driven. Costs for the past quarter, during which 58,000 miles were driven, are classi�ied as follows:

Item Cost Classi�ication

Fuel $3,200 Variable

Depreciation 11,200 Fixed

Insurance 3,900 Fixed

Maintenance 1,800 Variable

Parking 2,100 Fixed

The �ixed costs total $17,200, while the variable cost per mile is 8.62 cents [($3,200 + $1,800) ÷ 58,000]. Hence, the cost function would be expressed as:

Y = $17,200 + $.0862 (X)

The managing partner believes that costs should be stable for the coming quarter for which the brokers’ auto travel budget would be 65,000 miles. Accordingly, the estimated auto expenses should total $22,803 [$17,200 + ($.0862 × 65,000)]. The managing partner intends to investigate any signi�icant deviation from this total cost.

Account analysis is fairly accurate for determining cost behavior in many cases. Vendor invoices, for instance, imply that direct materials have a variable cost behavior; leasing costs are �ixed. A cell phone bill is a semi-variable cost. One portion is �ixed for the minimum monthly charge, and the remainder may be variable with data or minutes charges.

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Account analysis has limited data requirements and is simple to implement. The judgment necessary to make the method work comes from experienced managers and accountants who are familiar with the operations and management policies. Because operating results are required for only one period, this method is particularly useful for new products or situations involving rapid changes in products or technologies.

The two primary disadvantages of this method are its lack of a range of observations and its subjectivity. Using judgment generates two potential issues: (1) Different analysts may develop different cost estimates from the same data, and (2) the results of analysis may have signi�icant �inancial consequences for the analyst, therefore the analyst will likely show self-serving estimates. Another potential weakness in the method is that data used in the analysis may re�lect unusual circumstances or inef�icient operations, as is likely to occur with new products. These factors then become incorporated in the subsequent cost estimates. This method is also dependent on the quality of the detailed chart of accounts and transaction coding.

Engineering Approach

The engineering approach uses analysis and direct observation of processes to identify the relationship between inputs and outputs and then quanti�ies an expected cost behavior. A basic issue in manufacturing a product is determining the amount of direct materials, direct labor, and overhead required to run a given process. For a service, the question relates primarily to the labor and overhead costs.

One method of applying this approach to a product is to make a list of all materials, labor tasks, and overhead activities necessary for the manufacturing process. Engineering speci�ications and vendor information can be used to quantify the units of the various materials and subassemblies. Time and motion studies can help estimate the amount of time required for the tasks to be performed. Other analyses are used to assess the overhead relationships to the process. Once quantities and time are determined, those amounts are priced at appropriate materials prices, labor rates, and overhead rates.

A major advantage of the engineering approach is that it details each step required to perform a task. This permits transfer of information to similar tasks in different situations. It also allows an organization to review productivity and identify strengths and weaknesses in the process. Another advantage is that it does not require historical accounting data. It is, therefore, a useful approach in estimating costs of new products and services. The major disadvantage is the expensive nature of the approach. For example, time and motion studies require in-depth examinations of tasks and close observations of individuals performing each task. An additional disadvantage is that estimates made by the engineering approach are often based on near-optimal working conditions. Since actual working conditions are generally less than optimal, cost estimates using the engineering approach will generally understate the actual costs.

Scattergraph and Visual Fit

An approach that yields rough approximations to �ixed and variable costs is called scattergraph and visual �it. With the advent of personal computers, the mechanical nature of this approach loses its appeal. When the analyst has data, the computer can graph the observations and estimate cost behavior quickly. However, we present the details below because, in many cases, it can be used in a preliminary analysis and can easily be applied.

The �irst step in applying the approach is to graph each observation, with cost on the vertical axis and activity or cost driver on the horizontal axis. The second step is to �it visually and judgmentally a line to the data. Care should be taken so that the distances of the observations above the line are approximately equal to the distances of the observations below the line. Figure 6.8 shows a graph of maintenance cost and hours of operation for ten weeks of activity at Bleich Industries. The data for this graph are as follows:

Hours (X) Maintenance Cost (Y)

50 $120

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Hours (X) Maintenance Cost (Y)

30 110

10 60

50 150

40 100

30 80

20 70

60 150

40 110

20 50

Figure 6.8: A visually �itted cost function

The third step is to estimate the cost behavior from the plotted line. The variable cost per hour is indicated by the slope of the line, and the �ixed cost is measured where the line begins at zero hours of activity. In the maintenance cost example, the �ixed cost is at the Y-intercept and is $30. The variable costs can be calculated by subtracting �ixed costs from total costs at some point along the line. Let’s select 40 hours of operation. The cost indicated by the line at 40 hours is approximately $110. Compute variable costs as follows:

Total costs at 40 hours of operation $110

Less �ixed costs 30

Variable costs $80

$80 variable costs ÷ 40 hours = $2 per hour of operation

This analysis yields the following cost function:

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Y = $30 + $2 (X)

When used by itself, the scattergraph and visual �it approach is limited by the judgment of the person drawing the line through the data. Even reasonable people will disagree on the slope and intercept for a given graph. However, lines that are drawn visually will tend to be fairly consistent near the center of the data. Therefore, a visual �it may be a useful way to obtain rough approximations near the center of the data. Care should be taken with estimates away from the center. The further from the central area, the larger are the errors that may occur in estimates of �ixed and variable costs.

High-Low Method

Another method for obtaining rough approximations to �ixed and variable costs is the high-low method. The �irst step is to list the observed costs for various levels of activity from the highest level in the range to the lowest. This method chooses observations associated with the highest and the lowest activity levels, not the highest and lowest costs. The second step is to divide the difference in activity between the highest and the lowest levels into the difference in cost for the corresponding activity levels in order to arrive at the variable cost rate. As an example, suppose a manager for Edlin’s Pest Control Service wishes to estimate supplies costs as input for bidding on jobs. Its costs of supplies for several recent jobs, along with the hours of activity, are as follows:

Hours of Activity Supplies Cost

High 95 $397

90 377

87 365

82 345

78 329

75 317

66 281

58 239

Low 50 217

The difference in hours is 45 (95 – 50), and the difference in cost is $180 ($397 – $217). The variable supplies cost per hour is computed below:

The �ixed cost is estimated by using the total cost at either the highest or lowest level and subtracting the estimated total variable cost for that level:

Total �ixed cost = Total cost at highest activity – (Variable cost per unit × Highest activity)

or

Total �ixed cost = Total cost at lowest activity – (Variable cost per unit × Lowest activity)

If the variable cost is calculated correctly, the �ixed cost will be the same at both the high and low points. For the above illustration, the calculation of total �ixed cost is as follows:

Total �ixed cost = $397 – ($4 Variable cost per hour × 95 hours)

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= $397 – $380

= $17

or

Total �ixed cost = $217 – ($4 Variable cost per hour × 50 hours)

= $217 – $200

= $17

The cost function that results from the high-low method is:

Y = $17 + $4 (X)

If Edlin’s manager forecasts that a particular job would require 75 hours, the bid would include an estimate of $317 [$17 + ($4 × 75)] for supplies cost.

Occasionally, either the highest or lowest activity or the cost associated with one of those points is obviously an outlier to the remaining data. When this happens, use the next highest or lowest observation that appears to align better with the data. Sometimes only two data points are available, so in effect, these are used as the high and low points.

The high-low method is simple and can be used in a multiplicity of situations. Its primary disadvantage is that two points from all of the observations will only produce reliable estimates of �ixed and variable cost behavior if the extreme points are representative of the points in between. Otherwise, distorted results may occur.

If enough quality data are available, statistical techniques can provide more objective cost estimates than we have discussed thus far. These techniques are covered in section 6.10.

Ethical Considerations in Estimating Costs

All cost estimation methods involve some degree of subjectivity. With account analysis, managers judgmentally classify costs. In the engineering method, the manager must often subjectively adjust data obtained from near- optimal working conditions to normal working conditions. The scattergraph approach involves a subjective �itting of a line to data points. With the high-low method, one must decide whether the high and low points are representative data points.

The subjectivity inherent in cost estimation can lead to biased cost estimates. Indeed in certain instances, incentives exist for managers to bias cost estimates. In developing budgets or cost-based prices, managers may want to overestimate costs. In developing proposals for projects or programs, incentives may exist to underestimate costs. Managers must take care not to use subjectivity as an opportunity to act unethically.

Other Issues for Cost Estimation

An overriding concern with any cost estimation technique is that of extrapolating beyond the relevant range of activity. Cost behavior may change drastically once the activity falls below or rises above the relevant range. For instance, assume the relevant range of activity for Edlin’s Pest Control Service is 40 to 100 hours. We wish to predict the supplies cost for the coming time period during which 130 hours of activity are expected. Since this level is above the relevant range, the cost function we derived earlier may not be appropriate to use.

We have presumed that our cost data are suitably represented by a straight line (linear) and not by a curve. In some situations, the linear relationship may not be appropriate. Costs, for example, may not increase at a constant rate but instead may change at an increasing or a decreasing rate as the measure of activity increases. Hence, the

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cost data would be represented by a curve rather than a straight line. The shape of the line or curve can be revealed by plotting a suf�icient amount of data for various volumes of activity.

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6.8 Regression and Correlation Analyses Regression and correlation analyses are statistical techniques that can be used to estimate and examine cost functions. Regression analysis �its a line to the cost and activity data using the least squares method. Correlation analysis deals with the “goodness of �it” in the relationship between costs and activity as identi�ied by the regression line. Both analyses are important in �inding relationships and establishing the signi�icance of those relationships.

Linear Regression

Linear regression is a statistical tool for describing the movement of one variable based on the movement of another variable. In determining cost behavior, it is important to know if the movement in costs is related to the movement in activity. The cost behavior is expressed as a line of regression. A line of regression can be �itted precisely to a large quantity of data by the least squares method. The high-low method is a rough approximation computed from data taken only at the high and low points of the range, but the least squares method includes all data within the range. The line of regression is determined so that the algebraic sum of the squared deviations from that line is at a minimum.

We will explain the application of linear regression through an illustration. Suppose that the buildings manager of the Atlanta Juvenile Community Center (AJCC) is asked to assist in budgeting for building-related costs. During the past year, electricity costs for various hours of monthly activity in a particular building have been recorded as follows:

Hours (X) Electricity Cost (Y)

30 $500

50 650

20 300

10 300

60 900

50 750

40 650

60 700

30 450

10 350

40 600

20 450

The advent of the personal computer and spreadsheets has greatly simpli�ied the application of linear regression. By entering data on a spreadsheet and using a few function commands, the results appear on the screen. The data for our example of electricity cost and hours of activity yield the following results with a computer spreadsheet analysis:

Regression Output:

Constant 200

Std err of Y est 67.08

r2 0.886

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Regression Output:

No. of observations 12

X coef�icient(s) 10

The information necessary to obtain a cost function can be read from the output. The constant is the �ixed cost of $200. The X coef�icient is our variable cost per hour, $10. Hence, our cost function is:

Y = $200 + $10X

This cost function tells us that the total electricity cost is $200 plus $10 for each hour of electricity. The number of observations is given as a check. The remaining terms in the regression output will be discussed later.

The buildings manager of the AJCC can now use the derived cost function to budget the electricity cost. Suppose there is expected to be 35 hours of activity in the building during the next month. In that case, $550 will be budgeted for electricity cost [$200 + ($10 × 35)].

In measuring the relationship between the cost and activity, we are interested in more than just an equation for estimating cost. We also want to know the “goodness of �it” for the correlation of the regression line to the cost and activity data and the “reliability” of the cost estimates, as discussed below.

Goodness of Fit The relationship between cost and activity is called correlation. At times costs may be randomly distributed and are not at all related to the cost driver used in de�ining the relationship. This is illustrated in Figure 6.9.

Figure 6.9: No correlation

At the other extreme, the relationship may be so close that the data can almost be plotted on a line, as shown in Figure 6.10.

Figure 6.10: Positive correlation

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Between these extremes, the degree of correlation may not be so evident. A high degree of correlation exists when the regression line explains most of the variation in the data. The above example of electricity costs has all data lying relatively close to the regression line, as shown on the graph in Figure 6.11.

Figure 6.11: Explanation of correlation

The average cost is computed in the conventional way by adding the costs and dividing by the number of data points. In this case, the average is $550. Any variance between the line of regression and the average can be explained by hours of activity. The unexplained variances are the variances between the actual costs and the line of regression. In this illustration, a large part of the variance from the average can be explained by hours of activity; only a small amount is unexplained. Hence, a good correlation exists between cost and hours.

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The degree of correlation is measured by the correlation coef�icient, most frequently designated as r. A related measure, r2, is often used to assess the “goodness of �it” between the data and the regression line. The r2 �igure can vary from 0 to 1. An r2 close to 0 would indicate that the regression line does not describe the data. That is, the regression line is nearly horizontal, and little of the variation in Y is explained by the variation in X. If the regression line is very descriptive of the data, the r2 will be close to 1. Such is the case for the above example of electricity cost estimation. Recall that the regression output showed an r2 of 0.886. Thus, 88.6% of the variation in electricity costs could be explained by hours of activity.

Reliability Because a regression equation will not result in a perfect �it on the data observations, a measure of variability in the data is necessary with respect to the regression equation. The standard error of the estimate (Se) is a measure of the deviation between the actual observations of Y and the values predicted by the regression equation. In other words, Se gives an estimate of the amount by which the actual observation might differ from the estimate. For our example of electricity costs, the regression output showed an Se of 67.08, labeled as “Std Err of Y Est.”

Statistical data often form a pattern of distribution designated as a normal distribution. In a normal distribution, data can be plotted as a smooth, continuous, symmetrically bell-shaped curve with a single peak in the center of distribution. We will assume that the cost data in this section are normally distributed. A table of probabilities for a normal distribution shows that approximately two-thirds of the data (more precisely, 68.27%) lie within plus and minus one standard deviation of the mean. In our example, then, approximately two-thirds of the cost observations should lie within plus and minus one standard error of the estimate of the line of regression, or between $67.08 above the line of regression and $67.08 below it. To understand how this works with our data, examine the plot in Figure 6.12 of differences between the actual cost and predicted cost.

Figure 6.12: Graph of differences

An interrelationship exists between r2 and Se. For example, as the deviations between actual cost and predicted cost decrease, our measure for “goodness of �it” (r2) increases in amount and Se decreases in amount. That is, the

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higher the r2, the lesser the deviation, the higher the correlation, and the closer actual observations snug the line of regression. The signi�icance of this interrelationship is that the higher the r2 and the lower the standard error of the estimate, the more reliable is our estimate of b (the variable cost per hour).

Sources of Errors The cost equation derived from a set of data has a certain degree of error due to imperfections in the data, data collection, and other processing issues. These imperfections will appear in the difference between an actual cost and a cost predicted by the regression equation. Understanding the sources of errors is a step toward eliminating the impact of those errors on the results. The most common sources of errors fall into one of the following three categories: (1) major errors in the original data, (2) errors in keying data, and (3) inappropriate measures of activity.

Major errors in the original data are minimized through (1) reviewing the cutoff procedures that separate costs into periods, and (2) examining the data for procedural errors, such as classi�ication of transactions into the wrong account. For errors in keying data and calculation, look for cost outliers (i.e., observations with large differences between the actual cost and the cost predicted by the regression line). If multiple cost drivers are available in the data, try other cost drivers to locate one with a higher r2 value.

Control Limits

From the data given in our example, the �ixed electricity cost is estimated at $200, and the variable electricity cost is estimated to vary at the rate of $10 per hour. For 30 hours of activity, the total cost is estimated at $500. This is a predicted cost, however, and it is unlikely that the actual cost will be precisely $500. Because some variation in cost can be expected, management should establish an acceptable range of tolerance. Costs that lie within the limits of variation can be accepted. Costs beyond the limits, however, should be identi�ied and investigated.

In deciding upon an acceptable range of cost variability, management may employ the standard error of the estimate discussed earlier. Recall that a table of probabilities for a normal distribution shows that approximately two-thirds of the data lie within plus and minus one standard error of the estimate of the regression line. For the electricity cost illustration, the standard error of the estimate amounts to $67.08. At 40 hours of activity, for example, the cost is expected to lie between $532.92 and $667.08 about two-thirds of the time:

Upper Limit (+1 Standard Error)

Lower Limit (−1 Standard Error)

Regression prediction [$200 + ($10 × 40)]

$600.00 $600.00

Standard error of the estimate +67.08 −67.08

$667.08 $532.92

If more tolerance is permitted for control purposes, the limits may be extended. For instance, a 95% probability (also known as a con�idence interval) occurs for a range of costs of plus and minus 1.96 standard deviations. From the data given, the 95% con�idence interval is for a cost range between $468.52 and $731.48 at 40 hours of activity [$600 plus and minus $131.48 (1.96 × $67.08)]. Management must make a decision by balancing two alternatives:

1. A relatively narrow range of cost variation with a relatively low probability of a cost being within the zone 2. A relatively wide range of cost variation with a relatively high probability of a cost being within the zone

In other words, the wider the range, the fewer the costs that will be considered for investigation and the higher the likelihood that waste and inef�iciencies will go uncorrected.

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Multiple Regression

In many situations, more than one factor will be related to cost behavior. Electricity costs in our example above may vary not only with changes in the hours of activity but also with the number of people using the building, temperature changes, or other cost drivers. Or, telephone service costs may be a function of the basic monthly charge, in-state long distance calls, out-of-state long distance calls, and features such as call waiting or call forwarding. Insofar as possible, all factors that are related to cost behavior should be brought into the analysis. This will provide a more effective approach to predicting and controlling costs. In simple regression only one factor is considered, but in multiple regression several factors are considered in combination. The basic form of the multiple regression model is:

Y = a + b1X1 + b2X2 + . . . . . + bmXm

The Xs represent different independent variables, and the as and bs are the coef�icients. Any b is the average change in Y resulting from a one-unit change in the corresponding Xi. Output from a multiple regression analysis with three independent variables might look like the following:

Multiple Regression Output

Constant 995

Std err of Y est 146

R2 0.724

No. of observations 19

X1 X2 X3

X coef�icient(s) 0.735 0.121 0.885

Note that with multiple regression, the “goodness of �it” measure uses a capital R rather than the lower case r we saw with simple regression. Also, note that there are three X coef�icients given for the three independent variables. These represent b1, b2, and b3.

Sometimes a factor affecting the amount of cost is not (or only partially) quantitative in nature. For example, bank charges for various services may be different for senior citizens than for people under 65 years of age. A multiple regression model will have one independent variable that will have a value of 1 for senior citizens and 0 for other customers. These variables are called “dummy variables.”

Another concern in using a multiple regression model is the potential existence of a very high correlation between two or more independent variables. The variables move so closely together that the technique cannot tell them apart. We call this situation multicollinearity. For example, direct labor hours and direct labor costs would be highly correlated. Multicollinearity is not an issue if we are interested only in predicting the total costs. However, when we need accurate coef�icients, a de�inite problem exists. The coef�icients (the bs) in the model are variable costs for that independent variable, and accurate coef�icients can be used in pricing decisions and cost-volume- pro�it analyses.

Multicollinearity, when severe, will be indicated by one or more of the following symptoms:

1. A coef�icient is negative when a positive one is expected. 2. A coef�icient is insigni�icant which, in theory, should be highly signi�icant. 3. An unreasonably high coef�icient exists that does not make economic sense.

If one or more of the symptoms appear, we need to think through our theory supporting the equation. Remove one of the independent variables that is less critical to the setting. Adding two problem variables together may be a solution in some cases.

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Summary & Resources

Chapter Summary In planning pro�it, management considers sales volume, selling prices, variable costs, �ixed costs, and the sales mix. When the contribution margin is equal to �ixed costs, the company breaks even. A desired pro�it level can be attained when the contribution margin is equal to the �ixed costs plus the desired pro�it before income taxes. Break-even charts or pro�it-volume graphs are visual representations of pro�its or losses that can be expected at different volume levels.

In making plans, management can review various alternatives to see how they will affect pro�it. For example, what will likely happen if the selling price is increased or if the variable cost is decreased? Often a relatively small change in variable cost per unit will have a relatively large effect on pro�it. Prices may be cut to increase sales volume, but this will not necessarily increase pro�it.

Recent developments such as increased automation tend to increase the importance of �ixed costs in the total cost structure. With a relatively high contribution margin ratio and relatively high �ixed costs, a small percentage increase in sales volume can be translated into a substantial increase in pro�its. This principle is known as operating leverage. The reciprocal of the operating leverage factor is the margin of safety.

When more than one product line is sold, the relative proportion of total sales for each product line is known as the sales mix. To maximize pro�it, management will try to maximize the sales of product lines with higher contribution margin ratios. A break-even point and break-even units for each product line can be computed for any given sales mix.

Five methods for identifying variable and �ixed cost behavior are account analysis, the engineering approach, the scattergraph and visual �it method, the high-low method, and regression analysis. In account analysis, the analyst determines the cost behavior of a speci�ic cost by reviewing and interpreting managerial policies with respect to the cost and by inspecting the historical activity of the cost. The engineering approach uses analysis and direct observation of processes to identify the relationship between inputs and outputs and then quanti�ies an expected cost behavior. In the scattergraph and visual �it method, the analyst graphs each observation, with cost on the vertical axis and activity or cost driver on the horizontal axis. Then, the analyst visually and judgmentally �its a line to the data. The Y-intercept of the line is the estimate of �ixed cost, and the slope of the line is the estimate of variable cost per unit. The high-low method is a simple method in which the rate of cost variability is determined from data taken only at the high and low points of a range of data. Regression analysis �its a line to the cost and activity data using a statistical approach.

Key Terms

account analysis A method of estimating �ixed and variable costs by classifying accounts into one of these two categories.

break-even analysis An approach that examines the interaction of factors that in�luence the level of pro�its.

break-even chart A graph showing cost and revenue functions together with a break-even point.

break-even point The point where total revenue equals total costs.

con�idence interval A range with a speci�ied probability of including the parameter of interest.

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contribution margin ratio Contribution margin divided by total sales revenue.

correlation analysis Involves the goodness of �it in the relationship between costs and activity as identi�ied by the regression line.

cost estimation Determining expected or predicted costs.

cost-volume-pro�it (CVP) analysis An approach that examines the interaction of factors that in�luence the level of pro�its.

dependent variable The item one is attempting to estimate or predict from one or more other variables.

engineering approach An approach that uses analysis and direct observation of processes to identify the relationship between inputs and outputs and then quanti�ies an expected cost behavior.

high-low method An approach for estimating costs that uses only two data points—the highest and the lowest activity levels.

independent variable The item that is being used to predict or estimate another item.

least squares method A statistical method for estimation that derives a regression line by minimizing the squared distances between the line and the data points.

linear regression A method of regression analysis that uses a straight line to �it the data.

margin of safety The difference between sales revenue and the break-even point.

multicollinearity Existence of high correlation between two or more independent variables.

multiple regression Regression analysis using more than one independent variable.

normal distribution Data that can be plotted as a smooth, continuous, symmetrically bell-shaped curve with a single peak in the center of the data.

operating leverage Using �ixed costs to obtain higher percentage changes in pro�its as sales change.

pro�it-volume (P/V) graph A break-even chart that uses pro�its for the vertical axis.

regression analysis A statistical approach that �its a line to the cost and activity data using the least squares method.

regression line The cost function obtained from using regression analysis.

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sales mix A combination of sales proportions from the various products.

scattergraph and visual �it An approach to estimating �ixed and variable costs by visually obtaining a line to �it data points.

standard error of the estimate A measure of the deviation between the actual observations of the dependent variable and the values predicted by the regression equation.

Problem for Review Rodbell Roo�ing Co. installs residential roofs throughout Alabama. In 2018, the company installed 145 roofs at an average price of $30,000 per roof. Variable costs were $18,000 per roof, and total �ixed costs were $1,200,000.

In 2019, �ixed costs are expected to increase to $1,350,000, while variable costs should decline to $16,000 per roof due to a new source of materials and supplies. The company forecasts a 20% increase in number of installations for 2019; however, the average price charged to customers is not planned to change.

The 2020 forecast is for 20 more installations than in 2019, and �ixed costs are expected to jump by $240,000 more than in 2019. The average price and variable cost is not expected to change from 2019.

Questions:

1. For 2018, calculate the number of installations needed to break even. 2. For 2019, calculate the operating leverage factor. 3. What is expected to be the amount of pro�it change from 2019 to 2020?

Solution:

1. For 2019, the break-even point:

2. For 2019, the operating leverage factor:

Number of installations in 2019 = 1.2 × 145 = 174

Unit contribution margin in 2019 = $30,000 – $16,000 = $14,000

Total contribution margin in 2019 = 174 × $14,000 = $2,436,000

Pretax pro�it in 2019 = $2,436,000 – $1,350,000 = $1,086,000

Operating leverage factor in 2019 = $2,436,000 ÷ $1,086,000 = 2.24

3. Amount of pro�it change from 2019 to 2020:

Additional contribution margin =

20 additional installations × $14,000 contribution margin per unit = $280,000

Additional �ixed cost = $240,000

Additional pro�it = $280,000 – $240,000 = $40,000

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Questions for Review and Discussion 1. When the total contribution margin is equal to the total �ixed cost, is the company operating at a pro�it or at

a loss? Explain. 2. If the total �ixed cost and the contribution margin per unit of product are given, explain how to compute the

number of units that must be sold to break even. 3. Describe the components of a break-even chart. 4. Can two break-even points exist? If so, describe how the revenue and cost lines would be drawn on the

break-even chart. 5. Is it possible to compute the number of units that must be sold to earn a certain pro�it after income tax?

Explain. 6. What does the slope of the P/V graph represent? 7. De�ine margin of safety. How is a margin of safety related to operating leverage? 8. Why is cost estimation so important? 9. Describe the two major steps involved in the account analysis method of cost estimation.

10. Describe the steps for preparing an estimate of �ixed and variable costs using the scattergraph and visual �it method.

11. Describe the high-low method of cost estimation. 12. What is r2? What range of values can it take? 13. What is multiple regression? When would it be used in cost estimation? 14. What is multicollinearity? How does it pose problems in multiple regression analysis?

Exercises 6-1. Break-Even Point and Change in Fixed Costs. Schloss Spirits sells each bottle of a particular whiskey for $50. The variable costs are 60% of revenue. The �ixed costs amounted to $120,000 per year. Last year the store sold 7,500 of these bottles. During the current year, Schloss plans to sell 8,700 bottles, and �ixed costs will increase by $36,000.

Questions:

1. What was the break-even point last year? 2. This year, the break-even point will increase by how many bottles?

6-2. “What if” Prices. The following budget numbers from Cann Corporation were provided by the controller, Sue Ann Leonard:

Sales (12,000 units) $540,000

Variable costs (360,000)

Fixed costs (180,000)

Net income $ 0

Questions:

1. If Cann can reduce variable costs by $4 per unit, what price must be charged to earn $90,000? Assume that 12,000 units will still be sold.

2. If Cann can increase sales revenues by spending $20,000 more on advertising, what price must be charged to earn $120,000? Assume that 12,000 units will still be sold.

6-3. Changes to Break-Even Variables. Gerald Ruby & Co. sees its pro�it picture changing. Variable cost will increase from $4 per unit to $4.50. Competitive pressures will allow prices to increase only by $0.30 per unit to $8. Fixed costs ($200,000) and sales volume (60,000 units) likely will remain constant.

Questions:

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1. What will likely happen to the break-even point? 2. To maintain the same pro�it level, �ixed costs will have to change to what amount? 3. To maintain the same pro�it level, volume will have to change to what amount?

6-4. Break-Even Point and Target Pro�it. The Marla & Kerry Theatre Group operates �ive discount movie theatres in the Chicago area. All tickets are priced at $1.75. Variable costs are $1.10 per patron, and the �ixed costs per year total $900,000. The �ixed costs include concessions, but the variable costs do not. The concessions earn an average contribution margin of $0.60 per patron.

Questions:

1. How many patrons are required to break even? 2. If 800,000 patrons are expected for the year, what ticket price would be necessary to earn a pro�it of

$150,000?

6-5. Effects of Changes in Volume and Costs. Marnie’s Boutique sells umbrellas that have a contribution margin ratio of 35% of $440,000 annual sales (40,000 units). Annual �ixed expenses are $95,000.

Questions:

1. Calculate the change in net income if sales were to increase by 850 units. 2. The store manager, Laura Stein, believes that if the advertising budget were increased by $18,000, annual

sales would increase by $75,000. Calculate the additional net income (or loss) if the advertising budget is increased.

3. Laura Stein believes that the present selling price should be cut by 15% and the advertising budget should be raised by $12,000. She predicts that these changes would boost unit sales by 30%. Calculate the predicted additional net income (or loss) if these changes are implemented.

6-6. Break-Even Point and Pro�its. Sheila Hershey has noticed a demand for small tables for personal computers and printers. Retail of�ice furniture outlets are charging from $400 to $600 for a table. Sheila believes that she can manufacture and sell an attractive small table that will serve the purpose for $210. The cost per table of materials, labor, and variable overhead is estimated at $110. The �ixed costs consisting of rent, insurance, taxes, and depreciation are estimated at $25,000 for the year. She already has orders for 180 tables and has established contacts that should result in the sale of 150 additional tables.

Questions:

1. How many tables must Sheila make and sell to break even? 2. How much pro�it can be made from the expected production and sale of 330 tables? 3. How many tables are needed for a pro�it objective of $11,000?

6-7. Target Pro�it and Taxes. Gris, Inc. had the following results for October:

Fixed Variable Total

Sales ($200 per unit) $600,000

Cost of sales $180,000 $360,000 540,000

Net income before taxes $ 60,000

Taxes (40%) 24,000

Net income after taxes $ 36,000

Question:

For net income to be $60,000 after taxes in November, what will the sales in units need to be?

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6-8. Computation of Fixed Cost and Price. Matlin’s Ranch offers horseback riding lessons for children. “Wild Bill” Matlin has �igured that break-even revenues are $560,000, based on a contribution margin ratio of 35% and variable costs per rider of $6.50.

Questions:

1. Compute the total �ixed costs. 2. Compute the fee charged per rider.

6-9. Contribution Margin Ratio. In 2018, Simon’s Barber Shop had a contribution margin ratio of 22%. In 2019, �ixed costs will be $41,000, the same as in 2018. Revenues are predicted to be $250,000, a 25% increase over 2018. Simon’s Barber Shop wishes to increase pretax pro�it by $8,000 in 2019.

Question:

Determine the contribution margin ratio needed in 2019 for Simon’s Barber Shop to achieve its goal.

6-10. Multiple Products. Bettsak Security Systems installs three types of auto alarm systems. Last year, �ixed costs totaled $315,000, and target pretax pro�it was $190,000. Additional information for the past year was as follows:

Type of Alarm Unit Contribution Margin Number Sold

Best $50 1,000

Better 45 1,100

Good 38 1,300

Question:

Determine the sales volumes (number of alarm systems of each type) that were needed to achieve the target pro�it for the past year.

6-11. Multiple Product Analysis. The South Division of Euclid Products, Inc. manufactures and sells two grades of canvas. The contribution margin per roll of Lite-Weight canvas is $25, and the contribution margin per roll of Heavy-Duty canvas is $75. Last year, this division manufactured and sold the same amount of each grade of canvas. The �ixed costs were $675,000, and the pro�it before income taxes was $540,000.

During the current year, 14,000 rolls of Lite-Weight canvas were sold, and 6,000 rolls of Heavy-Duty canvas were sold. The contribution margin per roll for each line remained the same; in addition, the �ixed cost remained the same.

Questions:

1. How many rolls of each grade of canvas were sold last year? 2. Assuming the same sales mix experienced in the current year, compute the number of units of each grade

of canvas that should have been sold during the current year to earn the $540,000 pro�it that was earned last year.

6-12. Fixed Cost Increase and Margin of Safety. Joey Fink, the owner of Kay Manufacturing Company, is concerned about increased �ixed manufacturing costs. Last year, the �ixed manufacturing costs were $600,000. This year, the �ixed manufacturing costs increased to $750,000. The �ixed selling and administrative costs of $540,000 were the same for both years. The company operated in both years with an average contribution margin ratio of 30%. It earned a pro�it before income taxes of $910,000 last year.

Questions:

1. What was the sales revenue last year?

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2. How much would sales revenue have had to increase this year for the company to have earned the same pro�it as it did last year?

3. Calculate the margin of safety for each year. Which year was better?

6-13. Cost Segregation by High-Low Method. Betty Grus sells various ceramics and crafts at �lea markets in the area. She uses a motor home for transportation and lodging. She recognizes that travel costs with the motor home are relatively high and would like to estimate costs so that she can decide how far she can travel and still operate at a pro�it.

Records from one round trip of 150 miles show that the total cost was $320. On another round trip of 340 miles, the total cost was $472. A local round trip of 50 miles cost $240. She is convinced that the time and cost for trips of more than 300 miles are too high unless the sales potential is very high.

Question:

Calculate the variable cost per mile and the �ixed cost per trip by the high-low method.

6-14. Cost Prediction With Account Analysis. Muhammed Alley, a bowling alley located in Louisville, had the following costs during a recent month:

Expenses Total Amount Classi�ication

Wages $44,500 Variable

Supplies 9,200 Variable

Rent 12,000 Fixed

Advertising 3,700 Fixed

Utilities 20,000 Variable

Depreciation 11,300 Fixed

During the month, 1,593 customers patronized the bowling alley. Next month, 1,780 customers are expected to come.

Question:

Estimate Muhammed Alley’s total cost for next month.

6-15. Visual Fit and the Extremes. The cost of utilities at Harpaz Supply Store varies according to hours of operation, but a portion of the cost is �ixed. Hour and cost data for several months are given as follows:

Hours Total Cost

100 $ 800

200 700

300 800

400 900

500 1,000

600 1,100

700 1,200

800 1,300

900 1,600

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Questions:

1. Fit a line to the data by visual �it. 2. Using your line, compute the variable cost per hour and the �ixed cost per month. 3. Determine the variable cost per hour and the �ixed cost per month by the high-low method. 4. In which of the foregoing two variable costs per hour and two �ixed cost numbers do you have more

con�idence for making business decisions? Explain.

6-16. Cost Estimation and Break-Even Point. Water is supplied to Lake Tillem Township by pumping water from a lake to a storage tank at the highest elevation in town, from which it then �lows to the customers by gravity. The town council notes that the costs to pump water vary to some extent by the number of gallons pumped, but �ixed costs are also included in the pumping costs. A record of gallons consumed per month and total pumping cost per month is as follows:

Gallons Consumed (000) Pumping Cost Gallons Consumed (000) Pumping Cost

1,750 $29,100 1,800 $29,700

1,900 30,800 2,300 35,900

2,150 34,000 2,000 31,800

2,050 32,600 1,500 25,500

In addition to pumping costs, 1.1 cents in variable costs and $75,000 in �ixed costs are incurred to supply water to the residents. Lake Tillem charges its residents 4.6 cents per gallon consumed.

Questions:

1. Use the high-low method to obtain a cost function for Lake Tillem Township’s pumping costs. 2. At what level of water consumption would Lake Tillem Township break even?

6-17. Con�idence Interval. The Greenbelt Fire Department wants to examine the costs of operating its �ire engines (fuel, maintenance, etc.). Seventeen months of data were obtained on these costs as well as on the number of trips made (actual �ires, practice drills, and false alarms). A regression of costs on the number of trips yielded the following results:

Mean of X 22

Constant 11,000

r2 .59

X coef�icient 950

Se 3,125

Question:

Develop a 95% con�idence interval for the predicted cost if 18 trips are made.

6-18. Scattergraph and Visual Fit. Lewyn Financial Advisors uses the scattergraph and visual �it method to estimate its utilities costs. After plotting data for the past 15 weeks, the controller drew a cost function and saw that it hit the vertical axis at $6,500. He then picked a point on the cost function corresponding to $9,700 and 800 hours of activity for further analysis.

Question:

What amount of utilities cost would the controller predict for 920 hours of activity?

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Problems 6-19. CVP With Changes in Prices and Costs. Data with respect to a basic product line sold by Yozef Music Stores are as follows:

Selling price per unit $50

Cost per unit 30

Contribution margin per unit $20

The �ixed costs for the year are $360,000. The income tax rate is 40%.

Questions:

1. Determine the number of units that must be sold in order to break even. 2. If a pro�it before income taxes of $270,000 is to be earned, how many units of product must be sold? 3. If a pro�it after income taxes of $180,000 is to be earned, how many units of product must be sold? 4. If the selling price per unit is reduced by 10%, how many units must be sold to earn a pro�it of $8 per unit

before income taxes? 5. Assume that the selling price remains at $50. How many units must be sold to earn a pro�it of $8 per unit

before income taxes if the variable cost per unit increases by 10%? 6. Why does a 10% decrease in the selling price have more effect on the contribution margin than a 10%

increase in the variable unit cost?

6-20. Determining a Selling Price. Eileen Stewart and her brother, Ralph, would like to make extra money when they have time away from their studies at Pepper Pike University. They are skilled in carpentry and plan to build and sell rustic lawn chairs. Estimates of the cost to make and sell each chair are as follows:

Lumber and other materials $30

Labor (wages to student helpers) 15

Commission to stores selling the chairs 8% of selling price

Radio and direct mail advertising is estimated at $5,000. A pickup truck to transport the chairs can be rented for $1,000. Eileen and Ralph each plan to earn a pro�it of $4,500 for their efforts. This amount was calculated by considering what they could earn if they used their time in another way.

Eileen believes that 800 units can be made and sold. Ralph is more optimistic and believes that 900 units can be made and sold. Both agree that the price must be less than the commercial price of $98 per chair.

Questions:

1. Compute a selling price to obtain the desired pro�it if 800 chairs are sold. 2. Compute a selling price to obtain the desired pro�it if 900 chairs are sold. 3. Assume that the selling price is based on the sale of 800 chairs but that 900 chairs are actually sold. How

much additional pro�it will each of them make? 4. Assume that the selling price is based on the sale of 800 chairs but that only 700 chairs are actually sold.

Will Eileen and Ralph achieve their pro�it objectives? Explain.

6-21. Break-Even Comparisons. Dan and Elaine Miller, owners of Spira Motel, want to know potential maximum pro�its and the break-even occupancy for the operation. The motel is a low-cost operation to attract business people and families traveling on low budgets. A study of costs shows a difference between summer and winter operations. Swimming pool maintenance adds to summer costs while utilities (heat and light) add to winter costs. Variable costs have been determined on the basis of cost per room occupied per day and are as follows:

Cost per Room

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Cost per Room

Laundry $1.90

Heat and light (summer) 1.10

Heat and light (winter) 2.20

Repairs .75

Supplies 1.60

Taxes and insurance 3.60

Maintenance 1.50

Pool maintenance (summer only) .60

Fixed costs per month have been estimated as follows:

Housekeeping $14,000

Management 17,000

Desk service 2,700

Repairs and maintenance 1,600

Taxes 1,430

Insurance 1,120

Heat and light 1,000

Depreciation—motel 26,000

Depreciation—furnishings 12,500

Pool maintenance and personnel (summer only) 1,800

The motel has 300 rooms and charges $40 per room per night. Summer is relatively short and is de�ined as June, July, and August. All other months are designated as winter months. A month consists of 30 days for making calculations. Maximum capacity for a month would be 9,000 room days (300 rooms × 30 days).

Questions:

1. Compare the maximum operating net incomes that can be expected for a summer month versus a winter month.

2. How do the break-even points (in terms of room days) compare for summer versus winter? Also, state the break-even points as percentages of total capacity.

3. Based on advance reservations and normal expectations, the motel plans for 5,000 room days in August. Determine the estimated operating income for August. Also, determine the percentage of capacity expected for August.

6-22. CVP With a Sales Mix. Sharon Arts Festival rents four types of booths to exhibitors, providing them with space, tables, chairs, and some pre-festival publicity. Stan Harris, the festival organizer, has indicated that the booth rental fee is three times the amount of variable costs associated with the particular type of booth. Harris expects that the festival will incur �ixed costs of $9,200. The number of booths expected to be rented this year, as well as the related variable costs, are:

Booth Size Variable Cost per Booth Number of Booths

8' × 10' $25 15

10' × 12' 28 10

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Booth Size Variable Cost per Booth Number of Booths

10' × 15' 30 20

15' × 15' 35 5

Question:

Assuming that booths are rented according to the expected mix, determine the number of each type of booth that needs to be rented for the festival to break even.

6-23. Pricing to Break Even. Senkfor Township is inaugurating a youth soccer program. Estimates are that 70 children between the ages of 7 and 9 will enroll and that six teams will be formed. The program will be staffed by volunteer coaches, referees, and administrative personnel, so the only out-of-pocket costs involve the following:

Shirts $4.10 per shirt plus $20 screening charge

Balls $85 (total for all teams)

Goals $120 (total for all teams)

Cones $70 (total for all teams)

Shin guards $9.50 per pair (i.e., $9.50 per player)

The price obtained for the shirts presumes two colors (shirt color and lettering). The program director, Leslie Stewart, would like very colorful shirts. She has learned that a “rainbow” pattern having several additional colors would cost $1 extra per shirt plus an additional $100 screening charge. The township’s recreation director has asked Leslie to determine how much to charge each child so that the soccer program fully covers its costs.

Question:

If the “rainbow” pattern shirt is selected, what fee per child should Leslie suggest to the recreation director?

6-24. High-Low and Visual Fit. Kathleen Otwell, an insurance claims adjuster for Shoen�ield Casualty Company, notes that the cost to process a claim has both �ixed and variable components. She believes that she can estimate costs more accurately if she can separate the costs into their variable and �ixed components. The monthly record of the number of claims and the costs for the past year is as follows:

Month Number of Claims Cost

January 120 $20,600

February 134 20,670

March 142 20,710

April 156 20,780

May 160 20,800

June 220 21,100

July 250 21,250

August 330 21,650

September 114 20,570

October 280 21,400

November 274 21,370

December 230 21,150

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Questions:

1. Estimate the variable costs per claim and the �ixed costs per month by the high-low method. 2. Estimate the variable costs per claim and the �ixed costs per month by the scattergraph and visual �it

method. 3. Explain the differences between the two methods in the variable costs per claim and the �ixed costs per

month.

6-25. Account Analysis and Cost Prediction. A listing of accounts prepared by Cenker Video Arcade revealed the following data for October, during which time 9,500 video games were played:

Account Costs

Rent $1,600

Depreciation on equipment 70

Wages for part-time help 1,650

Insurance 120

Prizes 200

Supplies 85

Manager’s salary 2,000

Electricity 500

Telephone 100

Heat 250

Advertising 150

Question:

Estimate the cost for November, when 11,000 video games are expected to be played.

6-26. Control Limits. Harry Czinn, supervisor of the Maintenance Department at Severn Airport, has estimated that the department’s power cost varies at the rate of $0.80 per hour and that the �ixed cost for the month is $500. The standard error of the estimate from the line of regression is $60. Czinn investigates the cost of any month that is more or less than one standard deviation from the line of regression. Actual monthly hours and costs for the last year are as follows:

Month Hours Cost

January 600 $ 980

February 550 970

March 600 960

April 650 1,050

May 550 940

June 500 980

July 700 1,180

August 800 1,150

September 750 1,050

October 900 1,330

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Month Hours Cost

November 850 1,180

December 450 900

Questions:

1. Using the equation Y = a + b (X), what should be the cost for each month? 2. Calculate the difference between the actual cost and the predicted cost for each month. 3. Plot the differences in part (2) on a graph, and draw lines that represent the plus or minus one standard

error of the estimate. 4. For which month or months should the cost be investigated? Why?

6-27. Cost Estimation With Multiple Regression. Saylush Painters has gathered data on a random sample of 20 paint jobs. The company’s accountant, Fred Blair, feels that labor costs are related to the surface area painted (X1 = sq. ft. of surface area) and the length of the trim work needed to complete a paint job (X2 = edge trim, in feet). A multiple regression analysis was performed, and the results are as follows:

R2 .83

Constant 102.50

Coef�icient of X1 .127

Coef�icient of X2 .214

Standard error of estimate 77.23

Questions:

1. Does the regression line provide a good �it to the data? Brie�ly explain. 2. How much does it cost to paint an extra 400 sq. ft. of surface? 3. How much does it cost to get set up for a painting job? 4. The cost for a new job needs to be estimated. It will have 8,800 sq. ft. of surface area and 2,900 ft. of edge

trim. What is your estimate?

6-28. Linear Regression and Data Concerns. Larry Beck has a night job at a ballpark. He manages the late night clean-up crew at Nantahalla Field. As a student of the game and of garbage, he has selected a sample of 2018 games for study. The attendance �igures and clean-up costs, as well as output from a regression analysis, are given as follows.

Game Date Attendance Clean-Up Costs

April 28 25,216 $5,677

May 10 32,566 6,381

May 11 19,945 4,219

June 6 26,009 5,422

June 10 39,856 6,722

June 31 34,561 6,106

July 15 19,723 4,846

July 19 25,924 5,533

July 25 42,119 6,311

July 29 38,923 6,722

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Game Date Attendance Clean-Up Costs

August 21 26,912 4,909

August 23 21,902 4,771

September 5 36,205 6,508

September 7 26,931 5,456

September 22 19,636 4,323

Regression Output:

Constant 2642.63

Std err of Y est 339.05

r2 0.85125

No. of observations 15

X coef�icient(s) 0.10143

Questions:

1. What amount of clean-up cost would Beck budget for the 2019 opening day game, which is expected to have an estimated crowd of 50,000 fans?

2. How would you caution Beck about using the estimate obtained in part (1)—i.e., what concerns would you have about the data?

Case: Mendel Paper Company

Mendel Paper Company produces four basic paper product lines at one of its plants: computer paper, napkins, place mats, and poster board. Materials and operations vary according to the line of product. The market has been relatively good. The demand for napkins and place mats has increased with more people eating out, and the demand for the other lines has been growing steadily.

The plant superintendent, Marlene Herbert, while pleased with the prospects for increased sales, is concerned about costs:

“We hear talk about a paperless of�ice, but I haven’t seen it yet. The computers, if anything, have increased the market for paper. Our big problem now is the high �ixed cost of production. As we have automated our operation, we have experienced increases in �ixed overhead and even variable overhead. And, we will have to add more equipment since it appears that we need even more plant capacity. We are operating over our normal capacity as it is.

“The place mat market concerns me. We may have to discontinue printing the mats. Our specialty printing is driving up the variable overhead to the point where we may not �ind it pro�itable to continue with that line at all.”

Cost and price data for the next �iscal quarter are as follows:

Computer Paper Napkins Place Mats Poster Board

Estimated sales volume in units 30,000 120,000 45,000 80,000

Selling prices $14.00 $7.00 $12.00 $8.50

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Computer Paper Napkins Place Mats Poster Board

Materials costs 6.00 4.50 3.60 2.50

Variable overhead includes the cost of hourly labor and the variable cost of equipment operation. The �ixed plant overhead is estimated at $420,000 for the quarter. Direct labor, to a large extent, is salaried; the cost is included as a part of �ixed plant overhead. The superintendent’s concern about the eventual need for more capacity is based on increases in production that may reach and exceed the practical capacity of 60,000 machine hours.

In addition to the �ixed plant overhead, the plant incurs �ixed selling and administrative expenses per quarter of $118,000.

“I share your concern about increasing �ixed costs,” the supervisor of plant operations replies. “We are still operating with about the same number of people we had when we didn’t have this sophisticated equipment. In reviewing our needs and costs, it appears to me that we could cut �ixed plant overhead to $378,000 a quarter without doing any violence to our operation. This would be a big help.”

“You may be right,” Herbert responds. “We forget that we have more productive power than we once had, and we may as well take advantage of it. Suppose we get some hard �igures that show where the cost reductions will be made.”

Data with respect to production per machine hour and the variable cost per hour of producing each of the products are given as follows:

Computer Paper Napkins Place Mats Poster Board

Units per hour 6 10 5 4

Variable overhead per hour $9.00 $6.00 $12.00 $8.00

“I hate to spoil things,” the vice-president of purchasing announces. “But the cost of our materials for computer stock is now up to $7. Just got a call about that this morning. Also, place mat materials will be up to $4 a unit.”

“On the bright side,” the vice-president of sales reports, “we have �irm orders for 35,000 cartons of computer paper, not 30,000 as we originally �igured.”

Questions:

1. From all original estimates given, prepare estimated contribution margins by product line for the next �iscal quarter. Also, show the contribution margins per unit.

2. Prepare contribution margins as in part (1) with all revisions included. 3. For the original estimates, compute each of the following:

a. Break-even point for the given sales mix. b. Margin of safety for the estimated sales volume.

4. For the revised estimates, compute each of the following: a. Break-even point for the given sales mix. b. Margin of safety for the estimated sales volume.

5. Comment on Herbert’s concern about the variable cost of the place mats.

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Practice Problems in Action

Watch the videos below for a step-by-step tutorial on how to solve the following problem using Excel. The videos are best viewed in full-screen mode. For a transcript of the directions included in these tutorial videos click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/BUS630_2e/Chapter-6_Tutorial-Transcript_FINAL.pdf) .

Problem In this example, the establishment sells three products: burgers, fries, and drinks. The problem gives sales and cost data to �ind contribution margin, break-even points, and margin of safety. We will use a spreadsheet to determine the answers.

Cost and price data for the next �iscal quarter are as follows:

Burgers Fries Drinks

Estimated sales volume in units 37,250 27,940 35,200

Selling price $7.00 $2.50 $2.00

Product costs $3.25 $1.18 $0.74

Data, with respect to production per machine hour, and the variable cost per hour of producing each of the products are given as follows:

Burgers Fries Drinks

Units per hour 30 25 30

Variable overhead per hour $9.75 $8.01 $6.02

Variable overhead includes the cost of hourly labor and the variable cost of restaurant equipment operation. The �ixed restaurant overhead is estimated at $84,600 for the quarter. Direct labor, to a large extent, is salaried; the cost is included as a part of �ixed restaurant overhead.

In addition to the �ixed restaurant overhead, the establishment incurs �ixed selling and administrative expenses of $46,900 per quarter.

Questions 1. Prepare estimated contribution margin by product line and show contribution margin by unit for the next

�iscal quarter. 2. Compute break-even point for the given sales mix. 3. Compute margin of safety for the estimated sales volume.

Tutorial Video 1: Setting up the spreadsheet and calculating the contribution margin

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Video 2: Calculating the contribution margin per unit

Video 3: Calculating the break-even point

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Video 4: Calculating the margin of safety

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Learning Objectives

After studying Chapter 7, you will be able to:

Identify the major elements of a �inancial planning and control system.

De�ine responsibility accounting, including cost, pro�it, and investment centers.

Explain the major purposes of budgeting.

Identify the major human behavior factors that affect budgets and the budgeting process.

Understand the master budget components and their relationships.

Identify independent and dependent budget variables, and understand the basic format and calculation sequences necessary for preparation of budgets and supporting schedules.

Understand the role of �lexible budgeting, project budgeting, and probabilistic budgeting in planning and control.

Prepare and format schedules for all elements of the master budget.

7 Budgeting for Operations Management

Wavebreakmedia/iStock/Thinkstock

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Explain the impact on budgeting of JIT systems, activity-based costing, and �lexible manufacturing.

Budgeting: The Negatives and the Positives!

If you mention the words plans or budgets to Ann Davis, President of Internet Pathways, you get a reaction ranging from disdain to outright hostility. She has been heard to say:

“How can I plan? Things always change so fast!” “My business isn’t suited to anything so formal. My managers and I need to be �lexible, fast on our feet, and ready to change direction overnight, if we have to do so.” “The budget always says we can’t do it. I just say, ‘Do it!’” “The budget reports tell me where I’ve been, never where I’m going.” “That’s the accountant’s budget; it doesn’t tell me what my problems are and what to do about them!” “We can’t wait for approvals and reports. Budgets hold us back!”

Ann even has a coffee cup with “Budgets Are For Wimps!” printed on it. She believes that intuition and drive, not reports, got the company to where it is today.

“The easiest way to lose our edge is to start acting like paper shuf�lers!” she exclaims. Each of her comments has some truth in it; however, the comments together re�lect serious de�iciencies in the �irm’s management process—little or no planning, and little ability to measure performance.

A close friend says plans and budgets strike terror in Ann because her “style” is threatened. She likes to operate quickly, often keeping others in the dark. The friend says that she’s afraid to admit that she has little idea where the company is going.

Recently, a situation arose in which Ann thought employees were making too many “bad calls” on key decisions. She was surprised by the responses she got when she asked several department managers what was wrong. Each complained about lack of direction at the top, how management kept changing its mind, that there was no plan of action, and how employees felt they could not judge how each of them, and the company as a whole, was progressing.

A simple concept is a key to budgeting: Planning is not deciding what to do in the future; it is deciding what to do now to assure a future. This chapter discusses concepts, tools, and processes used in a planning and control system and illustrates an integrated master budget.

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7.1 Budgeting: A Planning and Control System Planning and control comprise an overall management system. Planning can be viewed as a framework for formulating short-term and long-term goals and objectives, predicting potential results under alternative ways of achieving them, and deciding how to attain the desired results. Control is the process of using feedback on actual operating results to compare to the plan, to evaluate performance in achieving the plans and goals, and to make changes. A budget is a plan showing what and how resources are to be used over a speci�ied time period.

A plan, act, control, and evaluate cycle is shown in Figure 7.1. The master plan is prepared, transactions are recorded, reports are prepared and analyzed, and the plan is reviewed and updated.

Figure 7.1: The planning and control cycle

A mission statement sets the purpose of the organization. Goals and objectives are statements about the organization’s future position and its long-term direction. They describe speci�ic performance targets within certain timeframes. A pro�it goal might be, for example, to earn an annual 15% aftertax return on shareholders’ equity or to generate sales of $1 billion by 2021. Once goals (direction and motivations) and objectives (quanti�ied performance targets) are set, action plans can be de�ined. The budgeting process determines the inputs needed to achieve the forecast outputs.

A planning and control system includes tools, methods, and attitudes. The following set of common elements appears:

Strategic planning process. This long-range planning effort de�ines the �irm’s mission (why the �irm exists), the long-range goals (what level of achievement it expects), and a strategic plan (what markets, price policies, resource needs, and production capabilities the �irm will have). Business plan and personal goal setting. Creating the annual business plan is the task of evaluating the �irm’s strengths, weaknesses, opportunities, and tactics to build �irm-wide priorities for the coming year. Also, each manager develops a personal set of goals and a plan of achievements that are consistent with the �irm’s business plan. Planning process and timetable. A budgeting schedule includes when to start the process, submit budgets, and review and approve budgets at various management levels—who does what and when.

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Responsibility accounting system. This is a planning and control system that combines responsibility centers, control reports, and cost drivers. Reward or incentive system. Rewards can provide incentives for managers who achieve their unit’s budget goals and/or MBO (management by objectives) targets. Tying performance to compensation appears to be an increasingly common practice. Financial modeling. Ability to evaluate alternative or “what if ” scenarios is now an expected part of any �inancial planning system. Simulation can test a plan to assess goal achievement and evaluate alternative actions. Participatory budgeting. It is assumed that every manager in the �irm is involved in planning and control. Often, budget objectives are set at the executive level, but budgets are constructed from the bottom up— sometimes called “grass roots” budgeting.

A budget period may be a week, month, quarter, year, or longer. But normally, a master budget is for a year’s activities and is divided into months or quarters. Long-term budgets may be for �ive or more years.

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7.2 Responsibility Accounting Responsibility accounting has no universal de�inition but does link authority and control. A key aspect of responsibility accounting is that managers prepare plans for their areas of responsibility and exert control over those activities by making decisions and evaluating results. A responsibility accounting system brings discipline to planning and control tasks. The same basic elements remain visible in the accounting systems of small �irms as in the sophisticated planning systems of large, complex organizations. The basic elements of responsibility accounting are:

Responsibility center designations—to segment the organization into small sets of similar activities. Control reports—to compare actual versus plan for expenses, revenues, and other �inancial and activity measures, such as cost drivers. Roll-up reporting capability—to summarize lower-level activities at higher levels along responsibility channels.

Strictly speaking, managers put more effort towards managing people who incur costs rather than actually controlling costs themselves. Controllable costs are tied to organizational structure, activities management, and performance assessment.

Responsibility Centers

From a �irm’s perspective, planning and control focus on responsibility centers. A responsibility center is an organizational unit that has a speci�ic manager with authority and control over spending, earning, or investing. Responsibility centers can be subdivided into three groups: investment centers, pro�it centers, and cost centers. Figure 7.2 illustrates these responsibility centers.

Figure 7.2: Responsibility centers: Investment, pro�it, and cost centers

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An investment center is a responsibility center where control exists over costs, revenues, and investments in assets used or managed. Managers must have the authority to acquire or dispose of assets. Typically, divisions of large �irms are considered to be investment centers and are viewed by top management essentially as separate business entities.

A pro�it center is a responsibility center where control exists over generating revenue and incurring its related costs. Often, sales organizations are pro�it centers—with product revenues, cost of sales, and marketing expenses. Managers with product-line responsibility might include both manufacturing and marketing departments. Branch or regional managers often have sales and expense control. The term revenue center can be used where a manager has revenue responsibility but controls few expenses, such as in a regional sales of�ice.

A cost center, or activity center as discussed in Chapter 4, is a responsibility center where control exists over incurring costs. Often, cost centers are de�ined by an organization chart and may be further subdivided into more cost centers if costs and activities can be better linked for cost determination and management purposes. A cost center is the smallest unit of an organization within which costs and activities are measured. Cost center managers control only costs, and as such they are evaluated only on costs, not revenues or pro�its.

Identifying Cost Centers

In many cases, cost centers parallel the boxes on the organization chart. Figure 7.2 illustrates the link between a �irm’s organization and its cost center coding. Activity groupings should be studied before cost centers are de�ined. Logical groupings are often created by a numbering system—de�ining different parts of the organization, levels of management, and superior/subordinates links. For example, the �irst digit indicates a group; the second, a division; the third, a functional area; and the last digit provides even greater detail if needed.

Design of the cost system is critical. If activities are segmented too �inely, too many cost centers are created, and key cost information is subdivided too �inely. However, data aggregation and summarization start here, and a greater danger is losing important cost relationships if cost and activity detail are too summarized. Cost centers de�ined too broadly lose detail needed in later analyses, and this detail can be recreated only at great cost.

Control Reports and Roll-Up Reporting

Control reports are prepared routinely for each cost center for a speci�ic time period. Figure 7.3 is a cost center report from a metal-forming factory. This is from Cost Center 3242 in Figure 7.2 and uses an account numbering system set up to detail the types of costs that will be tracked. This factory has nearly 40 cost centers and uses approximately 400 different expense accounts.

Several points should be made about the control report in Figure 7.3. The breakdown among controllable, semicontrollable, and allocated expenses is an excellent approach to signal which costs and variances are the responsibility of that cost center’s manager. Monthly and year-to-date comparisons of actual to budget costs report the current situation, annual trends, and magnitude and direction of variances from budget. Activity measures, including cost drivers that relate overhead costs to outputs, are reported at the bottom of the report.

Figure 7.3: Example of a cost center control report

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The overall performance of supervisor Kannisoni in controllable and semicontrollable categories was close to budget for September. But because of an extra large administrative allocation in account 6780, the cost center’s total overhead expenses appear to be about $6,000 over budget. While including allocated expenses may be useful for other purposes, it has little bene�icial budget impact and violates a basic responsibility accounting rule: Account for what you control.

Roll-up reporting aggregates results for each higher management level. Middle and upper levels of management receive reports containing summarized results for all cost centers under their control. The report in Figure 7.3 is reviewed by supervisor Kannisoni and his superior. Results from this cost center are summarized at the next higher level—in the control report for the manufacturing manager in Cost Center 3240 from Figure 7.2. All cost centers in Division 2, Pro�it Center 3200, are summarized in the director’s control report. Division 2 is then summarized in Group B vice president’s Investment Center 3000 control report, along with all divisions reporting to the Group B vice president. All responsibility center reports are eventually summarized into one �irm-wide control report for the president.

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7.3 Why Budget? Advantages of budgeting nearly always outweigh the costs and efforts required by the process. Although many reasons exist for budgeting, several key purposes are now discussed.

Formalize the Planning Process. Perhaps the foremost purpose of budgeting is to compel managers to think about the future. This forces them to set goals, consider future problem areas, and formulate strategies. Budgeting motivates managers to anticipate opportunities, problems, and actions, rather than to merely react.

Create a Plan of Action. The planning process brings together ideas, forecasts, resource availability, and �inancial realities to create a course of action to achieve the �irm’s goals and objectives. Build the plan, then use it!

Create a Basis for Performance Evaluation. Actual results lack meaning unless they are compared to some target or a budgeted number. A budget is a benchmark against which actual results are measured and managers’ performances are evaluated. Signi�icant variances between actual and planned require explanations and, often, corrective actions.

Promote Continuous Improvement. Redesigning processes, increasing productivity expectations, eliminating nonvalue-adding activities, and erasing quality problems are integral parts of planning for future performance. The budgeting system is where these improvement processes are quanti�ied and locked into operating plans.

Coordinate and Integrate Management’s Efforts. Budgeting processes open lines of communication within the organization: (1) up and down organizational lines of subordinates and supervisors and (2) across organizational lines to integrate functional tasks.

Aid in Resource Allocation. “We’ll do it, if we get budget approval to hire another person.” This is a typical comment about resources and budgets. Many resources are allocated during budget preparation time.

Create an “Aura of Control.” The expression “in control” can mean many things; however, in a management sense, effective controls ensure that managers understand their authority, responsibilities, and limits. A budget system can serve as a �iscal disciplinarian or a “money cop.”

Motivate Managers and Employees Positively. The motivational “good news” is:

People who help to prepare budgets for their domain will have a commitment to the budget and take pride in achieving “our” plans. Through the budget, managers can see how their parts of the puzzle �it together to form a whole—the �irm-wide plan. Promotions, raises, and incentives are based on job performance, which includes achieving budget targets.

Budgeting systems can promote improved teamwork, more involvement in process improvement, and greater goal congruency throughout the organization. If management, from the president down, treats budgets as important, each manager and employee will too.

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7.4 Behavioral Side of Budgeting While the goal is to motivate managers positively, budgeting can have a variety of impacts on people and organizations. Budgets have the potential of motivating workers to reach higher levels of ef�iciency and productivity or creating arti�icial barriers to progress.

Top-Management Support

Intense top-management involvement in planning and control processes is correlated with budgeting success at middle and lower management levels. Nothing will destroy the effectiveness of the budgeting process quicker than managers’ perceptions that their superiors do not support the process. Top-management actions must cement the impression that a major commitment exists for planning and budget-related performance evaluations.

Demonstration of support involves at least �ive important steps. First, establish clearly delineated lines of authority and responsibility. Second, involve managers in the planning process. Third, set appropriate goals and objectives that can be easily translated into plans and actions at lower management levels. Fourth, review, critique, and approve budgets thoroughly. And �ifth, follow up and review budget reports with the intent of encouraging budget updates and goal-oriented actions.

Budget Slack

Budget slack, also called “padding the budget,” occurs when managers intentionally request more resources than needed. If lower-level managers know from past experience that their budget requests will be cut by upper-level managers, the response is to in�late certain expenses or to “lowball” revenue estimates. In turn, upper-level managers, knowing that lower-level managers pad their budgets, automatically raise estimated revenues and cut budgeted expenses. The result is a vicious circle of lack of trust and counterproductivity.

Another problem arises during budget downsizing when upper management requires all segments to cut expenses by some arbitrary percentage, say 10%. Managers may make noneconomic decisions or resort to gamesmanship for self-preservation, perhaps creating protective slack for the next cuts. This approach suffers from three weaknesses: (1) Organizational differences are ignored, (2) speci�ic resource reallocations needed to support the �irm’s long-run goals are obliterated, and (3) executive management is viewed as capricious and uncaring. In its defense, if everyone “shares” the pain of budget reductions, a feeling of “together we can solve the problem” can be encouraged.

The most effective weapon against “slack” and “across the board” budget cutting is a careful and rigorous review of budgets by line managers. To be effective, reviewers must know the inner workings of the activities reporting to them. Nonaccounting managers must be able to read and interpret budget data and control reports.

Human Factors and Budget Stress

Budgets are bases for directing activities and establishing a discipline within an organization. The tightness of budgets necessarily depends on a number of factors, including the ability to predict future results for a given function, the manager’s experience, and the closeness of supervision. Some people need close guidance and a “fear of God” approach, while others operate best with broad degrees of freedom. Supervisors and upper-level managers must make careful judgments about how tight budget standards should be for each manager. Remember, the objectives are to generate the greatest bene�it from each manager’s area of responsibility and to maximize goal achievement for the whole organization.

Ethics of Budgeting

“Gamesmanship” often rears its head in budgeting. Budgets are future estimates. Management judgment is heavily involved. We expect ethical behavior, objective allocations of resources based on need and returns, and a

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managerial attitude of fairness and equity to permeate the organization. We have already mentioned the problem of budget slack—budgeting expenses too high or revenues too low to cover anticipated budget cuts. Other problems involve misstating to earn approval of projects, hiding overspending on one project by charging expenses to another project, blaming controllable budget variances on noncontrollable events, and pressuring subordinates, which encourages them to act unethically “to meet the budget.” In the public sector where budgets are legislated, spending unused appropriations near the end of a �iscal year on nonessential or wasteful activities to help justify budget requests for the next �iscal year is common and borders on unethical use of public funds.

Executive management must be alert to messages that the budget system sends to all employees. The discussions of “aura of control,” top-management support, budget slack, and human factors all combine to highlight the importance of a structured control system with clear responsibilities and feedback. Planning and control systems can move a �irm to a higher ethical plane and also create more dilemmas. Managers involved in the budget-setting process and in the control reporting process are the most effective weapons in upholding the integrity of the planning and control system.

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7.5 Master Budget—An Overview The annual budgeting effort is commonly called the master budget or, in some �irms, the pro�it plan or �inancial plan. Although a master budget usually covers a one-year period in detail, it may be prepared on a month-by- month basis for the year and may be extended in summary form for several years.

Master Budget Components

Master budget terminology and classi�ications may differ among organizations, but a common set is shown in �lowchart format in Figure 7.4 to describe it and its supporting schedules. A comprehensive example follows to illustrate each schedule and its format. Figure 7.4 references the appropriate master budget schedules shown later in the chapter.

Figure 7.4: Master budget components and their relationships

Operating Budgets. The operating budget is a formal document that takes a sales forecast and converts it into a plan of action. Planned operating results are summarized in a cash-�low forecast and forecast �inancial statements. The day-to-day activities of any business are the interdependent parts of an operating cycle. The operating cycle is a circular sequence of events from purchasing on account, paying those bills, generating sales, and collecting cash for the sales. The cycle can be viewed as a “cash-to-cash” process. The cycle continuously repeats itself.

Cash-Flow Forecast. Cash-�low forecasting is a key to cash management. Cash management is planning and controlling cash balances over time. Often, three timeframes can be identi�ied: long term, annual, and short term

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(which may be daily or weekly). Each �its into the �irm’s planning process.

Project Budgets. While much budgeting uses a 12-month timeframe to plan repetitive activities, a number of activities are project-related and have project budgets. Examples include capital spending for new construction and equipment, research and development programs, and information systems development projects. Project costs are planned around resources and the project’s time line. Project budgets, however, are integrated into annual plans as well.

Forecast (Pro Forma) Financial Statements. Forecast balance sheets and income statements summarize the �inancial results from operating, cash-�low, and project budgets for managers. Forecast income statements and balance sheets provide managers with information needed to judge how adequately the master plan achieves the �irm’s �inancial goals and objectives. Most �inancial goals are expressed as ratios of balance sheet and income statement numbers. The forecast �inancial data then become the basis for management’s evaluation of actual results. Information from internal planning processes to be released to stockholders and others external to the �irm is carefully structured, must meet external reporting requirements, and is called “�inancial forecasts” or “�inancial projections.”

Master Budget for Nonmanufacturing Organizations

How does a master budget differ for a merchandising or service organization? The basic budgeting concepts are essentially the same; however, variations do exist.

Merchandising Organizations. A merchandiser replaces production with purchases in Figure 7.4. The budget cycle for merchandisers will have the following different traits:

Often, multiple locations exist and have individual budgets. Budgets for all segments are consolidated into one sales and operating expense budget. Revenue and expense budgets for store operations are created. If distribution systems and warehousing are involved, these budgets must be linked to sales forecasts and store budgets. A greater proportion of managers are pro�it center managers (product lines, branches, or departments) with both revenue and expense responsibilities.

Most merchandising companies will concentrate on a gross margin or contribution margin plan, which combines sales and cost of sales budgets. Operating expenses may differ in nature in merchandising �irms, but the functional classi�ications of selling and administrative expenses remain.

Service Organizations. A service organization often depends heavily on human resources. Planning personnel capacity and staf�ing levels is critical. In many service organizations, personnel expenses, which include salaries and bene�its, account for well over 75% of all expenses. This is the case, for example, in school systems and accounting, legal, and consulting �irms. Here personnel may be organized by type of service, skill, customer, or project. Staf�ing plans using headcounts may be more valuable for planning and control than dollar plans.

In complex organizations such as hospitals and banks, budgets develop around services provided. Forecasts of customer or patient work volumes, equipment used, support services required, and revenue generated are developed in responsibility centers and are combined vertically and linked horizontally. In �inancial institutions, for example, interest income from loans and investments is forecast along with interest expense paid on deposits, yet operating expenses for the people who make loans and get deposits require traditional expense budgeting.

Nonpro�it Organizations. Many nonpro�it organizations operate similar to merchandising and service �irms. However, two characteristics of nonpro�it organizations require special attention: (1) lack of clearly de�ined outputs and (2) �ixed or legislated inputs or revenues. These commonly arise with governmental, educational, and philanthropic services. Budgets are determined by a legislative process with legal constraints placed on how much can be spent and what type of spending can be incurred. The outputs might be better �ire protection, natural resource conservation, or national defense. In certain areas, workloads can be de�ined, such as in issuing drivers’

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licenses or processing tax returns. Given the legislated revenue side, the budgeter’s tasks are to work with managers to de�ine desirable goals and outcomes, to allocate resources (people and dollars) to the programs that generate the greatest bene�it, and to evaluate performance based on comparisons of prede�ined goals and results for given benchmarks.

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7.6 The Starting Point and Beyond The executive team meets to set goals, targets, and assumptions. If executives emphasize planning, updating budgets, and evaluating performances using budget comparisons, all managers see that �inancial planning and control are major parts of the “corporate culture.” The controller sets the wheels in motion by providing time schedules, forecast support data, and forms. But given these basics, where is the starting point of the planning cycle? What is planned �irst?

Finding the Controlling Constraint

The starting point of the budget effort should always be the most constraining variable. Generally, this is sales. Most managers work to generate more sales. But other constraining variables might be:

Machine capacity in a specialized area (plastic extruding equipment in a plastic bottle plant) Floor space in a retail outlet (the �irst �loor in a major downtown department store) Salespersons’ time to make calls on customers (sales reps who must decide which clients to visit) Tables in a restaurant (where demand for reservations cannot be met)

When a variable other than sales limits growth, it becomes the starting point for planning. But, for most �irms, sales units or revenue is the limiting “resource.”

Sales Forecasting

A realistic sales budget is the foundation of a master budget. The sales forecast is based on a variety of interlocking factors, such as pricing policy, economic outlook, industry conditions, advertising, historical patterns, and the �irm’s strategic market position. A sales forecast is built using data from many sources, including:

Analysis of historical trends to create a momentum forecast Grass-roots forecasts, by product and by customer, prepared by salespersons Statistical analysis of sales and economic data Market research analysis of promotion, sales efforts, and market share

These approaches are not independent. More likely, all are involved in solving the forecasting problem. Each method tests the assumptions and the data of the others. The marketing plan and the sales forecast are interdependent. Figure 7.4 shows the reciprocal relationship by solid and dotted lines.

Using Activity-Based Costing Relationships

Activity-based costing sets formal links among resource inputs and their costs, operating activities, and outputs. The budgeting process must include these relationships in converting expected sales volumes into production and operating expense budgets. A carefully developed ABC system will greatly simplify the budgeting process by using the cost functions developed for product costing to plan expenses. From ABC studies come a much greater understanding of cost-causing relationships.

Quality assessment, JIT performance, and employee involvement and empowerment measures are parts of planning and evaluation processes. These are predominately nonmonetary indicators but still part of budgeting. Financial modeling can include these linkages in a computer-based simulation of operations and operating budgets.

Independent and Dependent Variables

The planning assumptions, management inputs, product cost and price data, sales forecasts, and all the formula- driven relationships are called independent variables; they can be changed by the planner or budget analyst. Most remaining values in budgets come from mathematical relationships, using the independent variables. These

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calculated values are called dependent variables. Independent variables are used to calculate dependent variables. For example, sales units, prices, and the percentage of sales collected in the month of sale are independent variables that can be combined to �ind cash collected, a dependent variable. In spreadsheet software logic, independent variables are constants or external inputs. The dependent variables are found by creating a cell formula.

“What if ” changes to independent variables will allow alternative scenarios to be tested through modeling. The impacts of the changes can be seen on the dependent variables—for example, net income.

Preparing and Formatting Budget Schedules

Budget preparation uses forecasts, planning assumptions, basic logical and mathematical relationships, and management experience and judgment. A few calculation guidelines help, such as:

While budgeting does not follow debit and credit rules, a �inal test of the master budget is whether the forecast balance sheet balances. Budget relationships are de�ined quantitatively to allow the same formulas to be repeated in later time periods, such as in spreadsheet cell formulas. Ideally, initial planning assumptions, management inputs, and beginning values (the independent variables) should be suf�iciently complete to calculate all other variables. Prepare schedules in the order of the sequential chain of events, such as the sales forecast, production plan, and then the purchases schedule. Align time periods by columns—month by month or quarter by quarter. This pattern allows repetitive calculations to be duplicated easily. Put independent variables in an initial schedule for easy access when making “what if ” changes for later analyses. Avoid circular reasoning. For example, sales may be a function of advertising. Yet, the advertising budget may be a percentage of sales.

Structure and format simplify budget preparation. Frequently, data from one period are needed in the prior or next period. Or, data in one schedule are used in a following schedule. A structure keeps data and calculations organized.

Assume that:

1. Sales for the �irst four months of 2020 for Dodaro & Associates are forecast to be $50,000, $60,000, $80,000, and $70,000, respectively.

2. Cost of sales is forecast to be 60% of sales. 3. Beginning inventory is $18,000. Ending inventory is expected to be 40% of next month’s cost of sales. 4. Cash from sales will be collected as follows (based on collection patterns of credit sales during recent

months): 60% in the month of sale and 40% in the month after the sale. Uncollectibles are ignored here. 5. Beginning accounts receivable is $40,000, all from December sales.

The format and data for cash receipts forecasting for 2020’s �irst quarter are:

January February March

Sales $50,000 $60,000 $80,000

Cash collections of receivables from:

December sales ($40,000 receivables) $40,000

January sales ($50,000 × .6 and × .4) 30,000 $20,000

February sales ($60,000 × .6 and × .4) 36,000 $24,000

March sales ($80,000 × .6) _______ _______ 48,000

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January February March

Total cash collected from sales $70,000 $56,000 $72,000

The January column contains all data needed to �ind cash collections for January. The sales row provides the data to �ind cash collections for January, February, and March. This column/row format can be used in all master budget schedules.

The format and data for forecasting purchases for the �irst quarter are:

An important pattern is established: sales plus ending inventory set the total amount needed, while beginning inventory and purchases meet the need.

Contemporary Practice 7.1: Budgeting in Greek Hotels

A survey of management accounting practices in 85 Greek hotel companies revealed that, “the majority of the Greek hotels use budgets for planning annual operations (98.8%), controlling cost (91.8%), coordinating activities of the various parts of the organization (80%), and evaluating the performance of managers (64.7 per cent).” There was a low adoption rate for �lexible budgeting (15.3%).

Source: Pavlatos, O. & Ioannis, P. (2009). Management accounting practices in the Greek hospitality industry. Managerial Auditing Journal, 81–98.

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7.7 Other Budgeting Techniques So far we have discussed budgeting in terms of a master budget and its components. The concept of budgeting can incorporate other tools where needed.

Flexible Budgeting

In Chapter 1, we introduced cost functions. We suggested that expense budgets can be based on a variable rate and a �ixed amount of costs. By knowing the cost function, we can plan costs for any activity level within our relevant range. This is a �lexible budget. Initially, when the master budget is prepared, an expected activity level is the basis for the budget, and this is sometimes referred to as a static budget because it is based on this expected level only. A �lexible budget, on the other hand, is based on whatever the actual activity level turns out to be.

For example, Kenny Silverboard provides local area delivery services. He is developing a home delivery service for local restaurants to be called Federation Foods. This would utilize the unused capacity in his delivery services. Activity is the number of deliveries. Following are expense items, which include variable, �ixed, and semivariable behaviors.

Expense Item Fixed Expenses Variable Expenses

Driver payments $1.50 per delivery

Supplies expense  .15

Added management expenses $3,000

Depreciation expense 1,000

Added communications expenses 600  .10

Miscellaneous expenses 400  .05

Totals $5,000 $1.80 per delivery

The cost function is: $5,000 + ($1.80 × deliveries). Kenny thought he would handle about 10,000 deliveries this year, but he only made 9,000. Figure 7.5 presents his original budget, a �lexible budget for the actual 9,000 deliveries, and a comparison of his actual expenses to the adjusted budget. The original budget is based on 10,000 deliveries, and, therefore, cannot be used to evaluate actual results. The �lexible budget is based on the actual activity level: 9,000 deliveries. Remember: Fixed expenses are �ixed, and variable expenses adjust to the actual activity level. For example, miscellaneous expenses are $400 plus 10,000 times $0.05, or $900, in the original budget, and are $400 plus 9,000 times $0.05, or $850, in the �lexible budget. Kenny is expected to spend no more than $850 for miscellaneous expenses since only 9,000 deliveries were made.

Figure 7.5: Flexible budgeting performance report for Federation Foods

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Flexible budgeting can also be tied to applying overhead in product costing. In Chapter 2, we developed rates to apply factory overhead to products. Applied overhead was found by using the cost function and actual activity. Actual overhead minus applied overhead produces either an overapplied or underapplied overhead variance. (See the master budget example later in this chapter.) This variance includes any spending variance and any mismatch in applying �ixed overhead. These variances are discussed in detail in Chapter 8.

Project Budgeting

Project budgets are oriented to speci�ic events or tasks and use time schedules to prepare annual operating budgets. Project budget examples include construction projects, information systems projects, engineering and design projects, entertainment events, and government defense contracts.

Project management has been a source of many cost and time overruns. Many projects are unique, one-time efforts. Research projects often present another management dilemma: working in technologically unknown areas with no predictable output or timetable. Project budgets link stages and segments of work, timetables, deadlines or decision points, and spending authorizations. Actual costs are compared with budget time and dollar amounts to monitor the project periodically and at speci�ic review points.

Two management concerns exist. How did we do? And, what should we do now? The �irst is control oriented, and the second is planning oriented. One looks back at resources used, and the other looks forward to completing the project. As an example, assume that a systems development project is budgeted at $90,000 and should take six months to complete. It is now three months into the project, and $40,000 has been spent. Keith Cunningham, the manager in charge, estimates that it is one-third done and will take another six months and $80,000 to complete. How should the current status be evaluated? If the project is now one-third complete, Cunningham is over budget in both time and money as follows:

Performance to Date Total Project

Original Budget

Original Budget Resources Used to Date

For Portion Completed

Budget Overrun to Date

Revised Projected Budget

Projected Budget Overrun

Costs $90,000 $40,000 $30,000 ($10,000) $120,000 ($30,000)

Time 6 months

3 months 2 months (1 month) 9 months (3 months)

Using the original budget, at this point the project is a month behind schedule and overspent by $10,000. If the total project budget is revised for time and dollars, the project will be $30,000 and three months over budget. Careful monitoring of project status (costs and accomplishment) is needed to meet time and dollar targets.

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Probabilistic Budgeting

Probabilities re�lect the likelihood that certain business conditions will occur. When risk exists that a particular variable may move within a range of values, probabilistic expressions of those outcomes help the budget to be more realistic. The sensitivity of pro�its to changes in variables, such as sales volume and prices, can be tested, and then management can focus on sensitive variables.

Ben Friedman, controller of Ariel Industries, can calculate expected values of sales, costs, and any other budgeted variable from probabilities assigned by senior managers in marketing, production, and other areas. Expected values are obtained by adding the products of all event values multiplied by their associated probabilities of occurrence. Assume, for example, that Ariel plans to sell a product next year for $20 a unit, with a variable cost of $14. Probability estimates have been made for three sales volume levels (i.e., three events).

Sales Volume (Units) Probabilities Expected Value (Units)

Conservative 150,000 × .20 = 30,000

Most likely 200,000 × .70 = 140,000

Optimistic 250,000 × .10 = 25,000

1.00

Expected sales volume (units) 195,000

The calculation of expected contribution margin is as follows:

Expected sales (195,000 units × $20) $3,900,000

Expected variable costs (195,000 units × $14) 2,730,000

Expected contribution margin $1,170,000

Price, volume, variable cost, �ixed costs, and many other variables can be assigned probabilities in many combinations re�lecting the levels of uncertainty. Past experience coupled with a careful analysis of the future can serve as a basis for establishing probability estimates. Admittedly, probability estimates will not be precise, but they should represent the best inputs managers can generate and be more accurate than rough approximations or intuitive estimates.

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7.8 A Master Budget Example To illustrate the master budget sequence of planning activity and schedule formats, a comprehensive example is presented. The �irm is Widman Products Company, a small manufacturer of wood-based products. In recent years, its primary product is a speaker’s podium, which is sold to chapters of the Effective Speakers Society of America (ESSA). Graduates of the Society’s speaker training programs are awarded a wooden podium as a symbol of public speaking prowess. Widman produces a high-quality product at a very competitive price. The product is called the “EXEC.”

In the Widman Products factory, wood is cut and assembled, a polyurethane �inish is applied, and packing and shipping are done. A small sales of�ice and administrative staff completes the organization.

Each year, Widman Products prepares a master budget on a quarterly basis and generally follows the structure shown in Figure 7.3. As in most budgeting situations, Widman Products’ dollar amounts are rounded to the nearest dollar. The model used to prepare the budget will track decimal places. When amounts are rounded throughout the budget example, certain columns or rows may appear to add incorrectly; however, overall accuracy is maintained.

Annual Goals and Planning Assumptions

Widman Products begins its planning process with a meeting organized by the controller at a local resort each August. All managers discuss their areas of responsibility and present strengths, opportunities, problems, and last year’s results. Financial and operating goals for 2020 are set, and planning guidelines are agreed upon.

Planning Assumptions. Certain data and relationships are needed to begin the planning process. These planning assumptions include beginning balances, product costs and prices, operating assumptions, and �inancing assumptions.

Product Cost and Pricing Data. The �irst planning data are EXEC quantities and costs. Materials, labor, and overhead are listed by each resource used. A list of materials is often called a bill of materials. Direct labor shows costs and hours. Schedule 1 shows these quantities and amounts. Amounts that are shown in bold are independent variables throughout the example.

Schedule 1: Product Quantities, Costs, and Prices

Product Costs Cost Quantity Per Unit

Materials:

Plywood (square feet) $0.275 15.00 $4.125

Trim (feet) 0.085 18.00 1.530

Total materials cost per unit $5.655

Direct labor:

Preparation and �inishing hours $12.00 1.00 $12.000

Factory overhead:

Variable – Based on direct labor hours $6.50 1.00 $6.500

Fixed – Based on machine hours 12.00 0.60 7.200

Total manufacturing overhead cost per unit $13.700

Total product cost per unit $31.355

Sales price $49.00

Manufacturing overhead is identi�ied as �ixed or variable. After analyses of activities and cost behaviors, direct labor hours was selected as the variable overhead cost driver. Much activity in the plant is linked to labor-intensive

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processes that generate the majority of variable overhead costs. The �ixed overhead cost driver is machine hours, because most �ixed overhead is generated by equipment costs.

Operating and Financing Assumptions. A variety of planning details are needed to prepare budget schedules. Most come from past experience, estimates of beginning balances, and 2020 forecasts. Schedule 2 presents the initial assumptions.

Schedule 2: Operating and Financing Assumptions for 2020

Inventory Data: Plywood (Sq Feet)

Trim (Feet) EXEC

December 31, 2019, inventory 10,000 6,000 700

Ending inventory (part of next quarter’s usage) 20% 10% 25%

Accounts receivable:

Beginning accounts receivable balance $40,000

Sales percentage collected this quarter 75%

Cash discount percentage for receipt of this quarter’s sales 2%

Accounts payable:

Beginning accounts payable balance $6,000

Purchases percentage paid this quarter 60%

Manufacturing activity base:

Normal labor hour activity rounded to the nearest 500 hours 11,500

Normal machine hour activity rounded to the nearest 500 hours (See Schedule 7 for budgeted variable rates and annual �ixed amounts)

7,000

Selling and administrative expense data:

Sales commissions: 4%; Shipping expenses (See Schedule 13 for annual budgeted selling and administrative expense amounts):

$1.30 per unit

Financial assumptions and balances:

Beginning cash balance $6,000

Cash balance: Minimum balance $5,000 Maximum balance: $10,000

Borrowing and investment incremental amount $5,000

Beginning taxes payable balance $2,000

Beginning interest payable balance $1,125

Quarterly principal payment on notes payable $3,000

Capital stock – Outstanding shares 24,000 shares

Paid-in-capital $240,000

Dividend rate – per share per quarter $0.05

Income tax rate (federal, state, and local) 40%

Interest rate on bank borrowings and investments (annual) (See December 31, 2019, Balance Sheet for beginning balances.)

9%

Project Expenditures: First Quarter Second Quarter Third Quarter Fourth Quarter

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Project Expenditures: First Quarter Second Quarter Third Quarter Fourth Quarter

Equipment purchases $8,000 $0 $10,000 $12,000

Research and development 0 0 0 4,000

Operating assumptions include percentages, speci�ic budgeted amounts for certain accounts to prepare overhead rates, and any other constant that will be needed in calculations. Borrowing details, cash policies, taxes, dividends, and beginning balance sheet �igures are the independent variables for �inancing assumptions. These starting points are needed to complete the cash-�low forecast and pro forma (or forecast) �inancial statements.

Sales Forecast

The sales forecast is the only remaining independent variable necessary. It is prepared using a �ive-quarter timeframe. A �ifth quarter of sales data is needed to complete a number of fourth quarter schedules. Physical quantities are independent variables. Dollar amounts are found by using the physical units and prices from Schedule 1.

From the sales dollars in Schedule 3 through the end of the master budget, all numbers are calculated using data and instructions in Schedules 1, 2, and 3. All values from this point are dependent variables using the independent variables. Note that the selling price implied in Schedule 3 is the $49 that comes from Schedule 1.

Schedule 3: Sales Forecast

First Quarter Second Quarter Third Quarter Fourth Quarter Total Fifth Quarter

Unit sales 2,400 2,800 3,000 3,200 11,400 3,000

Sales dollars $117,600 $137,200 $147,000 $156,800 $558,600 $147,000

Production Plan

A production plan, Schedule 4, is prepared using the beginning �inished podium inventory, the sales forecast, and the desired ending inventory levels. In this example, work in process inventory is assumed to be so small and unchanging that it is immaterial to both planning and product costing tasks. Key relationships in this production plan are the percentages of sales that should be on hand at the end of each quarter. Note the format of Schedule 4. Sales plus required ending inventory equal units needed. Then, by subtracting beginning inventory, the needed production volume is found. This sequence is common to many budgeting calculations.

Materials Requirements and Purchases Budget. Quantities of materials used in each unit (the bill of materials) are speci�ied in Schedule 1. Quantities of materials needed to meet production requirements are determined by multiplying the units to be made by the quantities of materials required for each unit. Then, this amount is added to the desired ending inventory amount to obtain the total needs.

Schedule 4: Production Plan

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total

Fifth Quarter

Unit sales 2,400 2,800 3,000 3,200 11,400 3,000

Ending �inished goods 700 750 800 750 750

Total units needed 3,100 3,550 3,800 3,950 12,150

Beginning �inished goods

(700) (700) (750) (800) (700) (750)

Production needed 2,400 2,850 3,050 3,150 11,450

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Schedule 5: Materials Requirements and Purchases Budget

Plywood Requirements (Sq Ft):

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total

Fifth Quarter

Ending inventory 8,550 9,150 9,450 8,850 8,850

Production requirements 36,000 42,750 45,750 47,250 171,750 44,250*

Total needs 44,550 51,900 55,200 56,100 180,600

Beginning inventory (10,000) (8,550) (9,150) (9,450) (10,000)

Purchases in square feet 34,550 43,350 46,050 46,650 170,600

Dollar cost of plywood purchases

$9,5011 $11,921 $12,664 $12,829 $46,915

Trim requirements (linear ft):

Ending inventory 5,130 5,490 5,670 5,310 5,310

Production requirements 43,200 51,300 54,900 56,700 206,100 53,100*

Total needs 48,330 56,790 60,570 62,010 211,410

Beginning inventory (6,000) (5,130) (5,490) (5,670) (6,000)

Purchases in linear feet 42,330 51,660 55,080 56,340 205,410

Dollar cost of trim purchases

$3,598 $4,391 $4,682 $4,789 $17,460

Total materials purchases $13,099 $16,312 $17,346 17,618 $64,375

1The purchase cost is actually $9,501.25. This number is rounded to the nearest dollar, $9,501. This is the �irst of several rounded amounts in the comprehensive example. Spreadsheet software tracks all signi�icant digits in calculations and rounds to the speci�ied level. Certain columns and rows that include rounded numbers may appear to add incorrectly. Budgeting rarely needs detail beyond whole dollars.

* Amount provided

Ending plywood inventory for the �irst quarter of 8,550 square feet is 20% (Schedule 2) of the second quarter’s production needs of 42,750 square feet. The 36,000 square feet of plywood needed for production in the �irst quarter is found by multiplying 15 square feet per unit (Schedule 1) times the 2,400 units to be produced (Schedule 4). Thus, the rules from Schedules 1 and 2 and the quantities from Schedule 4 determine all amounts needed to calculate the purchases requirements in Schedule 5.

In more complex production situations, the accumulation of parts and materials needs is called a bill of materials explosion. All uses of the same part in different products are summed to �ind the total usage across the entire product line for a time period. Computer software for production planning, such as Materials Requirements Planning (MRP), is used to calculate needs and to issue purchase orders when inventory levels reach certain points.

Direct Labor Budget. The direct labor budget is estimated �irst by the direct labor time required per unit (Schedule 1) times the units to be made (Schedule 4). Hours per podium are set by past experience or industrial engineering studies. At one hour per EXEC, the hours per quarter equal the units to be produced per quarter.

Labor cost per hour can be the “straight” wage rate, with all payroll taxes and fringe bene�its included in manufacturing overhead. Or the rate could be a “loaded” wage rate, which includes most fringes and expected overtime premiums.

Schedule 6: Direct Labor Budget

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total

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Schedule 6: Direct Labor Budget

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total

Total direct labor hours needed 2,400 2,850 3,050 3,150 11,450

Total direct labor payroll expense

$28,800 $34,200 $36,600 $37,800 $137,400

Factory Overhead Budgets. Planning factory overhead takes two forms: creating the expected overhead spending patterns (using a �lexible budget) and budgeting spending and applied overhead levels.

Cost Estimation Using ABC and Statistical Techniques. Detailed cost estimates come from several sources already discussed in prior chapters. Cost estimation techniques presented in Chapter 6 (regression analysis, high- low method, etc.) are used by managers and accountants to budget expenses that track well against one or more activity variables. More commonly, the same cost drivers used in Chapters 2 and 4 to build cost functions and assign costs to cost objectives are now applied to another cost objective—budgeting.

Factory Overhead Flexible Budget. Selecting activity bases for applying overhead, setting normal activity levels, planning variable and �ixed overhead items, and setting the overhead rates are all part of the annual budgeting process. Schedule 7 is the result. Independent variables (in bold) are the variable overhead rates and the �ixed overhead annual amounts. Separate cost drivers were selected for variable and �ixed overhead. The variable overhead cost driver is direct labor hours. Fixed overhead is applied using machine hours. Annual normal direct labor and machine hours are rounded (11,500 labor hours and 7,000 machine hours). Budgets are prepared for various ranges of activity, in both cases in increments of 500 hours around normal levels. Using budgeted expenses and normal activity levels given in Schedule 2, variable and �ixed overhead rates are set. These are calculated in Schedule 7 and added to product costs in Schedule 1.

Schedule 7: Factory Overhead Flexible Budget

Cost Driver Activity Levels

Normal

Variable cost driver: Direct labor hours 11,000 11,500 12,000

Fixed cost driver: Machine hours 6,500 7,000 7,500

Variable expenses: Rate/Hour

Supplies and other variable expenses $ 1.40 $15,400 $16,100 $16,800

Indirect labor and bene�its expenses 5.10 56,100 58,650 61,200

Total variable overhead expenses $ 6.50 $71,500 $74,750 $78,000

Fixed expenses: Amount

Depreciation expense $20,000 $20,000 $20,000 $20,000

Supervision salaries 41,000 41,000 41,000 41,000

Other �ixed overhead expenses 23,000 23,000 23,000 23,000

Total �ixed overhead expenses $84,000 $84,000 $84,000 $84,000

Total manufacturing overhead expenses $155,500 $158,750 $162,000

Overhead rates:

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Schedule 7: Factory Overhead Flexible Budget

Cost Driver Activity Levels

Normal

Variable rate per direct labor hour $ 6.50 $ 6.50 $ 6.50

Fixed rate per machine hour $12.00

Factory Overhead Operating Budget. With overhead rates and budgeted activity levels, quarterly budgets for manufacturing overhead and applied overhead are prepared. Again, direct labor and machine hour activity levels come from the hours per unit in Schedule 1 and the production plan. Variable expense budgets for each quarter are the expected spending levels given that activity level. Budgeted �ixed costs are merely divided equally among four quarters.

Near the bottom of Schedule 8 is the planned applied overhead. This will differ from the budgeted spending level because of the difference between budgeted �ixed cost and applied �ixed overhead. The quarter’s planned activity level for machine hours (1,440 hours) does not equal one quarter of the annual normal activity level (7,000 hours ÷ 4 quarters). Fixed overhead is budgeted at $21,000 for the quarter (one-fourth of $84,000). Using the �ixed overhead rate of $12.00 per machine hour developed in Schedule 7, the applied �ixed overhead is $17,280. Budgeted �ixed overhead is underapplied by $3,720, which is $21,000 minus $17,280 ($12 per hour × 310 hours).

Variable overhead is budgeted and applied at $6.50 per direct labor hour. Therefore, no budgeted overapplied or underapplied variable overhead exists.

Schedule 8: Factory Overhead Operating Budget

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total

Budgeted direct labor hour activity 2,400 2,850 3,050 3,150 11,450

Budgeted machine hour activity 1,440 1,710 1,830 1,890 6,870

Budgeted variable overhead expenses $15,600 $18,525 $19,825 $20,475 $74,425

Budgeted �ixed overhead expenses 21,000 21,000 21,000 21,000 84,000

Total budgeted factory overhead $36,600 $39,525 $40,825 $41,475 $158,425

Budgeted factory overhead cash out�low

$31,600 $34,525 $35,825 $36,475 $138,425

Applied factory overhead:

Variable overhead applied $15,600 $18,525 $19,825 $20,475 $74,425

Fixed overhead applied 17,280 20,520 21,960 22,680 82,440

Total applied overhead $32,880 $39,045 $41,785 $43,155 $156,865

Overapplied/(Underapplied) overhead

$(3,720) $(480) $960 $ 1,680 $(1,560)

Overapplied/(Underapplied) overhead YTD

$(3,720) $(4,200) $(3,240) $ (1,560) $(1,560)

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Supporting Schedules

Several supporting schedules are prepared by the accounting staff and are important to various forecasts and calculations. Assumptions about collections, payments, and ending balances were given in Schedule 2. We can now develop forecasts for accounts receivable (Schedule 9), inventories (Schedule 10), and accounts payable (Schedule 11).

Schedule 9: Accounts Receivable

First Quarter Second Quarter Third Quarter Fourth Quarter

Beginning balance $ 40,000 $ 29,400 $ 34,300 $ 36,750

Net sales 117,600 137,200 147,000 156,800

Total receivables 157,600 166,600 181,300 $193,550

Decreases in receivables:

Collections of prior quarter's sales $ 40,000 $ 29,400 $ 34,300 $ 36,750

Collections of this quarter's sales 86,436 100,842 108,045 115,248

Total cash collections of receivables $126,436 $130,242 $142,345 $151,998

Cash discounts 1,764 2,058 2,205 2,352

Total credits to receivables $128,200 $132,300 $144,550 $154,350

Ending balance $ 29,400 $ 34,300 $ 36,750 $ 39,200

Schedule 10: Ending Inventories—Cost Basis

Dec. 31, 2019

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

Materials inventory:

Plywood (square feet) $ 2,750 $ 2,351 $ 2,516 $ 2,599 $ 2,434

Trim (linear feet) 510 436 467 482 451

Total materials inventory $ 3,260 $ 2,787 $ 2,983 $ 3,081 $ 2,885

EXEC �inished goods inventory

21,949 21,949 23,516 25,084 23,516

Total inventories $25,209 $24,736 $26,499 $28,165 $26,401

Schedule 11: Accounts Payable

First Quarter Second Quarter Third Quarter Fourth Quarter

Beginning balance $ 6,000 $ 5,240 $ 6,525 $ 6,938

Purchases on account 13,099 16,312 17,346 17,618

Total payables $19,099 $21,552 $23,870 $24,556

Decreases in payables:

Payments of prior quarter’s purchases $ 6,000 $ 5,240 $ 6,525 $ 6,938

Payments of this quarter’s purchases 7,860 9,787 10,407 10,571

Total cash payments $13,860 $15,027 $16,932 $17,509

Ending balance $ 5,240 $ 6,525 $ 6,938 $ 7,047

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For accounts receivable, the percentage of net sales collected in the current quarter is 75% and cash discounts are 2% of collections of the current quarter’s net sales. Inventory values use quantities from Schedules 4 and 5 and costs from Schedule 1. For accounts payable, Schedule 2 indicates that 60% of purchases are paid in the current quarter.

Cost of Goods Manufactured and Sold Schedule

Now all the elements are in place to prepare a schedule of the cost of goods manufactured and sold. These costs are forwarded in summary form to the income statement.

Using Schedule 12, a useful proof can be made. With product costs from Schedule 1 and sales from Schedule 3, total costs of EXECs sold can be calculated quickly: $357,447. These numbers can be checked against the sums of materials, labor, applied overhead, and the changes in inventories. For each product in each quarter these numbers should match.

Schedule 12: Cost of Podiums Manufactured and Sold

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total

Materials inventory:

Plywood (square feet) $ 9,900 $11,756 $12,581 $12,994 $ 47,231

Trim (linear feet) 3,672 4,361 4,667 4,820 17,519

Total materials used $13,572 $16,117 $17,248 $17,813 $ 64,750

Direct labor 28,800 34,200 36,600 37,800 137,400

Factory overhead applied 32,880 39,045 41,785 43,155 156,865

Cost of EXECs manufactured $75,252 $89,362 $95,633 $98,768 $359,015

Plus: Beginning inventory 21,949 21,949 23,516 25,084 21,949

Less: Ending inventory (21,949) (23,516) (25,084) (23,516) (23,516)

Cost of EXECs sold $75,252 $87,794 $94,065 $100,336 $357,447

Overapplied/(Underapplied) overhead

(3,720) (480) 960 1,680 (1,560)

Adjusted cost of EXECs sold $78,972 $88,274 $93,105 $98,656 $359,007

Selling and Administrative Expense Budgets

Expenses of promoting, selling, and distributing the products are budgeted by combining the costs into a selling or marketing expenses budget (Schedule 13). Advertising and other sales expenses total $16,000. These are �ixed costs and are allocated to the four quarters. Also, sales salaries expenses, which are �ixed and total $30,000, are allocated to the four quarters.

Schedule 13: Selling and Administrative Expenses Budget

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total

Selling expenses:

Sales commission expenses $ 4,704 $ 5,488 $ 5,880 $ 6,272 $22,344

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Schedule 13: Selling and Administrative Expenses Budget

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total

Advertising and other sales expenses

4,000 4,000 4,000 4,000 16,000

Sales salaries expenses 7,500 7,500 7,500 7,500 30,000

Shipping expenses 3,120 3,640 3,900 4,160 14,820

Total selling expenses $19,324 $20,628 $21,280 $21,932 $83,164

Administrative expenses:

Wage and salaries expenses $15,000 $15,000 $15,000 $15,000 $60,000

Other administrative expenses 3,500 3,500 3,500 3,500 14,000

Total administrative expenses 18,500 18,500 18,500 18,500 74,000

Total selling and administrative expenses

$37,824 $39,128 $39,780 $40,432 $157,164

Project Budgets

Few project budgets exist in this example. Widman Products has a small capital investment and research and development budget, which is shown in Schedule 14. Equipment purchases are capitalized, and research and development costs are expensed.

Schedule 14: Capital Investment Project Budget

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total

Projects:

Equipment purchases $ 8,000 $ 0 $10,000 $12,000 $30,000

Research and development expenses

0 0 0 4,000 4,000

Total project expenditures $ 8,000 $ 0 $10,000 $16,000 $34,000

Cash-Flow Forecasts

Now that all operating and project budgets are in place, the time for summarizing has arrived. The �irst summary is the preparation of the cash-�low forecast. Nearly every schedule impacts cash. The basic structure is to list receipts and disbursements, sum to a cash balance, and show any planned investing or borrowing activities. In Schedule 15, a source document for each cash-�low item is cited.

Schedule 15: Cash-Flow Forecast

Source First

Quarter Second Quarter

Third Quarter

Fourth Quarter Total

Cash in�lows:

Collections from sales Schedule 9 $126,436 $130,242 $142,345 $151,998 $551,021

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Schedule 15: Cash-Flow Forecast

Source First

Quarter Second Quarter

Third Quarter

Fourth Quarter Total

Interest received Balance sheet

0 0 0 0 0

Total cash in�lows $126,436 $130,242 $142,345 $151,998 $551,021

Cash out�lows:

Purchases payments Schedule 11

$ 13,860 $ 15,027 $ 16,932 $ 17,509 $ 63,328

Direct labor payroll Schedule 6 28,800 34,200 36,600 37,800 137,400

Factory overhead Schedule 8 31,600 34,525 35,825 36,475 138,425

Selling and administrative expenses

Schedule 13

37,824 39,128 39,780 40,432 157,164

Interest payments Balance sheet

1,125 1,125 1,058 1,103 4,410

Income taxes payments Balance sheet

2,000 (834) 2,673 4,323 8,162

Dividend payments Schedule 2 1,200 1,200 1,200 1,200 4,800

Project budget payments Schedule 14

8,000 0 10,000 16,000 34,000

Note payable repayments Schedule 2 3,000 3,000 3,000 3,000 12,000

Total cash out�lows $127,409 $127,371 $147,068 $157,841 $559,689

Cash in�lows minus out�lows

$ (973) $ 2,871 $ (4,723) $ (5,843) $ (8,668)

Plus: Beginning cash 6,000 5,027 7,898 8,176 6,000

Cash available $ 5,027 $ 7,898 $ 3,176 $ 2,332 $ (2,668)

Less: Excess cash on hand 0 0 0 0 0

Plus: New borrowing needed

0 0 5,000 5,000 10,000

Ending cash balance $ 5,027 $ 7,898 $ 8,176 $ 7,332 $ 7,332

Cumulative borrowings $ 0 $ 0 $ 5,000 $10,000 $10,000

Cumulative investments $ 0 $ 0 $ 0 $ 0 $ 0

A key part of cash-�low forecasting is to anticipate cash de�icits or surpluses. If the cash balance falls below the minimum desired level (given in Schedule 2), bank borrowings or investment sales are needed. If the cash balance exceeds the maximum level, excess cash should be invested to ensure maximum earnings. Calculations at the bottom of Schedule 15 forecast that Widman Products will need to borrow cash.

The Completed Example: Forecast Financial Statements

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The operating data presented determine the forecast �inancial results. Consolidation of operating numbers into forecast �inancial statements is frequently the controller’s responsibility. These statements are reviewed carefully by the �irm’s executives. In this example, the source schedule for each account balance is listed to help explain the income statement and balance sheet numbers.

Forecast Income Statements. The forecast or pro forma income statement is a summary of the expected revenue and expense budgets. Management can compare its actual income statements with the forecast statements as the year progresses. If budgeted pro�its are to be realized, adjustments may have to be made. Perhaps the budget itself requires revision.

As can be seen, most amounts are summarized from earlier schedules. Only the interest income and expense and income tax expense are computed here from data in Schedule 2 and from amounts already calculated. All other amounts were taken from other budget schedules.

Forecast Balance Sheets. The forecast or pro forma balance sheet indicates the �irm’s �inancial position at a future date. Like the income statement, it is a summary statement that depends on individual budgets that have been prepared. The forecast balance sheet also serves as a point of reference during the year. Interim statements prepared at various dates can be compared with corresponding budget statements.

Widman Products Company—Forecast Income and Expense Statements

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total Source

Sales $117,600 $137,200 $147,000 $156,800 $558,600 Schedule 3

Cost of goods sold $ 75,252 $ 87,794 $ 94,065 $100,336 $357,447 Schedule 12

Factory variances (3,720) (480) 960 1,680 (1,560) Schedule 8

Net cost of goods sold $ 78,972 $ 88,274 $ 93,105 $ 98,656 $359,007

Gross margin on sales $ 38,628 $ 48,926 $ 53,895 $ 58,144 $199,593

Selling and administrative expense

$ 37,824 $ 39,128 $ 39,780 $ 40,432 $157,164 Schedule 13

Research and development expense

0 0 0 4,000 4,000 Schedule 14

Total operating expenses $ 37,824 $ 39,128 $ 39,780 $ 44,432 $161,164

Operating income $ 804 $ 9,798 $ 14,115 $ 13,712 $ 38,429 Schedule 11

Other: Interest income $ 0 $ 0 $ 0 $ 0 $ 0 Calculated

Interest expense (1,125) (1,058) (1,103) (1,148) (4,434) Calculated

Sales cash discounts (1,764) (2,058) (2,205) (2,352) (8,379) Schedule 9

Total other items $ (2,889) $ (3,116) $ (3,308) $ (3,500) $(12,813)

Net income before taxes $ (2,085) $ 6,682 $ 10,807 $ 10,212 $ 25,616

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Widman Products Company—Forecast Income and Expense Statements

First Quarter

Second Quarter

Third Quarter

Fourth Quarter Total Source

Income tax expense (834) 2,673 4,323 4,085 10,247 Calculated

Net income $ (1,251) $ 4,009 $ 6,484 $ 6,127 $ 15,369

Widman Products Company—Forecast Balance Sheets

Dec. 31, 2019

Mar. 31, 2020

June 30, 2020

Sept. 30, 2020

Dec. 31, 2020 Source

Assets:

Cash $ 6,000 $ 5,027 $ 7,898 $ 8,176 $ 7,332 Schedule 15

Short-term investments

0 0 0 0 0 Schedule 15

Accounts receivable 40,000 29,400 34,300 36,750 39,200 Schedule 9

Inventories 25,209 24,736 26,499 28,165 26,401 Schedule 10

Interest receivable 0 0 0 0 0 Income Stmt

Total current assets $ 71,209 $ 59,163 $ 68,697 $ 73,090 $ 72,933

Building and equipment

$360,000 $368,000 $368,000 $378,000 $390,000 Schedule 14

Accumulated depreciation

(100,000) (105,000) (110,000) (115,000) (120,000) Schedule 7

Total assets $331,209 $322,163 $326,697 $336,090 $342,933

Liabilities and equity:

Accounts payable $ 6,000 5,240 $ 6,525 $ 6,938 $ 7,047 Schedule 11

Taxes payable 2,000 (834) 2,673 4,323 4,085 Income Stmt

Bank borrowings 0 0 0 5,000 10,000 Schedule 15

Interest payable 1,125 1,125 1,058 1,103 1,148 Income Stmt

Total current liabilities

$ 9,125 $ 5,531 $ 10,255 $ 17,364 $ 22,280

Long-term notes payable

50,000 47,000 44,000 41,000 38,000 Schedule 15

Total liabilities $ 59,125 $ 52,531 $ 54,255 $ 58,364 $ 60,280

Capital stock $240,000 $240,000 $240,000 $240,000 $240,000 Schedule 3

Retained earnings 32,084 29,633 32,442 37,726 42,653 Schedule 15, Income Stmt

Total equity $272,084 $269,633 $272,442 $277,726 $282,653

Total liabilities and equity

$331,209 $322,163 $326,697 $336,090 $342,933

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Master Budget Summary

Several observations should be made about the master budget example. The budget should be tested for reasonableness, including:

A review of the reasonableness of critical independent variables (most often the sales forecast) as a key evaluation step A sensitivity analysis to determine whether small changes in key variables will cause major changes in pro�itability or cash �lows “What if ” analyses to determine whether a better combination of resource inputs could produce a stronger plan A budget review and approval by each manager involved in the planning effort An analysis to determine whether the management’s goals and objectives are realized

Many iterations may be needed to arrive at a budget that managers can accept, meets management’s goals, and pushes the �irm toward its long-range goals.

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7.9 Impacts of Contemporary Manufacturing Approaches The evolution of manufacturing approaches has, in some cases, had major impacts on budgeting. The following observations can be made:

Just-in-time systems reduce inventory needs and may even eliminate their role in production budgeting. Some �irms have reduced major component inventories to under two hours of production requirements. Shorter lead times place greater pressure on production planning. Small mistakes or delays can cause entire plants to stop—incurring nonproductive costs and lost output. Activity-based costing will likely increase the number of cost drivers and cost centers. Budgeting may actually be easier since costs and activity are more closely related. Flexible manufacturing and team production activities change the collection of cost data—where, how, and what. Costs will be regrouped for improved planning and control. Also, greater emphasis is placed on certain costs, such as costs of quality, manufacturing cycle times, value-added labor, and manufacturing throughput.

The reduction of lead times and buffers throughout the production process means planning grows in importance.

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Summary & Resources

Chapter Summary One major management function is to plan and control the activities of an organization. A planning and control system includes a strategic plan, a responsibility accounting system, a master budget, and �inancial modeling. Cost or activity, pro�it, and investment centers de�ine a manager’s sphere of responsibility. The glue that holds planning activities together is the budget. Purposes of budgeting are outlined.

Consideration is given to managers’ budget-related behavior and the impacts that budgets have on people. Areas of particular importance are top-management’s support of the budget, budgetary slack, budget stress, and ethical issues.

The master budget is an integrated set of schedules; it ties operating, project, and �inancial budgets together. The operating budget begins with the constraining variable, most commonly the sales forecast. All operating budgets are integrated into the cash-�low budget and forecast �inancial statements. Understanding how to organize budget data and to format budget schedules can ease the assimilation of the huge amount of budget data brought together to create an operating plan. A master budget example was developed to show the integrative nature of the various budget schedules.

Other budgeting approaches were presented. Flexible budgeting allows managers to be evaluated according to the actual activity they experience. Project budgeting prepares plans that span normal annual timeframes or are nonroutine in nature. Probabilistic budgeting gives managers an opportunity to bring into the budgeting process a range of estimates for key variables.

Key Terms

benchmark A comparison of operations, costs, or productivity.

bill of materials explosion The complete list of materials and quantities used for all production for a given time period.

budget A plan showing what and how resources are to be acquired and used over a speci�ic time period.

budget slack Excess resources built into the budget over the amount necessary to achieve the planned goals and objectives.

cash management Planning and controlling the levels of cash balances over a speci�ic time period.

control The process of comparing actual results with budgeted levels of performance in directing an organization.

expected value The average value of a variable that has had probabilities assigned to different values for that variable.

�inancing assumptions Budgeting assumptions in which the independent variables consist of borrowing details, cash policies, taxes, dividends, and beginning balance sheet �igures.

�lexible budget A budget based on a formula that expresses the budgeted costs at any activity level within the relevant range.

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forecast �inancial statements Financial statements based on budgeted or estimated amounts that are presented in the same format as historical �inancial statements.

goals and objectives Speci�ic performance targets that provide a quantitative and time framework for achievement within any environmental constraints facing the organization.

investment center A responsibility center where control exists over costs, revenues, and investments in assets used or managed.

long-range goals Statements about the desired position of the organization in the extended future or about the direction important variables should take in determining the long-run destiny of the organization.

master budget An integrated plan that combines the operating budget, �inancial budget, and any project budgets.

mission statement The statement of purpose of the organization.

operating assumptions Budgeting assumptions that consist of percentages, speci�ic budgeted amounts for certain accounts, and any other constant needed in calculations.

operating budget A formal document that summarizes the expected results of an organization’s revenue and expense transactions for a future period.

operating cycle A circular sequence of events from purchasing on account to paying those bills with cash collected from sales.

planning The process of formulating short-term and long-term goals and objectives, predicting potential results under alternative ways of achieving them, and deciding how to attain the desired results.

planning assumptions Management assertions about the future that are used as a given in the budgeting process.

pro forma (or forecast) �inancial statements Financial statements based on budgeted or estimated amounts that are presented in the same format as historical �inancial statements.

pro�it center A responsibility center where control exists over both the incurrence of costs and the generation of revenues.

pro�it plan A term used to describe the master budget of an organization, re�lecting the primary focus of the master budget —the management of revenues and expenses.

project budget A budget oriented to a speci�ic event rather than a time period.

responsibility accounting A system where managers prepare plans for their areas of responsibility and exert control over those activities by making decisions and evaluating results.

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responsibility center Any unit of an organization where control over incurrence of cost, revenue, or investment is found.

revenue center A responsibility center where control exists over the generation of revenues, but few expenses are controlled.

roll-up reporting Summarizes lower-level activities when reporting to higher levels along the responsibility channel.

sales forecast Estimated future sales based on a variety of interlocking factors.

strategic plan The process of deciding on organizational goals and strategies to achieve them.

Problem for Review The production manager of JRS Enterprises, Samuel Schwartzben, maintains an inventory of materials equal to production needs for the next month because of the possibility of delays in shipments from his Korean supplier. Each unit takes 4 pounds of materials, which cost $3 per pound. The target for �inished goods inventory is 20% of the following month’s sales. Budgeted sales in units for the �irst �ive months of 2020 are:

Month Budgeted Sales Month Budgeted Sales

January 12,000 April 16,000

February 16,000 May 20,000

March 15,000

At December 31, 2019, 60,000 pounds of materials and 3,000 units of �inished goods were on hand.

Question:

Prepare a budget for production in units and a budget for purchases in pounds and dollars for the �irst three months of 2020.

Solution:

Production plan in units:

January February March April May

Sales 12,000 16,000 15,000 16,000 20,000

Ending inventory (20 % of next month) 3,200 3,000 3,200 4,000

Total units needed 15,200 19,000 18,200 20,000

Beginning inventory available 3,000 3,200 3,000 3,200

Production required 12,200 15,800 15,200 16,800

Purchases budget:

January February March April

Production required 12,200 15,800 15,200 16,800

Pounds per unit × 4 × 4 × 4 × 4

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January February March April

Pounds required 48,800 63,200 60,800 67,200

Ending inventory (next month’s production requirements) 63,200 60,800 67,200

Total pounds needed 112,000 124,000 128,000

Beginning inventory available 60,000 63,200 60,800

Materials purchases in pounds 52,000 60,800 67,200

Cost per pound × $3 × $3 × $3

Materials purchases in dollars $156,000 $182,400 $201,600

Questions for Review and Discussion 1. Reread the vignette about Ann Davis at the beginning of the chapter. Respond to each of her comments

about budgeting. Give a possible reason for why she thinks that way. What retort could you give to each comment?

2. Identify and explain at least �ive purposes of budgeting. 3. What are the similarities and differences among an activity center, a cost center, a pro�it center, and an

investment center? 4. Explain why variable and �ixed costs behave differently when a budget is “�lexed” from the expected to the

actual level of activity. 5. For what kinds of business activities are project budgets useful? 6. Why are the human behavioral concerns important in budgeting? Identify and explain the concerns. 7. If Widman Products Company were a wholesaler and not a manufacturer, how would the master budget

sequence as presented change? 8. From the master budget example, identify the independent variables. Which schedules contain only

dependent variables? 9. Explain why preparing the cash-�low forecast requires that all operating and project budget schedules be

completed �irst. 10. What does “what if ” analysis mean?

Exercises 7-1. Materials Requirements. Tendler & Co. produces plastic buckets. The following budget data are available:

a. Ending �inished goods inventory: 20% of next quarter’s sales. b. Ending materials inventory: 30% of next quarter’s production needs. c. Forecast sales for each quarter of next year are 1,000, 1,100, 1,200, and 1,300 buckets, respectively. d. Two pounds of plastic are needed for each bucket. January 1 inventories are at the correct planned levels.

Question:

How many pounds of plastic must be purchased for the �irst two quarters of next year to meet the bucket sales forecast?

7-2. Forecast Cash Payments. Jaret’s Shoe Shop is preparing its cash budget for the month of November. The following information is available about its operation:

November beginning inventory $18,000

Estimated November cost of goods sold 90,000

Estimated November ending inventory 16,000

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Estimated November payments for purchases made prior to November 21,000

Estimated November payments for purchases made in November 80%

Question:

What are the estimated cash payments in November for Jaret’s Shoe Shop?

7-3. Cash Receipts. Hampshire Company, located in Manchester, U.K., prepared the following sales budget for the �irst six months:

January February March April May June

Sales units 6,000 7,000 7,500 8,500 7,800 8,300

Units sell for £20 each. Twenty percent of sales is for cash, and the remainder is on account. The �irm forecasts collection of sales on account to be 60% in the month of sale with the remainder collected in the next month. Beginning receivables at January 1 is £40,000.

Questions:

1. Find the forecast cash receipts for each month. 2. If more customers use credit cards, causing cash sales to increase to 40% of total sales, by how much is

cash increased in the second quarter?

7-4. Purchases and Payments. Cumberland Company sells course note packets for classes with high enrollments at Coventry University. Each packet sells for $10, and the purchase cost is $6 per packet. The �irm keeps an inventory of 40% of next month’s forecast sales. Each month, it pays suppliers 70% of the current month’s purchases, and the remainder is paid in the following month. The Spring semester’s sales budget is:

January February March April May

Sales $6,000 $4,000 $3,000 $6,000 $1,000

Questions:

1. Calculate Cumberland’s budgeted purchases per month through April. 2. Show Cumberland’s cash payments to suppliers per month from February through April.

7-5. Flexible Budgeting. PeeWee’s Bicycle Co. operates a repair shop on May�ield Road. The owner has calculated his overhead costs per year to be $10,000 plus $10 per bicycle repaired. In late 2019, he prepared a budget for repairing 500 bikes in 2020. He actually repaired 550 bikes in 2020 and spent $15,200 for overhead expenses.

Question:

Comment on each of the following statements about 2020 activities.

a. His cost function is ($10,000 / 500) + $10, or $30 per bike. b. His original budget for 2020 (prepared in late 2019) was $15,500. c. His spending was $200 over his original budget; therefore, he did not control costs well. d. His spending was $300 under his adjusted budget; therefore, he did control costs well.

7-6. Expected Value of Pro�it. The sales manager of the Bleier Corporation’s Economic Forecasting Department has estimated that a 40% probability exists that sales volume for next year will be 600,000 units with a selling price of $7 per unit. A 60% probability exists that sales will be 500,000 units with a selling price of $8 per unit. Variable cost per unit is estimated at $6 (with a probability of 20%) or $5 (with a probability of 80%). Fixed costs for the next year have been estimated at $800,000.

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Question:

Compute the expected value of forecast net income for next year.

7-7. Budget Comments. Comment brie�ly on the following quotes about budgeting from a �inancial planning textbook:

a. “One major criticism of budgeting is that it is used as a ‘cost reduction’ tool rather than a ‘cost control’ tool. The objective of the budget is to control costs at an ef�icient level of operation.”

b. “There are generally three bene�its from allowing employees to participate in developing the budget: (1) Employees tend to accept the budget as their own plan of action. (2) Participation tends to increase morale among employees and toward management. (3) Employee cohesiveness is increased, and productivity will also increase if dictated by the group norm.”

c. “Even though budgets are quantitative tools, considerable emotion is connected to budgeting. The individual in control often sees the budget as a means of getting things done. People being controlled often have feelings of anxiety because their success and promotion are tied directly to the budget.”

7-8. Purchases and Cash Payments. A production plan by quarter for ADS Company is:

First quarter 24,000 units Third quarter 32,000 units

Second quarter 30,000 Fourth quarter 42,000

Four units of materials are used in producing each unit of product. Each unit of materials costs $0.60. Ending materials inventory is to be equal to 25% of production requirements for the next quarter. This requirement was met at the beginning of the year. Production for the �irst quarter following the budget year is estimated at 28,000 units. Accounts payable for materials purchased is estimated at $38,400 at the beginning of the current budget year. Forecast accounts payable at the end of the quarter should equal 40% of the purchases during the quarter.

Questions:

1. Determine the units of materials to be purchased each quarter. 2. Determine the cost of materials purchases by quarter. 3. Estimate the payments to be made each quarter for materials.

7-9. Basic Budget Relationships. Analyze the following situations.

a. Evan Corporation has a $75,000 balance in its accounts receivable account at the beginning of the budget month. Sales on account this month should be $160,000, and 70% of those sales should be collected in the month of the sale. In addition, 60% of the beginning balance in accounts receivable is expected to be collected this month. What is expected to be the budget month’s ending balance of accounts receivable?

b. Henry Supply, a wholesaler, estimated sales of $750,000 for the third quarter and $800,000 for the fourth quarter. The estimated gross pro�it rate is 40%. The June 30 inventory is $120,000. The targeted inventory at the end of the third quarter is to be 20% of fourth quarter sales volume. What quantity of inventory should be purchased in the third quarter?

c. Schneider’s Wholesale Apparel is budgeting for the year. The beginning accounts receivable and partial sales data are given below:

First Quarter Second Quarter

Accounts Receivable $200,000 Sales $600,000 $800,000

Sales are all on credit, and 80% are collected in the quarter of sale. The remainder is collected in the next quarter. What are budgeted cash collections in the second quarter?

Question:

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Find the requested amount in each situation.

7-10. Various Budget Schedules. Sloviter Candies is preparing a budget for the second quarter of the current calendar year. The March ending inventory of merchandise was $106,000, which was higher than expected. The company prefers to carry ending inventory amounting to the expected sales volume of the next two months. Purchases of merchandise are paid half in the month of purchase and half in the month following purchase, and the balance due on accounts payable at the end of March was $24,000. Budgeted sales are as follows:

April $50,000 July $72,000

May 48,000 August 56,000

June 60,000 September 60,000

Questions:

1. Assume that a 25% gross pro�it margin is budgeted. Prepare a budget schedule that shows the following for April, May, and June:

a. Cost of goods sold b. Purchases required c. Cash payments for merchandise

2. Assume that the accounts receivable balance on April 1 was $35,000 and that three-fourths of all customers pay in the month of sale and one-fourth in the month following the sale. Prepare a budget showing the cash receipts from accounts receivable for April, May, and June.

7-11. Adequacy of Cash Flow With “What Ifs.” Marcy Lynn is preparing a budget of cash receipts and disbursements for Newman Food Services, Inc. Some sales are for cash, and the remainder is billed on a contract basis. Sales for April to August are:

Cash Sales Billed Sales Total Sales

April $65,000 $40,000 $105,000

May 72,000 46,000 118,000

June 84,000 68,000 152,000

July 88,000 72,000 160,000

August 86,000 70,000 156,000

Of the billed sales, 65% is collected during the month of sale; the other 35% is collected the next month.

Food costs amounting to 75% of sales must be paid during the month of sales. Monthly operating costs are $24,000. The cash balance at May 1 amounted to $7,000. If the cash balance is more than $20,000 on August 31, Marcy and the other shareholders will receive the excess as dividends.

Questions (use of spreadsheet software is recommended):

1. Prepare a budget of cash receipts and disbursements for each month, May to August, inclusive. 2. Compute the amount, if any, that can be paid in dividends at the end of August. 3. What is the impact on possible dividend payments in the following situations?

a. “What if ” competitive pressures cause food costs to increase to 80% of sales? b. “What if ” collections of billed sales slow to 50% in the month of sale and 50% in the next month?

7-12. Cash Budgeting. Benporath Corporation, a Melbourne, Australia, �irm, is preparing a cash budget for 2020 using the following data:

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a. Each month, 70% of sales is on credit. Of credit sales, 60% is collected in the month of sale and 40% in the next month.

b. Cost of goods sold is 70% of sales. Of purchases, 60% is paid when purchased; and the remainder is paid in the next month.

c. Planned inventory is 40% of the next month’s sales. Budgeted purchases in February were A$60,000. d. Operating expenses are A$30,000 per month, including A$2,000 of depreciation expense. These are paid

when incurred. e. Forecast cash balance as of March 1 is A$20,000, which is the target level.

Budgeted sales, in Australian dollars, for a portion of 2020 are: February A$90,000, March A$120,000, April A$110,000, and May A$100,000.

Questions:

1. Create a cash forecast for March. 2. If Benporath plans to buy a computer system for A$20,000, can the �irm pay for it and keep a “safe” cash

level? What are the main risks?

7-13. Managerial Behavior and Budget Ethics. Shulamith Corporation has seen a new revision of the budget system each year for the past �ive years. Bonuses followed strong budget performances. The following are changes made during the past few years:

Change 1: One year top management felt that, since wages were 60% of total expenses, the budget should simply focus on keeping next year’s headcounts equal to or below the current year’s level. Most managers did this by shifting work to outside contractors. Change 2: Concern over customer service caused top management to budget the number of back orders issued because an item was not available from existing inventory. A trip to Tahiti was given to managers with zero actual back orders. Change 3: Because corporate expenses were viewed as being too high, the president, Jonathan Klein, decided to allocate all home of�ice expenses to the nine divisions. Each division head budgeted down to “net income” and was evaluated on the comparison of actual to planned “net income.” Change 4: Also, at the �inal budget approval stage for the last several years, Klein forced each division to reduce its total expenses by an even 5% across the board. This year, Klein increased the across-the-board cuts to 10%.

Question:

Comment on Shulamith Corporation’s approach to budgeting and the possible impacts each change might have on the budget process and managers’ behavior.

Problems 7-14. Responsibility Accounting and Roll-up Reporting. Greenblatt Packaging Corporation has two plants, one in Los Angeles and one in Singapore. Each plant has a forming and a packing department. Production for the forming department of the Los Angeles Plant is estimated at 1,600 tons for June. The budgeted costs per ton are as follows:

Direct materials $8

Direct labor 15

Factory overhead (half �ixed and half variable) 10

Total per ton $33

Total budgeted production costs for the packing department are $33,000 for June. Budgeted costs for the plant manager’s of�ice are $57,000.

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Budgeted costs for the Singapore plant total $67,000. The vice president of production, Fred Horn, is responsible for both plants and has $54,000 of budgeted expenses. Budgeted expenses for the company’s vice president of marketing’s of�ice are $112,600. The president’s of�ice budget is $60,000.

In June, 1,500 tons were produced, and actual expenses were as follows:

President’s of�ice $62,300 Los Angeles plant:

Vice president of marketing 109,800 Plant manager’s of�ice $58,300

Vice president of production 55,500 Packing department 34,900

Singapore plant – total costs 70,100 Forming department:

Direct materials 10,600

Direct labor 23,400

Overhead 13,200

Question:

Prepare responsibility reports showing the appropriate budget, actual expenses, and variances from budget for each of the following:

a. Forming department in Los Angeles plant b. Plant manager for the Los Angeles plant c. Vice president of production d. President of the company

7-15. Cash Forecasting. Jeff Snow is preparing his budgets. He has written the following on a pad of legal paper:

Forecast Sales Actual December 31 Balance Sheet Data

January $70,000 Cash $8,000

February 90,000 Accounts Receivable 20,000

March 80,000 Inventory 40,000

April 60,000 Accounts Payable 45,000

Other data are as follows:

a. Sales are on credit with 40% collected in the month of sale and 60% in the next month. b. Cost of sales is 60% of sales. c. Other variable costs are 10% of sales, paid in the month incurred. d. Inventories are to be 80% of next month’s budgeted sales requirements. e. Purchases are paid in the month after purchase. f. Fixed expenses are $3,000 per month; all are paid in the month incurred.

Question:

Prepare a cash budget for February.

7-16. Budgeted Income Statement for a Service Organization. Gal Motel is a low-priced motel in southern California. It has 50 rooms, each with two double beds. The rates are $48 for one person, $10 for the second person, and $3 each for the third and fourth persons. Rollaway beds are available for $2 per night.

During April, the motel manager, Dora Ludwig, expects an 80% occupancy rate. Past experience suggests that 20% of the rooms rented will be to only 1 person, 20% to 2 persons, 30% to 3 persons, and 20% to 4 persons. Ten

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percent will have 5 persons and use rollaway beds.

Laundry costs average $2 per person per night. Cleaning workers earn $15 per hour, and it takes 30 minutes to clean each room. Other variable operating costs (utilities, for example) are $8 per occupied room per night. Maintenance and grounds personnel costs are about $4,000 per month. Two clerks each have a salary of $3,300 per month. Depreciation is $2,000 per month. Other cash �ixed expenses are $3,500 per month.

Questions:

1. Prepare a budgeted income statement for April. 2. Suggest an average occupancy percentage needed to break even if the average number of people staying in

a room is three.

7-17. Production and Inventories. Freedman Company has irregular sales volume during the year, and management is planning to produce at a uniform rate with inventories increasing or decreasing throughout the year. A sales budget in product units is forecast for the �irst six months of the year, as follows:

Months Units Months Units

January 40,000 April 25,000

February 25,000 May 40,000

March 20,000 June 50,000

The production cycle is short, and work in process inventories are insigni�icant. An inventory of 10,000 units was on hand at January 1, and 20,000 units of inventory are planned for June 30.

Questions:

1. Prepare a production schedule that will have level production each month while showing the expected inventories at the end of each month.

2. Comment on the problems this approach creates. Why is it attractive?

7-18. Project Management. In the Hurwitz Corporation, an advertising project is forecast to cost $100,000, generate $200,000 in additional variable contribution margin, and take 6 months to complete.

It is now 4 months into the project, and $60,000 has been spent. Hurwitz estimates that it is one-third done and that it will take another 8 months and $100,000 to complete the project. Current estimates now show that the forecast additional variable contribution margin will be $160,000.

Questions:

1. How does Hurwitz report the project relative to the budget? 2. How does Hurwitz report this project in its “plan of action,” if approved for continuation?

7-19. Expected Cash Flow. Mara Equipment Company is planning to expand beyond the industrial market of its materials handling equipment to produce trailers for the sports and recreation markets. The president, Joey Pollack, estimates that the company must invest $1,800,000 in new equipment up front. He wants to know how much cash �low can be provided by operations next year to apply toward acquiring the equipment and how much of the cost will have to be �inanced.

His sales staff estimates revenue next year at $8,500,000. However, if economic conditions deteriorate, sales revenue may be only $6,500,000.

Cost of goods sold has historically been 70% of revenue. A possibility exists that the company will have to absorb cost increases that cannot be passed along to customers. In this case, the cost of goods sold will be 80% of revenue.

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With sales down to $6,500,000, the cost of goods sold will de�initely be 80% of revenue. Probabilities of occurrence have been estimated for each of three alternatives as follows:

Operating Revenues and Cost of Goods Sold Expenses Probabilities

Sales at $8,500,000, cost of goods sold at 70% $1,050,000 30%

Sales at $8,500,000, cost of goods sold at 80% 1,200,000 50%

Sales at $6,500,000, cost of goods sold at 80% 1,100,000 20%

Depreciation of $280,000 is included in operating expenses under each alternative, and depreciation of $350,000 is included in cost of goods sold for each alternative. Income taxes are estimated at 40% of income before income taxes.

In making the transition, equipment will be sold for $600,000, net of income taxes. A payment of $350,000 must be made on long-term notes payable. Joey wants dividends of $300,000 to be paid under each alternative.

Questions:

1. What is the “worst case” cash-�low scenario that Joey could face? 2. Prepare a statement to show the forecast cash �low provided by operations under each assumption and the

expected value of cash �lows. 3. Continue the forecast statement to show how much additional cash will be needed to �inance the new

project after considering the information given. Show the impact of all three assumptions on expected cash �lows.

7-20. Budgeted Cost of Goods Manufactured. Ayal Plastic Products had inventories of 75,000 pounds of raw materials and 25,000 units of �inished product on January 1. Sales forecasts for the �irst six months are as follows:

January 40,000 units April 70,000 units

February 55,000 May 60,000

March 50,000 June 70,000

Ayal maintains a �inished goods inventory equal to 40% of the forecast sales of the next month and a raw materials inventory equal to 30% of the next month’s production requirements. Each unit of product requires 3 pounds of raw materials at $5 per pound.

The budgeted direct labor cost is $8 per hour, and each �inished unit requires 30 minutes. Variable factory overhead is 40% of raw materials costs. Fixed factory overhead, including depreciation of $10,000, totals $90,000 per month and is applied using units. Normal volume is 60,000 units per month.

Questions (use of spreadsheet software is recommended):

1. Prepare a budgeted cost of goods manufactured schedule. Include supporting schedules needed to calculate product cost components and unit costs.

2. Analyze the overhead �lexible budget and amounts applied. 3. Comment on the following:

a. “What if ” �inished goods inventory level is only 20% of next month’s sales? b. “What if ” normal capacity is 50,000 units per month?

7-21. Cash Flows and “What If.” Dennis Christopher, a member of the board of directors of Riley Markets, Inc., is concerned about the ability of the company to repay a loan in the amount of $250,000 that matures on June 30, 2020. In addition to the principal of the loan, the company must pay interest of $50,000.

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The cash balance at January 1, 2020, is $82,000. Sales for December 2019 through June 2020 are budgeted as follows:

Net Sales

December 2019 $236,000

January 2020 137,000

February 142,000

March 182,000

April 170,000

May 156,000

June 148,000

Cash sales each month are equal to approximately 30% of net sales. Collections on accounts receivable are expected as follows:

a. 60% collected during the month of sale b. 40% collected in the following month

Total cash disbursements are estimated at $115,000 each month.

Questions (use of spreadsheet software is recommended):

1. Prepare a cash budget for each month and in total for the six months of 2020. 2. Will the company be able to pay the loan with interest and still maintain a cash balance of no less than

$60,000 on June 30? Explain. 3. If actual sales are 10% lower than the forecast each month while cash expenses drop by only $5,000 per

month, what will happen to the company’s ability to pay off the loan and keep the cash balance at the desired level?

4. If the sales and expenses fall as in Part (3) and collections patterns change to 40% collected in the current month and 60% in the following month, what will happen to the company’s cash situation?

7-22. Budgeted Balance Sheet. The balance sheet for Spaner Stores, Inc. at December 31, 2019, is:

Assets: Liabilities and Equity:

Cash $82,000 Accounts payable $62,000

Accounts receivable 112,000

Inventory 136,000 Capital stock 300,000

Building and �ixtures, net 358,000 Retained earnings 326,000

Total assets $688,000 Total liabilities and equity $688,000

Cash receipts for the year are collections on accounts receivable amounting to $846,000. Cash payments are budgeted at $838,000. Included in those payments is $126,000 for various expenses that do not �low through accounts payable. Credits to accounts payable for the year are estimated at $715,000, all merchandise purchases. All cash payments are for expenses or purchases. Depreciation expense is $75,000. Net credit sales are estimated at $930,000. The inventory of merchandise is expected to increase to $147,000 by the end of the year.

Question:

From the information given, prepare a budgeted balance sheet at December 31, 2020. Prove the retained earnings balance by computing the net income. Income tax is estimated at 40% and will be paid after December 31, 2020.

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7-23. Forecast Balance Sheet. Ira’s Electronics designs and assembles electronic systems used by a variety of organizations. Its principal products are medical measurement systems and instrumentation systems for chemical analyses.

As a member of the budgeting team, your assignment is to prepare the budgeted balance sheet, based on information provided by other team members. The latest actual balance sheet shows:

Beginning Balance Sheet, December 31 (in Millions)

Current Assets: Current Liabilities:

Cash $479 Accounts payable $249

Accounts receivable 590 Accrued income taxes 132

Inventories 511 Other liabilities 280 $661

Prepaid expenses 30 Long-term debt 143

Total current assets $1,610 Total liabilities $804

Plant and equipment $1,397 Shareholders’ equity:

Less: depreciation 462 Common stock $356

Net plant and equipment 935 Retained earnings 1,385 1,741

Total assets $2,545 Total liabilities and equity $2,545

Cindy Feuer, another member of the team, has given you the following budgeted income statement for the coming year:

Forecast Income Statement (in Millions)

Sales revenue $3,253

Cost of goods sold 1,583

Gross pro�it $1,670

Operating expenses:

Marketing $590

General and administrative 358

Research and development 343 1,291

Net income before taxes $379

Provision for income taxes 134

Net income after taxes $245

The controller, Gail Kessler, has also furnished you with a number of assumptions, policies, and other information as follows:

1. The company has made arrangements to acquire plant and equipment during the year for $339 million. Long-term debt will �inance $18 million, and cash will be used for the remainder.

2. All sales are on credit. Collections on credit sales for the year are scheduled to be $3,218 million. 3. Changes in several account balances are planned.

a. Inventories will decrease by $15 million. b. Other accrued liabilities will increase by $70 million. c. Prepaid expenses will increase by $10 million.

4. Depreciation expense in the forecast income statement totals $105 million. 5. Payments of accounts payable will total $2,682 million and on accrued income taxes will be $179 million.

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6. Common stock will be sold to employees in a special stock purchase plan for $34 million. 7. Dividends of $29 million will be declared and paid during the year.

Questions:

1. Prepare a forecast year-end balance sheet. 2. Does the proposed �inancing of new plant and equipment strain the cash position? Explain. 3. Identify several danger areas in the forecast that might cause the asset acquisition to be dif�icult to �inance.

What other sources of cash might exist?

7-24. Probabilistic Budgeting. Busch Manufacturing Company is in the process of preparing its operating budget for next year. Phyllis Neal, controller, wants to include in the budget documents a budgeted income statement based on probabilities. In visiting with selling, production, and administrative personnel, Neal has obtained estimates and probabilities for each area.

Unit sales estimates, with associated selling prices and probabilities, are:

Units Selling Price Probability

800,000 $25 .20

700,000 28 .30

600,000 32 .40

500,000 36 .10

Variable manufacturing costs will either be $8 per unit, with a probability of 80%, or $10 per unit, with a probability of 20%. Fixed manufacturing costs have a 90% chance of being $4,000,000 and a 10% chance of being $5,000,000. Variable selling and administrative expenses are estimated at $2, $3, or $4, with probabilities of 20%, 70%, and 10%, respectively. Fixed selling and administrative expenses have a 60% chance of amounting to $5,000,000 and a 40% chance of being $6,000,000.

Question:

Prepare a budgeted income statement based on expected values.

Case: Chester & Wayne

Chester & Wayne is a regional food distribution company. Mr. Chester, CEO, has asked your assistance in preparing cash-�low information for the last three months of this year. Selected accounts from an interim balance sheet dated September 30 have the following balances:

Cash $142,100 Accounts payable $354,155

Marketable securities 200,000 Other payables 53,200

Accounts receivable 1,012,500

Inventories 150,388

Mr. Wayne, CFO, provides you with the following information based on experience and management policy. All sales are credit sales and are billed the last day of the month of sale. Customers paying within 10 days of the billing date may take a 2% cash discount. Forty percent of the sales is paid within the discount period in the month following billing. An additional 25% pays in the same month but does not receive the cash discount. Thirty percent is collected in the second month after billing; the remainder is uncollectible. Additional cash of $24,000 is expected in October from renting unused warehouse space.

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Sixty percent of all purchases, selling and administrative expenses, and advertising expenses is paid in the month incurred. The remainder is paid in the following month. Ending inventory is set at 25% of the next month’s budgeted cost of goods sold. The company’s gross pro�it averages 30% of sales for the month. Selling and administrative expenses follow the formula of 5% of the current month’s sales plus $75,000, which includes depreciation of $5,000. Advertising expenses are budgeted at 3% of sales.

Actual and budgeted sales information is as follows:

Actual: Budgeted:

August $750,000 October $826,800

September 787,500 November 868,200

December 911,600

January 930,000

The company will acquire equipment costing $250,000 cash in November. Dividends of $45,000 will be paid in December.

The company would like to maintain a minimum cash balance at the end of each month of $120,000. Any excess amounts go �irst to repayment of short-term borrowings and then to investment in marketable securities. When cash is needed to reach the minimum balance, the company policy is to sell marketable securities before borrowing.

Questions (use of spreadsheet software is recommended):

1. Prepare a cash budget for each month of the fourth quarter and for the quarter in total. Prepare supporting schedules as needed. (Round all budget schedule amounts to the nearest dollar.)

2. You meet with Mr. Chester and Mr. Wayne to present your �indings and happen to bring along your PC with the budget model software. They are worried about your �indings in Part 1. They have obviously been arguing over certain assumptions you were given.

a. Mr. Wayne thinks that the gross margin may shrink to 27.5% because of higher purchase prices. He is concerned about what impact this will have on borrowings. Comment.

b. Mr. Chester thinks that “stock outs” occur too frequently and wants to see the impact of increasing inventory levels to 30% and 40% of next quarter’s sales on their total investment. Comment on these changes.

c. Mr. Wayne wants to discontinue the cash discount for prompt payment. He thinks that maybe collections of an additional 20% of sales will be delayed from the month of billing to the next month. Mr. Chester says, “That’s ridiculous! We should increase the discount to 3%. Twenty percent more would be collected in the current month to get the higher discount.” Comment on the cash-�low impacts.

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Practice Problems in Action

Watch the video below for a step-by-step tutorial on how to solve the following problem using Excel. The video is best viewed in full-screen mode. For a transcript of the directions included in this tutorial video click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/BUS630_2e/Chapter-7_Tutorial-Transcript_FINAL.pdf) .

Problem The CFO of a regional food distribution company has asked for your assistance in preparing cash-�low information for the next month. Selected accounts from an interim balance sheet dated May 31 have the following balances:

Cash $85,260

Marketable Securities 12,000

Accounts Receivable 607,500

Inventories 90,232

Accounts Payable 212,493

The CFO provides you with the following information based on experience and management policy. All sales are credit sales and are billed the last day of the month of sale. Customers paying within 10 days of the billing date may take a 2 percent cash discount. Forty percent of the sales is paid within the discount period in the month following billing. An additional 25 percent is paid in the same month but does not receive the cash discount. Twenty percent is collected in the second month after billing; the remainder is uncollectible. Additional cash of $35,000 is expected in July from renting storage space in the factory.

Actual and budgeted sales information is as follows:

Sales

Actual Budget

May $450,000 July $496,080

June $472,500

The company will acquire equipment costing $30,000 cash in July. Accounts payable for July is projected to be $409,773.

The company would like to maintain a minimum cash balance at the end of each month of $72,000. Any excess amounts go �irst to repayment of short-term borrowings and then to investment in marketable securities. When cash is needed to reach the minimum balance, the company policy is to sell marketable securities before borrowing.

Question Prepare a cash budget for July. Prepare supporting schedules as needed. (Round all budget schedule amounts to the nearest dollar.)

Tutorial Video: Creating a cash budget

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