balakrishnan mgrl solutions ch04

Chapter 4 Solutions

PAGE 4-2

Chapter 4

TECHNIQUES FOR ESTIMATING FIXED AND VARIABLE COSTS

Solutions

Review Questions4.1

Because the statement groups costs by business function rather than variability. That is, the traditional income statement combines fixed (non-controllable) and variable (controllable) costs.

4.2

Revenues less variable costs. It is the amount that contributes toward recovering fixed costs and earning a profit.4.3

The GAAP-based income statement, which is used for external reporting, groups costs by business function, separating product costs from period costs (as discussed in Chapter 3). In contrast, the contribution margin statement groups costs by variability, separating fixed costs from variable costs.

4.4

Yes, along with revenues and variable costs.

4.5

By separating out fixed costs, which relate to the costs of capacity resources and usually do not change in the short-term, from revenues and variable costs, which vary with activity volume and usually are controllable in the short term.

4.6

Account classification, the high-low method, and regression analysis.4.7 (1) Sum the costs classified as variable to obtain the total variable costs for the most recent period; (2) Divide the amount in (1) by the volume of activity for the corresponding period to estimate the unit variable cost; and (3) Multiply (2) by the change in activity to estimate the total controllable variable cost.4.8 The primary advantage is that it can provide very accurate estimates because it forces us to examine each cost account in detail. The primary disadvantages are that the method is time-consuming and subjective.4.9

The two observations pertaining to the highest and lowest activity levels. These two values are most likely to define the normal range of operations.4.10

The primary advantage is that the high-low method is easy to use and only requires summary data. The primary disadvantages are that it only uses two observations (throwing away much of the data) and yields only rough estimates of the fixed costs and unit variable costs.

4.11

While the high-low method only uses two observations, regression analysis uses all available observations to come up with a line that best fits the data.

4.12

(1) R-square, which indicates the goodness of fit this statistic is between 0 and 1, with values closer to 1 indicating a better fit; (2) p-value, which indicates the confidence that the coefficient estimate reliably differs from 0.

4.13

The relevant range is the normal range of operations, where we expect a stable relationship between activity and cost.4.14

We compute a segment margin by subtracting traceable fixed costs related to the segment (e.g., a product, customer, geographical region) from its contribution margin. The two margins differ by the traceable fixed costs.4.15

(1) products; (2) customers; (3) stores; (4) geographical regions; and, (5) distribution channels are some of the many ways an organization might segment its contribution margin statement.

Discussion Questions

4.16 A 5% decrease in selling price would result in a larger decrease in unit contribution margin than a 5% increase in variable costs. To see why, keep in mind that unit selling price is a larger number than unit variable cost (otherwise, unit contribution margin will not be positive). Therefore, a 5% decrease in selling price will also be proportionately larger than a 5% decrease in variable cost. For example, if the unit selling price is $10 and the unit variable cost $6, then the unit contribution margin is $4 (= $10 - $6). With a 5% decrease in selling price, the selling price decreases by $0.50 to $9.50; the unit contribution margin also decreases by the same $0.50 to $3.50 (= $9.50 - $6). With a 5% increase in variable costs, the unit variable cost increases by $0.30 to $6.30, and the unit contribution margin decreases by the same $0.30 to $3.70 (= $10 6.30).

4.17 Investors are external users of the financial reports prepared by firms. Investors might prefer the income statement using the gross margin format because the cost of goods sold as reported in this format includes allocated fixed costs such as depreciation, factory overhead and so on. These allocated fixed costs represent a rough measure of the opportunity cost of capacity resources. Thus, investors get an idea of profitability after taking into account the opportunity cost of the usage of capacity resources.

4.18 A key aspect of the contribution margin statement is that it clearly separates fixed costs from variable costs associated with various decision options. Because contribution margin is revenues less variable costs, the decision maker can correctly compute the contribution margin associated with each decision option. In the short run, fixed costs do not change, and therefore contribution margin constitutes the right basis for decision making. In the long run, however, many fixed costs become controllable and relevant for decision making.

4.19 As is often said, A picture is worth a thousand words. Plotting the data helps in quickly assessing the behavior of various cost items i.e., whether a cost is fixed or variable with respect to the volume of production, just by inspection. Plotting the data also helps us determine the appropriate technique to use to estimate fixed and variable costs. Moreover, plots often reveal a few data points that do not appear to conform to the general pattern emerging from other data points. Such outliers or extreme observations are typically the result of recording errors or unusual activities in a specific period. We can identify and eliminate such observations from consideration because they are not likely to reflect typical behavior.

4.20 The reason for plotting is to examine how a cost item increases in activity volume. Some months may have high activity volumes and other months may have low activity volumes in no particular order. But we would like to know how costs vary as the activity volume increases or decreases. For this reason, if we sort by activity volume and plot it on the X-axis, and plot the corresponding cost on the Y-axis, the resulting plot will indicate how cost increases as the activity volume increases along the X-axis.

4.21 Account classification requires us to examine each cost account in detail, and provides very accurate estimates. Often, this analysis requires us to plot each cost account and examine the graph and exercise some judgment to determine its behavior. Grant proposals often require the proposal preparers to exercise considerable judgment. They typically involve a manageable number of line items so that an accurate line-by-line estimation of costs using the account classification method is not such a tedious task.

4.22 Large projects are often unique and dissimilar. Smaller and routine decisions tend to be more alike. Therefore using mechanical methods such as the high-low method work reasonably well for small and routine decisions. On the other hand, such methods will likely result in much greater estimation errors for large projects. And, erroneous estimation of costs can in turn prove quite costly if they lead to bad decisions relating to large projects. Even though tedious, the account classification method is more suited for large and unique projects.4.23 One can visually verify that high and low data points are representative by making sure they do not seem to be outliers with respect to the rest of the data points. That is, these points do not seem out of step or pattern with other points. 4.24 One reason could be that either the high data point or the low data point (or both) is an outlier. Another reason could be a change in the fixed cost that may have occurred in the interim. The high-low method will not be able to detect this change. The accounting classification method will.

4.25 True the high-low method relies completely on just two data points to separate fixed costs and variable costs. If one of these points turns out to be an outlier, the estimates can be completely off. In contrast, a regression detects the cost behavior using all available data points. Consequently, each individual observation has far less influence on the estimates than the high or low data points in the high-low method.

4.26 Yes, going back to obtain historical data from many years does increase the number of data points we use in a regression. However, we would be assuming that the cost structure the mix of fixed and variable costs stays the same over all these years. In practice, firms change with time. Fixed costs change as more capacity is added or some capacity is reduced. Unit variable costs may decrease as production becomes more efficient. Therefore, the longer is the time period, the less applicable is the assumption that the cost structure remains the same. And, such cost structure changes limit the extent to which we can use historical data for estimation purposes.

4.27 We can use number of batches and number of products as additional variables in the right hand side of the regression equation along with the activity volume. In such a regression, we can interpret the intercept as facility level costs because these costs do not vary at all.

4.28 In estimating the revenues and costs using this kind of a two-part fee structure, it becomes necessary to estimate the number of families, average family size, and the number of individual memberships. Revenues would be determined by the number of families multiplied by the family membership fee plus the number of individual memberships multiplied by the individual membership fee. On the cost side, one needs to estimate the total membership as number of families multiplied by the average family size plus number of individual members, and then multiply this total membership by the cost of serving each member. In principle, this setting is similar to situations in which firms bundle their products for market penetration (e.g., a vacation package comprising of airline tickets, hotel costs, and cruises, as opposed to just airline tickets, hotel costs and cruises). Bundles are priced differently than individual products, and bundling is an integral part of the marketing strategy.

4.29 Yes, it does! Such a contribution margin statement will help measure how much contribution each major customer makes to the fixed costs of the company. It will help in customer-related decisions such as whether to keep or drop a particular customer, whether some customer-specific promotions and discounts can improve the contribution from that customer and so on. Customer Profitability Analysis is an important strategic tool that we will discuss in Chapter 10.

4.30 If a grocery store stops selling 1% lowfat milk, its revenues from 2% lowfat milk is likely to go up, as customers who routinely buy 1% lowfat milk settle for the next best option. This is an example of a positive spillover effect. On the other hand, if an automobile repair shop stops doing routine maintenance services, it is likely to lose revenues from other repair issues that typically crop up during routine maintenance services. This is an example of a negative spillover effects. Yes, spillover effects are controllable and must be considered in the decision to drop the 1% lowfat milk in the case of the grocery store, and the routine maintenance service in the case of the automobile repair shop.

4.31 Here is the income summary of operating segments of General Electric Corporation extracted from its 2006 Annual Report.

Exercises

4.32 Unit contribution margin = Price all variable costs

We first calculate price = ($15,000 revenue/500 units) = $30 per unit. Given that variable manufacturing costs = $10 per unit and variable selling costs = $2 per unit, then unit contribution margin = $30 - $10 - $2 = $18 per unit.

Contribution margin = number of units unit contribution margin

Thus, contribution margin = 500 units $18/unit = $9,000.

The following is the contribution margin statement.

Contribution Margin Income Statement

Revenue500 units $30 per unit$15,000

Variable manufacturing costs500 units $10 per unit 5,000

Variable selling costs500 units $2 per unit1,000

Contribution margin$9,000

Fixed manufacturing costs6,000

Fixed selling costs2,000

Profit$1,000

4.33The following table presents the required statement.

Ajax Corporation

Contribution Margin Income Statement for the most recent Year

Revenue$1,525,000

Cost of goods sold900,000

Sales commissions91,500

Variable cost of transport in6,500


Fixed transportation cost18,000

Administration costs220,000

Selling costs148,500

Profit$140,500

Notice that the contribution margin statement regroups the costs into fixed and variable costs. Moreover, because it is a merchandiser, Ajax buys and sells goods without substantially transforming them. Thus, its cost of goods sold is a variable cost; this cost is the amount Ajax would have paid its suppliers. We obtain sales commissions as 6% of sales revenue (0.06 $1,525,000 = $91,500). We then back out fixed selling costs as the remainder ($240,000- $91,500 = $148,500).

4.34The following table presents the required statement.

Jindal Corporation

Contribution Margin Statement for the most recent Year

Revenue$2,435,000

Variable cost of goods sold998,010

Sales commissions121,750

Contribution margin$1,315,240

Fixed manufacturing costs248,750

Fixed administration costs425,000

Fixed selling costs437,200

Profit$204,290

Notice that the contribution margin statement regroups the costs into fixed and variable costs. We obtain sales commissions as 5% of sales revenue (0.05 $2,435,000 = $121,750) and back out fixed selling costs as the remainder ($558,950 - 121,750 = $437,200).

Note: The instructor can point out that inventories would substantially complicate this problem. The complication arises because GAAP (which governs the gross margin statement) classifies fixed manufacturing costs as product costs, whereas the contribution margin statement classifies them as period costs. We address this issue in Chapter 9.

4.35The following table provides the required detail.

ItemEstimateDetail

Student related variable costs $2,500 50 = $125,000Variable in number of students

Faculty related costs2 faculty $150,000 = $300,000Variable in number of faculty hired

Administration costs1 person $60,000 = $60,000Variable in number of staff hired.

Building maintenanceNo changeFixed for this decision.

Total$335,000

Notice that we would find it difficult to make this estimate using techniques such as the high-low method. Each cost element has a different driver, and major cost items such as faculty and staff costs are step functions.4.36 A simple analysis is to argue that the cost per unit is total product cost / total units (=$400,400/10,000 units), or $40.04. Adding 2,500 units a month for 2 months would add 5,000 units $40.04 = $200,200 to Megas cost.

However, this approach is incorrect. It does not distinguish between controllable and non-controllable costs. And, as we know from Chapter 2, the cost of making the additional units should only include controllable costs. How should we estimate controllable costs though? The following table identifies controllable costs, making the usual assumption that all variable costs are controllable and fixed costs non-controllable over the short term.

Variable items

Materials and components

These costs vary proportionately with the number of units made. The logic is easy to see for items such as materials, freight out, and labor. However, costs of supplies and oils also vary with production volume, even though these are indirect cost. These costs are the products variable overhead. The sales commissions also vary because revenue varies with volume.

Direct labor

Supplies

Oils and lubricants

Freight out

Sales commissions

Fixed costs items

Machine depreciationNone of these costs change if we change production volume, especially in the short-term.

Plant heating and lighting

Plant rental

Sales office administration

Corporate office costs

We estimate the total variable costs as $273,500 or $27.35 per unit. (Add up all of the variable cost amounts to obtain $273,500 as the cost of 10,000 units.) Thus, the expected increase in costs from adding 2,500 units a month for 2 months is 5,000 units $27.35 = $136,750.4.37

a. The following is the required statement.

Singapore Executive MBA Program

MidWest University

Tuition revenue$1,400,000 40 students $35,000

Partner fees490,000 Traced

Text books etc128,000 $200 per course 40 students 16 classes


Instructor salaries320,000 $20,000 16 courses

Instructor travel 72,000 $4,500 16 courses

Program assistance81,0001.5 FTE $54,000 per FTE

Program related travel19,5003 trips $6,500 per trip

Program margin $289,500

Associate Dean (allocated)22,50010% of salary

Deans time (allocated)17,5005% of compensation

Profit $249,500

This statement, which incorporates the cost hierarchy, shows that for each student enrolled in the class, the program generates 782,000/40 students = $19,550 in contribution margin. These costs and revenues are controllable for the decision to add students to the program.

Program related costs amount to $320,000 + $72,000 + $81,000 + $19,500 = $492,500. These costs are controllable for the decision of whether to keep or drop the program.

Finally, there is some allocated cost ($40,000) which is not likely controllable for any decision concerning the program. After all, the dean is unlikely to reduce her salary if the program shuts down.

b. For this decision, we only consider controllable costs and benefits, at the participant level. Notice that we cannot directly use the contribution margin statement because the revenue has changed, which changes some costs as well.

Increase in tuition revenue$75,000

Partner fees26,250

Textbooks 9,600

Net gain$39,150

Thus, it appears that the Dean should accept this offer. However, the Dean also needs to consider long-term and other spillover effects. For example, other students might also demand the same discount once word gets out about the fee concession. Further, there is a strong price-quality association with graduate degrees (particularly Executive MBA programs). Thus, lowering the price also might harm the programs image. Finally, the class is already at a good size; additional members might put it over the top in terms of a manageable class size. Overall, the decision is not clear-cut.

Note: The instructor can point out that account analysis is most useful for this decision. The high-low method or regression analysis is needlessly complex for a decision that only affects a few costs and revenues.

4.38 a.Silk Flowers and Mores shipping costs likely contain both fixed (e.g., employee costs) and variable (e.g., cartons, tape, and postage) elements. For convenience, let UVC (Unit variable cost) represent the variable cost per flower arrangement. Using the high-low method and the data provided, we have:

HIGH (February) $33,750 = Fixed costs + (UVC ( 7,500)

LOW (January) $27,500 = Fixed costs + (UVC ( 5,000)

Now we can solve for the unit variable cost.

UVC = $33,750 - $27,500 = $6,250 = $2.50 per flower arrangement sold.

7,500 5,000

2,500Substituting our estimate of UVC into either equation, we find that Fixed costs = $15,000. For example,

Fixed costs = $33,750 ($2.50 per arrangement 7,500 arrangements) = $15,000

Thus, Silk Flowers & Mores monthly shipping cost equation is:

Total shipping costs per month = $15,000 + ($2.50 ( Number of flower arrangements sold)

b. Once we have our cost equation, we can plug in the anticipated sales volume to obtain an estimate of shipping costs. For June, we have:

Estimated June shipping costs = $15,000 + ($2.50 ( 5,500) = $28,750.

Additionally, based on the data provided, a volume of 5,500 flower arrangements appears to be well within Silk Flower and Mores relevant range of activity.

c. Stated simply, management would like to know the cost of free shipping. As estimated in part [b], at a volume of 5,500 arrangements, management should expect free shipping to cost $28,750 for the month of June. This number allows management to make an informed comparison between the costs and the benefits of offering free shipping (presumably, offering free shipping increases sales volume and contribution margin). Moreover, separating costs into fixed and variable components helps managements assess those costs that vary with the number of flower arrangements sold and those that do not.

Instructors also may wish to point out to students that management of Silk Flowers & More would be likely to refine their shipping costs equation to incorporate factors such as the type of package shipped (small versus large), the type of flowers shipped (some may required more packaging materials and labor), and the distance shipped. Such refinements allow management to estimate the profit of the various types of floral arrangements sold and the various customers that they serve (e.g., profit by region of the country). This may lead management to restrict free shipping to some product lines.

For a salient example, consider Amazon.com, which offers free shipping. However, only some products in Amazon.com qualify for free shipping. A book usually does, but a plasma TV usually does not. In addition, Amazon requires a minimum order size to qualify for free shipping. Exploring the rationale for these practices underscores how cost structure influences a firms policies and procedures.

4.39 a. We can use the two data points to decompose supervision costs into fixed and variable components. Specifically, using the cost information from January and March (the months with the lowest and highest activity levels), we have:

(January): $27,500 = FC + (Cost per labor hour ( 2,400)

(March):$32,540 = FC + (Cost per labor hour ( 3,360).

Solving for the unit variable cost, or Cost per Labor Hour, we have:

Cost Per Labor Hour = $32,540 - $27,500 = $5,040 = $5.25 per Labor Hour

3,360 2,400 960By substituting the cost per labor hour = $5.25 into the cost equation for January (using March will also work), we find that

FC = $27,500 (2,400 ( $5.25) = $14,900.

Thus, we express total supervision costs as: Total supervision costs = $14,900 + ($5.25 ( Number of labor hours)

Notice that we use the observations with the highest activity level. We do not use the data for May even though it has the highest cost.

b.We can use the two data points to decompose total supervision costs into fixed and variable components. Specifically, using the cost information from January and May (the months with the lowest and highest activity levels), we have:

(January): $27,500 = FC + (Cost per machine hour ( 5,040)

(May):

$32,630 = FC + (Cost per machine hour ( 6,750).

Solving for the unit variable cost, or Cost per Machine Hour, we have:Cost Per Machine Hour = $32,630 - $27,500 = $5,130 = $3.00 per Machine Hour

6,750 5,040 1,710By substituting the cost per machine hour = $3.00 into the cost equation for January (using May will also work), we find that

FC = $27,500 (5,040 ( $3.00) = $12,380.

Thus, we express total supervision costs as:

Total supervision costs = $12,380 + ($3.00 ( Number of machine hours).

c. We believe that the equation based on labor hours might better represent cost behavior because supervision is likely related to the number of workers. However, there usually is a strong correlation between labor and machine hours in many settings. Thus, we could justify either equation.

d. A manager might believe neither equation to be valid because the data indicate that supervision might be a step cost. For instance, the cost did not change when the number of labor hours increased from 2,400 to 2,560 but jumped $2,500 when the labor hours increased from 2,560 to 2,880. Such jumps and intuition lead us to conclude that supervision costs might be step costs, which means that our task changes to estimating the step size. (This material might be covered in an advanced class.)

4.40 a. We can use the two data points in the condensed income statements to decompose Frame & Shows total costs into fixed and variable components. Specifically, using the cost information from years 1 and 2, we can express Frame & Shows total costs as:

(Year 1): $310,000 = FC + variable cost per frame 3,000

(Year 2):$332,500 = FC + variable cost per frame ( 3,500.

Solving for the unit variable cost, or variable cost per frame, we have:Variable cost per frame = $332,500 - $310,000 = $22,500 = $45.00 per frame

3,500 3,000 500By substituting variable cost per frame = $45 into the cost equation for Year 1 (using year 2 will also work), we find that

FC = $310,000 (3,000 ( $45) = $175,000.

Thus, we express Megans annual cost equation as:

Total Costs = $175,000 + ($45 ( Number of items framed).

b. The cost of participating in the Thieves Market equals the sum of the controllable fixed and variable costs associated with this decision alternative.

The controllable fixed cost associated with participating in the Thieves Market is the $2,500 booth fee. Megans annual fixed costs of $175,000 are not controllable for this short-term decision.

The controllable variable cost equals the number of framings multiplied by the variable cost per framing. Megan expects to sell 150 framings at the market. From the cost equation we developed in part [a], the estimated variable cost per framing is $45. Consequently, Megans expected controllable variable costs = $45 ( 150 = $6,750.

Adding the controllable fixed cost to the controllable variable costs, we have:

Cost of participating in the Thieves Market = $2,500 + $6,750 = $9,250.

To determine the expected profit from participating in the Thieves Market, we need to determine the revenue from participating in the market. Since revenue = selling price ( number of framings, we can use the data in either Year 1 or Year 2 to find the average selling price. Using the data from Year 2, we find that the sales price per frame = $318,000/3,000 = $106.

Thus, the revenue from 150 frames = 150 ( $106 = $15,900.

Subtracting the cost from the revenue associated with participating in the Thieves Market, we find that Megans profit is expected to increase by $15,900 $9,250 = $6,650. Participating in the Thieves Market therefore appears to be a steal!

4.41 a. Following the procedure outlined in the text, we find the following:

CoefficientsStandard Errort StatP-value

Intercept$15,320.95689.884422.207990.0002

Number of shipment$2.4459460.10683422.894890.000183

R-Square =0.992

Based on the above data, we estimate the monthly shipping cost equation as:

Total shipping costs per month = $15,320.95 + ($2.446 ( Number of flower arrangements sold)We note that the regression has a high R-square (the Excel output shows an adjusted R-square of 0.992) indicating an excellent fit. Moreover, the p values are low, indicating a statistically meaningful relation between the cost driver (the number of shipments) and the cost. This statistical relation confirms our intuition about an economic relation between the cost driver and the cost.

b. Once we have our cost equation, we can plug in anticipated sales volume to obtain an estimate of shipping costs. For June, we have:

Estimated June shipping costs = $15,320.95 + ($2.445 ( 5,500) = $28,768.45.

Additionally, based on the data provided, a volume of 5,500 flower arrangements appears to be well within Silk Flower and Mores relevant range of activity.

Note: The instructor can observe that while we obtain similar answers with the high-low and the regression method for estimating costs, this is often not the case.

4.42 We would argue that the second equation is likely to be a better predictor of monthly materials handling costs. We base our conclusion on the following reasons.

Equation 2 has a much higher R-square (76.34%) than equation 1 (54.17%). The higher R-square indicates a better fit, meaning that the cost driver (the independent variable in the regression equation) number of material moves is able to explain more of the variation in the dependent variable (monthly materials-handling costs) than the independent variable value of materials handled.

The p-values of the coefficients are low in both equations, indicating that all estimates reliably differ from zero. However, the p-values are lower in equation 2 than in equation 1, again indicating a stronger association between material moves and materials-handling costs than the association between the value of materials and materials-handling costs.

We have to consider more than just R-squares and p-values when choosing an activity. For example, we need to consider whether there is a cause-effect relationship between the activity and the cost. The answer for our problem is not obvious. We can visualize the number of moves being the cause for materials-handling costs. We also can conceive of the value of materials being correlated with handling expenses because we are likely more careful with more expensive materials. However, there could be situations where the association between value of materials and handling cost is weak. Ultimately, we will have to rely on situation specific knowledge to make the choice.

Overall, this exercise highlights that we can employ many independent variables in a regression and that the choice among the resulting equations must rely on both statistical and economic criteria. More sophisticated multiple-regression models can portray the joint effect of many independent factors.

4.43 a. Using Excel, we obtain the following regression equation and output:

Regression Statistics

R Square34.57%

Observations12

CoefficientsStandard Errort statisticp-value

Intercept13,059.781991.1536.5589070.00

Cases shipped 2.1530.9368292.2988160.04

b. This equation indicates a somewhat poor fit. The fit is not excellent as the R-square value is only around 35%. Moreover, the explanatory variable is only marginally significant (p of 0.04). OConner would be well advised to consider alternate drivers and/or to collect more data to refine its estimates.

4.44 a. The GAAP income statement classifies costs according to their function it groups costs by whether they pertain to manufacturing (product costs) or non-manufacturing (period costs) activities. The GAAP income statement also aggregates the data to the firm level because the income statement pertains to the firm as a whole and not any particular product, geographical region, or customer. (Note: Generally, investors buy and sell shares in the entire firm and not individual pieces of the firm. A few firms do issue tracking shares that permit an investor to invest in specified operations only.)

In contrast, a contribution margin statement groups costs as per their variability, presenting the data at the sub-unit level. The sub-unit, which can be products (as in the Caylor example), divisions, regions, or customers, depends on the decision context.

Re-grouping costs per their variability gives rise to the following income statement for Caylor:

Product Contribution Margin Statement

Caylor Company

For the most recent Year

RX-560VR-990Total

Revenues1$5,400,000$12,000,000$17,400,000

Variable costs (Manufacturing)2540,0002,000,0002,540,000

Variable costs (SG&A)3 720,0008,000,0008,720,000

Contribution margin$4,140,000$2,000,000$6,140,000

Traceable fixed costs (Manufacturing)$500,000$500,000$1,000,000

Traceable fixed costs (SG&A)1,000,0001,350,0002,350,000

Product (Segment) margin$2,640,000$150,000$2,790,000

Common fixed costs (manufacturing)$1,300,000

Common fixed costs (SG&A)1,200,000

Profit before Taxes$290,000

1 $5,400,000 = 180,000 $30; $12,000,000 = 2,000,000 $6.

2 $540,000 = 180,000 $3; $2,000,000 = 2,000,000 $1.

3 $720,000 = 180,000 $4; $8,000,000 = 2,000,000 $4.

b. The product contribution margin statement is much more informative for decision making than the GAAP income statement. The product contribution margin statement shows that RX-560 is clearly more profitable than VR-990. (The GAAP income statement obscures this fact). Thus, management of Caylor may wish to increase its emphasis on RX-560 and de-emphasize VR-990. Additionally, we clearly see the traceable fixed and variable costs associated with producing each drug; this information can facilitate special order decisions, pricing decisions, and keep or drop decisions.

Note: Caylors profit before taxes is the same regardless of which way we group revenues and costs. This equivalence occurs because of the absence of inventory. As discussed in a later chapter (Chapter 9), inventory can cause the two income numbers to differ.

4.45 a. The following table provides the required calculations:

Omega CorporationMonthly Contribution Margin Statement

(by Geographical Region)

EasternWesternTotal

Revenue $2,000,000$600,000$2,600,000

Variable manufacturing costs11,300,000370,0001,670,000

Variable selling costs250,00016,00066,000

Contribution margin$650,000$214,000$864,000

Traceable fixed costs250,000225,000475,000

Segment margin$400,000($11,000)$389,000

Common fixed costs275,000


1 $1,300,000 = ($1,000,000 0.55) + ($1,000,000 0.75); $370,000 = ($400,000 0.55) + ($200,000 0.75)

2 $50,000 = ($1,000,000 0.03) + ($1,000,000 0.02); $16,000 = ($400,000 0.03) + ($200,000 0.02)

b. The following table provides the required information:

Omega CorporationMonthly Contribution Margin Statement

(by Product)

StandardDeluxeTotal

Revenue $1,400,000$1,200,000$2,600,000

Variable manufacturing costs1770,000900,0001,670,000

Variable selling costs242,00024,00066,000

Contribution margin$588,000$276,000$864,000

Traceable fixed costs275,000225,000500,000

Product margin$313,000$51,000$364,000


Net Income$114,000

1 $770,000 = ($1,000,000 0.55) + ($400,000 0.55); $900,000 = ($1,000,000 0.75) + ($200,000 0.75).

2 $42,000 = ($1,000,000 0.03) + ($400,000 0.03); $24,000 = ($1,000,000 0.02) + ($200,000 0.02).c. The contribution margin statements clearly show that the Eastern region currently is more profitable than the Western region and that the standard product is more profitable than the deluxe product. Thus, management may need to devote more efforts to increasing the profits associated with the deluxe line. (Management may also use the information to support a strategy of emphasizing the standard line given the low contribution margin of the deluxe line relative to the standard line).

Similarly, management may need to devote even more resources to the Western region to ensure that its expansion efforts are successful. Alternatively, management may decide, based on the geographic contribution statement (i.e., the loss in the Western region), to discontinue its presence in the Western region.

4.46 a. Atman expects to spend 8 20,000 hours = 160,000 hours to assemble 8 satellites. Its expected cost is 160,000 hours $25 per hour = $4,000,000.b. The following table provides the average hours required with learning

Unit number

Average Hours per unit

1

20,000 (Given)

2

18,000 (=20,000 0.9)

4

16,200 (=18,000 0.9)

8

14,580 (=16,200 0.9)

Thus, the total labor hours needed are 116,640 (8 14,580) and the associated cost is $2,916,000 ($25 116,640).

Note: Some students erroneously think of 14,580 hours as the time needed for the eighth unit (i.e., the marginal time for the eighth unit) rather than the average time per unit for the first eight units. In this context, we note that it is possible to re-express an average cost learning equation (which we illustrate) into a marginal cost learning equation. However, such transformations are beyond the scope of this book.

c. Incorporating learning effects reduces Atmans expected cost by more than 25%! Ignoring this factor could lead to a gross overbid, potentially costing Atman the job.

Problems

4.47 a. The classification of each of Amys costs is as follows:

Cost ItemCost Hierarchy ClassificationExplanation

$1,200 variable costs per personUnit levelVaries directly with the number of persons taking the tour.

$98,000 cost per tour

Batch levelVaries with the number of tours.

$50,000 central office and administration costsFacility levelRequired to sustain the business.

One might be tempted to classify Amys $50,000 in central office costs as product-level costs because, at the present time, Amy only offers tours to Southeast Asia. These costs, however, probably are best classified as facility-level because they are required to sustain Amys business. They probably wont change even if, for example, Amy starts offering tours to Europe.

b. The table below presents Amys total quarterly costs under each scenario:

Cost item2 tours with 40 persons each5 tours with 50 persons eachDetail

Variable costs$96,000$300,0002 40 $1,200; 5 50 $1,200

Cost of tours$196,000$490,0002 $98,000; 5 $98,000

Fixed expenses$50,000$50,000Facility-level cost

Total costs$342,000$840,000

c. Based on our cost classifications, the controllable cost of offering any particular tour = $98,000 + ($1,200 number of persons on the tour). With 35 persons, this cost = $98,000 + ($1,200 35) = $140,000. Furthermore, with 35 persons Amy receives 35 $4,000 = $140,000 in tour revenue. Thus, Amy just breaks even when 35 persons are in the tour and loses money with fewer than 35 persons. This explains why Amy has this stipulation.

4.48 Let us begin by classifying the items as being controllable or not for this decision.

ItemClassification

Direct materialsControllable

Direct labor Controllable

Departmental overhead: DirectControllable

Departmental overhead: Indirect Not controllable

Factory overheadNot controllable

Selling & administration overhead Not controllable

How can we make the above classification? Notice the per-unit amounts for the controllable costs are the same at different production volumes. This equality suggests that these costs are proportional to production volume, or that they are variable. Thus, these costs are likely controllable for this decision.

Indirect overhead declines on a per-unit basis as volume increases. This is a classic sign of a fixed cost. Indeed, we can verify that the amount is $31,000 for both volumes.

We now consider the two allocated amounts: factory overhead and selling costs. From Chapter 3, we know that allocations take an indirect cost and split it among cost objects in proportion to the number of cost driver units. Suppose we allocate rent (a fixed cost) in proportion to labor hours. Suppose further that we increase production of a product (with one labor hour per unit) from 1,000 units to 2,000 units. The number of labor hours used by this product will then double. The mechanics of the allocation then mean that the amount allocated for rent will also double because the allocated cost is proportional to the number of driver units! Thus, a casual examination of cost per unit at the different volumes might well conclude that rent is a variable cost because the allocation process has made a fixed cost look like a variable cost.

This phenomenon is at work here. Indeed, note that factory overhead is constant per unit, suggesting that it is variable. But, appearances could be deceiving. The allocated amount per unit is the same for different volumes because we calculate the allocated amount as 100% of a controllable cost (labor). However, the total amount the firm spends on factory overhead is likely the same at both volumes. Thus, factory overhead is not controllable for this decision. A similar logic applies to selling and administration overhead.

With this classification, we have the controllable costs as $2.50 + 2.14 + $0.45 = $5.09 per unit. Thus, increasing production by 1,500 units will increase costs by $7,635.Note: This problem underscores that allocated costs, particularly when presented as a cost per unit, have the potential to confuse. If you encounter an allocated amount in a product cost report, do not consider just the amount allocated to an individual unit of the product or to the product line alone to determine whether the cost is controllable. Rather, consider whether the total expenditure on the cost (across all products) by the firm will change due to the decision.

4.49 a. The table below classifies each of Comfort Pillows cost items as being controllable or non-controllable for accepting the department stores order. The table also presents the increase in the cost item, if any, as a result of accepting the order and the detail supporting this calculation. That is, the status quo is not accepting the order.

Cost ItemControllable?Cost for store orderDetail

FabricControllable. The cost will increase if the order is accepted.

$12,5005,000 pillows $2.50 per pillow.

FillControllable. The cost depends on whether the order is accepted.

$90,0005,000 pillows $18 per pillow.

Industrial sewing machines Non-Controllable. The cost is the same regardless of whether the order is accepted.

$0

LaborControllable. The cost will increase if the order is accepted.

$30,0005,000 pillows hour per pillow $12 per hour

Plastic wrap & other packing Controllable. The cost increases if the order is accepted.

$2,5005,000 pillows $0.50 per pillow

Cartoning & cratingControllable. This batch-level cost changes because of the order.

$2,000(5,000/25) $10

TransportationControllable. Similar to cartoning and crating, this is a batch-level cost.

$3,000(5,000/2,500) loads $1,500 per load

Purchasing & manufacturing supportControllable. This cost will increase since only 12,000 pillows per month are being produced currently.$15,000Accepting the order will mean that Comfort will produce 17,000 pillows in the coming month, thereby triggering an additional $15,000 in cost.

Advertising brochuresNon-Controllable. The cost is the same whether the order is accepted or not.

$0

Office expensesNon-Controllable. The cost is the same whether the order is accepted or not.

$0

Sales & supportControllable. These costs will increase if the order is accepted.

$1,000Additional $1,000 will be incurred.

Total cost$156,000

The controllable cost per pillow is therefore: $156,000/5,000$31.20

Markup at 25%

0.25 $31.20

$ 7.80

Price per pillow

$39.00

b. The point to note here is that, on a per-pillow basis, the batch- and order- (product-) level costs will change. The following table (which only shows the controllable costs) highlights this point.

ItemPer-pillow cost 5,000 pillowsPer-pillow cost

4,000 pillowsDetail

Fabric$2.50$2.50$2.50 per pillow

Fill$18.00$18.00$18.00 per pillow

Labor cost$6.00$6.00 hour $12 per hour

Plastic wrap & other packing $0.50$0.50$0.50 per pillow

Cartoning & crating$0.40$0.40Although this is a batch cost, notice that the per- unit cost has not changed because both orders are divisible by 25, which is the batch size.

Transport$0.60$0.75$3,000/5,000; $3,000/4,000. Still need two trips even though the order is smaller.

Purchasing & manufacturing support$3.00$3.75$15,000/5,000; $15,000/4,000

Sales & support$0.20$0.25$1,000 / number of pillows.

Cost per pillow$31.20$32.15

The revised price per pillow is therefore $40.19 = $32.15 (1 + 0.25).

Notice that the unit cost has increased due to the presence of batch- and order-(product-) level costs. Because the batch size is smaller than the step size for transportation costs under the revised order, the unit cost will increase. Similarly, the product costs related to purchasing and manufacturing support and sales support are spread over a smaller volume level, thereby increasing the cost per pillow.

4.50 a. By inspection, we see that the highest and lowest activity levels (pizzas sold) occurred in the fourth and first quarter, respectively. Accordingly, we have:

HIGH (Fourth quarter): $190,000 = FC + (40,000 ( cost per pizza sold)

LOW (First quarter):

$115,000 = FC + (25,000 ( cost per pizza sold).

Solving for the UVC, or cost per pizza sold, we find

UVC = $190,000 - $115,000 = $75,000 = $5.00 per pizza

40,000 25,000 15,000Substituting UVC into either equation, we find that FC = $10,000. Thus, Pizzeria Paradises total quarterly cost equation is:

Total Quarterly Costs = $10,000 + ($5.00 ( number of pizzas).

b. As shown in part [a], our estimate of Pizzeria Paradises fixed costs is indeed negative. Clearly, Pizzeria Paradise will not incur negative fixed costs (i.e., receive money) if it produces 0 pizzas in a quarter. What we need to keep in mind is that any estimated cost model is only valid within a particular range of activity usually defined by the range in the data used to estimate the model. Projections outside of this range may not be accurate because the linear approximation implied by the model may no longer be valid.

In the Pizzeria Paradise example, we estimated the cost model using activity levels between 25,000 and 40,000 pizzas. However, interpreting the $10,000 as a fixed cost requires that we apply the model at a value of 0 pizzas. This value is well outside the relevant range. The model likely is only applicable for activity levels between 25,000 and 40,000 pizzas.

c. Using the model developed in part [a], our estimate of total costs at a volume of 50,000 pizzas is:

Estimated Quarterly Costs = $10,000 + ($5.00 ( 50,000) = $240,000.

Building on the discussion in part [b], we need to be concerned about this estimate because it falls outside the range of data used to estimate the cost equation. Thus, we should issue a caveat to management that our estimate may not be valid because it falls outside the relevant range. In addition, it probably also is worth pointing out issues related to drawing inferences and/or estimating cost from just a years worth of data particularly the startup year. It will be important to closely monitor Pizzeria Paradises cost patterns in the coming months/quarters as the business settles into a more stable pattern.

4.51 a. By inspection, we see that the highest and lowest activity levels (ZAP kits sold) occurred in the fourth and second quarter, respectively. Accordingly, we have:

HIGH (Second quarter): $268,200 = FC + 9,600 ( Variable cost per kit.

LOW (Fourth quarter): $181,500 = FC + 4,500 ( Variable cost per kit

Solving for the UVC, or variable cost per kit, we find

UVC = $268,200 - $181,500 = $86,700 = $17.00 per kit

9,600 4,500 5,100Substituting UVC into either equation, we find that FC = $105,000. Thus, ZAPs quarterly cost equation is:

Total Quarterly Costs = $105,000 + ($17.00 ( number of kits sold).

b. The following graph depicts the relation between total quarterly costs and ZAP kits sold:

One of the observations, 9,600 ZAP kits for Quarter 2, does not appear to be in the same relevant range or fall along the same line as the other three observations. This observation may reasonably be classified as an outlier or extreme observation and may unduly influence our cost model.

c. This information confirms our intuition. The observation for the second quarter is not representative of the model that governs the other observations. Thus, we need to re-estimate the quarterly fixed costs and the variable cost per ZAP kit sold.

After eliminating the second quarter, the third and fourth quarter have the highest and lowest activity levels, respectively. Thus, we have:

(Third quarter): $192,000 = FC + (6,000 ( variable cost per kit),

(Fourth quarter):$181,500 = FC + (4,500 ( variable cost per kit).

Solving, we find UVC = $7.00 and FC = $150,000. Thus, our cost equation is:

Total Quarterly Costs = $150,000 + (number of kits sold ( $7.00).

Using this cost equation on the second quarters activity level, we would expect second quarter total costs to be: $150,000 + (9,600 ( $7) = $217,200. Because actual total costs were $268,200 during the second quarter, our model suggests that ZAP spent $51,000 on advertising. This conclusion, though, should be tempered because the activity level of 9,600 kits is likely beyond the relevant range over which we estimated the cost equation.

Other questions to consider are whether there were any step increases in staff whether production, order fulfillment, or marketing to go along with the increases in units sold. d. Graphing the data and ensuring data reliability are crucial steps before employing any model to estimate costs. Graphing the data is an excellent way to gain intuition regarding the relation between activity levels and costs. Graphs also alert the user to outliers and potential non-linearity in the relation between activity levels and costs. Advanced users also check the data to ensure that the cost and the activity are recorded in the same time interval. For example, some of the costs associated with one months activity may be recorded in another month. In this case, we must adjust the data so that the activity and the associated cost line up in the same observation.

4.52 a. The cost of employees is a step cost. Specifically, Carlton needs to hire one person until the number of cars detailed reaches 900 per year (900 = 3 cars per day ( 300 days a year). Beyond 900 cars, Carlton needs to hire two people, until the volume reaches 1,800 cars, at which point he needs to hire three people, and so on. Thus, the step size is 900 cars detailed and every 900 cars per year triggers a step-increase in the employee costs. In other words, employee costs are fixed from 0 to 900 cars, from 901 to 1,800 cars, from 1,801 to 2,700 cars, and so on.

Realistically, Carlton may need to hire more than one person even if demand were fewer than 900 cars per year because of seasonal and/or daily variations in demand for example, it is likely that many more people will want their car detailed in June than in January. In addition, if Carlton can hire part-time employees (say, on a daily basis), the step-size becomes much smaller. For every 3 cars demanded, he needs to pay for an additional day. The step is now an hour instead of a full-time employee. With a sufficient reduction in the granularity of a resource (e.g., the minimum size for purchase), one can turn a fixed cost into a variable cost. While such reduction appears feasible in this business, it may not be technologically or economically feasible in other businesses.

b. First, we write out Carltons annual cost equation:

Total Costs = fixed costs + (# of employees ( cost per employee) + (variable cost per car detailed ( # of cars detailed).

Using the data for years 1 and 2, we can estimate the variable cost per car detailed. Such estimation is feasible because both the fixed costs and the employee costs are the same for both years.

(Year 1): $129,000 = fixed costs + (2 ( cost per employee) + (1,200 ( VC per car)

(Year 2): $137,000 = fixed costs + (2 ( cost per employee) + (1,600 ( VC per car)

Because the employee costs are the same for these two years, we can solve for the UVC, or detailing cost per car, as we have in the past, and find:

UVC = $137,000 - $129,000 = $8,000 = $20.00 per car detailed

1,600 1,200 400We can now use our variable cost estimate in the cost equations for years 2 and 3, where we do have variation in the number of employees (which is necessary so that the employee costs do not, excuse the pun, wash in our estimation). We also could use years 1 and 3 in our estimation.

(Year 2): $137,000 = fixed costs + (2 ( cost per employee) + (1,600 ( $20)

(Year 3): $183,000 = fixed costs + (3 ( cost per employee) + (2,400 ( $20).

First we simplify these equations:

(Year 2): $137,000 = fixed costs + (2 ( cost per employee) + ($32,000)

(Year 3): $183,000 = fixed costs + (3 ( cost per employee) + (48,000).

Subtracting $32,000 and $48,000 from both sides of the respective equations leads us to the following set of equations.

(Year 2): $105,000 = fixed costs + (2 ( cost per employee)

(Year 3): $135,000 = fixed costs + (3 ( cost per employee)

We now can solve for the UVC, which in this case is the annual cost per employee.

UVC = $135,000 - $105,000 = $30,000 = $30,000 per employee

3 2

1We can now plug in the cost per employee and the variable cost per car detailed into any of the years to estimate Carltons annual fixed costs. Using, for example, year 1 we have:

(Year 1): $129,000 = fixed costs + (2 ( $30,000) + (1,200 ( $20).

Solving, we find fixed costs = $45,000. Thus, Carltons annual cost equation is:

Total Costs = $45,000 + (# of employees ( $30,000) + ($20 ( # of cars detailed).

Please note that we need at least three data points to solve this problem. This occurs because there are three unknowns in the cost model: (1) fixed costs, (2) the cost per employee, and (3) the variable cost per car detailed. In general, we need at least as many data points as unknowns in cost estimation.

4.53 a. Based on the data provided, we have:

HIGH (September) $560,000 = FC + (15,000 ( variable cost per pillow)

LOW (March) $420,000 = FC + (10,000 ( variable cost per pillow)

Solving for the UVC, or variable cost per pillow, we find

UVC = $560,000 - $420,000 = $140,000 = $28.00 per pillow

15,000 10,000 5,000Substituting our estimate of UVC into either equation, we find that FC = $140,000. Thus, Comfort Pillows monthly total cost equation is:

Total costs per month = $140,000 + ($28.00 ( number of pillows sold)

b. For a short-term order like the one from the store, fixed costs generally are non-controllable as Comfort would incur theses costs whether the order is accepted or not. The variable cost is the estimate of the additional cash outflow from making one more pillow and, thus, would be the controllable amount.

With a 25% markup and using the estimate of the variable cost, the price per pillow would be $28.00 (1 + 0.25) = $35.00.

Notice that this price is $4.00 less than the $39.00 price in part [a] of the previous problem and is independent of the volume of pillows ordered.c. The difference stems from variations in the detail considered. The account classification method considered details such as changes in batch size and, as a result, is likely to be more accurate. For instance, the method yielded different cost estimates at differing volume levels (as expected with any batch processes). The high-low method, in contrast, classifies all costs as fixed or variable. Consequently, it misclassifies some costs and does not represent their behavior well. This method may yield a good and easy to compute first approximation but is not as reliable. Moreover, it is likely that, under the high-low method, some of the costs that were classified as batch- or product-level under the account classification method would be classified as fixed. The estimates between the high-low method and the account classification method will be close when the magnitudes of the batch- and product-level costs are small relative to the magnitudes of the fixed and variable costs.

4.54 a. The following graph depicts the relation between the total costs of making course packets and class size:

The relation between the number of students and the total cost of making course packets indeed appears to be linear. The plot indicates that the observed data points deviate only slightly from a straight line this deviation could arise from measurement error or from other factors such as the number of pages in a course packet that determine the cost of a course packet.b. Using Excel, we obtain the following regression equation and output:


R-Square98.85%

Adjusted R-Square98.57%

Observations6


Intercept143.1338.12117.6240.00

Class size 3.8770.20818.5910.00

We estimate the fixed costs of preparing a course packet at $143.133 per class and the variable cost at $3.877 per student. (Note: the high fixed costs relate to obtaining copyright permission, assembling the master packet, and charges for the copy machine and machine operator).

Thus, the cost equation is:

Cost of making packets for a class = $143.133 + $3.877 Class size.c. The reported regression results indicate an excellent fit. The R-square is 98.8%, consistent with a high association between the number of students and the cost of course packets. Economically, the story is plausible as a greater number of students increases the number of copies made and, in turn, cost.

We might be able to improve the accuracy of the estimate by adding the size of the course packet (in number of pages), although the high association for Watson could be because the size of the course packet does not vary much across classes. More data might help shed light on the costs and benefits associated with adding other explanatory variables to the regression equation.

4.55 a. Using Excel, we obtain the following regression equation and output:


R Square1.1%

Adjusted R Square0.0%

Observations9


Intercept787.933379.4632.0764420.076486

Machine hours0.0078470.027710.2831920.785222

Thus, the cost equation is:

Maintenance hours = 787.933 + (0.007847 Machine hours)

This equation indicates a lack of relation between machine hours and maintenance hours. The R-square is extremely low (1%) and the coefficient on machine hours is not significant.

b. As discussed in part [a], the equation indicates a poor fit between machine hours and maintenance hours. The R-Square is low (1%) and the p-value for machine hours is 0.78, meaning that it is statistically indistinguishable from zero. The result is surprising because we expect a greater number of machine hours to lead to more maintenance.

Franks practice alerts us to one potentially source of error. It is possible that maintenance hours lag machine hours. That is, if there is high machine usage in quarter 1, the associated maintenance may occur in quarter 2. If we regress (as we did in part [a]) the maintenance hours in quarter 1 with the machine hours in quarter 1, we will not capture this association because of the lag effect.

c. In this specification, we lag the machine hours by one quarter to match up machine hours and maintenance hours. That is, we will treat the machine hours for quarter 1, 2007 as the predictor for the maintenance done in quarter 2 of 2007, the machine hours in Q2, 2007 as the predictors for maintenance in Q3, 2007 and so on.

Estimating the equation after such aligning of data yields:


R Square86.95%

Adjusted R Square84.78%

Observations8


Intercept-39.6145151.3295-0.261780.802249

Machine hours (in prior quarter)0.0690390.0109156.325140.00073

Maintenance hours = 787.933 + (0.007847 Prior quarter Machine hours)

This equation indicates an excellent fit, as shown by the high value for the R-square and the low p-value for the independent variable (prior quarter machine hours). Notice, however, that we lose one observation because we employ lagged data.

In essence, this problem highlights the importance of understanding the data and their economic relations before employing statistical methodologies.

4.56 a. The following graph depicts the relation between advertising costs (y-axis) and sales revenue (x-axis).

The graph indicates that the relation between advertising expenditures and sales revenue is reasonably linear.b. Using Excel, we obtain the following regression equation and output:


R-Square75.6%


Observations8


Intercept-94,515.173659.78-1.283130.24

Sales Revenue0.24460.0567074.3150950.00

This equation indicates a good fit between the two variables. The R-square is at a high level and the coefficient for the independent variable has a low p-value.

c. Using the equation from part [b], we have:

Advertising cost = - $94,515 + (0.2446 $1,750,000) = $333,535.

We urge caution when using this estimate. First, we are using the equation to predict costs for a value that could be outside of the relevant range for the model. Second, the direction of the economic linkage between sales and advertising is ambiguous. One can plausibly argue that advertising expenses trigger sales and not vice versa. Moreover, there could be a lag between the time of advertising and the sales realization. Thus, while the cost equation may be a good fit statistically, the economic underpinnings of this model are debatable.

4.57 a. The key is to realize that the service department currently is incurring the variable costs associated with all of the repairs, regardless of whether the repairs are internal or external. However, revenue is only recognized on sales made to external customers (no revenue is recorded for repairs to cars purchased for inventory or courtesy repairs to used cars sold). If the service department could charge the used car department for these repairs (i.e., as if it were a separate stand-alone service station), then its revenues would double (since half of their time is spent on such repairs). Meanwhile, its variable costs would stay at the same level. In addition, the used car costs would increase by $200,000, reflecting the value of the services received. The revised contribution margin statement below reflects these changes:

Used CarsServiceTotal

Revenue$2,500,000$200,000$2,700,000

Revenue used cars-----------200,000200,000

Variable costs1,200,000200,0001,400,000

Service costs 200,000-----------200,000

Contribution Margin$1,100,000$200,000$1,300,000

Traceable fixed costs750,000250,0001,000,000

Segment Margin$350,000($50,000)$300,000



Notice that Carousels overall profit has not changed it remains at $100,000. The revised income statement simply paints a truer picture regarding the stand-alone revenues and costs associated with each of Carousels departments. Moreover, the service department is not performing as poorly as previously thought.

b. Based on the nature of the common fixed costs, it is unlikely that these costs will decrease if the service department is closed. All other revenues and costs associated with the service department, however, likely will go away. As calculated in part [a], the service department is losing $50,000 before considering common fixed costs thus, all other things being the same, Carousels profit is expected to increase by $50,000 if the service department were closed. This effect also can be seen (and verified) by constructing an income statement with used car sales only. We present such an income statement below (again, this income statement assumes that the used car department will pay for minor repairs on the cars it buys and still provide courtesy repairs and maintenance on used car purchases all of this will be done via an independent service station at market price, or $200,000 as calculated earlier):

Used Cars

Revenue$2,500,000

Variable costs*$1,400,000

Contribution margin$1,100,000

Traceable fixed costs$750,000

Common fixed costs$200,000


* = $1,200,000 + $200,000

Again, we see that Carousels overall income is expected to increase by $50,000 to $150,000.

There are, of course, other factors that should be considered, perhaps the most important of which relates to the effect on used car sales. For example, it is quite possible that closing the service department will decrease used car sales. That is, the service department likely entices customers to look at and purchase a car (e.g., someone who is waiting on a repair might roam the used car lot). Other considerations relate to whether the entire service departments traceable fixed costs will go away (e.g., those related to equipment or space) and whether some of the common fixed costs will go away (e.g., the general managers salary may decrease since his/her responsibilities have decreased).

c. A 10% decrease in used car sales implies that used auto revenues, variable costs, and contribution margin will all decrease by 10%. However, it is unlikely that, at least in the short term, either traceable fixed costs or common fixed costs will decrease. With this, our revised income statement for used cars looks as follows:

ItemUsed CarsDetail

Revenue$2,250,000$2,500,000 ( .90

Variable costs$1,260,000$1,400,000 ( .90

Contribution margin$990,000$1,100,000 ( .90

Traceable fixed costs$750,000

Common fixed costs$200,000


Here, we see that Carousels overall income decreases by $60,000 to $40,000. Assuming the accuracy of the various estimates underlying the revised income statement, Carousel should not close the service department. This problem underscores the importance of considering interdependencies among departments and/or products oftentimes it is difficult to evaluate products or departments on a stand alone basis. Moreover, the contribution margin statement helps us assess these interdependencies.

4.58 a. The total variable costs are comprised of materials, labor, and variable overhead. Because materials and variable overhead are expected to remain the same for each of the 32 guidance systems, we calculate the sum of these costs as:

Total expected materials and variable overhead costs = 32 ( ($400,000 + $200,000) = $19,200,000.

We need to factor in the 90% learning curve to estimate the total labor costs of producing the 32 guidance systems. The following table shows the average labor cost per guidance system as well as the total labor cost, assuming a 90% learning curve.

Number of Guidance SystemsAverage Labor Cost per systemTotal Labor Cost*

1$600,000

(given)$600,000

2$540,000

(600,000 ( .90)$1,080,000

4$486,000

(540,000 ( .90)$1,944,000

8$437,400

(486,000 ( .90)$3,499,200

16$393,660

(437,400 ( .90)$6,298,560

32$354,294

(393,660 ( .90)$11,337,408

Thus, the total expected variable costs = $19,200,000 + $11,337,408 = $30,537,408.

b. Bid = 1.50 ( total variable costs = 1.50 ( 30,537,408 = $45,806,112.

In turn, the expected contribution margin = bid total variable costs = $45,806,112 $30,537,408 = $15,268,704.

c. The revenue that FlyWell will receive from the contract = .50 ( $45,806,112 = $22,903,056.

To determine the contribution margin, we need to determine the total variable costs of producing the 16 systems. For materials and variable overhead, we have: 16 ( ($400,000 + $200,000) = $9,600,000. For labor costs, we have (from the table in part [a]) $6,298,560. Thus, FlyWells total costs = $9,600,000 + $6,298,560 = $15,898,560 and the actual contribution margin = $22,903,056 $15,898,560 = $7,004,496, less than the 50% of the anticipated contribution margin of $15,268,704.

Furthermore, the actual markup percentage = 7,004,496/15,898,560 = 44%.

The actual markup is lower than the 50% target. This is because the cost of producing the first 16 systems is higher than the cost of producing the next 16 systems. If Flywell had known that the order was for 16 systems only, it should have priced the 16 systems at a total of $23,847,840 (= $15,898,560 ( 1.50) to achieve a 50% markup. If the government scales back the order volume, FlyWell should attempt to renegotiate the price because of learning effects, expected total costs (and profit) depend crucially on volume.

4.59 a. To arrive at the unit selling price, we first need to determine the learning rate. Next, we need to calculate the total labor hours required to complete batches 1 through 16 and batches 1 through 32. Third, we need to calculate the average time to complete a batch for batches 17 through 32. Finally, we use the average time to arrive at the unit selling price. Each of these steps is detailed below.

Step 1: Determine the learning rate

The problem provides the actual time to complete batches 1 and 2. To determine the learning rate, we need the average time for batches 1 and 2.

Total time to complete batches 1 and 2:32,000 + 22,400 = 54,400

Average time to complete batches 1 and 2:54,400/2 = 27,200

Average time to complete batch 1:

32,000 (given)

Learning rate

27,200/32, 000 = 0.85 or 85%Step 2: Determine the total time to complete batches 1-16 and batches 1-32

The following table shows the cumulative average labor hours per batch as well as the cumulative total labor hours, assuming an 85% learning curve.

Number of BatchesCumulative Average Labor HoursCumulative Total Labor Hours*

132,000

(given)32,000

227,200

(32,000 ( .85)54,400

423,120

(27,200 ( .85)92,480

819,652

(23,120 ( .85)157,216

1616,704.20

(19,652 ( .85)267,267.20

3214,198.57

(16,704.20 ( .85)454,354.24

* = cumulative average labor hours ( number of batches

Step 3: Determine the average time to complete batches 17-32

Total time for batches 1-32

454,354.24 hours


267,267.20 hours


187,087.04 hours (454,354.24 267,267.20)

Average time for batches 17-3211,692.94 hours (187,087.04/16 batches)

Step 4: Determine the unit selling price

Materials cost

$150,000.00(given)

Variable overhead cost$ 50,000.00(given)

Labor cost

$292,323.50(11,692.94 labor hours ( $25 per labor hour)

Total variable cost

$492,323.50

Markup

$369,242.63($442,323.50 ( .75)

Price for batch

$861,566.13

Price per unit

$8,615.66($861,566/100 units per batch)

b. We can calculate Zerons expected profit in year 1 as follows:

Revenue$861,566 ( 16$13,785,058

Materials costs$150,000 ( 16($2,400,000)

Variable overhead costs$50,000 ( 16 ($800,000)

Labor costs$267,267.20 ( $25 ($6,681,680)

Fixed costs($3,000,000)

Profit in year 1$903,378

c. We can calculate Zerons expected profit in year 2 as follows:

Revenue$861,566.13 ( 16$13,785,058

Materials costs$150,000 ( 16($2,400,000)

Variable overhead costs$50,000 ( 16 ($800,000)

Labor costs$187,087.04 ( $25 ($4,677,176)

Fixed costs($3,000,000)

Profit in year 2$2,907,882

Notice the sharp increase in profit from year 1 to year 2 even though the firm has sold the same number of units and for the same unit price. The increase is attributable to the decrease in labor costs. Generally, the profit per unit will steadily increase for products subject to a learning effect.

Note: Some instructors may wish to discuss the financial accounting implications of costs subject to learning. Oftentimes, firms will smooth reported profit by estimating the total profit over the product life and then using a reserve account (called deferred learning costs) to recognize the difference between the average profit and the actual profit for the period. This asset account will accumulate balances in the early years (less cost than actually incurred will be recognized in the income statement). The balances decline in later years and will be zero at the end of the project (more cost than actually incurred will be recognized in the income statement).

Mini Cases

4.60 a. The following graph depicts the relation between Yin-Yangs total costs and cups of yogurt sold.

b. We want to estimate the following cost equation:

Total monthly costs = Fixed costs + (Variable cost per cup of yogurt ( cups of yogurt).

For convenience, write the variable cost per cup of yogurt = UVC or unit variable cost. Using the data from January and February, we have:

January: $5,500 = FC + (UVC ( 1,000)

February: $6,200 = FC + (UVC ( 1,200).

Solving for UVC, we have:UVC = $6,200 - $5,500 = $700 = $3.50 per cup

1,200 1,000 200Substituting the value for UVC into the January cost equation yields

FC = $5,500 (1,000 cups ( $3.50 per cup) = $2,000.

Thus, we would model Yin-Yangs cost function as:

Total monthly costs = $2,000 + ($3.50 ( cups of yogurt).

The following graph shows this estimate vis--vis the actual data:

Note: The first data points for January and February are hidden behind the estimated line.

c. Again, we want to estimate the following cost equation:

Total monthly costs = Fixed costs + (Variable cost per cup of yogurt ( cups of yogurt).

The months with the highest and lowest total costs are December and January, respectively. Accordingly, we have:

December: $8,500 = FC + (UVC ( 1,100)

January: $5,500 = FC + (UVC ( 1,000).

Solving for UVC, we have:UVC = $8,500 - $5,500 = $3,000 = $30.00 per cup

1,100 1,000 100Substituting the value for UVC into the January equation yields

FC = $5,500 (1,000 cups ( $30.00 per cup) = $24,500.

Thus, Yin-Yangs cost function would be modeled as:



Note: The first two actual data points (for December and January) are hidden behind the first two points of the estimated line.

d. The months with the lowest and highest activity levels are January and August, respectively. Accordingly, we have:

January: $5,500 = FC + (UVC ( 1,000)

August: $8,125 = FC + (UVC ( 2,500).

Performing procedures analogous to those in parts [b] and [c] we find UVC = $1.75 and FC = $3,750. Thus, Yin-Yangs cost function would be modeled as:



e. Using Excel, we obtain the following regression equation and output when we include the data for December:


R-Square34.5%


Observations12


Intercept5223.91796.466.550.00

Cups sold1.030.442.290.04

This equation indicates a questionable fit between the two variables. The R-square is somewhat low and the p-value for the independent variable is only marginally significant.

The picture changes dramatically if we exclude the outlier (the observation for December). We obtain the following:


R-Square96.3%


Observations11


Intercept4074.47186.19021.8830.00

Cups sold1.5780.10215.4240.00

This equation indicates an excellent fit between the two variables. The R-square is at a high level and the coefficient for the independent variable has a low p-value.

f. Using the highest and lowest activity levels (i.e., the cost equation estimated in part [d]) appears to lead to the best estimate of Yin-Yangs cost structure. The differences between the actual and predicted costs using this estimate are rather small, indicating a very good (exceptional) fit. This estimate clearly leads to a better specification of costs than the estimates arrived at in parts [b] and [c] even though the month of January was used in all of our specifications. Notice that we get markedly different specifications depending on the other month chosen.

The estimate in part [b] is biased because there is little difference in the January and February activity levels only 200 cups of yogurt. Small deviations in cost vis--vis the true underlying cost structure can lead to a biased estimate of variable costs (because the denominator is small) and, in turn, fixed costs. For example, assume one of Yin-Yangs employees was sick for a week in January with the flu and that other employees had to cover for his/her absence. Assume the sick employee was scheduled to work for 30 hours and would have made $200 for the week. This relatively small change would have resulted in a variable cost estimate of $2.50 rather than $3.50 and a fixed cost estimate of $3,200 rather than $2,000.

The estimate in part [c] is biased because the December cost data appears to be an outlier (an extreme observation). For example, Ying-Yang could have paid its employees a Christmas bonus and/or paid its annual property taxes in December. While these costs would be incurred and recorded in December, they do not relate to cups of yogurt sold in December. Including data tainted by such features might lead to inaccurate measures of fixed and variable costs indeed, we see that our estimate of fixed costs is negative $24,500.

By itself, a negative fixed cost estimate is not enough to conclude that cost estimates are incorrect. However, it is suggestive of errors, particularly when the relevant range is close to zero. Moreover, this aspect of the problem illustrates that there is often more bias, or measurement error, in total costs than in activity levels. Costs can be erratic and lumpy; accounting systems can fail to capture the relation between spending and consumption. This reinforces why activity levels, rather than costs, typically are the basis for selecting data points.

More generally, instructors may wish to note that accounting conventions (e.g., cash accounting) may result in costs for one month being recorded in another month. Because the high-low method uses only two observations, it is particularly susceptible to this kind of error. Using the two activity levels rather than the two cost levels reduces such concerns. These kinds of classification error have smaller effects on analyses that use all available data, such as the regression method.

However, the exercise on the regression, part [e], shows the effect of an outlier even on methods such as regression. This one observation skews the data considerably, underscoring the importance of plotting data before analyzing it using regressions.

4.61 a. The high and the low observations correspond to year 3 and year 2, respectively. Writing out the cost equation for these two data points, we have:

$1,475,000 = Fixed costs + (Variable cost per participant 5,000 participants)

$1,122,500 = Fixed costs + (Variable cost per participant 3,500 participants)

Solving for the UVC, or variable cost per participant, we find

UVC = $1,475,000 - $1,122,500 = $352,500 = $235 per participant

5,000 3,500 1,500Variable cost per seminar participant = $235.00Plugging this estimate into the high or the low value equation, we have:

Fixed costs = $300,000Thus, we estimate Brads total annual cost equation as:

Total costs = $300,000 + ($235.00 ( number of seminar participants)

b. If Brad offers 20 seminars under the new format, then he will have 20 seminars 230 participants per seminar = 4,600 participants for the year. Let us plug this number into the cost equation to estimate total costs:

Total costs = $300,000 + ($235 4,600) = $1,381,000.

In turn, total revenues are:

Total revenues = $350 per participant 4,600 participants = $1,610,000.

Subtracting total costs from total revenues, we find:

Profit before taxes = $1,610,000 $1,381,000 = $229,000.

Comparing this profit estimate to Brads profit with offering 35 seminars under the current format, it appears that Brad would make substantially less money ($229,000 versus $421,875) if he were to switch his seminar format.

c. Our classification of each cost is as follows: We note that the central office and administration costs of $250,000 could be classified as either product-level or facility-level costs, depending on how they are viewed. If the costs relate solely to running seminars, then they would rightfully be classified as product-level costs. If the costs relate to Brads entire business, which not only includes seminars but also includes selling books and tapes, then they would be facility-level costs.

Cost ItemCost Hierarchy ClassificationExplanation

Variable costs Unit levelVaries with the number of participants

The cost for each seminar Batch levelVaries with the number of seminars

Cost of seminar coordinatorProduct levelRequired for offering seminars.

Central office and administrationProduct level/Facility levelRequired to sustain the business.

d. This question helps us see that the high-low method does not account well for batch- and product-level costs. Let us re-estimate Brads costs and profit using account classification:

ItemDetail35 Seminars

(125 per seminar) 20 Seminars

(230 per seminar)

Total number of participants# of seminars 125 persons per seminar; # of seminars 230 persons per seminar.4,3754,600

RevenueNumber of participants $400; Number of participants $350.$1,750,000$1,610,000

Variable costs $75 total number of participants328,175345,000

Costs for setting up the seminars$20,000 number of seminars; $25,000 number of seminars.700,000500,000

Cost of seminar coordinator$50,000 given50,00050,000

Annual fixed operating costs $250,000 given250,000250,000

Profit before Taxes$421,875$465,000

The above detailed analysis suggests that Brads profit actually will be $465,000 if he switches to the new seminar format. Moreover, Brads profit will increase by $465,000 $421,875 = $43,125 if he switched to the new format.

e. The methods do lead to dramatically different answers. Based on our analysis in part [b], it appeared that Brad would forego roughly $200,000 in profit if he were to switch his seminar format. In part [d], however, we find that Brads profit would actually increase if he were to switch formats.

Why do the two methods yield such different answers? The answer is that the high-low method implicitly classifies batch-level and product-level costs as being variable (unit level) or fixed (facility level).Thus, any cost estimates using the high-low method implicitly assume no change in the production technology that is, the batch size will stay the same and the cost per batch or product will not change. For Brad, as long as the batch size stays at 125 participants per seminar, our cost and profit estimates will be the same under the two methods notice that our profit estimates under the high-low method and the account classification method are equivalent for 35 seminars with 125 participants per seminar.

The proposed seminar format changes the batch size from 125 to 230. Thus, Brad can accommodate the same (or more) participants with fewer seminars that is, the number of batches decreases. In turn, the batch-level costs will decrease. (Equivalently, the batch cost per participant decreases.) While the account classification method includes the consequent decrease in cost, the high-low method, however, is still estimating costs as if there were only 125 participants per seminar (or, approximately 4,600/125 = 36.8 seminars). Consequently, this method over-estimated costs by approximately $320,000 = (16 phantom seminars $20,000 per seminar).

Note: The instructor can use this exercise to note that methods such as the high-low method estimate parameters of the cost function from historical data. Using these estimates to project future costs implicitly assumes that the underlying cost structure is stable. (An additional assumption, not covered in this case, is that we are operating within the relevant range.) If the assumption is not valid, poor decision making can occur. The account classification method is less subject to this error because it examines each cost item individually.

4.62 a. Mollys response indicates that she believes all of her costs are variable. That is, she appears to believe that it costs $16.50 per CD regardless of the number of CDs sold. Molly does not appear to realize that some of her costs are fixed, and therefore invariant to sales volume (CDs sold), while some of her costs are variable and, indeed, increase proportionally with sales volume. Many of Mollys costs are likely to be fixed, including costs associated with leasing the land and building, having full-time employees, a computer network, etc.

For this particular decision, Mollys fixed costs are not controllable since she is operating within the relevant range of activity. Thus, only variable costs will differ between the decision to keep the selling price at $16.95 per CD or lower it to $14.95 per CD.

Going a step further, we would suggest that Mollys decision should be made on the basis of whether the increase in revenue associated with reducing the selling price is more than the increase in variable costs associated with reducing the selling price.

b. The following graph depicts the relation between Mollys total costs and CDs sold.

The graph appears to confirm our intuition from part [a]. Indeed, a portion of Mollys costs appear to vary directly with the number of CDs sold and a portion appears to be fixed. Based on the plotted data, it appears that we can reasonably represent Mollys costs by a straight line with a positive slope and a positive intercept. That is, Mollys total costs can reasonably be represented as:

Total Costs = Fixed costs + (variable cost per CD ( # of CDs sold).c. The high-low method stipulates choosing the highest and lowest levels of activity. For Molly, this corresponds to December and August, respectively. Accordingly, we have:

HIGH (December):$170,000 = fixed costs + 12,000 CDs sold ( Variable cost per CD

LOW (August):$125,000 = fixed costs + 6,000 CDs sold ( variable cost per CD.

Solving for the UVC, or variable cost per pillow, we find

UVC = $170,000 - $125,000 = $45,000 = $7.50 per CD sold

12,000 6,000 6,000 Plugging this estimate into either equation yields fixed costs = $80,000. Thus, Mollys monthly cost equation is:

Total Monthly Costs = $80,000 + (# of CDs sold ( $7.50).

The following graph shows this estimate in terms of the actual data:

The estimated cost equation appears to fit the data extremely well as the differences between actual and predicted costs are very small. This good fit indicates a strong relation between the number of CDs sold and total costs.

d. As a first step, it probably is useful to restate Mollys model in terms of annual costs. This requires us to multiply monthly fixed costs by 12. The variable cost per CD, however, remains unchanged. Thus, we have:

Total Annual Costs = ($80,000 ( 12) + (# of CDs sold ( $7.50).

Total Annual Costs = $960,000 + (# of CDs sold ( $7.50).

If reducing the selling price to $14.95 increases volume by 30%, then annual CD sales are expected to be: 1.30 ( 106,900 = 138,970. In turn, our estimate of Mollys total annual costs = $960,000 + (138,970 ( 7.50) = $2,002,275.

At this new level of volu

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