Solution manual cost accounting by LauderbachCOST ANALYSIS

CHAPTER 3 COST ANALYSIS 31 Cost Classification (a) Committed (b) Committed (c) Discretionary, but in some companies could be committed (Intel, Microsoft, et. al.) (d) Committed (e) Discretionary (f) Committed (g) Discretionary 32 Limitations of HighLow Method The procedure would not work well because the two points used to determine the pattern of cost behavior are outside the relevant range. The results will probably understate the fixed component and overstate the variable component. Total costs at shutdown (all fixed costs) are almost certainly less than fixed costs in the relevant range and total costs at 100% of capacity will reflect inefficiencies from sacrificing efficiency to increase output. The company will hire inexperienced workers, expedite deliveries of materials, and take other actions that will increase costs. If they can sell all that they can make, the company will be very profitable, and cost control is not likely to be a high priority 33 Methods of Cost Behavior Analysis The highlow method is quick and easy, but uses only two observations and so is seriously deficient. It assumes that the two selected points are representative. It gives no indication of how accurate predictions are likely to be The scatterdiagram method is better than the highlow method. It uses more observations, it allows a visual, informal analysis of goodness of fit, and it allows users to spot outliers or problematic patterns of cost (such as curvilinear behavior or kinks that indicate two or more cost functions) Regression analysis gives more precise results than scatterdiagrams, gives formal measures of goodness of fit, and permits the use of more than one independent variable. By itself, it does not allow the user to spot outliers or problematic cost patterns 31 34 Cost Classification It needs to be made clear with respect to what decision a cost is avoidable. You might wish to ask for other decisions or types of decisions for which each cost might be avoided. (a) Avoidable and direct (b) Unavoidable, but direct (c) Avoidable and direct (d) Unavoidable and indirect (e) Unavoidable and indirect The cost is avoidable, but not with respect to decisions about the SouthCentral region (f) Avoidable and direct The pattern that emerges is that avoidable costs are typically direct, indirect costs usually unavoidable, but not necessarily vice versa. Chapter 5 discusses situations in which indirect, common costs might be avoided, essentially when dropping a segment so greatly reduces workload that a service department might be reduced 35 Cost Classification BDirectness and Avoidability (a) Avoidable and direct (b) Unavoidable and indirect (c) Unavoidable, but direct (d) Unavoidable and indirect (e) Avoidable and direct (f) Unavoidable and indirect 36 Accuracy of Predictions (5 minutes) Indirect labor is much easier. The observations lie along a line while supplies cost is widely dispersed. If a cost line were fitted visually in each graph and costs predicted based on the formula for that line, the actual costs of supplies will be farther from that line than the actual costs of indirect labor 37 Mixed Costs (10 minutes) 1. $64,230 fixed, $0.57 per hour variable $90,450 $85,890 = $4,560/8,000 = $0.57 per hour variable component 46,000 38,000 Fixed cost = total cost total variable cost Using the high volume, Fixed cost = total cost total variable cost = $90,450 (46,000 x $0.57) = $90,450 $26,220 = $64,230 32 Using the low volume, = $85,890 (38,000 x $0.57) = $85,890 $21,660 = $64,230 2. $89,880 $64,230 + ($0.57 x 45,000 hours) 3. The controller wants to be able to predict costs, and also must take part in decisions about pricing, whether to accept particular types of business, and others 38 Cost Behavior (10 minutes) 1. Variable component = cost at high volume cost at low volume high volume low volume = $29,840 $21,150 = $8,690/$220,000 = 0.0395, or 3.95% $560,000 $340,000 Fixed component = Total cost variable cost, using the high volume, F = $29,840 (0.0395 x $560,000) F = $29,840 $22,120 F = $7,720 2. Excel output follows SUMMARY OUTPUT Regression Statistics Multiple R 0.783200 R Square 0.613403 Adjusted R Square 0.558175 Standard Error 1,829.53 Observations 9 Intercept Monthly Service Revenues Standard Coefficients Error t Stat Pvalue Lower 95% Upper 95% 11,928.34 3,946.01 3.023 0.019 2,597.52 21,259.17 0.02902 0.00871 3.333 0.013 0.00843 0.04960 The results are quite different. The regression line is $11,928 + 0.029 x sales as opposed to $7,720 + 0.0395 x sales. The fixed component is higher and the variable component lower than the highlow method gives. The high and low observations appear to be nonrepresentative of the entire set. Of course, its reliance on two observations is a major weakness of the highlow method 3. The equation is reasonably good. An r2 of .613 and a standard error of $1,830 are decent measures of goodness of fit. The 95% confidence interval for the variable cost does not include zero. Given that service revenues average nearly $450,000, the average predicted cost will be about $25,000, so 68% of observations should be within $1,830, or about 7.4% 33 39 Cost Analysis, HighLow Method (20 minutes) 1. Cost of Goods Sold Selling Administrative Cost at high volume $54,000 $ 8,800 $9,400 Cost at low volume 48,000 8,500 9,200 Change in cost $ 6,000 $ 300 $ 200 Divided by change in volume $10,000 $10,000 $10,000 Equals variable cost percentage 60% 3% 2% Total cost at sales of $90,000 $54,000 $ 8,800 $ 9,400 Variable cost portion ($90,000 x variable cost percentage) 54,000 2,700 1,800 Fixed portion of cost $ $ 6,100 $ 7,600 2. Income Statement Sales $100,000 Variable costs: Cost of goods sold at 60% $60,000 Selling expenses at 3% 3,000 Administrative expenses at 2% 2,000 Total variable costs at 65% 65,000 Contribution margin at 35% 35,000 Fixed costs: Selling $6,100 Administrative 7,600 Total fixed costs 13,700 Income $ 21,300 Note to the Instructor: Students will use different formats in requirement 2. Some might find only the total for each component and place only that total on the statement. Alternatives offer the opportunity to discuss the idea of preparing statements and internal reports in a form most likely to be understood and useful to their readers. The point to be made is that information provided by accountants does not fulfill its function if the managers receiving it cannot use it to fulfill their functions. A useful analogy of "different reports for different people" is found in financial accounting, where the formats change for reports to stockholders, the many governmental units, regulatory agencies, trade associations, etc. You might wish to make the point that, for a nonmanufacturing company, cost of goods sold should be wholly variable (not mixed, as it can be for a manufacturer). Of course, cost of sales might not be exactly the same percentage of sales from period to period even if selling prices are constant. Changes in the percentage of cost of sales to sales between two periods could result from a change in purchase prices or sales mix (covered in Chapter 4) 310 Understanding Regression Results (1015 minutes) The memorandum should contain the following major points The equation tells us that parttime consultants cost has a fixed component of $101,187 per month and a variable component of $0.0898 per 34 dollar of consulting revenue. Therefore, to predict the cost, we multiply expected revenue by $0.0898 and add $101,187. For example, at $900,000, Y = $101,187 + ($0.0898 x $900,000) = $182,007 The slope tells us the variable component of the cost, so we can use it to determine the probable increase (or decrease) in costs that would accompany an increase (or decrease) in business The coefficient of determination, r2 of 0.6266, or 62.66%, is the percentage of the variation in parttime consultants cost that is associated with changes in revenue. The value is relatively high for such data and so indicates that the fit is good The standard error of the estimate, tells us how close our predictions are likely to be to the actual results. In this case, we expect predictions to be within $9,329 about 68% of the time, and within $18,658 (2 x $9,329) about 95% of the time. (This is a bit rough and does not tell us the confidence interval for a single prediction but for the average. This point is probably not important to most classes.) It is also helpful to understand what the results do not tell you. The equation is not necessarily the best available. Some other factor might predict better. Multiple regression with some other factors might give better results in the form of a higher rsquared and a lower standard error. The intercept, $101,187, is not the estimate of total cost at zero revenue. The data were collected in the range of $800,000 to $1,200,000, and it is unsafe to extrapolate outside that range Note to the Instructor: Students often ask what a good value is for r2. The best answer, that it depends on the data, is not too satisfying. Anything above .50 is probably quite good for cost data in a complicated environment. Evaluating the standard error requires examining the relationship of the error to the total cost. For instance, at $1,000,000 hours (midpoint of range) predicted cost is $190,987. The standard error of $9,329 is about 5% of predicted cost, which is a pretty good fit. 311 Interpreting Behavior Patterns (1015 minutes) 1. The first step is to determine just what the behavior is. The first set of observations shows a relatively low fixed cost and a rapidly increasing total cost. This indicates that variable cost is relatively high. The second segment shows a jump above the level of the first segment, with a flattening of the total cost line, indicating a decline in variable cost per unit of activity. The third segment shows much the same: a jump in the level of costs, with a further flattering of the slope of the cost line One possible explanation for the observed behavior is that "variable" costs per unit drop as volume increases, with increases in stepvariable costs accounting for the jumps. If the cost were total manufacturing cost, a possible explanation is that materials were subject to quantity discounts and were a large proportion of total costs, with jumps in cost occurring because of stepvariable costs such as supervision Another possible explanation is that the company has three alternative methods of production, with increasing amounts of machinery causing the jumps in cost and increased efficiency in the use of labor and materials causing 35 the flattenings of the cost lines. It is unlikely that the firm could actually operate from near zero to near full capacity in this manner at short notice, unless the machinery could be rented at short notice. Hence, the cost behavior under this explanation should be viewed as relatively long term 2. Planning for the costs should be relatively simple if the range within which the company expects to operate was relatively certain. Three different lines would be drawn and used in prediction, depending on the range in which volume was expected to occur. A single line could not be a good predictor. 312 HighLow Method for Manufacturing Company (20 minutes) 1. Cost of sales: 30% of sales $$ variable, $340.0 fixed S&A expenses: 20% of sales $$ variable, $150.0 fixed Cost of Sales S&A Expenses Cost at high volume $688.0 $382.0 Cost at low volume 670.0 370.0 Differences $ 18.0 $ 12.0 Divided by difference in sales $ 60.0 $ 60.0 Variable components 30% 20% Cost at high volume $688.0 $382.0 Less variable cost: $1,160.0 x 30% 348.0 $1,160.0 x 20% 232.0 Fixed components $340.0 $150.0 2. April May Sales $1,100.0 $1,160.0 Variable costs: Manufacturing at 30% $330.0 $348.0 S&A at 20% 220.0 550.0 232.0 580.0 Contribution margin 550.0 580.0 Fixed costs: Manufacturing 340.0 340.0 S&A 150.0 490.0 150.0 490.0 Income $ 60.0 $ 90.0 Several comments apply here. First, some students do not understand that recasting income statements does not change profit, only the form of the statement. Second, the contribution margin format allows us to do CVP analysis, which we could not with the functional income statements. We can, for example, determine the breakeven point because we know that contribution margin is 50% (100% 30% 20%) and total fixed costs are $490.0: $490.0/50% = $980.0 We can also calculate sales volumes required for target profits and do other planning that is impossible without knowledge of cost behavior 313 Relationships (15 minutes) 36 1. (b) $600,000 $400,000 + $200,000 (a) $2.00 $8 selling price less $6 contribution margin per unit ($600,000/100,000) (c) $230,000 $200,000 current income + additional contribution margin of $30,000 (5,000 x $6), or 105,000 x $6 = $630,000 total contribution margin less $400,000 fixed costs = $230,000 2. (d) $250,000 $50,000/20% (c) 25,000 units $250,000/$10 (b) $6 $10 x (100% 40%) (a) $50,000 ($250,000 x 40%) $50,000 profit 3. (c) $60,000 $400,000 x 15% (a) 10,000 Sales $400,000 Total contribution margin ($60,000 + $90,000) 150,000 Variable costs $250,000 Variable cost per unit $25 Number of units sold ($250,000/$25) 10,000 (b) $15 $150,000 CM/10,000 units 314 PerUnit Analysis (1015 minutes) 1. $432,000, $5.40 x 80,000. You might want to reemphasize that fixed costs come in total, not perunit, and that this multiplication is necessary because you must work backwards 2. 85,000 units Total fixed costs $432,000 Desired profit 180,000 Total required contribution margin $612,000 Divided by contribution margin per unit ($12 $4.80) $7.20 Units required 85,000 3. $13.54 per unit Desired income $180,000 Fixed costs from requirement 1 432,000 Required total contribution margin $612,000 Divided by expected unit volume 70,000 units Equals required perunit contribution margin $8.74 rounded Plus expected variable cost per unit 4.80 Required price $13.54 4. $9,600 increase in profit. Either the total or incremental approaches could be used here. Using the total approach, Expected total contribution margin ($7.20 x 83,000) $597,600 Expected fixed costs ($432,000 + $12,000) 444,000 Expected total profit 153,600 Profit expected without additional expenditure (80,000 x $1.80) 144,000 Increase in profit $ 9,600 Using the incremental approach, 37 Additional contribution margin ($7.20 x 3,000 units) $ 21,600 Added fixed costs 12,000 Increase in profit $ 9,600 Note to the Instructor: You might wish to ask the class how many additional units the company must sell to make the advertising campaign just pay for itself. The calculation is similar to that of an indifference point, or even of a breakeven point. $12,000/$7.20 = 1,667 units Because 1,667 is well below the expected 3,000 units, the company is probably welladvised to go ahead. Had the indifference point been, say, 2,800 units, a reasonable manager might believe that the risk is too great because a relatively small shortfall would wipe out the additional profit 315 Percentage Income Statement (1520 minutes) 1. $80,000 $800,000 x 10% 2. $160,000 fixed costs, $533,333 breakeven point, ($160,000/30%) and $266,667 margin of safety ($800,000 $533,333) Variable costs are 70% of salescost of sales of 60% plus 10% commissionso contribution margin is 30%. To find fixed costs, Total costs at $800,000 sales $800,000 $80,000 profit $720,000 Total variable costs ($800,000 x 70%) 560,000 Total fixed costs $160,000 3. $50,000 Contribution margin ($700,000 x 30%) $210,000 Fixed costs 160,000 Profit $ 50,000 Or, the decreased sales of $100,000 decrease profit by $30,000 ($100,000 x 30% CM%), from $80,000 to $50,000 4. 5.55% The easiest way to approach this requirement is to use the basic profit equation. Cost of sales remains at $480,000, ($800,000 x 60%) S $480,000 .1S $160,000 = $120,000 .9S = $760,000 S = $844,444 Percentage increase = 5.55% ($44,444/$800,000) As proof, Sales $844,444 Cost of sales, as before 480,000 Gross margin 364,444 Commission ($844,444 x 10%) 84,444 Contribution margin 280,000 Fixed costs 160,000 Profit $120,000 316 Cost Behavior Graphs (15 minutes) 38 Unofficial answers to this CPA problem are as follows: 1. C 2. F 3. K 4. B 5. A 6. D 7. J 8. E or H 9. L (Item 9 is different from the original CPA problem.) 10. G Many of the answers assume that the use of the cost element is at least partly variable with production. Item 3 is an example. The cost of water as the use of water increases is described by graph K. It is assumed that increases in production cause proportional increases in the amount of water consumed. It is possible, but unlikely, that the use of water is relatively constant whatever production is. It is also possible that 1,000,000 gallons or more is the base amount, with additional water being related to production. Note to the Instructor: Although we did not show the vertical segments of stepvariable costs in the text, students have had little difficulty with cost graphs such as item 7. You might wish to point out that graph J is technically incorrect because the cost is discontinuous, jumping from one level to another. This poses no real problem in a practical situation because the portions of discontinuity are quite small. In this case, a single machinehour at the breaking point gives the jumps, and it is unlikely that any company could be so precise in its hiring practices Some students will wonder why the second segment of the line in graph H (item 8) tilts upward instead of being parallel to the horizontal axis. The reason seems to be that although the labor force is "constant in number," it could be changing in composition because of turnover. It is also possible that some workers earn annual wages of less than $8,500. Graph E is a good answer if (a) there is no turnover and all workers earning more than $8,500 317 CVP Review (20 minutes) 1. 183 sweaters, rounded ($5,000 + $6,000)/($100 $40) = $11,000/$60 Use the highlow method to determine fixed and variable costs: At 150 units, costs are (150 x $100) $4,000 = $11,000 At 200 units, costs are (200 x $100) $7,000 = $13,000 Variable costs = ($13,000 $11,000)/(200 – 150) = $40 Fixed costs = $13,000 – ($40 x 200) = $5,000 2. $113.33 rounded Sales variable costs fixed costs = profit (S x 150) ($40 x 150) $5,000 = $6,000 (S $40) = $11,000/150 S = $40 + 73.33 3. 150 sweaters, same as now Some alert students will see that the supplier receives $40 either way at the $100 price. Some will go through calculations such as the following $100 $30 (10% x $100) = $60 new contribution margin, same as now ($5,000 + $4,000)/$60 = 150 The proposed agreement gives the supplier the same total compensation at the $100 selling price. At higher selling prices the supplier will take a larger share. In all likelihood, Mia will raise prices in the future, making the proposed arrangement more attractive to the supplier, less attractive to Mia 39 318 Profit Improvement Alternatives (15 to 25 minutes) To: Leslie Meriwether From: Student Date: Today Subj: Profit improvement We can achieve our target profit by (a) increasing selling price, (b) decreasing variable cost,(c) decreasing fixed costs, and (d) increasing sales volume. The required changes in these items appear below: (a) Increase selling price to $10.60, an increase of $0.60 per unit With no change in fixed or variable costs, a $60,000 increase in profit ($100,000 desired vs. $40,000 earned last year) requires a $60,000 increase in contribution margin at a volume (current level) of 100,000. Hence, an increase of $0.60 ($60,000/100,000) is necessary Competition will determine whether we can achieve the expected volume with the higher price (b) Reduce variable cost per unit to $5.40, a decrease of $0.60 per unit The logic here is the same as in requirement (a). Contribution margin must increase by $0.60 per unit, and with a constant selling price of $10 the perunit variable cost must decline $0.60 from $6 We might change suppliers to reduce variable costs, but such a step could reduce the quality of the product. We should look for activities/costs that do not add value to the product (c) Fixed costs must decrease by $60,000, to $300,000 If profit is to increase $50,000 and contribution margin is to remain the same, fixed costs must be reduced by an amount equal to the desired increase in profit We can easily reduce some fixed costs, but again the question is whether we might run into other difficulties. We can always reduce discretionary costs such as advertising, but perhaps at the cost of reduced sales. We could cut other costs that might harm us in the long run. Such costs include employee training and maintenance (d) Increase sales to 115,000, an increase of 15%. Here again, if profit is to increase $60,000 without a change in fixed costs, total contribution margin must also increase by that amount. If selling price ($10) and variable cost per unit ($6) remain constant, contribution margin remains at $4, and it will require 15,000 more units ($60,000/$4) to produce the desired increase in profit Increasing unit sales without increasing costs could be difficult. An expanding market would help, as would better service to our customers and a higherquality product. Achieving these improvements without increasing costs might not be possible 310 319 Interpreting Data (1015 minutes) The assistant merely connected the high and low points with his line, not considering the intervening observations. Moreover, the high and low points are at volumes far removed from the other observations, so we should question whether they are within the relevant range. Because the cost is maintenance, we might even expect a relatively higherthannormal cost at low activity because there is then more time for performing the work. Similarly, at the high point we might expect lowerthannormal costs because of the inability to perform work then, as well as managers' unwillingness to take limos in for service during a peak period. The assistant's line shows observations in almost equal numbers above and below, but the line would fit the majority (all but the high and low) of the observations better if it were tilted up and pushed down on the vertical axis. A line hitting the vertical axis at $100 and with a slope of $1.55 fits nicely. At 500 hours, the cost is about $875. This line ignores the extreme points. If the extreme points are to be considered, the line would tilt less and the fixedcost component would be higher than $100. Putting a couple of alternatives on the board will help students see the differences that would arise from differing interpretations of the particular observations 320 Delta Airlines CVP Relationships (20 minutes) 1. The key is to find revenues and costs at breakeven to be able to use the highlow method Revenue and cost at breakeven = $14,881 ($16,741/.729) x .648 So, $15,003 $14,881 = $ 122 = 6.56% variable component $16,741 $14,881 $1,860 2. The fixed component is $13,905 million, $14,881 ($14,881 x $0.0656) 3. $1,953 million Revenue, $16,741/.729 x .739 $16,971 Operating expenses Variable at 6.56% $ 1,113 Fixed 13,905 Total operating expenses 15,018 Operating income $ 1,953 4. The lesson is that an airline, or any other company with very high fixed costs and low variable costs, lives and dies by volume. The calculation in requirement 3 shows that each percentage point adds over $215 million ($1,953 $1,738 = $215) to operating income. Of course, each drop reduces operating income by the same amount. 311 321 Using Multiple Regression (20 minutes) 1. $75,992 $49,272 + ($1.78 x 12,000) + ($2.68 x 2,000) 2. $30.90, calculated as follows: Materials $ 6.00 Labor, 2 hours x $10 20.00 Variable manufacturing overhead (2.0 x $1.78) + (.50 x $2.68) 4.90 Total variable cost $30.90 3. $5.89 Reduced labor, $10 x .50 $5.00 Reduced variable overhead $1.78 x .50 0.89 Total reduction $5.89 Note to the Instructor: You might expand on the important idea that, as item 3 shows, when a company reduces labor time, it reduces not only labor cost but also any variable manufacturing overhead driven by direct labor time 322 Understanding Regression Results (15 minutes) 1. $209,345, $118,645 + ($0.907 x 100,000) 2. No, because zero hours is outside the relevant range. This point is very important, yet often overlooked. It is not safe to predict costs below 75,000 nor above 140,000 hours 3. $40.815 (45 x $0.907) per batch of 100, or $0.40815 per unit 4. This question refers to measures of goodness of fit. The r 2 of 79.25% indicates quite a good fit because 79.25% of the variation in power cost is associated with changes in machine hours. The specific requirement of the question gets at the meaning of the standard error. Actual cost should be within $9,497 of predicted cost about 68% of the time and within $18,994 (2 x $9,497) about 95% of the time. At 100,000 hours, $18,994 is only 9.1% of predicted cost of over $209,345 (part 1). 5. No. There could be another simple regression equation or a multiple regression equation that predicts better. Only if the correlation is perfect, r2= 1, Standard error = zero, can you say that there is none better 323 Review Problem, Including Income Taxes (3540 minutes) 1. $10 ($500,000 sales/50,000 units) 2. $2.50 ($10 selling price $7.50 variable cost) variable cost = $375,000/50,000 units = $7.50 3. 24,000 units ($60,000 fixed costs/$2.50 contribution margin 4. $7,500 (3,000 units x $2.50 contribution margin per unit) 5. 48,000 units ($60,000 target profit + $60,000 fixed costs)/$2.50 6. $400,000 $60,000 fixed costs/(25% contribution margin 10% ROS) 312 7. 54,000 units Desired aftertax profit $ 45,000 Divided by 60% = pretax profit $ 75,000 Fixed costs 60,000 Required contribution margin $135,000 Divided by $2.50 unit CM = 54,000 units 8. 60,000 units Desired aftertax return 9% Divided by 60% = pretax return 15% Sales = $60,000/(25% 15%) = $600,000 $600,000/$10 selling price = 60,000 units 9. $10.20 per unit Desired aftertax profit $ 45,000 Divided by 1 tax rate 0.60 Required pretax profit $ 75,000 Fixed costs 60,000 Required contribution margin $135,000 Divided by unit volume 50,000 Equals required unit contribution margin $ 2.70 Plus variable cost 7.50 Selling price $ 10.20 10. $10.36 per unit, let P = selling price 50,000P – (50,000 x $7.50) $60,000 = 0.16P x 50,000 P = $10.357 11. $625,000 Contribution margin, $10.00 ($7.50 + $0.50) $2.00 Contribution margin percentage, $2/$10 20% Required contribution margin, $60,000 + $65,000 $125,000 Divided by 20% equals required sales $625,000 324 Cost Formula, HighLow Method (5 minutes) The variable cost rate is about 5.2% of sales, and fixed costs are about $412 Sales Wages High $18,100 $1,350 Low 5,050 675 Difference $13,050 $ 675 Change in cost divided by change in volume ($675/$13,050) = 5.2% rounded Substituting 5.2% in the total cost formula at the low volume level: Fixed costs + Variable costs = Total costs F + (5.2% x $5,050) = $675 F = $412 rounded Note to the Instructor: This relatively simple problem emphasizes three important points. First, the observations used in calculating the variable and fixed components of a mixed cost are the high and low points for the 313 independent variable, not for the dependent variable. (Students misunderstanding this point will use sales volumes of $1,950 and $15,040.) Second, the points to be used must be within the relevant range. (Students misunderstanding this point will use sales volumes of $1,950 and $18,100.) The third, and more general, point demonstrated by this problem is the need to understand the facts of the situation. A grasp of the facts is necessary if the student is to question whether the observations for sales volumes of $2,000, $17,000, and $18,000 are outside the relevant range, given that the low and high cost observations occur at $1,950 and $18,100. In this case, the owner calls in parttime help based on the estimate of sales for the coming week, and it is to be expected that the owner's estimates are sometimes off by a wide margin. Errors in estimates result in wages being higher or lower than predicted using a formula based on actual sales. Thus, when actual sales were $15,040, the owner might have expected much larger volume in one or more weeks and committed to more parttime help (who had to be paid!). Similarly, the facts given about the period with $1,950 sales suggest that that level of volume is below the relevant range and should be disregarded 325 Fixed Costs and Decisions (25 Minutes) This is a straightforward problem that allows you to discuss several important points at an early stage in the course. The idea of opportunity cost and loss of sales are treated in Chapter 5, but the introduction here of these points is relatively simple. Moreover, you need not even use the term opportunity cost in connection with this problem Considering only quantitative issues, Keith is better off staying open. An income statement assuming that he closes shows the following Rent on building $1,550 Depreciation on fixtures 600 Utilities, minimum 450 Net loss $2,600 Adding the $2,600 loss to the $350 profit that he could earn staying open, Keith is $2,950 better off remaining open The final recommendation depends on what Keith means by "net at least $2,500 for the month." If he means that he wants to be at least $2,500 better off staying open, he should stay open, but if he means that he wants to show a profit of $2,500, he should close. Whatever the intention of Keith's stated decision criterion, he should be advised to recognize the effect of a onemonth closing on the profit for a full year. That is, the cost to him of closing is $2,950, not just the $350 profit given up. Moreover, Keith might have reason to believe that closing could affect future sales. Some semiregular customers might find another restaurant they like better. Some might be put off by the closing and stay away longer than their normal intervals. 314 326 Alternative Cost Structures   A Movie Company (30 minutes) Note to the Instructor: This problem can be answered either by computing profits at each level of admissions or by using the breakeven points from problem 243 1. (a) Blockbusters: Normal contract $180 million $200 million Revenues (40%) $72,000,000 Variable costs 3,600,000 Contribution margin 68,400,000 Fixed costs 65,000,000 Profit $ 3,400,000 $80,000,000 4,000,000 76,000,000 65,000,000 $11,000,000 Special contract $180 million $200 million Revenues (40%) Variable costs Contribution margin Fixed costs Profit $72,000,000 14,400,000 57,600,000 50,000,000 $ 7,600,000 $80,000,000 16,000,000 64,000,000 50,000,000 $14,000,000 In either case, Blockbusters will prefer the special contract. As problem 243, requirement 3 showed, the special contract will be preferred by Blockbusters only when revenues to the producer are less than $100 million (b) Drift will prefer the normal contract. At $180 million, the normal contract would pay Drift $23.6 million ($20 million salary + 3.6 million variable) while the special contract would pay Drift $19.4 million. At $200 million Drift’s pay would be $24 million under the normal contract and $21 million under the special contract 2. (a) Blockbusters will prefer the normal contract Revenues Variable costs Contribution margin Fixed costs Profit Normal $120,000,000 6,000,000 114,000,000 65,000,000 $ 49,000,000 Special $120,000,000 24,000,000 96,000,000 50,000,000 $ 46,000,000 (b) Drift will prefer the special contract. The normal contract would pay $26 million while the special contract would pay $29 million 327 Regression Analysis (15 minutes) The point here is that observations are so widely scattered that the regression equation is virtually worthless. The r2 is 0.019. Because regression analysis always gives an equation (unless the independent variable has the same value for every observation), people sometimes count on it more than is desirable. The following Excel output provides relevant measures SUMMARY OUTPUT 315 Regression Statistics Multiple R 0.137572 R Square 0.018926 Adjusted R Square (0.121227) Standard Error 48,652.19 Observations 9 Intercept Units Produced Standard Coefficients Error t Stat Pvalue Lower 95% Upper 95% 262,203.39 74,407.37 3.524 0.010 86,258.05 438,148.73 13.1961 35.9103 0.367 0.724 (71.7181) 98.1104 Notice also that with a standard error of the regression equation of $48,652, the 68% confidence interval is very wide. The variable, Units Produced, is not statistically significant 328 CVP Analysis with Changes in Costs (2025 minutes) 1. $200,000 (350,000 x [$20 $8]) $4,000,000 2. $21 The increase in material cost is $1.00 ($4.00 x 25%), so the price increase must cover the increase in variable costs. Some students will simply add the $12 per unit contribution margin to the new perunit variable cost of $9 to arrive at the $21 price. Some students will solve from scratch. Sales = $4,000,000 + (350,000 x $9) + $200,000 = $7,350,000 $7,350,000/350,000 = $21 3. (a) $22.50 ($9.00/40%) The current contribution margin percentage is 60%, ($20 $8)/$20, so the variable cost ratio is 40%. The new variable cost is $9, so the selling price is $9 divided by 40%. Some students will have trouble with this part, which is not explicitly illustrated in the text. However, all it requires is understanding that 100% minus the contribution margin percentage is the variable cost percentage. (b) Profit will be higher because contribution margin per unit will be higher ($22.50 x 60% = $13.50, rather than $12). This requirement emphasizes that contribution margin per unit and contribution margin percentage are different. Assuming no change in unit volume, if prices are increased so as to maintain the perunit contribution margin, profit is maintained at the previous level. If prices are increased so as to maintain the contribution margin percentage, perunit contribution margin increases and so profit increases. 329 Cost Structures and Average Costs (25 minutes) 1. Sally: 100,000 x ($10 $9) = $100,000 Sam: 200,000 x ($10 $9) = $200,000 2. Computations: Sally Sam 316 Total costs at 200,000 units 200,000 x $6 $1,200,000 200,000 x $9 $1,800,000 Total costs at 100,000 units 100,000 x $9 900,000 Total costs at 80,000 units 80,000 x ($10 + $0.50) 840,000 Changes in total costs $300,000 $ 960,000 Changes in volume 100,000 120,000 Unit variable costs $3 $8 Total variable costs at 200,000 units 200,000 x $3 $600,000 200,000 x $8 $1,600,000 Total fixed costs $1,200,000 $600,000 $600,000 $1,800,000 $1,600,000 $200,000 Contribution margin $10 $3 $7 $6 $4 $2 3. Sally: $600,000/($10 $3) = 85,714 Sam: $200,000/($10 $8) = 100,000 4. Since the selling price is the same for each division, they will show equal profits when they have equal costs. Letting V represent the volume, Sally Sam $600,000 + $3 x V = $200,000 + $8 x V $400,000 = $5 x V 80,000 = V Since this volume is less than the breakeven for either division, this is the sales level where they will show equal losses. At volumes greater than 80,000, Sally will show a higher profit. 330 Avoidable Costs (20 to 25 minutes) 1. The equation prepared by Halton's friend is incorrect unless Halton purchases and sells exactly 200 arrangements (so that there are no losses as a result of purchasedbutunsold arrangements). In effect, the equation ignores Halton's purchasing situation. Halton turns a normally variable cost into a fixed (and unavoidable) cost because he cannot sell units after a week. CVP analysis assumes saleability of purchased units Note to the Instructor: Before going on to the next question, it might be useful to explore the implications of accepting the proposed equation, even for planning purposes. For example, the nature of the product is such that some will be less desirable than others by the end of the week, so that lateintheweek sales might not be as expected. (And, of course, if the product is not arrangements but groups of flowers of various types, it is certainly possible that the flowers available for arranging at the end of the week will not be appropriate for the sales opportunities available at that time.) An important point to remember is that we are dealing with average data here (purchase and sales prices), which suggests some need to provide leeway in planning. And, in addition to the previous considerations, Halton should recognize that if he buys and sells 200 arrangements, he could lose the contribution margin from sales orders that he cannot meet 317 2. The purchase cost of the arrangements (or the flowers, as the case may be) cannot be readily classified. Once a specific quantity has been bought, the total purchase cost becomes an unavoidable fixed cost, the variable cost per sale becomes zero, and contribution margin equals selling price 3. About 234 units if 300 units are purchased and 267 if 400 are purchased. Incorporating the idea expressed in the Note to the Instructor for requirement 1, the purchase cost becomes another fixed cost and the target sales volumes can be computed as follows: If purchases are 300, target sales volume = $3,000 + ($10 x 300) + $1,000 = 234 units, rounded $30 $0 If purchases are 400, target sales volume = $3,000 + ($10 x 400) + $1,000 = 267 units, rounded $30 $0 Another approach is to rely on the basic idea that revenues costs = profit Using this simple approach: If purchases are 300, and letting Q = the number of units sold: $30Q $10Q $3,000 $10(300 Q) = $1,000 Q = 234 units If purchases are 400, and letting Q = number of units sold: $30Q $10Q $3,000 $10(400 Q) = $1,000 Q = 267 units In line with the comments offered under the Note to the Instructor in requirement 1, some students might well ask why Halton does not just order 200 units to avoid the problem of unsold units. The issue is, of course, balancing risk and reward, and a risk of $10 (on average) for a potential reward of $30 (again, on average) is likely to be quite attractive 331 Cost EstimationService Business (35 minutes) The pattern of behavior, as shown in the scatterdiagram, is that the cost is relatively constant from 2,800 to 3,500 hours. It then rises at a rate of about $1.80 to $1.95. Several reasons could explain the behavior. Because we have no observations below 2,800 hours, we do not know whether the $3,000 or so cost that we see from 2,800 to 3,500 hours is fixed or a step in a function of a stepvariable cost. It might be that Jarvis keeps a steady parttime force until he finds that volume is rising and he then needs to add workers or increase the hours of the existing ones 318 Calculated variable cost rates in different ranges: Range Rate 3,500 4,800 $1.77 ($5,400 $3,100)/(4,800 3,500) 4,800 5,200 1.95 ($6,180 $5,400)/(5,200 4,800) 5,200 5,600 1.80 ($6,900 $6,180)/(5,600 5,200) 3,500 5,600 1.81 ($6,900 $3,100)/(5,600 3,500) The rates are fairly constant, indicating that a pattern does exist over the upper range of volume Cost $7,000 x 6,000 x x 5,000 4,000 x x 3,000 x x 1,000 2,000 3,000 4,000 5,000 6,000 Hours 332 CVP Analysis for an Airline (25 minutes) 1. 20,000 passengers or 53.33% of capacity of 37,500 Fixed costs: Overall per month $ 130,000 Flight costs at 250 flights (250 x $4,000) 1,000,000 Total fixed costs 1,130,000 Desired profit 70,000 Required contribution margin $1,200,000 Divided by perpassenger CM ($66 $6) $ 60 Number of passengers required 20,000 Divided by capacity (250 x 150) 37,500 Equals percentage of capacity required 53.33% 2. 16,667 passengers or 55.56% of capacity of 30,000 Fixed costs: Overall per month $ 130,000 Flight costs for 200 flights (200 x $4,000) 800,000 Total 930,000 Desired profit 70,000 Required contribution margin $1,000,000 Divided by perpassenger CM ($66 $6) $ 60 Number of passengers required 16,667 Divided by capacity (200 x 150) 30,000 Equals percentage of capacity 55.56% 319 3. Flight costs are an example of a cost that varies with an activity other than sales. The flight cost is fixed from the point of view of a specific flight, but is variable with the number of flights 4. The most obvious characteristic of the airline's cost structure is the high level of fixed costs. For such companies, volume is the key to successful operations. For example, with the data given in requirement 1, the breakeven point is 18,833 passengers, or 50.22% of capacity [$130,000 + (250 x 4,000)]/($66 $6) Thus, an increase of slightly over three percentage points (53.33% 50.22%) in capacity utilization produces a $70,000 change in profit. This is an increase of only 1,167 passengers. Another increase of 1,167 passengers doubles profit to $140,000 Note to the Instructor: A point of particular interest in this problem is the behavior of flight costs, which are variable but not with sales. Note also that the number of planes available has no direct bearing on the problem. Some students try to incorporate that number in their solution, at first as a determinate of capacity. The particular plane used for one of the 200 or 250 flights has no bearing on the costs or capacity. The total fixed cost is affected by the number of planes owned to provide the capacity expressed as the number of flights 333 Promotional Campaign (20 minutes) 1. $5,850,000 Subscription revenue to Ajax 20,000,000 x 15% x $35 x 25% $26,250,000 Costs $10,000,000 + $10,400,000 20,400,000 Profit $ 5,850,000 2. 11.66% Ajax has a contribution margin per $35 order of $8.75 ($35 x 25%). The breakeven point in number of orders is 2,331,429 ($20,400,000/$8.75), or 11.66% response rate (2,331,429/20,000,000) Note to the Instructor: You might want to mention that the prize money in these giveaways is paid over a lengthy time, often 20 years. You might, even before covering Chapter 8, ask the class what effect the delayed payment has on the profitability of the campaign. Though they have not yet studied the time value of money, most students will see that the campaign would be more profitable because Ajax can invest the money for a long time. 334 Brain Teaser   Calculating Contribution Margin Percentage (1025 minutes) 1. 40% (1 minus the 60% variablecost percentage computed below) First, convert the 6% aftertax ROS to a l0% beforetax ROS [ 6%/(1 40%)], which means that total costs are 90% (1 10%) of current sales. Knowing the margin of safety and that, at the breakeven point, total costs equal total sales, the basic facts are: Sales Total Costs = Profit Current sales S 90%S 10%S Breakeven sales 75%S 75%S 0 320 This matrix can be converted to the typical highlow matrix as: Sales Total Costs High volume 1.00 .90 Low volume .75 .75 Difference .25 .15 Change in total cost divided by change in volume = .15/.25 = 60% 2. $36,000 Again, converting the aftertax 6% ROS to a 10% beforetax ROS, and applying the basic formulas regarding sales, costs, and breakeven, the basic facts are: Sales Total Costs = Profit Current sales $120,000 $108,000 $12,000 Breakeven sales 75% of current sales 90,000 90,000 0 Difference $ 30,000 $ 18,000 $12,000 Change in total cost divided by change in volume = $l8,000/$30,000 = 60% Applying the variable cost percentage to the current sales volume (the break even volume could also be used, of course): Total costs = variable costs + fixed cost $108,000 = (60% x $120,000) + fixed cost $108,000 $72,000 = fixed cost $36,000 = fixed cost 335 Cost Structure and Risk (20 minutes) Monthly 5 Years Annual sales $250,000 $250,000 Variable costs 100,000 100,000 Contribution margin 150,000 150,000 Fixed costs: 12 x $6,000 72,000 12 x $5,200 62,400 Annual profit $ 78,000 $ 87,600 If sales and variable costs materialize as forecast, Gladack will earn $9,600 more annually under the fiveyear lease. However, the acceptance of the product (and hence the product's useful life) is also relevant If, for example, the product stops selling after four years, the company will be unable to avoid the last year's lease payment of $62,400, while the added profit under the fiveyear lease will be only $38,400 ($9,600 x 4 years). The president should therefore be interested in determining the indifference point, how long the product would have to sell to equate the costs and profits under the two choices. The calculations, with M = the number of months the company must use the machine are: Cost of MonthtoMonth Lease Cost of FiveYear Lease $6,000M = $5,200 x 12 x 5 M = 52 Thus, if the company uses the machine for 52 months, it shows the same 321 total cost and total profit under either alternative. At this point you might wish to bring up the time value of money, saying that even if the company uses the machine for exactly 52 months, it is better off with the yearyear lease because its cash payments are delayed under that choice. That is, the company saves $800 per month for 52 months, a total of $41,600. It pays the $41,600 during the last eight months at $5,200 per month, so that the present value of the savings of the fiveyear lease is positive. The 52 month period is only eight months short of five years, so by taking the five year lease the company is accepting the risk that the product will be profitable for nearly the entire life of the lease. The lower the indifference point, the more attractive the fiveyear lease The commitment for the fiveyear period cuts both ways. There is no guarantee that the lease will remain at $6,000 per month for the five years under the monthly option. The lessor could raise the rent at any time, as the problem states (the lessor can cancel the lease, which amounts to saying that it could also raise the rent). Thus, the fiveyear lease does protect the company against the risk of increased rent Note to the Instructor: This is a good problem to point out the uncertainties with which businesspeople must regularly deal. Here the president is facing uncertainty regarding consumer acceptance and at the same time must deal only with estimates of revenues and variable costs. If a decision is based on the best information available at the time, the president need not regret the choice. If subsequent information does not agree with reasonable estimates at the time of the decision, it is the estimates that were wrong (or "bad"), not the decision 336 Loss per Unit (20 minutes) 1. $4 per unit. The total loss at 40,000 units is $120,000 ($3 x 40,000) and at 50,000 units is $80,000 ($1.60 x 50,000). The change in the loss is $40,000, which, when divided by 10,000 units, gives $4 per unit 2. $280,000. At sales of 40,000 units, total contribution margin is $160,000 (40,000 x $4) and the loss is $120,000. Fixed costs are therefore $280,000 greater than contribution margin. At 50,000 units, contribution margin is $200,000 ($4 x 50,000), and the loss is $80,000, also giving $280,000 for fixed costs 3. 70,000 units ($280,000/$4) 337 CVP AnalysisMeasures of Volume (30 minutes) This problem focuses on identifying a measure of sales volume that is suitable for use in CVP analysis. Requirement 3 will give many students a great deal of trouble and affords an opportunity to discuss alternative ways to express revenues and costs 1. At 100 loaves per month the company will earn $12,000, selling 450,000 board feet of good output (5,000 x 90% x 100 loaves) 322 Revenue: Good output (450,000 bd. ft. x $.30) $135,000 Scrap (50,000 x $.11) 5,500 Total revenue ($1,405 per loaf) 140,500 Variable costs: Price of loaf ($900 x 100) $90,000 Cutting costs ($175 x 100) 17,500 Total variable costs 107,500 Contribution margin ($330 per loaf) $ 33,000 Fixed costs 21,000 Income $ 12,000 2. 63.6 loaves ($21,000/$330 contribution margin per loaf) It is theoretically possible for the company to process part of a loaf because the production process could be viewed as more or less continuous. A loaf could be 35% or so processed at the end of a month. Such an answer would be calculated anyway if loaves per day were asked for, with 22 working days in a month 3. There are alternative ways to approach this part. The easiest is to divide contribution margin per loaf of $330 (requirement 1) by 4,500 good board feet per loaf, giving $.0733 contribution per good board foot. It is also possible to work directly with board feet. It is easier to treat scrap sales as variable cost reductions, than as revenue Revenue per good board foot $0.3000 Variable cost per loaf $1,075 Less scrap sales per loaf (500 x $.11) 55 Net variable cost 1,020 Divided by 4,500 good board feet 0.2267 Contribution margin per board foot $0.0733 The sales of good board feet required to earn $15,000 are 491,132 [($21,000 + $15,000)/$.0733] 338 Measures of Volume (50 minutes) The first step is to scan the data to identify likely correlations. Thus, selling expenses are more probably related to sales than to labor hours, and the last two listed observations confirm this intuitive conclusion. The following results are from Excel spreadsheets Production costs = $5,397 + $7.50 per labor hour r2 = .991, Std Error = $238 Selling expenses = $1,997 + $0.101 per sales dollar r2 = .998, Std Error = $52 Administrative expenses = $2,681 + $0.058 per sales dollar r2 = .918, Std Error = $208 The fits are all excellent, indicating that we have the right drivers. We 323 tested other possible combinations. The r2 for production costs against sales is .18: for selling expenses against labor hours it is .38. Fits of other combinations, such as selling expenses to DLH are low. We have only six observations (to keep data entry to a minimum), so we cannot be as happy as we would with 25 or so, but with such good fits we have equations that should predict well. We must guard against regressing everything in sight on everything else, always a temptation when we have a datarich environment and virtually unlimited computing capability. 339 Selecting a Regression Equation (1015 minutes) The memo should make the following points The equation using machine hours will provide better predictions than the one using direct labor hours. Labor hours is not a statistically significant variable (notice the 95% confidence interval includes a value of zero). Moreover, the equation using machine hours will give reasonable results and so we should use it Labor Hours Machine Hours Standard error $19,272 $10,105 r2 .24 .79 variable cost significant? no yes The machinehour equation is better on the important measures of goodness of fit. We should get reasonable predictions using the machinehour equation We might do even better by using both variables in a multiple regression analysis. If we do, we must take care to check for multicollinearity. If machine hours and labor hours are themselves correlated, we would have a problem 340 ValueAdding and NonValueAdding Activities and Costs (30 minutes) This assignment is virtually the same as 114, except that 114 asks about differences between a company's operations and JIT operations. MUL warehouses materials and components. A JIT manufacturer orders stock as needed, eliminating the handling and storage. MUL goes to great lengths to get the best prices on materials and components. A JIT manufacturer is more concerned about quality and meeting delivery schedules. MUL deals with many suppliers, while a JIT manufacturer deals with relatively few MUL inspects all incoming shipments. Instead, like a JIT manufacturer it should stop inspecting once it determines that a vendor delivers defect free components. MUL also inspects for deterioration before it puts components into process. Keeping lower inventories would eliminate this activity MUL maintains inventories at work stations, has long setup times, and considerable moving of goods during production. These activities could be eliminated by paying more attention to quality so that there would be no need to hold inventories at stations. Using manufacturing cells would reduce (perhaps eliminate) setup times and eliminate moving semifinished product around the factory. 324 MUL inspects at the end of production. It also makes 10% more units than needed as a buffer against defects. The company's workers could instead inspect product continually, making it possible to keep little inventory and eliminate separate inspection. MUL tries to trace defects, which adds no value. If its workers inspected continually it would not have that activity MUL's cycle times are high. It could reduce them by adopting JIT principles, as indicated above. 325 ... component 46,000 38,000 Fixed cost = total cost total variable cost Using the high volume, Fixed cost = total cost total variable cost = $90,450 (46,000 x $0.57)... Change in cost divided by change in volume ($675/$13,050) = 5.2% rounded Substituting 5.2% in the total cost formula at the low volume level: Fixed costs + Variable costs = Total costs F + (5.2% x $5,050) = $675... One possible explanation for the observed behavior is that "variable" costs per unit drop as volume increases, with increases in stepvariable costs accounting for the jumps. If the cost were total manufacturing cost, a possible explanation is that materials were subject to quantity discounts and

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