ORIE_350_Homework__9_Solutions

ORIE_350_Homework__9_Solutions - ORIE 350 Homework#9...

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Unformatted text preview: ORIE 350 Homework #9 Solutions 1. If the first FSAE car built took 400 assembly hours, and the doubling parameter had value 0.80, how long did it take the FSAE team to assemble the 10th car? Given: s = 0.80 K = 400 hours Calculations: n= log s log 0.80 -0.09691 = = = -0.032193 log 2 log 2 0.3010 Zu = Ku n We want the value of Z for the 10th car, so u = 10 and Z10 = 400 ( 10 ) -0.0321928 = 190.6 It takes 190.6 hours to assemble the 10th car. 2. A contractor manufactures large backup power systems . Given the following data, estimate the cost of units 5, 6, and 7. Unit 1: Unit 2: Unit 3: Unit 4: Step 1: Take the logs of both u and Z u 1 2 3 4 Z 7,815,000 7,424,000 7,205,000 7,053,000 log u 0 0.3010 0.4771 0.6021 log Z 6.89293 6.87064 6.85763 6.84837 $7,815,000 $7,424,000 $7,205,000 $7,053,000 Next, we see that using the log form of the learning equation, we get a straight line: log Zu = log K + n log u with log K = intercept n = slope Plotting log Z versus log u, we obtain: 6.9 6.88 6.86 6.84 6.82 6.8 6.78 6.76 6.74 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 We see the intercept is 6.89293, so solve for K log K = 6.89293 K = 106.89293 = 7,815, 018 Measuring the slope, we find it is - 0.074, so n = - 0.074 Then we are ready to calculate Z5, Z6, and Z7. Z5 = 7,815, 018 ( 5 ) Z6 = 7,815, 018 ( 6 ) Z7 = 7,815, 018 ( 7 ) -0.074 -0.074 -0.074 . = $6,937,551 = $6,844,580 = $6, 766,946 3.27 (ABC versus traditional costing.) a. Using the Three Cost Drivers Rate Direct Materials.................... Direct Labor........................... Overhead Costs: Number of Production Standard High $ 125,000a $ 114,000 $ 239,000 $ 160,000b $ 80,000 $ 240,000 Grade Total Runs................................ $ 10,000c $ 200,000f $ 100,000 $ 300,000 Number of Quality Tests................................ 12,000d 144,000g 216,000 360,000 Number of Shipping Orders............................. 1,466.67e 146,667h 73,333 220,000 Total Overhead...................... $ 490,667 $ 389,333 $ 880,000 Total Costs............................. $ 775,667 $ 583,333 $ 1,359,000 Total Unit Cost...................... $2.42i $4.86i aData given in the text. bData given in the text. c$10,000 per run = $300,000 in production costs/30 total runs. d$12,000 per test = $360,000 in quality costs/30 total tests. e$1,466.67 per order = $220,000 in shipping costs/150 shipping orders. f$200,000 = $10,000 per production run X 20 runs for Standard. g$144,000 = $12,000 per quality test X 12 tests for Standard. h$146,667 = $1,466.67 per order shipped X 100 orders shipped for Standard. i$2.42 = $775,667 total costs for Standard/320,000 units produced; $4.86 = $583,333 total costs for High Grade/120,000 units produced. 3.27 continued. b. Using Direct Labor as the Allocation Base Rate Direct Materials....................... Direct Labor............................. Total Overhead (Labor Standard Grade High Total 239,000 240,000 $ 125,000a $ 114,000 $ 160,000b 80,000 Dollar Allocation).................. 3.66667c 586,667d 293,333 880,000 Total Costs................................ $ 871,667 $ 487,333 $ 1,359,000 Total Unit Cost......................... $2.72e .06 $4 aData given in the first table. bData given in the first table. c3.66667 = $880,000 total overhead/$240,000 total direct labor costs. d$586,667 = 3.66667 X $160,000. e$2.72 = $871,667/320,000 Standard units produced. c. By allocating overhead on the basis of direct labor costs, the company has been understating the cost to manufacture HighGrade units and overstating the cost to manufacture Standard units. As a result, ABC shows that the Standard unit is more profitable than originally thought and the HighGrade unit is less profitable: Traditional Costing Method Price................. Cost.................. Profit................ Standard $ 3.60 .72 2 0 $ .88 HighGrade $ 5.80 .06 4 1 $ .74 ABC Standard $ 3.60 .42 2 1 $ .18 HighGrade $ 5.80 .86 4 $ .94 3.40 (Choosing an ABC system.) a. FreeWheeler, Ltd. Income Statement Featherweight Peak Raider Total Sales.................................. $ 760,000 $ 1,120,000 Direct Costs: Direct Materials............. $ 300,000 $ 480,000 Direct Labor................... 28,800 48,000 Variable Overheada.......... 104,400 167,040 Contribution Margin......... $ 326,800 $ 424,960 Plant and Administration. Other Fixed Overhead...... Operating Profit................ aOverhead rate = $10.44 = $522,000/50,000 hours. $104,400 = $10.44 X 10,000 hours; $167,040 = $10.44 X 16,000 hours; $250,560 = $10.44 X 24,000 hours. b. FreeWheeler, Ltd. $ 950,000 $ 2,830,000 $ 400,000 $ 1,180,000 108,000 184,800 250,560 522,000 $ 191,440 $ 943,200 176,000 280,000 $ 487,200 Income Statement Featherweight Peak Raider Total Sales.................................. $ 760,000 $ 1,120,000 $ 950,000 $ 2,830,000 Direct Costs: Direct Materials............. $ 300,000 $ 480,000 $ 400,000 $ 1,180,000 Direct Labor................... 28,800 48,000 108,000 184,800 Variable Overhead: Machine Setupa............. 10,400 18,200 23,400 52,000 Order Processingb.......... 32,000 48,000 48,000 128,000 Warehousingc................. 46,500 46,500 93,000 186,000 Depr of Machineryd....... 16,800 26,880 40,320 84,000 Shippinge........................ 4,800 19,200 48,000 72,000 Contribution Margin......... $ 320,700 $ 433,220 $ 189,280 $ 943,200 Plant Administration........ Other Fixed Overhead...... Operating Profit................ 176,000 280,000 $ 487,200 a$10,400 = $52,000/80 production runs X 16 production runs; etc. b$32,000 = $128,000/1,600 X 400; etc. c$46,500 = $186,000/800 X 200; etc. d$16,800 = $84,000/50,000 X 10,000; etc. e$4,800 = $72,000/15,000 X 1,000; etc. c. The activitybased costing method provides a more detailed breakdown of costs. This additional information should enable management to make better decisions. For example, if management wants to reduce costs then activitybased costing will identify the activities on which management should focus its cost reducing efforts. For example, warehousing costs are high and particularly high for the Raider in view of its sales volume. Some costs may have no relationship to any volume or activity base. To artificially allocate these costs would distort the accounting information used for pricing, evaluation, etc. A preferable method of handling these costs might be to require a "contribution margin" from each product that must cover a portion of unallocated costs. d. 5.21 (Cost behavior when costs are semivariable.) a. Slope = = $1. Intercept = ($15,000 $12,000)/(9,000 packages $6,000 packages) = a cost data point (slope X distance from data point to zero) = $15,000 [$1 X (9,000 packages 0)] = $15,000 $9,000 = $6,000. Costs Shipping Department $15,000 12,000 6,000 6,000 9,000 Number of Packages Shipped b. c. The variable cost per package shipped is $1. (See Part a.) Fixed cost is $6,000 (the point where the line crosses the vertical axis). (See Part a.) 5.25 (Average cost calculations.) a. b. c. Average fixed cost = $40,000 1,000 memberships = $40. Average variable cost per membership = $80. Average cost per membership = $120 (= $40 + $80). 5.33 (Multiple linear regression.) a. The regression equation is: Costs = $25,419 + $13.480 Beer Produced + $0.685 Raw Materials + $69.724 Batches + $0.920 Water + $19.984 CIPs + $514.560 New Products Therefore, the cost driver rates are: Beer Produced............................................ Raw Materials............................................ Batches....................................................... Water.......................................................... CIPs............................................................ New Products............................................. b. $13.480 per hL $0.685 per kg $69.724 per Batch $0.920 per hL $19.984 per CIP $514.56 per New Product The estimated costs of doing business given the following activity levels (i.e., cost driver volumes) are computed using the cost driver rates computed above. Activity 1,650 hL 25,500 kg 100 10,800 hL 120 1 Level X X X X X X Beer Produced Raw Materials Batches Water CIPs New Products Intercept Activity $ $ $ $ $ $ Rate 13.480 0.685 69.724 0.920 19.984 514.560 Total Estimated Costs for the Month c. = $ 22,242 = 17,468 = 6,972 = 9,936 = 2,398 = 515 25,419 $ 84,950 Cost Target water consumption was 105,820 hL (= 21,164 hL beer produced X 5 hL water). Actual water consumption was 141,972 hL. The difference is 36,152 hL. Thus, $33,260 (= 36,152 hL water X $0.92) would have been saved if the company achieved its target. (Approximately $1,848 per month.) Multiple linear regression is a useful tool. As ORIE 350 is a junior-level class, it was not unreasonable to expect that you would have seen regression before. Regrettably, many of you had not. While regression is listed in the catalog descriptions of at least one sophomore class, apparently the topic was not actually covered. It is difficult to introduce this topic in ORIE 350, as the sections do not meet in a computer lab. If you plan to work in business, please make sure to take some sort of elective (ORIE 451 is one) in which a computer lab is utilized and where linear regression is used. Regression is often taught in a statistics class, but not always, so be careful in your course selection. ...
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