Cost managment∶accounting and control 第十五章解答手册.doc

348 CHAPTER 15 PRODUCTIVITY MEASUREMENT AND CONTROL QUESTIONS FOR WRITING AND DISCUSSION 1 Total productive efficiency is the point where technical and allocative efficiency are achieved It is the point where the optimal quantity of inputs is used to produce a given output 2 Technical efficiency means that for any mix of inputs no more of any one input is used than necessary Allocative efficiency means that the least costly and most technically efficient mix is chosen 3 Productivity measurement is a quantitative assessment of productivity changes 4 If the productivity ratio output input has only one input then it is a partial measure If all inputs are included then it is a total measure of productivity 5 An operational productivity measure is expressed in physical terms whereas a financial productivity measure is expressed in dollars 6 Partial measures can be misleading since they do not consider possible trade offs among inputs They do however allow some assessment of how well individual factors are being used and additionally often serve as input to total measures Total measures are preferred because they provide a measure of the overall change in productivity and they allow managers to assess trade offs among inputs 7 A base period serves as a standard or benchmark for assessing changes in productive efficiency 8 Profile measurement and analysis computes a series of operational partial productivity measures and compares this series with the corresponding series of the base period to assess the nature of the productivity changes Profile analysis does not indicate whether productivity changes are good or bad when trade offs among inputs exist No value is attached to productivity changes 9 Profit linked productivity measurement and analysis is an assessment of the amount of profit change from the base period to the current period attributable to productivity changes 10 Profit linked productivity measurement allows managers to assess the economic effects of productivity improvement programs It also allows valuation of input trade offs a critical element in planning productivity changes 11 The price recovery component is the difference between the total profit change and the change attributable to productivity effects 12 Activity productivity analysis measures changes in the productivity of individual activities It does this by measuring the inputs and outputs of each activity and comparing the results against a base period Both profile and profit linked measures are possible The approach is limited because it can be applied only to value added activities 13 Process productivity analysis measures process productivity by calculating two components and then summing these two components The first component is simply activity productivity The second component is activity output efficiency For the second component process output is defined and individual activity output is viewed as process input Both profile and profit linked measurement and analyses are possible This approach can be used to assess changes in efficiency for both value added and non value added activities 349 EXERCISES 15 1 1 Combinations B and C are technically efficient Combination B can produce the same output for less of each input than Combination A Similarly Combination C can produce the same output for less of each input than Combination D Comparing B and C shows that trade offs exist among the inputs and so it is not possible to say that B is more technically efficient than C or vice versa 2 Once the technically efficient input combinations are identified then the least costly combination should be chosen Input prices are used to value the trade offs B uses more materials but less labor and energy than C Combination B 8 110 10 180 2 540 3 760 Combination C 8 92 10 190 2 570 3 776 Combination B is the best choice based on allocative efficiency 15 2 1 Output input ratios Combination C1 Materials 4 000 14 000 0 29 Labor 4 000 7 000 0 57 Yes there is improvement Current productivity is Materials 4 000 16 000 0 25 Labor 4 000 8 000 0 50 Since 0 29 0 25 and 0 57 0 50 Combination C1 dominates the current input combination and productivity would definitely improve Cost comparison Current combination 5 16 000 10 8 000 160 000 Combination C1 5 14 000 10 7 000 140 000 Value of productivity 20 000 This improvement is all attributable to technical efficiency The same output is produced with proportionately less inputs Note that the inputs are in the same ratio 2 1 and that Combination C1 reduces each input in the same proportion 350 15 2Concluded 2 Output input ratios Combination C2 Materials 4 000 15 000 0 27 Labor 4 000 6 000 0 67 Compared to the current use productivity is better for both materials and labor 0 27 0 25 and 0 67 0 50 Compared to Combination C1 however C2 has lower productivity for materials 0 27 0 57 Trade offs must be considered 3 Cost of Combination C2 5 15 000 10 6 000 135 000 Cost of Combination C1 See Req 1 above 140 000 Difference 5 000 Combination C2 is a less costly input combination than C1 It saves 5 000 of input cost per quarter Thus less resources are used by C2 than C1 and moving from C1 to C2 would be a productivity improvement The same output is produced at a lower cost This is an example of improving allocative efficiency 15 3 Productivity profiles 2009 Power 96 000 12 000 8 Materials 96 000 24 000 4 2010 Power 120 000 6 000 20 Materials 120 000 27 000 4 44 The profile reveals that productivity did improve Each output input ratio in 2010 is greater than its 2009 counterpart 15 4 1 Profit linked measurement PQ PQ PAQAQ P PQ P AQ P Power15 000 30 0006 000 12 000 18 000 Materials30 000300 00027 000270 00030 000 330 000 282 000 48 000 120 000 8 15 000 120 000 4 30 000 Profits increased by 48 000 due to productivity changes 351 15 4Concluded 2 Price recovery Total profit change Productivity induced change Total profit change 2010 4 120 000 2 6 000 10 27 000 198 000 2009 3 96 000 1 12 000 8 24 000 84 000 114 000 Price recovery 114 000 48 000 66 000 Price recovery is the profit change that would have been realized without any changes in productivity Thus without the productivity increase the company would have shown increased profits of 66 000 15 5 1 Productivity profiles Year BeforeYear After Materials 100 000 25 000 4120 000 20 000 6 0 Labor 100 000 5 000 20120 000 2 000 60 0 Capital 100 000 10 000 10120 000 300 000 0 4 Based on the profiles we see that materials and labor productivity increased as expected and that capital productivity decreased The increase in materials and labor productivity was caused by reducing materials and labor usage by using more capital input Since a trade off exists it is difficult to say whether the outcome is good or bad using profile analysis Valuation of the trade off is needed 2 Profit linked measurement P 5 10 and 10 respectively PQ PQ PAQAQ P PQ P AQ P Materials 30 000 150 00020 000 100 000 50 000 Labor 6 00060 0002 00020 00040 000 Capital 12 0001 200300 00030 000 28 800 211 200 150 000 61 200 120 000 4 120 000 20 120 000 10 Profits increased by 61 200 due to productivity changes Assuming that this outcome will persist the trade off is favorable and automating was a good decision 352 15 6 1 Productivity profile analysis Status QuoaProject IbProject IIc Materials 0 500 600 55 Labor 1 251 502 00 Energy 2 503 003 00 a100 000 200 000 100 000 80 000 100 000 40 000 b120 000 200 000 120 000 80 000 120 000 40 000 c120 000 220 000 120 000 60 000 120 000 40 000 Both projects improve technical efficiency because more output is produced per unit of input for all inputs A recommendation cannot be made without valuing trade offs 2 Profit linked productivity measurement P 8 10 and 2 Project I PQ PQ PAQAQ P PQ P AQ P Materials 240 000 1 920 000200 000 1 600 000 320 000 Labor 96 000960 00080 000800 000160 000 Energy 48 00096 00040 00080 00016 000 2 976 000 2 480 000 496 000 Project II PQ PQ PAQAQ P PQ P AQ P Materials 240 000 1 920 000220 000 1 760 000 160 000 Labor 96 000960 00060 000600 000360 000 Energy 48 00096 00040 00080 00016 000 2 976 000 2 440 000 536 000 120 000 0 50 120 000 1 25 120 000 2 5 The analysis favors Project II Price efficiency is concerned with valuing trade offs of technically efficient combinations The objective is to choose the least costly and most technically efficient combination In this example trade offs were valued that included both improvements in technical and allocative efficiency The objective is to choose the project that offers the most improvement whether it be from technical or allocative efficiency or both Once these trade offs were valued it became clear that Project II was better than Project I 353 15 7 1 Productivity profiles Base YearaCurrent Yearb Materials0 751 00 Labor3 002 00 a600 000 800 000 600 000 200 000 b720 000 720 000 720 000 360 000 2 Income statements Base YearCurrent Year Sales 9 000 000 10 800 000 Materials 4 000 000 4 320 000 Labor 1 600 000 2 880 000 Gross profit 3 400 000 3 600 000 Change in income 3 600 000 3 400 000 200 000 3 Profit linked measurement P 6 and 8 respectively PQ PQ PAQAQ P PQ P AQ P Materials960 000 5 760 000720 000 4 320 000 1 440 000 Labor240 0001 920 000360 0002 880 000 960 000 7 680 000 7 200 000 480 000 720 000 0 75 720 000 3 00 Change attributable to productivity 480 000 4 Price recovery component 200 000 480 000 280 000 In the absence of productivity changes input costs would have increased by 2 080 000 7 680 000 5 600 000 This increase would not have been offset by the 1 800 000 increase in revenues producing a 280 000 drop in profits This is the price recovery component the amount by which profits will change without considering any productivity changes The productivity improvement adds an additional 480 000 increase in profits so that total profits increased by 200 000 480 000 280 000 Thus the productivity improvement helped offset the profit drop due to input price increases 354 15 8 1 Productivity profiles Paying bills activity Base YearMost Recent Year Clerks 20 00064 000 PCs 20 00064 000 Supplies 28 Moving materials activity Base YearMost Recent Year Labor 21 67 Forklifts 4 0002 500 Supplies 52 50 The productivity profile for the paying bills activity indicates an overall improvement in activity efficiency all partial ratios improved Since this is a value added activity this means that activity performance has improved The moving materials activity indicates a drop in activity productivity Less output and less inputs were used to perform the activity This is a non value added positive effect The productivity ratios fail to reveal this though unless it can be shown that reduction of non value added activities always leads to a decline in productivity ratios which seems unlikely Thus changes in profiles for non value added activities are difficult to interpret The best way to deal with non value added activities is to include them as part of the productivity analysis of the process to which they belong 2 Profit linked measure P 25 000 5 000 and 1 respectively PQ PQ PAQAQ P PQ P AQ P Clerks 16 400 0005 125 000 275 000 PCs 1680 000525 00055 000 Supplies 160 000160 00040 00040 000120 000 640 000 190 000 450 000 320 000 20 000 320 000 20 000 320 000 2 Significant savings have come from process innovation 355 PROBLEMS 15 9 1 Profit linked measure purchasing expressed in thousands where P 2 40 000 and 10 respectively PQ PQ PAQAQ P PQ P AQ P Supplies 60 12060 120 0 Clerks 0 031 2000 0251 000200 Capital 1 2001201 2001200 1 440 1 240 200 120 2 120 4 000 120 0 10 where the partial ratios for purchasing for 2008 are 2 100 000 50 000 4 000 100 000 25 and 0 10 100 000 1 000 000 Profit linked measure receiving in thousands where P 2 40 000 and 10 respectively PQ PQ PAQAQ P PQ P AQ P Supplies 48 9630 60 36 Clerks 0 062 4000 052 000400 Capital 960963 000300 204 2 592 2 360 232 180 3 75 180 3 000 180 0 1875 where the 2008 ratios are 3 75 150 000 40 000 3 000 150 000 50 and 0 1875 150 000 800 000 Profit linked measure paying bills in thousands where P 2 40 000 and 10 respectively PQ PQ PAQAQ P PQ P AQ P Supplies 90 1805 10 170 Clerks 0 124 8000 014004 400 Capital 600601 000100 40 5 040 510 4 530 180 2 180 1 500 180 0 30 where the 2008 partial ratios are 2 150 000 75 000 1 500 150 000 100 and 0 30 150 000 500 000 356 15 9Concluded 2 Activity output efficiency in thousands where P 12 00 14 40 and 28 00 respectively PQ PQ PAQAQ P PQ P AQ P Purchasing 120 1 440120 1 440 0 Receiving 1802 5921802 5920 Paying bills 1805 0401805 0400 9 072 9 072 0 3 600 000 30 3 600 000 20 3 600 000 20 where the partial ratios are 30 3 000 000 100 000 and 20 3 000 000 150 000 3 Sum of the two components Resource efficiency component Purchasing 200 000 Receiving 232 000 Paying bills 4 530 000 4 962 000 Activity output efficiency 0 Total process productivity change 4 962 000 The sum of the two components gives the change in profits attributable to changes in process productivity This shows that even though the procurement output s demands for the output of the three activities remains unchanged significant improvements in activity resource efficiency have increased the overall efficiency of the procurement process Notice that the biggest increase came from the paying bills subprocess This can be explained in large part by the elimination of the non value added activity of resolving discrepancies 357 15 10 1 Productivity profile Current system Materials 50 000 200 000 0 25 Labor 50 000 100 000 0 50 Computerized system Materials 50 000 175 000 0 29 Labor 50 000 75 000 0 67 Materials and labor productivity increase with the acquisition as claimed by the production manager 2 To compare the alternatives all inputs must be considered Productivity profiles CurrentComputerized Materials0 250 29 Labor0 500 67 Capital0 500 10 Energy1 000 40 The productivity profiles indicate a mixed outcome some ratios improve and some do not Trade offs therefore must be valued 3 Profit linked measurement where P 4 9 10 and 2 50 respectively PQ PQ PAQAQ P PQ P AQ P Materials200 000 800 000175 000 700 000 100 000 Labor100 000900 00075 000675 000225 000 Capital100 00010 000500 00050 000 40 000 Energy50 000125 000125 000312 500 187 500 1 835 000 1 737 500 97 500 Since output is the same PQ equals the inputs for the current system The trade offs are favorable The computerized system will increase profits by 97 500 358 15 11 1 Productivity profile MaterialsaLaborb 2009 0 502 0 2010 0 602 4 a18 000 36 000 24 000 40 000 b18 000 9 000 24 000 10 000 The profiles indicate an overall productivity increase and thus support the effectiveness of the new process 2 Profit linked measurement where P 4 50 and 10 respectively PQ PQ PAQAQ P PQ P AQ P Materials 48 000 216 00040 000 180 000 36 000 Labor 12 000120 00010 000100 00020 000 336 000 280 000 56 000 24 000 0 5 24 000 2 Increase in profits due to productivity 56 000 3 Price recovery component Total profit change 2010 Revenues 16 24 000 384 000 Materials 4 50 40 000 180 000 Labor 10 10 000 100 000 Profit 104 000 2009 Revenues 16 18 000 288 000 Materials 4 36 000 144 000 Labor 9 9 000 81 000 Profit 63 000 Total profit change 104 000 63 000 41 000 Price recovery component 41 000 56 000 15 000 Without the productivity improvement profits would have dropped 15 000 The increase in sales would not have recovered the increase in the cost of inputs 359 15 12 1 Productivity profile MaterialsLabor 2009 1 670 83 Change I 1 431 25 Change II 2 001 00 Optimal 2 501 25 Change I shows an improvement in labor productivity and a decline in material productivity For Change II both material and labor productivity ratios improved Which change should be implemented depends on the value of the productivity trade offs of Change I versus the value of the productivity improvements of Change II Profile analysis does not reveal these values 2 Cost 2009 33 000 60 66 000 15 2 970 000 Change I 38 500 60 44 000 15 2 970 000 Change II 27 500 60 55 000 15 2 475 000 Optimal 22 000 60 44 000 15 1 980 000 Cost of productive inefficiency 2009 2 970 000 1 980 000 990 000 Change I 2 970 000 1 980 000 990 000 Change II 2 475 000 1 980 000 495 000 Potential improvement for 2007 Change I 2 970 000 2 970 0000 0 Change II 2 970 000 2 475 000 495 000 Change I improves the technical use of labor but does so by trading off materials for labor inputs The optimal combination defines the relative mix ratio as 1 2 The mix ratio for Change I is 7 8 Notice that the 2009 mix ratio is 1 2 Thus moving to Change I decreases allocative efficiency while improving technical efficiency by using less labor in fact the amount of labor used corresponds to the optimal level Change II on the other hand has a mix ratio of 1 2 which is the same as the 2009 and optimal input combination Therefore there is no reduction in trade off efficiency and reducing the amount of each input required to produce the same output is all attributable to improving technical efficiency 3 The profit linked measurement approach will provide the same outcome without requiring knowledge of the optimal input combination Since the output is the same for both years the inputs that would have been used in 2010 without any productivity change are the same as 2009 usage Thus the profit linked measure is simply the difference between the cost of the inputs for the two years Change I 2 970 000 2 970 000 0 Change II 2 970 000 2 475 000 495 000 360 15 13 1 Productivity profiles 200820092010 Handling goods 0 100 200 50 Entering data 3 004 005 00 Detecting errors 1 002 004 00 With respect to the demand for activity output process productivity has improved for 2009 and 2010 for every activity More process output is being produced per unit of activity input The changes definitely improved process productivity Comparing multiyear profiles allows managers to see whether improvement is ongoing and to evaluate whether prior year gains are being maintained Trends in productivity data are useful for measur