Productivity and Profitability Assessment using Financial Statements. Diego PRIOR

Productivity and Profitability Assessment using Financial Statements Diego PRIOR 1

SESSION 1.DEFINITION OF THE ECONOMIC AND FINANCIAL VARIABLES NEEDED TO APPLY THE ANALYSIS. MODEL OF BALANCE SHEET. OSIRIS DATABASE ASSETS Current Assets Stocks Debtors Others Cash & Cash Equivalent Fixed Assets Tangible Fixed Assets Intangible Fixed Assets Other Fixed Assets Total Assets LIABILITIES Current Liabilities Loans Creditors Other Non Current Liabilities Long Term Debt Other Non Current Liabilities Shareholders Funds (EQUITY) Capital Other Total Shareh. Funds & Liab. MODEL OF INCOME STATEMENT. OSIRIS DATABASE Operating Revenue / Turnover Sales (-) Costs of Goods Sold (=) Gross Profit (-) Other Operating Items (-) Depreciation/Amortization (=) Operating P/L Financial Revenue Financial Expenses (+) Financial P/L (+) Other non Oper./Financial Items (=) P/L before Tax (-) Taxation (=) P/L after Tax (+) Extraord. & Oth. Items (=) P/L for Period Costs of Goods Sold = (Material Costs) + (Costs of Employees) 2

CHAPTER 01. BASIC DEFINITIONS PROFITABILITY: = 100 = 100 = 100 = 100 PRODUCTIVITY: = 3

OCCUPANCY RATE:. 100 INPUTS MIX: = 10 ; =30 : inputs mix 1 = 30 ; =10 : inputs mix 2 Impact on costs? INPUT (x) PRODUCTION PROCESS OUTPUT (y) 4

PRODUCTIVITY: EXERCISE 1: = = Unit Output Input A 100 10 B 150 13 C 200 16 D 300 23 E 500 27 Unit Output Input Productivity A 100 10 10.00 B 150 13 11.53 C 200 16 12.50 D 300 23 13.00 E 500 27 18.51 5

EFFICIENCY: = 100 Unit Output Input Productivity Efficiency A 100 10 10.00 54.02 % B 150 13 11.53 62.29 % C 200 16 12.50 67.53% D 300 23 13.00 70.23% E 500 27 18.51 100.00% Output orientation to achieve efficiency Input orientation to achieve efficiency 6

FINANCIAL STATEMENTS: Physical magnitudes money Output price = =30 Input price = =1000 (fixed input) A B C D E Total assets 10000 13000 16000 23000 27000 User cost (w x ) (depreciation 20 %; financial cost 10 %) A B C D E (+)Revenues 3000 4500 6000 9000 15000 (-) Expenses 3000 3900 4800 6900 8100 (=) Profit/L 0 600 1200 2100 6900 7

= 100 A B C D E 100 0% 4.61% 7.5% 9.13% 25.5% Compute ROA for the output orientation strategy: (25.5 %) Compute ROA for the input orientation strategy = 100 A B C D E 100 0% 13.33% 20.00% 23.33% 46.00% 8

= 100 A B C D E 100 100% 115.38% 125.00% 130.43% 185.18% EXERCISE 2: 1. Determine productivity, efficiency, ROA, ROS and profitability ratio for year 2 (p x = 1000). 2. Estimate ROA after the output and the input orientation to reach the efficient frontier. Unit Output Input p y w x A 100 10 30 30.00 % B 130 13 25 35.00 % C 210 16 35 33.00% D 280 23 35 35.00% E 550 27 40 30.00% 9

SESSION 2. ASSESSMENT OF THE ECONOMIC PERFORMANCE: PROFITABILITY RATIOS CONTENTS OSIRIS DATABASE Consolidated data Parent company Subsidiary Segment data KEY RATIOS Return on Shareholders Funds (%) = = = 100 Profit Margin (%)= = = 100 10

Return on Total Assets (%)= = = 100 = Solvency Ratio (%) = = + /.+. 100 Price Earning Ratio = = 100 EBIT = Operating Profits/Losses EBITDA = EBIT + Depreciation/Amortization 11

01. CONTENTS INCOME FUND REPORT Total debt to total capital Cash flow to total debt EBITDA interest coverage ROE Market capitalization OPERATING STATISTICS: = # h # 365 = = # # 365 12

Earnings manipulation Income smoothing Accounting choice Taking a big bath DEFINITION OF ROE AND ROA FOR THE ANALYSIS FIRM A FIRM B TOTAL ASSETS 1000 1000 Non Current Liabilities 600 0 Shareholders Funds 400 1000 INCOME STATEMENT FIRM A FIRM B Oper. Rev. / Turn. Sales 300 300 (-) Costs of Goods Sold 100 100 (=) Operating P/L 200 200 (-) Financial Expenses (10%) 40 - (=) P/L before Tax 160 200 (-) Taxation (30 %) 48 60 (=) P/L for Period 112 140 13

EXERCISE: 1. Estimate ROE and ROA 2. Estimate the leverage effect 3. Comment the movements from year 1 to year 2 4. Explore the changes needed for year 3 to achieve a ROE of 10% Year 1 Year 2 TOTAL ASSETS 1000 1500 Non Current Liabilities 400 900 Shareholders Funds 600 600 INCOME STATEMENT Year 1 Year 2 Oper. Rev. / Turn. Sales 300 450 (-) Costs of Goods Sold 100 300 (=) Operating P/L 200 150 (-) Financial Expenses 40 135 (=) P/L before Tax 160 15 (-) Taxation 48 4.5 (=) P/L for Period 112 10.5 14

DEFINITIONS P/L FOR PERIOD ROE = -------------- EQUITY P/L FOR PERIOD + FINANCIAL EXPENSES.(1-t) ROA = ----------------------------------------- TA P/L FOR PERIOD + FINANCIAL EXPENSES.(1-t)- EXTRAORD.ITEMS NROA = --------------------------------------------------------- TA EXTRAORD.ITEMS EXROA = -------------- TA OPERATING P/L.(1-t) OROA = ------------------- TA (FINANCIAL REVENUE + OTHER NON OPER.ITEMS).(1-t) NOROA = ------------------------------------------------ TA Cost of Financial expenses.(1-t) Debts i = ------------------------ Liabilities Liabilities Leverage f = ----------- Equity Operating Revenue Sales turnover turn = ----------------- TA OPERATING P/L.(1-t) Net margin m = ------------------- Operating Revenue OPERATING P/L.(1-t) = [GROSS PROFIT (OTHER OPERATING ITEMS + + DEPRECIATION(AMORTIZATION)].(1-t) GROSS PROFIT.(1-t) Gross margin gm = ------------------ Operating Revenue Rate of fixed [OTHER OPERATING ITEMS +DEPRECIATION(AMORTIZATION)].(1-t) costs fc = --------------------------------------------------------- Operating Revenue 15

FORMULATION ROE = ROA + f.(roa - i) ROA = NROA + EXROA NROA = OROA + NOROA OROA = m. turn m = gm-fc 16

SESSION 3. MULTIFACTOR PRODUCTIVITY AND PROFIT MARGINS PRODUCTIVITY OPERATING P/L.(1-t) Net margin m = --------------------- Operating Revenue GROSS PROFIT.(1-t) Gross margin gm = --------------------- Operating Revenue Rate of fixed [OTHER OPERATING ITEMS + DEPRECIATION(AMORTIZATION)].(1-t) costs fc = ------------------------------------------------------------ Operating Revenue m = gm - fc GROSS PROFIT.(1-t) (Operating Revenue Costs of Goods Sold).(1-t) gm = ------------------- = ------------------------------------------------= Operating Revenue Operating Revenue and: Operating Revenue Costs of Goods Sold = [----------------- - -------------------].(1-t) = Operating Revenue Operating Revenue Costs of Goods Sold = [ 1 - -------------------].(1-t) Operating Revenue m = [1 c fc] 17

PRODUCTIVITY INDEX: OUTPUTS Y PRO = -------- = - INPUTS X OUTPUTS 1 Y 1 PRO 1 = --------- = -- INPUTS 1 X 1 OUTPUTS 0 Y 0 PRO 0 = --------- = -- INPUTS 0 X 0 PRO 1 Y 1 /X 1 Y 1 /Y 0 PRO g = ------ = ----- = ---- PRO 0 Y 0 /X 0 X 1 /X 0 PRICES INDEX: OUTPUTS PRICE P PRI = -------------- = - INPUTS INPUTS W OUTPUTS PRICE 1 P 1 PRI 1 = --------------- = -- INPUTS PRICE 1 W 1 OUTPUTS PRICE 0 P 0 PRI 0 = --------------- = -- INPUTS PRICE 0 W 0 PRI 1 P 1 /W 1 P 1 /P 0 PRI g = ------ = ----- = ----- PRI 0 P 0 /W 0 W 1 /W 0 18

PRODUCTIVITY, PRICES INDICES AND OPERATING COST RATES Costs of Goods Sold W.X c = -------------------- = ---- Operating Revenue P.Y Costs of Goods Sold W 1.X 1 c 1 = -------------------- = ----- Operating Revenue P 1.Y 1 Costs of Goods Sold W 0.X 0 c 0 = -------------------- = ----- Operating Revenue P 0.Y 0 c 0 c 1 = --------- PRO g.pri g PRODUCTIVITY, PRICES INDICES AND FIXED COST RATES W f.x f fc = ----- P.Y W f1.x f1 fc 1 = ------ P 1.Y 1 W f0.x f0 fc 0 = ------ P 0.Y 0 fc 0 fc 1 = ---------- PRO fg.pri fg 19

MULTIPLE INPUTS CASE PRODUCTIVITY INDEX: OUTPUTS Y PRO = -------- = ---- INPUTS ΣW.X OUTPUTS 1 Y 1 PRO 1 = --------- = ----- INPUTS 1 ΣW 0.X 1 OUTPUTS 0 Y 0 PRO 0 = --------- = ----- INPUTS 0 ΣW 0.X 0 PRO 1 Y 1 /ΣW 1.X 1 Y 1 /Y 0 PRO g = ------ = -------- = ------------ PRO 0 Y 0 /ΣW 0.X 0 ΣW 0.X 1 /ΣW 0.X 0 PRICES INDEX: OUTPUTS PRICE P PRI = -------------- = ---- INPUTS INPUTS ΣW.X OUTPUTS PRICE 1 P 1 PRI 1 = --------------- = ----- INPUTS PRICE 1 ΣW 1.X 1 OUTPUTS PRICE 0 P 0 PRI 0 = --------------- = ----- INPUTS PRICE 0 ΣW 0.X 1 PRI 1 P 1 /ΣW 1.X 0 P 1 /P 0 PRI g = ------ = -------- = ------------ PRI 0 P 0 /ΣW 0.X 0 ΣW 1.X 1 /ΣW 0.X 1 20

SESSION 4. EXTENSIONS OF THE MULTIFACTOR PRODUCTIVITY INDEX: BENCHMARKING 21

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ORIGINAL DATA 12 10 3 8 9 5 6 2 6 10 4 4 2 1 7 8 0 0 2 4 6 8 10 12 25

BENCHMARK ON CRS TECHNOLOGY 12 10 3 8 9 5 6 2 6 10 4 4 2 1 7 8 0 0 2 4 6 8 10 12 26

BENCHMARK ON VRS TECHNOLOGY 12 10 3 8 9 5 6 2 6 10 4 4 2 1 7 8 0 0 2 4 6 8 10 12 27

ESTIMATION OF THE ECONOMIES OF SCALE 12 10 3 8 9 5 6 2 6 10 4 4 2 1 7 8 0 0 2 4 6 8 10 12 28

EXERCISES ON THE MEASUREMENT OF THE TOTAL FACTOR PRODUCTIVITY 01_profits_partial_and_TFP Partial factor productivity quantification Year 1 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 10.000 4.800 2.400 selling price (pv) 15,00 21,40 39,00 Variable inputs: x w (x).(w) t w (x).(w) t w (x).(w) Labor cost 0,22 19,60 4,31 0,25 19,60 4,90 0,42 19,60 8,23 Material cost 1,05 3,60 3,78 1,16 3,60 4,18 1,40 3,60 5,04 Energy 0,52 5,90 3,07 0,64 5,90 3,78 0,82 5,90 4,84 Total variable costs 11,16 12,85 18,11 Contribution margin 3,84 8,55 20,89 Year 2 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 12.000 5.500 1.800 selling price (pv) 16,00 20,00 40,00 Variable inputs: x w (x).(w) t w (x).(w) t w (x).(w) Labor cost 0,20 22,00 4,40 0,30 22,00 6,60 0,40 22,00 8,80 Material cost 1,00 4,40 4,40 1,10 4,40 4,84 1,30 4,40 5,72 Energy 0,50 5,80 2,90 0,60 5,80 3,48 0,80 5,80 4,64 Total variable costs 11,70 14,92 19,16 Contribution margin 4,30 5,08 20,84 Year 3 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 11.000 5.600 2.000 selling price (pv) 15,50 20,20 42,00 Variable inputs: x w (x).(w) t w (x).(w) t w (x).(w) Labor cost 0,25 23,00 5,75 0,25 23,00 5,75 0,35 23,00 8,05 Material cost 1,30 4,60 5,98 1,05 4,50 4,73 1,15 4,50 5,18 Energy 0,60 5,95 3,57 0,55 5,90 3,25 0,80 5,90 4,72 Total variable costs 15,30 13,72 17,95 Contribution margin 0,20 6,48 24,06 PERFORMANCE ANALYSIS Year 1 Year 2 Sales y pv value y pv value output 1 10.000 15,00 150.000 12.000 16,00 192.000 output 2 4.800 21,40 102.720 5.500 20,00 110.000 output 3 2.400 39,00 93.600 1.800 40,00 72.000 total sales 346.320 374.000 Variable costs x w value x w value Labor 4.408 19,60 86.397 4.770 22,00 104.940 Materials 19.428 3,60 69.941 20.390 4,40 89.716 Energy 10.240 5,90 60.416 10.740 5,80 62.292 (-) Total variable costs 216.754 256.948 (=) Contribution margin 129.566 117.052 (-) Overhead (fixed)costs 75.000 84.000 (=) Profits 54.566 33.052 29

Partial factor productivity (partial factor productivity) Productivity in year 1 and year 2 Year 1 Year 2 OUTPUT 1 OUTPUT 2 OUTPUT 3 OUTPUT 1 OUTPUT 2 OUTPUT 3 Labor 4,55 4,00 2,38 5,00 3,33 2,50 Material 0,95 0,86 0,71 1,00 0,91 0,77 Energy 1,92 1,56 1,22 2,00 1,67 1,25 Productivity changes between period 1 and period 2 OUTPUT 1 OUTPUT 2 OUTPUT 3 ratio change (%) ratio change (%) ratio change (%) Labor 1,10 10,00% 0,83-16,67% 1,05 5,00% Material 1,05 5,00% 1,05 5,45% 1,08 7,69% Energy 1,04 4,00% 1,07 6,67% 1,03 2,50% Total factor productivity OUTPUT 1 OUTPUT 2 OUTPUT 3 change (%) % of cost change (%) % of cost change (%) % of cost Labor 10,00% 38,64% -16,67% 38,13% 5,00% 45,46% Material 5,00% 33,87% 5,45% 32,49% 7,69% 27,83% Energy 4,00% 27,49% 6,67% 29,38% 2,50% 26,71% TFP: 6,66% -2,62% 5,08% % of revenues 43,31% 29,66% 27,03% cumulated TFP: 3,48% Required: 1. From year 1 to year 2 TFP have increase but profits drop. Are these movements compatible? 2. Compute profits for year 3 and TFP change between years 2 and 3 (fixed costs for year 84.000). 30

02_MACROECONOMIC APPROACH CASE STUDY 1 VARIABLE COST AND NET MARGIN Year 1 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 10.000 4.800 2.400 selling price (pv) 15,00 21,40 39,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,22 19,60 4,31 0,25 19,60 4,90 0,42 19,60 8,23 Material cost 1,05 3,60 3,78 1,16 3,60 4,18 1,40 3,60 5,04 Energy 0,52 5,90 3,07 0,64 5,90 3,78 0,82 5,90 4,84 Total variable costs 11,16 12,85 18,11 Contribution margin 3,84 8,55 20,89 Year 2 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 12.000 5.500 1.800 selling price (pv) 16,00 20,00 40,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,20 22,00 4,40 0,30 22,00 6,60 0,40 22,00 8,80 Material cost 1,00 4,40 4,40 1,10 4,40 4,84 1,30 4,40 5,72 Energy 0,50 5,80 2,90 0,60 5,80 3,48 0,80 5,80 4,64 Total variable costs 11,70 14,92 19,16 Contribution margin 4,30 5,08 20,84 Year 3 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 15.000 8.600 1.700 selling price (pv) 18,00 25,00 38,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,15 23,00 3,45 0,25 23,00 5,75 0,35 23,00 8,05 Material cost 0,90 5,00 4,50 1,00 5,00 5,00 1,10 5,00 5,50 Energy 0,50 5,60 2,80 0,55 5,60 3,08 0,60 5,60 3,36 Total variable costs 10,75 13,83 16,91 Contribution margin 7,25 11,17 21,09 PROFIT AND LOSS ACCOUNT Year 1 Year 2 Year 3 Sales y pv value y pv value y pv value output 1 10.000 15,00 150.000 12.000 16,00 192.000 15.000 18,00 270.000 output 2 4.800 21,40 102.720 5.500 20,00 110.000 8.600 25,00 215.000 output 3 2.400 39,00 93.600 1.800 40,00 72.000 1.700 38,00 64.600 total sales 346.320 374.000 549.600 Variable costs x w value x w value x w value Labor 4.408 19,60 86.397 4.770 22,00 104.940 4.995 23,00 114.885 Materials 19.428 3,60 69.941 20.390 4,40 89.716 23.970 5,00 119.850 Energy 10.240 5,90 60.416 10.740 5,80 62.292 13.250 5,60 74.200 (-) Total variable costs 216.754 256.948 308.935 (=) Contribution margin 129.566 117.052 240.665 (-) Overhead (fixed)costs 12.500 11.350 15.000 (-) Depreciation costs 62.500 72.650 85.503 (=) Profits 54.566 33.052 140.162 EFFICIENCY ANALYSIS CASE STUDY BALANCE SHEET Year 1 Year 2 Year 3 Land 15.000,00 16.500,00 17.325,00 Machinery and equipment 500.000,00 581.250,00 684.030,00 Inventories 150.000,00 170.000,00 153.868,00 Accounts receivable-trade 100.000,00 89.350,00 111.700,00 Cash and cash equivalents 15.000,00 16.500,00 17.325,00 Total Assets 780.000,00 873.600,00 984.248,00 inflation rate 10 % 5 % 31

MACROECONOMIC APPROACH Erik Hörnell (1992), Improving productivity for competitive advantage, Pitman Publishing. Year 1 Value Added quantification Revenues Year 1 Revenues y pv value output 1 10000 15 150000 output 2 4800 21,4 102720 output 3 2400 39 93600 total sales 346320 x w value Materials 19428 3,6 69941 Energy 10240 5,9 60416 (-) Intermediate consumption 130357 (=) Brut Value Added 215963 x w value (-) Labor costs 86397 Labor 4.408 19,60 86.397 (=) Brut Operating Surplus 129566 (-) Depreciation costs 62500 Productivity = (Value added)/(total hours or work) (-) Overhead (fixed)costs 12500 Productivity = 48,99 (=) Profits 54566 Revenues Interm. Cons. Increase 1. Increase in units produced ( 10 %) 380952,00 143392,48 53,89 0,10 2. Increase in quality (prices 10 %) 380952,00 130356,80 56,85 0,16 3. Costs reduction ( 10 %) 346320,00 117321,12 51,95 0,06 Inflation 10 % 380952,00 143392,48 53,89 0,10 Innovation (changes in output mix) 32

03_APC, 1975 (RATIO FORM) CASE STUDY Year 1 VARIABLE COST AND NET MARGIN OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 10.000 4.800 2.400 selling price (pv) 15,00 21,40 39,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,22 19,60 4,31 0,25 19,60 4,90 0,42 19,60 8,23 Material cost 1,05 3,60 3,78 1,16 3,60 4,18 1,40 3,60 5,04 Energy 0,52 5,90 3,07 0,64 5,90 3,78 0,82 5,90 4,84 Total variable costs 11,16 12,85 18,11 Contribution margin 3,84 8,55 20,89 Year 2 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 12.000 5.500 1.800 selling price (pv) 16,00 20,00 40,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,20 22,00 4,40 0,30 22,00 6,60 0,40 22,00 8,80 Material cost 1,00 4,40 4,40 1,10 4,40 4,84 1,30 4,40 5,72 Energy 0,50 5,80 2,90 0,60 5,80 3,48 0,80 5,80 4,64 Total variable costs 11,70 14,92 19,16 Contribution margin 4,30 5,08 20,84 Year 3 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 15.000 8.600 1.700 selling price (pv) 18,00 25,00 38,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,15 23,00 3,45 0,25 23,00 5,75 0,35 23,00 8,05 Material cost 0,90 5,00 4,50 1,00 5,00 5,00 1,10 5,00 5,50 Energy 0,50 5,60 2,80 0,55 5,60 3,08 0,60 5,60 3,36 Total variable costs 10,75 13,83 16,91 Contribution margin 7,25 11,17 21,09 PROFIT AND LOSS ACCOUNT Year 1 Year 2 Year 3 Sales y pv value y pv value y pv value output 1 10.000 15,00 150.000 12.000 16,00 192.000 15.000 18,00 270.000 output 2 4.800 21,40 102.720 5.500 20,00 110.000 8.600 25,00 215.000 output 3 2.400 39,00 93.600 1.800 40,00 72.000 1.700 38,00 64.600 total sales 346.320 374.000 549.600 Variable costs x w value x w value x w value Labor 4.408 19,60 86.397 4.770 22,00 104.940 4.995 23,00 114.885 Materials 19.428 3,60 69.941 20.390 4,40 89.716 23.970 5,00 119.850 Energy 10.240 5,90 60.416 10.740 5,80 62.292 13.250 5,60 74.200 (-) Total variable costs 216.754 256.948 308.935 (=) Contribution margin 129.566 117.052 240.665 (-) Overhead (fixed)costs 12.500 11.350 15.000 (-) Depreciation costs 62.500 72.650 85.503 (=) Profits 54.566 33.052 140.162 EFFICIENCY ANALYSIS CASE STUDY BALANCE SHEET Year 1 Year 2 Year 3 Land 15.000,00 16.500,00 17.325,00 Machinery and equipment 500.000,00 581.250,00 684.030,00 Inventories 150.000,00 170.000,00 153.868,00 Accounts receivable-trade 100.000,00 89.350,00 111.700,00 Cash and cash equivalents 15.000,00 16.500,00 17.325,00 Total Assets 780.000,00 873.600,00 984.248,00 inflation rate 10 % 5 % 33

APC, 1975 (RATIO FORM) Revenues year 2: 374.000,00 profitability ratio year 2: 1,455547 Variable costs year 2: 256.948,00 change in profitability ratio: 0,910993 (profitability index) Revenues year 1: 346.320,00 profitability ratio year 1: 1,597759 Variable costs year 1: 216.753,60 Deflacted revenues year 2: y2 pv1 y2.pv1 output 1 12000 15 180000 output 2 5500 21,4 117700 output 3 1800 39 70200 367900 Deflacted variable costs year 2: x2 w1 x2.w1 Labor 4770 19,6 93492 Materials 20390 3,6 73404 Energy 10740 5,9 63366 230262 Productivity index y2.pv1/y1.pv1 Deflacted revenues year 2: 367.900,00 y2.pv1 1,062312 Revenues year 1: 346.320,00 y1.pv1 0,999991 x2.w1/x1.w1 Deflacted variable costs year 2: 230.262,00 x2.w1 1,062321 Variable costs year 1: 216.753,60 x1.w1 0,910993 (profitability index) Price recovery index y2.pv2/y2.pv1 Revenues year 2 : 374.000,00 y2.pv2 1,016581 Deflacted revenues year 2: 367.900,00 y2.pv1 0,911001 x2.w2/x2.w1 Variable costs year 2: 256.948,00 x2.w2 1,115894 Deflacted variable costs year 2: 230.262,00 x2.w1 34

04_AMERICAN PRODUCTIVITY CENTER, (1975), Kaplan (1982) Year 1 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 10.000 4.800 2.400 selling price (pv) 15,00 21,40 39,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,22 19,60 4,31 0,25 19,60 4,90 0,42 19,60 8,23 Material cost 1,05 3,60 3,78 1,16 3,60 4,18 1,40 3,60 5,04 Energy 0,52 5,90 3,07 0,64 5,90 3,78 0,82 5,90 4,84 Total variable costs 11,16 12,85 18,11 Contribution margin 3,84 8,55 20,89 Year 2 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 12.000 5.500 1.800 selling price (pv) 16,00 20,00 40,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,20 22,00 4,40 0,30 22,00 6,60 0,40 22,00 8,80 Material cost 1,00 4,40 4,40 1,10 4,40 4,84 1,30 4,40 5,72 Energy 0,50 5,80 2,90 0,60 5,80 3,48 0,80 5,80 4,64 Total variable costs 11,70 14,92 19,16 Contribution margin (m) 4,30 5,08 20,84 PERFORMANCE ANALYSIS Year 1 Year 2 Sales y pv value y pv value output 1 10.000 15,00 150.000 12.000 16,00 192.000 output 2 4.800 21,40 102.720 5.500 20,00 110.000 output 3 2.400 39,00 93.600 1.800 40,00 72.000 total sales 346.320 374.000 Variable costs x w value x w value Labor 4.408 19,60 86.397 4.770 22,00 104.940 Materials 19.428 3,60 69.941 20.390 4,40 89.716 Energy 10.240 5,90 60.416 10.740 5,80 62.292 (-) Total variable costs 216.754 256.948 (=) Contribution margin 129.566 117.052 (-) Overhead (fixed)costs 75.000 84.000 (=) Profits 54.566 33.052 35

Sales-activity variance y 2 y 1 m 1 (y 2 -y 1 ).m 1 output 1 12.000 10.000 3,84 7.680 output 2 5.500 4.800 8,55 5.984 output 3 1.800 2.400 20,89-12.534 (1) Total change in output quantity 1.130 Sales-volume variance y 2 y 1 m 1average (y 2 -y 1 ).m average output 1 12.000 10.000 7,53 15.066 output 2 5.500 4.800 7,53 5.273 output 3 1.800 2.400 7,53-4.520 Total change in sales-volume variance 15.819 Sales-mix variance y 2 y 1 m 1 (y 2 -y 1 ).(m 1 -m 1average ) output 1 12.000 10.000 3,84-7.386 output 2 5.500 4.800 8,55 711 output 3 1.800 2.400 20,89-8.014 Total change in sales-mix variance -14.690 Price-recovery variance Sales-price variance pv 2 pv 1 y 2 (pv 2 -pv 1 ).y 2 output 1 16,00 15,00 12.000 12.000 output 2 20,00 21,40 5.500-7.700 output 3 40,00 39,00 1.800 1.800 Total change in sales-price variance 6.100 Input-cost variance w 1 w 2 x 2 (w 1 -w 2 ).x 2 input 1 19,60 22,00 4.770-11.448 input 2 3,60 4,40 20.390-16.312 input 3 5,90 5,80 10.740 1.074 Total change in input-cost variance -26.686 (2) Total change in price-recovery variance -20.586 Productivity variance Labor t 1 t 2 w 1 y 2 (t 1 -t 2 ).w 1.y 2 output 1 0,22 0,20 19,60 12.000 4.704 output 2 0,25 0,30 19,60 5.500-5.390 output 3 0,42 0,40 19,60 1.800 706 Total change in labor productivity variance 20 Materials t 1 t 2 w 1 y 2 (t 1 -t 2 ).w 1.y 2 output 1 1,05 1,00 3,60 12.000 2.160 output 2 1,16 1,10 3,60 5.500 1.188 output 3 1,40 1,30 3,60 1.800 648 Total change in materials productivity variance 3.996 Energy t 1 t 2 w 1 y 2 (t 1 -t 2 ).w 1.y 2 output 1 0,52 0,50 5,90 12.000 1.416 output 2 0,64 0,60 5,90 5.500 1.298 output 3 0,82 0,80 5,90 1.800 212 Total change in energy productivity variance 2.926 (3) Total productivity variance 6.942 Total change in contribution margin (1)+(2)+(3) -12.514 36

05_ACCOUNTING MODEL (Kaplan, 1982) Year 1 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 10.000 4.800 2.400 selling price (pv) 15,00 21,40 39,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,22 19,60 4,31 0,25 19,60 4,90 0,42 19,60 8,23 Material cost 1,05 3,60 3,78 1,16 3,60 4,18 1,40 3,60 5,04 Energy 0,52 5,90 3,07 0,64 5,90 3,78 0,82 5,90 4,84 Total variable costs 11,16 12,85 18,11 Contribution margin 3,84 8,55 20,89 Year 2 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 12.000 5.500 1.800 selling price (pv) 16,00 20,00 40,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,20 22,00 4,40 0,30 22,00 6,60 0,40 22,00 8,80 Material cost 1,00 4,40 4,40 1,10 4,40 4,84 1,30 4,40 5,72 Energy 0,50 5,80 2,90 0,60 5,80 3,48 0,80 5,80 4,64 Total variable costs 11,70 14,92 19,16 Contribution margin 4,30 5,08 20,84 PERFORMANCE ANALYSIS Year 1 Year 2 Sales y pv value y pv value output 1 10.000 15,00 150.000 12.000 16,00 192.000 output 2 4.800 21,40 102.720 5.500 20,00 110.000 output 3 2.400 39,00 93.600 1.800 40,00 72.000 total sales 346.320 374.000 Variable costs x w value x w value Labor 4.408 19,60 86.397 4.770 22,00 104.940 Materials 19.428 3,60 69.941 20.390 4,40 89.716 Energy 10.240 5,90 60.416 10.740 5,80 62.292 (-) Total variable costs 216.754 256.948 (=) Contribution margin 129.566 117.052 (-) Overhead (fixed)costs 75.000 84.000 (=) Profits 54.566 33.052 37

PERFORMANCE ANALYSIS Year 1 Year 2 Sales y pv value y pv value changes output 1 10.000 15,00 150.000 12.000 16,00 192.000 42.000 output 2 4.800 21,40 102.720 5.500 20,00 110.000 7.280 output 3 2.400 39,00 93.600 1.800 40,00 72.000-21.600 total sales 346.320 374.000 27.680 Variable costs x w value x w value Labor 4.408 19,60 86.397 4.770 22,00 104.940-18.543 Materials 19.428 3,60 69.941 20.390 4,40 89.716-19.775 Energy 10.240 5,90 60.416 10.740 5,80 62.292-1.876 (-) Total variable costs 216.754 256.948-40.194 (=) Contribution margin 129.566 117.052-12.514 (-) Overhead (fixed)costs 75.000 84.000-9.000 (=) Profits 54.566 33.052-21.514 change in revenues change in output quantity y 2 y 1 pv 1 (y 2 -y 1 ).pv 1 output 1 12.000 10.000 15,00 30.000 output 2 5.500 4.800 21,40 14.980 output 3 1.800 2.400 39,00-23.400 Total change in output quantity 21.580 change in output price pv 2 pv 1 y 2 (pv 2 -pv 1 ).y 2 output 1 16,00 15,00 12.000 12.000 output 2 20,00 21,40 5.500-7.700 output 3 40,00 39,00 1.800 1.800 Total change in output price 6.100 Total change in revenues 27.680 change in variable costs change in input quantity x 1 x 2 w 1 (x 1 -x 2 ).w 1 input 1 4.408 4.770 19,60-7.095 input 2 19.428 20.390 3,60-3.463 input 3 10.240 10.740 5,90-2.950 Total change in input quantity -13.508 change in input price w 1 w 2 x 2 (w 1 -w 2 ).x 2 input 1 19,60 22,00 4.770-11.448 input 2 3,60 4,40 20.390-16.312 input 3 5,90 5,80 10.740 1.074 Total change in input prices -26.686 Total change in variable costs -40.194 Total change in contribution margin -12.514 38

06_Adjusted kaizen costs Year 1 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 10.000 4.800 2.400 selling price (pv) 15,00 21,40 39,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,22 19,60 4,31 0,25 19,60 4,90 0,42 19,60 8,23 Material cost 1,05 3,60 3,78 1,16 3,60 4,18 1,40 3,60 5,04 Energy 0,52 5,90 3,07 0,64 5,90 3,78 0,82 5,90 4,84 Total variable costs 11,16 12,85 18,11 Contribution margin 3,84 8,55 20,89 Year 2 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 12.000 5.500 1.800 selling price (pv) 16,00 20,00 40,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,20 22,00 4,40 0,30 22,00 6,60 0,40 22,00 8,80 Material cost 1,00 4,40 4,40 1,10 4,40 4,84 1,30 4,40 5,72 Energy 0,50 5,80 2,90 0,60 5,80 3,48 0,80 5,80 4,64 Total variable costs 11,70 14,92 19,16 Contribution margin 4,30 5,08 20,84 PERFORMANCE ANALYSIS Year 1 Year 2 Sales y pv value y pv value output 1 10.000 15,00 150.000 12.000 16,00 192.000 output 2 4.800 21,40 102.720 5.500 20,00 110.000 output 3 2.400 39,00 93.600 1.800 40,00 72.000 total sales 346.320 374.000 Variable costs x w value x w value Labor 4.408 19,60 86.397 4.770 22,00 104.940 Materials 19.428 3,60 69.941 20.390 4,40 89.716 Energy 10.240 5,90 60.416 10.740 5,80 62.292 (-) Total variable costs 216.754 256.948 (=) Contribution margin 129.566 117.052 (-) Overhead (fixed)costs 75.000 84.000 (=) Profits 54.566 33.052 39

Yasuhiro Monden (1997), Sistemas de reducción de costes Productivity Press Adjusted kaizen costs vc 1 vc 2 (vc 1 -vc 2 ).y 1 output 1 11,16 11,70-5.400,00 output 2 12,85 14,92-9.926,40 output 3 18,11 19,16-2.520,00 kaizen cost variation -17.846,40 40

07_Kurosawa (1991), AIPR system Year 1 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 10.000 4.800 2.400 selling price (pv) 15,00 21,40 39,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,22 19,60 4,31 0,25 19,60 4,90 0,42 19,60 8,23 Material cost 1,05 3,60 3,78 1,16 3,60 4,18 1,40 3,60 5,04 Energy 0,52 5,90 3,07 0,64 5,90 3,78 0,82 5,90 4,84 Total variable costs 11,16 12,85 18,11 Contribution margin 3,84 8,55 20,89 Year 2 OUTPUT 1 OUTPUT 2 OUTPUT 3 units (y) 12.000 5.500 1.800 selling price (pv) 16,00 20,00 40,00 Variable inputs: t w (t).(w) t w (t).(w) t w (t).(w) Labor cost 0,20 22,00 4,40 0,30 22,00 6,60 0,40 22,00 8,80 Material cost 1,00 4,40 4,40 1,10 4,40 4,84 1,30 4,40 5,72 Energy 0,50 5,80 2,90 0,60 5,80 3,48 0,80 5,80 4,64 Total variable costs 11,70 14,92 19,16 Contribution margin 4,30 5,08 20,84 PERFORMANCE ANALYSIS Year 1 Year 2 Sales y pv value y pv value output 1 10.000 15,00 150.000 12.000 16,00 192.000 output 2 4.800 21,40 102.720 5.500 20,00 110.000 output 3 2.400 39,00 93.600 1.800 40,00 72.000 total sales 346.320 374.000 Variable costs x w value x w value Labor 4.408 19,60 86.397 4.770 22,00 104.940 Materials 19.428 3,60 69.941 20.390 4,40 89.716 Energy 10.240 5,90 60.416 10.740 5,80 62.292 (-) Total variable costs 216.754 256.948 (=) Contribution margin 129.566 117.052 (-) Overhead (fixed)costs 75.000 84.000 (=) Profits 54.566 33.052 41

Kurosawa (1991), AIPR system Profit variance (R 2 -R 1 ): -21.514 Price recovery variance y 2 pv 2 pv 1 y 2.(pv 2 -pv 1 ) output 1 12.000 16,00 15,00 12.000 output 2 5.500 20,00 21,40-7.700 output 3 1.800 40,00 39,00 1.800 6.100 x 2 w 2 w 1 -x 2.(w 2 -w 1 ) Labor cost 4.770 22,00 19,60-11.448 Material cost 20.390 4,40 3,60-16.312 Energy 10.740 5,80 5,90 1.074-26.686 -(F 2 -F 1 ) -9.000 Total price recovery variance -29.586 Productivity variance y 2 y 1 pv 1 pv 1.(y 2 -y 1 ) output 1 12.000 10.000 15,00 30.000 output 2 5.500 4.800 21,40 14.980 output 3 1.800 2.400 39,00-23.400 21.580 x 2 x 1 w 1 -w 1.(x 2 -x 1 ) Labor 4.770 4.408 19,60-7.095 Materials 20.390 19.428 3,60-3.463 Energy 10.740 10.240 5,90-2.950-13.508 Total productivity variance 8.072 42

Decomposition on productivity variance Technical progress y 2 pv 1 pv 1.y 2 output 1 12.000 15,00 180.000 output 2 5.500 21,40 117.700 output 3 1.800 39,00 70.200 367.900 π 1 1,1870 x 2 w 1 -π 1 w 1. x 2 Labor 4.770 19,60-110.978 Materials 20.390 3,60-87.133 Energy 10.740 5,90-75.217-273.328 -π 1.F 1-89.027 Total variance due to technical progress: 5.545 Expansion or Scale effect x 2 w 1 π 1. w 1. x 2 Labor 4770 19,6 110.978 Materials 20390 3,6 87.133 Energy 10740 5,9 75.217 273.328 π 1.F 1 89.027 -y 1.pv 1-346.320 -w 1.(x 2 -x 1 ) -13.508 Total variance due to expansion or scale effect 2.526 43