CA Final Gr. II Paper - 5 (Solution of May & Question of November ) Paper - 5 : Advanced Management Accounting

Transcription

1 Solved Scanner Appendix CA Final Gr. II Paper - 5 (Solution of May & Question of November ) ISBN Paper - 5 : Advanced Management Accounting Chapter - 1: Developments in the Business Environment May [5] (a), (b) (a) (i) Selling Price (`) Variable Cost (60) (70) Contribution (`) Units 15,000 15,000 Total Contribution A 6,00,000 7,50,000 Fixed Cost Set up Cost (4,000 8) (32,000) - (7,500 12) - (90,000) Distribution Cost (60,000) (24,000) Step fixed cost (32,000) (75,000) Unanalyzed Fixed Cost (32,000) (32,000) A B B 1,56,000 2,21,000 Profit (A - B) 4,44,000 5,29,000 1

2 Solved Scanner Appendix CA Final Gr. II Paper (ii) BEP = = = 800 units Setup Cost (fixed for 2,000 units); 1 Production Run; ` 4,000/- Step Cost (fixed for 2,000 units); ` 4,000/- Distribution Cost will have to be recovered on the basis of 30 units. Let BEP (unit) - K 40 K = ` 32,000 + ` 8,000 + Boxes ` 120 (b) K = 1, units Refining, 1, will have boxes or say 38 boxes. The last box will cost ` 120 which is equivalent to contribution from 3 units. Hence, BEP is 1,114 units. Particulars ` / Toy Component A 8.50 Component B 7 Labour 24 (0.4 hr ` 60) Product Specific overhead 13.5 Additional Material 10 Royalty (100 15%) Profit (100 25%) Cost Structure is not within the target cost, i.e = 75, cost need to be reduced to ` 3.

3 Solved Scanner Appendix CA Final Gr. II Paper May [7] (c) (i) Research and Development Cost Investment (ii) Rent/Utilities Operating costs (iii) Raw materials used for production Through put contribution (iv) Depreciation Operating cost (v) Labour Cost Operating costs (vi) Stock of raw materials Investments (vii) Sales Throughput contribution (viii) Cost of equipments and buildings Investment Nov [1] {C} (d) MK international Ltd. has developed a new product RIO which is to be launched soon. The company anticipates to sell 1,25,000 of these units at a sale price of ` 400 per unit over the product life cycle of three years. The other data pertaining to Product RIO are as under: Research and development cost ` 32,50,000 Manufacturing cost per unit ` 175 Fixed manufacturing cost per year ` 12,75,000 Marketing cost per unit ` 90 (including 4% commission on sales) Fixed marketing cost per year ` 6,72,000 Administration cost ` 6,60,000 per year Warranty expenses 4 replacement parts per 50 units at ` 30 per part Calculate: (i) The life cycle cost of the product RIO (ii) The revised life cycle cost if the MK international Ltd. increases sales by 12% through 5% reduction in sale price along with increase in fixed manufacturing cost by ` 1,20,000 per year. (iii) Should the company go for reduction in sale price? (6 marks)

4 Solved Scanner Appendix CA Final Gr. II Paper Nov [3] (a) A Company produces three products P, Q and R for which the standard cost per unit and quantities produced are as under: Products P Q R Units produced and sold 36,000 48,000 96,000 Direct material cost per unit (`) Direct labour cost per unit (`) Machine hours per unit (hours) Total production overheads are absorbed on machine hour basis. The rate is ` 60 per machine hour. The Company has analysed its operations and determined that five activities act as cost drivers for overheads. Data relating to five activities are given below: Activity Area Cost driver Cost of each activity as % of total production overhead cost Store receiving Number of requisitions 25% Machine set up Number of set ups 20% Machine running Machine hours worked 25% Packing Packing time in hours 16% Storage Area in square metres 14% The investigation into the production overhead activities for the period revealed the following: Activity P Q R Number of requisitions 1,200 1,500 3,900 Number of machine set ups Packing hours 3,000 4,800 10,200 Storage (Sq metres) 10,800 12,000 19,200 Required: (i) Calculate total production overheads. (ii) Prepare product cost statement showing per unit cost under traditional absorption costing method. (iii) Calculate the cost driver rates.

5 Solved Scanner Appendix CA Final Gr. II Paper (iv) Prepare product cost statement showing per unit cost under activity based costing method. (v) What is the difference in costs due to adoption of traditional absorption costing method and activity based costing method? (10 marks) Nov [7] (e) Classify the following items under appropriate categories of quality costs viz. Prevention cost, Appraisal cost, Internal failure cost and External failure cost. (i) Reinspection of product reworked. (ii) Testing of material of special nature from outside laboratory. (iii) Employee time spent on reviewing and assessing the quality of output regarding material supplied. (iv) Customer survey for assessing the feedback on quality of product sold. (v) Calibration of testing equipment. (vi) Warranty claim processing (vii) Repurchase of components to create replacements. (viii) Loss of customer due to supply of low quality product. (4 marks) Chapter - 2: Cost Concepts, CVP Analysis and Decision Making May [1] {C} (a), (c) (a) (i) Total Machine hours required A B C Total P = 7050 Q = 8700 Machine hours of Q is limiting factor for manufacturing. Total Hours available 7800 (-) Required for B (compulsory) (1,200 3) (3600) 4200 (-) Required for C (1500) 2700 (-) Required for A (2700) (2700 3) = units of A required to be purchased but as the purchase price of A & C is lower than production cost company should purchase both component instead of manufacturing. (ii) Total manufacturing cost of A is ` 302 & purchase cost ` 280, total manufacturing cost of C is ` 166 & purchase cost ` 161. In this case purchase of both product is beneficial to company provided company can avoid fixed cost relating to A & C.

6 Solved Scanner Appendix CA Final Gr. II Paper (c) Statement showing cost reduction programme envisaged (Reduction in fixed expenses product-wise) Particulars X Y (a) Sale (`) (10, ) 40,00,000 (12, ) 48,00,000 (b) Selling Price per unit (Revised) 8,000 9,000 (c) Sales unit (a/b) (d) BEP (%) 80% 75% (e) Margin of safety (%) 20% 25% (f) Margin of safety (`) (a e) 8,00,000 12,00,000 (g) Previous fixed cost (given) 10,00,000 15,00,000 (h) New P/V Ratio (same as old) (given) 25% 30% (i) Break even sales (400 8,000) 32,00,000 (400 9,000) 36,00,000 (j) Revised fixed cost (i h) 8,00,000 10,80,000 (k) Reduction in fixed cost (g - j) 2,00,000 4,20,000 So cost reduction program is envisaged in reduction of fixed cost from previous level by ` 2,00,000 in Mobile - X and ` 4,20,000 in Mobile - Y.

7 Solved Scanner Appendix CA Final Gr. II Paper Notes: 1. In the absence of information it is assumed that the number of units to be sold for X and Y to break-even as well as the total number of units of X and Y to be sold during the year are same. 2. The revised P/V ratio are as per the previous year as given in the problem May [2] (a) ABC Ltd. Cost Sheet of Gadget ` ` Upper part: Material (15 kg. ` 10) 150 Labour Lower part: Material (15 kg. ` 10) 150 Labour Add: Welding Charges 20 Total Cost of Manufacturing 440 Add: Profit 240 Sales Price 680 (i) If ABC wants to retain the same level of profit per unit as in own manufacture, it has to achieve manufacturing cost of ` 440. ` Target Cost 440 Less: Cost of upper part 210 Less: Transportation Cost 6 Less: Welding Charges 20 Price of Lower Part 204 ABC will pay ` 204 per lower part to the supplier for retaining the same level of profit per unit. (ii) Present Capacity Revenue is ` 60,00,000/- (25,000 units ` 240) If Supplier is used, 50,000 units of Gadgets can be sold. For, Additional Revenue

8 Solved Scanner Appendix CA Final Gr. II Paper Let Price for Lower Part per unit- K 50,000 units {` 680 (` K + ` 236*) > ` 60,00,000 50,000 units {` 444 ` K) > ` 60,00,000 K < 324 (*) Cost of Upper Part plus Transportation Cost plus Welding Charges An amount less than ` 324 will be paid for the lower part May [7] (e) A company wishes to manufacture smart watches that can be interactive with mobile phone computers and CCTV. It is planning to do research on the compatibility. It has done market survey and is satisfied about the demand being sufficient for making the product profitable. Some facility can be made available by discontinuing its existing line of telephone instruments division. So the classification of R&D costs, cost of Market Survey and the profit of the Telephone Instruments Division are as follows: No. Costs Classification Category (i) R&D costs indicated above Relevant cost (ii) Cost of Market survey Sunk cost (iii) The profit of the Telephone Instruments Division Opportunity cost Nov [1] {C} (a) AB company produces three products X, Y and Z by using Indigenous and Imported raw materials. The relevant information available from the records of the Company is as under: Product X Product Y Product Z Selling price in ` per unit Direct materials in ` per unit Direct ` 40 per hour Variable ` 12 per labour hour Maximum Sales Potential (in units) 1,500 2,500 2,500

9 Solved Scanner Appendix CA Final Gr. II Paper The Company also has an agreement to supply 1,000 units of Product X to a vendor which has to be executed. Out of direct materials, 60% is imported raw material and it is purchased at ` 24 per kg. Prepare a statement showing Contribution of these three products assuming availability of imported raw materials is restricted to 24,000 kgs per year. (5 marks) Nov [6] (b) JC Company produces electronic product and factory is working in Special Economic Zone (SEZ). The expected capacity utilization is 60% and turnover for the year is ` 660 lakh. If the company works at 100% capacity, the sales cost relationship will be as follows: Factory cost : 65 per cent of sales value Prime cost : 75 per cent of factory cost Selling and administrative cost : 20% of sales value and being 80% variable The factory overheads will vary according to operating capacity in the following manner: Operating capacity 60% 80% 100% 120% Factory overheads (` in lakhs) The Government of India gives 10% subsidy on the export order amount and it is expected that currency fluctuation trends will be positive by 8% in next financial year. The Company receives an offer from abroad for a value of ` 150 lakhs. The prime cost of this order is estimated at ` 96 lakhs and selling and administrative expenses applicable to this order is ` 7,20,000. The order will occupy 40% of the capacity of the plant. To complete the export order, quality maintenance cost of ` 1,20,000 will also be incurred. The Marketing Director estimates that the company s own sales will increase to 80% of the capacity by the time of materialization of new order. The factory overheads will increase by ` lakhs (for increase from 80% to 120% capacity). The maximum demand in local market can be extended up to 120% with export order. The export order cannot accepted partly.

10 Solved Scanner Appendix CA Final Gr. II Paper Required: (i) Prepared a profitability statement at the capacity level of 60%, 80% and 100%. (ii) Should the company accept the export order? (8 marks) Nov [7] (c) Identify the type of cost in each of the following independent situations. Also state whether it is relevant or irrelevant. (i) A company has invested ` 50 lakh in a project. Company could have earned ` 4 lakh by investing the amount in Government securities. (ii) Company has purchased a new machine for ` 50 lakh and entered into three year maintenance contract at ` 25,000 per year. (iii) A special drilling machine has to be hired on monthly charges of ` 50,000 for two months for the Construction project. (iv) There are 15 skilled workers in the production department of X Ltd. currently under utilized. It is the policy of the company to continue to pay skilled workers at ` 15,000 per month in full. Acceptance of the new project will reduce the idle time of skilled workers. (4 marks) Chapter - 3 : Pricing Decisions May [1] {C} (b) Sl. No. I RP/EP/MP III Pricing IV (i) (ii) (iii) Me - too Products (MP) Revolutionary Product (RP) Evolutionary Product (EP) The me - too products are price takers as the price is determined by the market mainly by the competitive forces. Revolutionary Product may enjoy the premium price as a reward for its innovation and taking first initiative. The Evolutionary Products are price takers as the price is determined by the market mainly by the competitive forces.

11 Solved Scanner Appendix CA Final Gr. II Paper May [7] (b) The Frequency table indicating the frequency of occurrence of defects in decreasing order of their occurrence will be as follows: Defect Type No. of Items (%) Cumulative (%) Scratches on the surface Rough edges of lenses Non uniform grinding of lenses Frame colors shade differences Power mismatches End frame not equidistant from the centre Spots/Stains on lenses The Pareto Chart is constructed for defect type: Pareto Chart

12 Solved Scanner Appendix CA Final Gr. II Paper The purpose of Pareto Chart in this example is to direct attention to area where best returns can be achieved by solving most of the quality problems, perhaps just with a single action. In this case, use of good quality raw material say plastic may solve some percentage and handled property some percentage may be overcome Nov [7] (a) (i) Define Pricing Strategy (ii) State the Market Entry Strategies of pricing applicable in the following situations: (1) Inelastic demand (2) Mass Production (3) Assured profit (4) Elastic demand (4 marks) Chapter - 4 : Budget and Budgetary Control May [4] (a) (i) The Production Budget for the month of May, 2017 (in quantity) Particulars Product Super (in tons) Product Normal (in tons) Sale (+) Closing Stock ( ) Opening Stock (40) (20) Production (ii) Material Purchase Budget May 17 (tons) Particulars Grade A Requirement for Production (180 70%) Grade B (180 30%) Grade C (75 40%) Grade D (75 60%) Add: Budgeted Inventory (31 st May) Total Requirements Less: Actual Inventory (1 st May)

13 Solved Scanner Appendix CA Final Gr. II Paper Quantity to be purchased Add: Lose of Weight* (Seasoning) Quantity to be purchased (Gross) (*) Quantity to be purchased 15% / 85% May [7] (d) (i) The principal budget factor is the factor that limits the activities of functional budgets of the organisation. The early identification of this factor is important in the budgetary planning process because it indicates which budget should be prepared first. In general sales volume is the principal budget factor. So sales budget must be prepared first, based on the available sales forecasts. All other budgets should then be linked to this. So from above we can say that it is necessary to start preparing a functional budget only after identifying the principal budget factor. (ii) Production budget cannot be prepared directly from sales budget without a consideration of stake holding policy. The production budget must be prepared first and all other budgets follow it. The production budget as prepared shows the estimates about future production activities. Production budget provides the estimation of the production will be made for a certain time period from production activities. So that yes, it is necessary to make a flexible production cost budget before the commencement of production activities of a certain production period Nov [4] (b) MH hotel has a capacity of 50 rooms, each of which can accommodate one or two guests. Guests staying in hotel are provided with free facilities like sports centre, kids zone, swimming pool etc. The details in the budget for the year ending are narrated below: (i) Standard room rent of ` 3,500 per night during high season i.e. May, June, July, December and January and for the remaining months (low season) standard room rent of 1,800 per night will be charged. (ii) Average room occupancy per night during high season is 80% and during low season is 50%.

14 Solved Scanner Appendix CA Final Gr. II Paper (iii) The hotel is registered with number of internet based hotel providers. It is expected that subject to capacity available, an average of 15 rooms per night can be sold through them. These bookings will be in addition to the occupancy level stated in point (ii). The internet service provider will pay 60% of the standard booking rate. (iv) Variable cost per room night will be ` 1,075 per room night. (v) Fixed cost will be ` 12,00,000 per month. However, when occupancy is 100%, fixed cost will increase by ` 9,000 per night. Prepare budgeted profitability statement for the year ending showing the details fo revenue, costs and profits. (8 marks) Nov [5] (b) A company manufactures two products X and Y. The current pattern of sales of Product X and Product Y is in the ratio of 5 : 3. The budgeted data for the quarter ending is as under: Particulars Product X Product Y Direct material cost per unit ` 161 ` 176 Direct labour cost per unit ` 75 ` 90 Variable overheads per unit ` 30 ` 50 Commission on sales 4% of selling price 5% of selling price P/V ratio 20% 16% Stock as on ,400 units 1,050 units The annual fixed overheads amounts to ` 25,36,000 and it is assumed to be occurred evenly throughout the year. The Company desires profit of ` 4,50,000 per quarter. Closing stock is to be maintained at 20% of the budgeted sales. Required: (i) Calculate sales quantity to be sold during quarter ending (ii) Prepare production budget in units for the quarter ending (8 marks) Chapter - 5 : Standard Costing May [4] (b) (i) Direct Material Usage Variance: Direct Material Usage Variance = (Standard Quantity Actual Quantity) Standard Rate = (2,64,000 3,30,000) 12 Direct Material Usage Variance = 7,92,000 (A)

15 Solved Scanner Appendix CA Final Gr. II Paper (ii) Direct Material Price Variance: Direct Material Price Variance = (Standard Price Actual Price) Actual Quantity = (12 11) 3,30,000 Direct Material Price Variance = 330,000 (F) (iii) Direct Labour Efficiency Variance: Direct Labour Efficiency Variance = (Standard hours Actual hours) Standard Rate = (5,28,000 5,28,000) 9 Direct Labour Efficiency Variance = NIL (iv) Direct Labour Rate Variance: Direct Labour Rate Variance = (Standard Rate Actual Rate) Actual hours = (9 10) 5,28,000 Direct Labour Rate Variance = 5,28,000 (A) (v) Variable Overhead Cost Variance: Variable Overhead Cost Variance = (Standard input for actual output Actual input for actual output) = (79,20,000 81,84,000) Variable Overhead Cost Variance = 2,64,000 (A) (vi) Sales Margin Volume Variance: Sales Margin Volume Variance = (Standard unit Actual unit) Standard Rate of Margin (Profit) = (60,000 66,000) 159 Sales Margin Volume Variance = 9,54,000 (F) Working Note: 1. Calculation for Material (Standard input for Actual Output) Standard Actual Material Kg. Rate Amount Kg. Rate Amount 2,64, ,68,000 3,30, ,30, Calculation for Labour (Standard hours for Actual Output) Standard Actual Labour Hours Rate Amount Hours Rate Amount 5,28, ,52,000 5,28, ,80,000

16 Solved Scanner Appendix CA Final Gr. II Paper Calculation for Variable Overhead Cost: Standard input for actual output = = 79,20, Calculation for Sales Margin: (i) Calculation for Profit on Sales Particulars Standard Actual Sales 1,80,00,000 2,14,50,000 + Number units Sales Price p.u. 60, , (-) Material Cost p.u. (-) Labour Cost p.u. (-) Variable Cost p.u. (12) (9) (120) (11) (10) (124) Sales Margin (Profit) p.u (ii) Sales Margin Sales Margin Standard Actual Unit Rate Amount Unit Rate Amount 60, ,40,000 66, ,18,80, Nov [5] (a) S. Ltd. produces and sells a single product. The product is manufactured by mixing two raw materials Q and R. The standard cost date of the product is as follows: Raw material input: Q 3 ` per kg R 7 ` 6.00 per kg ` ` Raw material cost per kg of input ` Yield 96% Raw material cost per kg of output ` Fixed production overheads per kg of output ` 8.00 Total standard cost per kg of output `

17 Solved Scanner Appendix CA Final Gr. II Paper The budgeted and actual data are as follows: Budgeted data Actual data Sales 72,000 kg Sales 71,000 kg Production 70,000 kg Production 69,000 kg Opening 2,000 kg Cost per kg of Q ` Inventory (valued at standard cost) Cost per kg of R ` 5.80 Selling price per kg ` 200 Selling price per kg ` Fixed production overheads ` 5,60,000 Fixed production overheads incurred Input of Q ` 5,08,000 2,21,000 kg Input of R 4,79,000 kg The fixed production overhead absorption rate is based on the budgeted production. Calculate Sales price variance, Sales volume variance, Material price variance, Material mix variance, Material yield variance, Fixed overhead expenditure variance and Fixed overhead volume variance. (8 marks) Chapter - 7 : Transfer Pricing May [6] (a) Basic Workings Statement Showing Contribution per unit (`) Particulars Division A Division B AC PC RAC External Demand (units) 18,000 unlimited 6,000 Selling Price (A) , Direct Material Imported Component Direct Labour & Overheads Variable Cost (B)

18 Solved Scanner Appendix CA Final Gr. II Paper Contribution (A) (B) Hours Contribution/ Hour Division A Allocation of Hours on the basis of contribution/hour Production of AC = 18,000 units Hours Required = 72,000 hrs (18,000 units 4.0 hrs.) Balance Hours Available = 48,000 hrs (1,20,000 hrs. - 72,000 hrs.) Production of PC Note = 48,000 units Analysis of Hours Available and Required in Division B Particulars Hrs. Required for 10 p.u. Hrs. Required for 2 p.u. If Requirement 6,000 units 12,000 units 15,000 units 60,000 hrs. 1,20,000 hrs. 1,50,000 hrs. 12,000 hrs. 24,000 hrs. 30,000 hrs. Total Hrs. Available 6,00,000 hrs. 6,00,000 hrs. 6,00,000 hrs. Division B s required hours are less than the available hours (considered various scenarios). Hence, the same has no impact on the figures arrived specifically for point (iii), (iv) & (v). (i) Minimum Transfer Price per unit If Requirement of B is 12,000 units Transfer Price = Variable Cost + Opportunity Cost = ` = ` 345 (ii) Minimum Transfer Price per unit If Requirement of B is 15,000 units Transfer Price = Variable Cost + Opportunity Cost = ` = ` 366 (iii) Maximum Price (B will Offer A)

19 Solved Scanner Appendix CA Final Gr. II Paper The price being paid to Outside Supplier less Cost of Modification = ` 450 ` 70 = ` 380 (iv) & (v) Division B is not in a position to sell more than 6,000 units as given in the question and therefore any transfer of component from Division A of over 6,000 units will NOT be in the overall interest of the company. Although Division B has spare hours of 5,40,000 hours (6,00,000-60,000) which will not help it to increase its sales. If division B able to sell entire units transferred, then Company would be able to save ` 35 per unit. Cost of Modified AC vs Cost of Imported Component Particulars Modified AC (`) Imported Component (`) Transfer Price AC Cost of Modification (2 hrs. ` 35) Cost of Import Effective Cost per unit Nov [6] (a) ABC miners operates two divisions, one in Japan and other in United Kingdom (U.K). Mining Division is operated in Japan which is rich in raw emerald. The other division is United Kingdom Processing Division. It processes the raw emerald into polished stone fit for human wearing. The cost details of these divisions are as follows: Division Japan Mining Division United Kingdom Processing Division Per carat of raw emerald Per carat of polished emerald Variable Cost 2,500 Yen 150 Pound Fixed Cost 5,000 Yen 350 Pound Several polishing companies in Japan buy raw emerald from other local Mining

20 Solved Scanner Appendix CA Final Gr. II Paper Companies at 9,000 Yen per carat. Current Foreign Exchange Rate is 50 Yen = 1 Pound. Income Tax rates are 20% and 30% in Japan and the United Kingdom respectively. It takes 2 carats of Raw Yellow emerald to yield 1 carat of Polished Stone. Polished emerald sell for 3,000 Pounds per carat. Required: (i) Compute the transfer price for 1 carat of raw emerald transferred from Mining Division to the Processing Division under two methods - (a) 200% of Full Costs and (b) Market Price. (ii) 1,000 carats of raw emerald are mined by the Japan Mining Division and then processed and sold by the U.K. Processing Division. Compute the after tax operating income for each division under both the Transfer Pricing Methods stated above in (i). (8 marks) Chapter - 9 : Cost Sheet, Profitability Analysis and Reporting May [6] (b) (i) A B C D No. of Pizzas 1,500 2,500 4,800 4,000 Contribution Total contribution 1,08,000 1,67,500 3,12,000 2,40,000 (-) Normal delivery cost (40,000) (75,000) (32,000) (1,00,000) (Km 20 No. of delivery) (-) Rush delivery cost (Rush delivery 200) - (8,000) (4,000) (6,000) 68,000 84,500 2,76,000 1,34,000 (ii) Additional cost Normal ( ) 26,000 Rush (200 20) 4,000 30,000 (+) Existing Delivery Cost 40,000 70,000 (+) Current profit of A 68,000 Sales 1,38,000 ( ) Units 2,300 Contribution per unit 60 PH can reduce price per unit to ` 60 for A Nov [4] (a) UV Limited manufactures a product ZED. It currently

21 Solved Scanner Appendix CA Final Gr. II Paper operates at 70% capacity. It has received an export order which will utilize 50% of the capacity of the factory. The order has to be either taken in full or rejected totally. The order has to be executed at a price of ` 86 per unit and company has to incur additional cost of packing and forwarding of ` 2.50 per unit on the goods exported. 3% will be payable to overseas agent. Other information available is as under: Sale value 63,000 ` 95 per unit ` 59,85,000 Direct ` per unit ` 26,52,300 Variable manufacturing overheads ` 4,41,000 Variable selling & distribution overheads (including 2% commission on domestic sales) ` 4,34,700 Fixed overheads ` 6,75,000 P/V ratio 20% Following three alternatives are available to the management: (i) Continue with the current domestic sale and reject the export order. (ii) Accept the export order by reducing the domestic sale. (iii) Increase the capacity by 10% by installing a new machine costing ` 2,50,000. Fixed overheads will increase by ` 96,000. Opportunity cost of investment is 15%. Overtime is to be paid at one and a half time the normal rate to meet the balance of the required capacity. Required: (i) Prepare Statement of profitability for each of the above three alternatives. (ii) Which is the best alternative in terms of profitability? (8 marks) Chapter - 10 : Linear Programming May [7] (a) (i) Introducing stock/surplus/artificial variables In case of Maximization... Z = 3x 1 + 4x 2 + 0S 1 + 0S 2 - MA 2... (1) Subject to, 2x 1 + 3x 2 + S 1 = (2) 4x 1 + 3x 2 - S 1 + A 2 = (3)

22 Solved Scanner Appendix CA Final Gr. II Paper x 1, x 2, S 1, S 2, A (4) *For Equation - (1) Coefficients of S 1, S 2 and A 2 are 0, 0 and - M respectively. *For Equation - (3) Coefficients of S 1, S 2 and A 2 are 0, -1 and 1 respectively. (ii) In any maximization problem, this tableau must satisfy the following requirements: All the Stock Variables (and Surplus variables as well) must form part of the initial solution mix (basis). The table must contain as many rows as there are constrains. The elements in the columns of variables appearing in the basis must form a unit vector. If S 2 is included in the basis, the elements of the S 2 will be 0 and -1 and thus not a unit vector. This is contrary to the non-negativity restriction i.e. all variables must have a positive value. This problem is solved by adding an Artificial Variable (denoted by Ai) to the equation, that is, a variable that has a positive value. Artificial variables do not represent any quantity relating to the decision problem and must not be present in the final solution (if at all they do, it represents a situation of infeasibility). Accordingly, in the initial tableau we will place A 2 along with S 1 to eliminate the impact of first. *Note: In the absence of information it is assumed that, let S 1 be the variable introduced to restate (2) as an equality and let S 2 and A 2 be variables to restate (3) as an equality Nov [1] {C} (b) The simplex tableau for a maximization problem of linear programming is given below: c j Product Mix x 1 x 2 s 1 s 2 Quantity 5 x s c j z j c j - z j Answer the following questions giving reasons in brief:

23 Solved Scanner Appendix CA Final Gr. II Paper (i) If s 1 is slack in machine A (in hours/week) and s 2 is slack in machine B (in hours/week), which of these machines is being used to the fullest capacity? (ii) A customer would like have to one unit of product x 1 and is willing to pay more than the normal price in order to get it. How much should the price be increased in order to maintain same level of profit? (iii) Machine A (associated with slack s 1 in hours/week) has to be shut down for repairs for 2 hours next week. What will be the effect on profits? (iv) How much would you be prepared to pay for another hour (per week) of machine A and machine B? (4 marks) Nov [7] (b) Explain the following terms in relation to Simplex method of Linear Programming problem: (i) Multiple optimal solution (ii) Infeasible solution (iii) Degeneracy (iv) Unbounded solution (4 marks) Chapter - 11 : Transportation Problem May [3] (b) (i) Initial Solution. Factory Destination F 1 F 2 F 3 Demand D /25/0 30 D /0 30 D /0 Supply 35/0 55/25/0 30/0 120 (ii) No. of solutions M + N Here, Degeneracy exist. (iii)

24 Solved Scanner Appendix CA Final Gr. II Paper (iv) (v) Destination Factory F 1 V 1 = 3 F 2 V 2 = 6 F 3 V 3 = 10 D V 1 = D V 2 = D 3 e 2 30 V 3 = We will get some values, because Δ ij matrix shows opportunity cost and that will remain some in all cases. Factory Destination F 1 F 2 F 3 Demand D /25/0 D /0 D /0 Supply 35/0 55/30/0 30/ Nov [2] (a) XYZ chemical company has three plants located in a state. The daily chemical production at each plant is as follows: Plant- I : 12 million litres Plant- II : 2 million litres Plant- III : 20 million litres Each day, company must fulfil the needs of its four distribution centres. Minimum requirements at each centre are as follows: Distribution centre 1 : 14 million litres Distribution centre 2 : 10 million litres Distribution centre 3 : 6 million litres Distribution centre 4 : 4 million litres Cost in hundreds of rupees of shipping one million litres from each plant to

25 Solved Scanner Appendix CA Final Gr. II Paper each distribution centre is given in the following table: Distribution Centre D1 D2 D3 D4 Plant P P P Required: (i) Find initial basic feasible solution for given transportation problem by using Vogel s approximation method if the object is to minimize the total cost. (ii) Is this the degenerate solution? (6 marks) Chapter - 12 : Assignment Problem May [1] {C} (d) R 1 C 1 appears at the intersection of R 1 and C 1. Hence, it will have its zero replaced by minimum of a, b, c, or d in the next operation since the number of lines to cover zeros is less than 3. In the next step, a or b or c or d will have one zero. Then, number of lines will be 3, the order of the matrix. Assignments will be made to the Zeros. Hence, R 1 C 1 cannot figure in this. Interpretation An assignment of R 1 C 1 will eliminate the use of other costs available on R 1 and C 1 entirely. The left over will be a, b, c, or d combinations which are more than zero. Hence, R 1 C 1 taking on assignment will be non-optimal Nov [7] (d) State with reason whether the following statements are true or false in relation to assignment problem: (i) There cannot be multiple optimal solutions in an assignment problem. (ii) In 4 6 minimisation problem. We can solve it by introducing one dummy row in given matrix. (iii) In a problem relating to sales maximization, we have to convert the given matrix into minimization by subtracting lowest element among all the elements of given matrix from all the elements of that matrix. (iv) When there is a restriction of assignment in a particular cell, then we put M to avoid assignment in that cell. (4 marks) Chapter - 14 : Programme Evaluation and Review Technique

26 Solved Scanner Appendix CA Final Gr. II Paper May [2] (b) Activity Duration (EFT-EST) EST EFT LST LFT TF C/ T A ,000 B ,000 C ,000 D ,000 E ,000 F ,000 G ,000 H ,000 I ,000 (i) Critical path always 0 Total float. A E F G I Duration = 26 days. (ii) LFT C 12 D 10 H 24 B 12 (iii) Step Crashing Activity Days Cost I A 1 1,000 II F 1 6,000 III G 1 7,000 Activity E cannot be crashed since zero duration is not possible. (iv) Activity Increase duration by. B 2 (3 1) Total float after crashing C 0 (1 1) ( ) Extra Days for H Concept: After crashing total float for B is 3 days and for C is 1 day. As the B and C are succeeding to H, if H uses 1 float then total float of B and C are reduced by Nov [2] (b) A small project consisting of eight activities has the following

27 Solved Scanner Appendix CA Final Gr. II Paper characteristics: Activity Time (Weeks) Optimistic Pessimistic Most likely Required: (i) Draw the project network and find out the critical path and expected completion time. (ii) Calculate the standard deviation and variance of the project. (iii) What is the probability of the project completion at least 2 weeks earlier than the expected time? (iv) If the project due date for completion is 27 weeks, what is the probability of not meeting the due date? (v) If the project manager wants to be 90% sure of the completion, how many weeks before the due date should he commence the project? Value of Z = , Z 0.58 = , NT (Z) 0.40 = 1.28 (10 marks) Chapter - 15 : Simulation Nov [3] (b) MN Ltd. is a confectionery company and it sells confectionery items. Past data of demand per day with frequency is given below:

28 Solved Scanner Appendix CA Final Gr. II Paper Demand (in kgs) No. of days The company has scope to meet 12 kg demand per day. The life of the product is one day. It will be produced according to demand. It cannot hold as inventory. The contribution is ` 10 per kg. Using the following random numbers, simulate 10 days demand for the confectionery items. 35,52,90,13,23,73,34,57,35,83 Required: (i) Allocate random numbers and simulate for 10 days. (ii) Calculate average demand of confectionery items per day fulfilled. (iii) Calculate amount of loss (Due to not fulfilling the demand). (6 marks) Chapter - 16 : Learning Curve Theory May [3] (a) (i) The usual learning curve model is y = ax b Where y = Average time per unit for x units a = Time required for first unit x = Cumulative number of units produced b = Learning coefficient Time required for first 250 units: y = 40 (250) y = y = hrs. Total time for 250 units = 250 units hrs. = 1,691 hrs. Time required for first 249 units: y = 40 (249) y = y = hrs.

29 Solved Scanner Appendix CA Final Gr. II Paper Total time for 249 units = 249 units hrs. = 1, hrs. Time required for 1,000 units: Total time for first 250 units = 1,691 hrs. Total time for next 750 units= (1,691 1, ) hrs. 750 units = 3,579 hrs. Total time for 1,000 units = 1,691 hrs. + 3,579 hrs. = 5,270 hrs. (ii) Labour Efficiency Variance = (Std. Hrs. Actual Hrs.) Std. Rate = (5,270 hrs. 6,000 hrs.) ` 96 = 70,080 (A) (iii) Labour Efficiency Variance = (Std. Hrs. Actual Hrs.) Std. Rate = (40 hrs. 1,000 units 6,000 hrs.) ` 96 = 32,64,000 (F) Nov [1] {C} (c) RST Co. manufactures products purely carried out by labour. It has 25 direct workers who work for 25 days a month of 8 hours a day. However, the company may resort to overtime if required, at one and half the normal rate of wages. The company has received an order of 8,000 units of a new product at a price of ` 160 to be executed within 30 days. The contract stipulates a penalty of ` 10,000 per day for delivery beyond 30 days. It is estimated that at the current level of efficiency, each unit requires one hour for the first 2,000 units. Company expects 90% learning curve for this type of work. The cost data is as under: Direct materials ` 75 per unit Direct labour (1 hour/unit) ` 30 per unit Variable overhead Fixed overhead ` 12 per direct labour hour ` 1,20,000 per month (Fixed overheads are to be incurred evenly throughout the month)

30 Solved Scanner Appendix CA Final Gr. II Paper Calculate: (i) Overtime hours if the option of overtime is exercised to avoid the penalty. (ii) The cost and profit under both the options i.e. to pay the penalty by working in normal hours or to work overtime to avoid penalty. (5 marks) Shuchita Prakashan (P) Ltd. 25/19, L.I.C. Colony, Tagore Town, Allahabad Visit us:

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