Accounting Managerial Accounting [ADVANCED HIGHER] Lindsay Mitchell abc
The Scottish Qualifications Authority regularly reviews the arrangements for National Qualifications. Users of all NQ support materials, whether published by LT Scotland or others, are reminded that it is their responsibility to check that the support materials correspond to the requirements of the current arrangements. Acknowledgement Learning and Teaching Scotland gratefully acknowledge this contribution to the National Qualifications support programme for Accounting. First published 2005 Learning and Teaching Scotland 2005 This publication may be reproduced in whole or in part for educational purposes by educational establishments in Scotland provided that no profit accrues at any stage. ISBN-10: 1-84399-098-9 ISBN-13: 978-184399-098-7
CONTENTS Introduction 5 Section 1: Activity-Based Costing (ABC) 7 Section 2: Multi-Product Break-Even Analysis 33 Section 3: Contract Costing Statements 49 MANAGERIAL ACCOUNTING (AH) 3
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INTRODUCTION This pack contains notes and exercises for three topics activity-based costing, multi-product break-even analysis and contract costing. Activity-based costing and multi-product break-even analysis are both new topics for Advanced Higher and it is intended that the enclosed material will provide guidance to tutors as to what students are expected to know when covering the topics. Contract costing appeared in the old Higher Accounting and Finance arrangements but is now included in the Advanced Higher content. As no previous material on this topic has been produced it is hoped that this package will fill the gap. Each topic contains notes, exercises and full solutions. MANAGERIAL ACCOUNTING (AH) 5
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SECTION 1 ACTIVITY-BASED COSTING (ABC) Activity-Based Costing (ABC) In your studies in Higher Accounting one of the major topics in the Cost/Management Accounting part of the syllabus was the treatment of overhead costs within a business. This involved the allocation and apportionment of overheads among cost centres and the subsequent absorption of these cost-centre overheads into the cost units produced in the cost centres. The whole process described above can best be illustrated by the following diagram. Overhead Costs Allocation Apportionment using selected basis Single Cost Centre Multiple Cost Centres Production Cost Centres Service Cost Centres Re-apportionment using selected basis Cost Units using appropriate absorption rate The above approach is sometimes referred to as the traditional approach to overhead absorption. Activity-based costing has been developed within the last 20 30 years in an effort to avoid defects in the traditional system. MANAGERIAL ACCOUNTING (AH) 7
ACTIVITY-BASED COSTING (ABC) The main characteristics of the traditional system are as follows: it was developed in manufacturing industry there were typically a narrow range of products production processes were much simpler than now direct material and labour costs were the main production costs overhead costs were relatively small inaccuracies due to arbitrary nature of process were therefore relatively unimportant. Activity-Based Costing (ABC) has therefore emerged due to the following: product ranges have increased overhead costs have become more significant manufacturing concerns no longer dominate service organisations account for a much larger share of economic activity production is more complex and capital intensive. The main ideas behind ABC are: costs are caused by activities for example ordering, material handling, scheduling, machining, assembling, etc. production of products or supply of services creates the demand for these activities costs are therefore assigned to products or services on the basis of consumption of these activities. 8 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) Therefore ABC involves a number of stages: 1. Identify the major activities of the organisation. 2. Identify the factors which affect the cost of an activity. These factors are known as COST DRIVERS, e.g. the number of purchase orders might be considered as the cost driver for the costs of a purchasing department. 3. Collect the associated costs of each activity. This is known as the COST POOL. 4. Allocate costs to products/services based on the demand created for the cost drivers. As with the traditional approach, ABC can be illustrated by a diagram: Identify major activities Create cost pool for each activity Identify cost driver for each activity Produce absorption rate for each pool based on cost driver Overhead cost per unit Let us now look at an example which will show both the traditional approach to the treatment of overheads and then how ABC would treat the same situation. MANAGERIAL ACCOUNTING (AH) 9
ACTIVITY-BASED COSTING (ABC) Example Deeside plc manufactures three products, A, B and C in their factory and use a factory-wide absorption rate for absorbing overheads based on direct labour hours. The following information relates to Period 5 of Year 3. Product A B C Production (units) 12,000 8,000 4,000 Direct Material Cost p.u. 40 30 20 Direct Labour Hours p.u. 4 6 2 Direct labour is paid at 8 per hour. The overhead costs for Period 5 are as follows: Machining 312,000 Set-up 56,000 Assembling 80,000 Goods Receiving 128,000 Dispatch 100,000 676,000 (a) Calculate the factory-wide absorption rate for Period 5. (b) Calculate the cost p.u. of each product under the traditional approach to treatment of overheads. The company is considering using ABC as a method of arriving at the cost per unit of their products and the following information is available for this purpose: The overheads have been investigated and while Machining costs will be absorbed on the basis of machine hours, cost drivers have been identified for the other overheads. Overhead Set-up Assembling Goods Receiving Dispatch Cost Driver No. of production runs No. of production orders No. of receipts No. of production orders 10 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) The following additional information is also available: Product A B C Machine hours per unit 2 3 1 No. of Production runs 1 2 5 No. of Material receipts 3 5 24 No. of Production orders 3 2 5 (c) (d) Calculate a cost driver absorption rate for each of the above overheads. Calculate the cost per unit for each product under the ABC system. This question contains a lot of information and lots of figures and therefore it is important to read it carefully with a view to deciding which information relates to each part of the question. The purpose of this question is to show how the traditional method of overhead absorption works and then to demonstrate the Activity-Based Costing approach. At the end of the question we will compare the two methods and see if we can explain the differing results they produce. MANAGERIAL ACCOUNTING (AH) 11
ACTIVITY-BASED COSTING (ABC) Solution (a) This opening part of the question asks us to calculate a factorywide overhead absorption rate (sometimes called a blanket rate ), based on labour hours. You should recall that the calculation of an overhead absorption rate divides the relevant overhead (which may be for a cost centre or, as in this case, for the whole factory) by the relevant units of the base selected. (There were actually six possibilities, i.e. per unit, % on material, % on wages, % on prime cost, per labour hour or per machine hour.) In this question we are using labour hours and therefore the calculation is as follows: Overhead Absorption Rate = Factory Overheads Labour Hours Although we know the total factory overheads we need to calculate the total labour hours, i.e. A 12,000 4 = 48,000 B 8,000 6 = 48,000 C 4,000 2 = 8,000 104,000 We can now calculate the factory-wide rate 676,000 = 104,000 = 6.50 per labour hour 12 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) (b) In this next part we are asked to calculate the total cost per unit for each product using the traditional approach. This total cost will be the sum of the two direct costs material and labour, plus overheads. The question gives us the material cost p.u. for each product, but we will have to calculate the figures for labour and overheads. For labour this will be the number of labour hours per unit multiplied by the labour rate per hour. For overheads it will be the number of labour hours per unit multiplied by the overhead absorption rate calculated in part (a), i.e. Cost per unit A B C Material 40 30 20 Labour 32 (4 8) 48 (6 8) 16 (2 8) Overheads 26 (4 6.50) 39 (6 6.50) 13 (2 6.50) 98 117 49 The remaining parts of the question now introduce the Activity-Based Costing technique. (c) This part asks us to calculate cost driver absorption rates for the separate overheads. The total overhead of the factory has been broken down into five activities. For the first of these, machining, a traditional-style absorption rate is to be used, i.e. machine hour rate. Machine Hour Rate = Machine Overhead Machine Hours Once again we know the overhead but need to calculate the machine hours, i.e. A 12,000 2 = 24,000 B 8,000 3 = 24,000 C 4,000 1 = 4,000 52,000 Therefore the calculation is 312,000 Machine Hour Rate = 52,000 = 6 per m/c hour MANAGERIAL ACCOUNTING (AH) 13
ACTIVITY-BASED COSTING (ABC) For the other activities, which comprise the factory overheads, appropriate cost drivers have been identified and we can use these to calculate the relevant absorption rate. The cost drivers identified are the number of production runs, the number of production orders and the number of receipts. Therefore before we go any further we must calculate the relevant figure for each driver. Production Runs A 1 B 2 C 5 8 Production Orders A 3 B 2 C 5 10 Receipts A 3 B 5 C 24 32 Now we can calculate the absorption rate for each activity, based on the relevant cost driver. Set-up = 56,000 8 = 7,000 per run Assembling = 80,000 10 = 8,000 per order Goods Receiving = 128,000 32 = 4,000 per receipt Dispatch = 100,000 10 = 10,000 per order 14 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) (d) The final part requires us to use these figures to produce a cost per unit for each product. Therefore we need to calculate the overhead cost per unit to add to the material and labour costs which we calculated in part (b). Machinery overhead is the simplest, i.e. machine hours per unit multiplied by machine hour rate. A 2 6 = 12 B 3 6 = 18 C 1 6 = 6 For the other overhead activities we need to relate the cost driver absorption rate to the units produced. A B C Set-up 7,000 14,000 (7,000 2) 35,000 (7,000 5) 12,000 8,000 4,000 = 0.58 = 1.75 = 8.75 Assembling 24,000 ( 8,000 3) 16,000 (8,000 2) 40,000 (8,000 5) 12,000 8,000 4,000 = 2 = 2 = 10 Goods 12,000 ( 4,000 3) 20,000 (4,000 5) 96,000 (4,000 24) Receiving 12,000 8,000 4,000 = 1 = 2.50 = 24 Dispatch 30,000 (10,000 3) 20,000 (10,000 2) 50,000 (10,000 5) 12,000 8,000 4,000 = 2.50 = 2.50 = 12.50 Therefore using ABC total cost per unit for the products would be as follows: A B C Direct Materials 40 30 20 Direct Labour 32 48 16 Machinery 12 18 6 Set-up 0.58 1.75 8.75 Assembling 2 2 10 Goods Receiving 1 2.50 24 Dispatch 2.50 2.50 12.50 90.08 104.75 97.25 MANAGERIAL ACCOUNTING (AH) 15
ACTIVITY-BASED COSTING (ABC) Contrast these figures with the ones produced in the answer to part (b) of the question. The most striking change is in the increase in the cost per unit of Product C, although there is also a less substantial decrease in the cost per unit of the other two products. The increase in the cost of C has arisen because most of the charges relating to C were not identified under the traditional absorption system. The cost drivers identified in the ABC system are responsible for generating these charges and thus we can suggest that the ABC system produces a more accurate cost for each product. The following examples will provide practice in applying the ABC system. Solutions are provided at the end of this section. 16 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) Question 1 Your company currently produces and sells 4 products, Alpha, Beta, Gamma and Delta. The following information relates to Period 3. Alpha Beta Gamma Delta Production (units) 180 150 120 180 Costs per unit: Direct material 46 58 35 70 Direct labour 21 14 7 14 Machine hours per unit 4 3 2 3 Number of production runs 6 5 4 6 Number of requisitions raised 30 30 30 30 Number of orders completed 18 15 12 18 Currently the production overhead is absorbed by the machine-hour rate method and the following are the total production overhead costs for Period 3. Machine Department 24,540 Set-up costs 6,300 Receiving costs 7,200 Inspection costs 3,150 Despatch costs 7,560 48,750 Cost drivers have been identified as follows: Set-up costs Stores receiving Inspection Despatch Number of production runs Number of requisitions raised Number of production runs Number of orders completed You are required to calculate: (a) (i) The machine-hour rate currently used to absorb the production overhead. (ii) The total cost per unit for each product if overheads are absorbed by the method in (a)(i). (b) The cost per unit for each product using an ABC approach. MANAGERIAL ACCOUNTING (AH) 17
ACTIVITY-BASED COSTING (ABC) Question 2 Jomit plc has budgeted for the following overhead costs for Period 6. Material receipt costs 31,200 Power costs 39,000 Material handling costs 27,300 The company produces 3 products, P, Q and R for which the following budgeted information is available for Period 6. Product P Q R Output (units) 4,000 3,000 1,600 Material batches 20 10 32 Per Unit Direct material (kg) 4 6 3 Direct material ( ) 6 5 9 Direct labour (hours) 0.2 0.5 1.0 Number of power operations 6 3 2 Direct labour rate per hour 8 8 8 Currently the overhead costs are each absorbed using a rate per direct labour hour. However, the company is considering applying overheads using an ABC approach and has identified drivers for the activities as follows: Material receipt costs Power costs Material handling costs number of batches of material number of power operations kg of material handled You are required to calculate: (a) (b) The total cost per unit for each product using the current overhead absorption method. The total cost per unit for each product using the ABC method. 18 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) Question 3 Your company currently produces a range of three products, D, E and F to which the following details relate for Period 2. D E F Production (units) 1,500 2,500 14,000 Material cost per unit 18 10 20 Labour hours per unit 1 3 2 Machine hours per unit 3 2 6 Labour costs are 8 per hour and production overheads are currently absorbed in the conventional system by reference to machine hours. Total production overheads for Period 2 have been analysed as follows: Set-up costs 327,250 Handling costs 187,000 Machining costs 140,250 Inspection costs 280,500 935,000 (a) Calculate the cost per unit for each product using conventional methods. The introduction of an ABC is being considered and to that end the following volume of activities have been identified with the current output levels. D E F Number of set-ups 90 138 576 Number of material issues 16 28 116 Number of inspections 180 216 804 (b) Calculate the cost per unit for each product using the ABC approach. MANAGERIAL ACCOUNTING (AH) 19
ACTIVITY-BASED COSTING (ABC) Question 4 The following table summarises the details of the production levels, costs and cost drivers for Abtronics Ltd who have traditionally absorbed overheads into production on the basis of a labour hour absorption rate. They wish to move to an ABC system. Product P Q R Material cost per unit 20 15 10 Labour hours per unit 4 6 3 Machine hours per unit 4 3 6 Number of production runs 6 14 40 Number of production orders 45 30 75 Number of orders delivered 30 20 50 Number of receipts 12 28 80 Production (units) 15,000 10,000 4,000 Labour hours are paid for at 10 per hour. Overheads Cost Driver Machining 684,000 machine hours Set-up costs 60,000 production runs Receiving costs 240,000 number of receipts Packing costs 300,000 number of orders delivered Engineering costs 450,000 number of production orders 1,834,000 (a) (b) Calculate the cost per unit for each product using the traditional overhead absorption approach. Calculate the cost per unit using the ABC approach. 20 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) Question 5 Param plc has incurred the following overheads in its factory during Period 6. Quality control 90,000 Process set-ups 135,000 Purchasing 105,000 Order processing 120,000 Occupancy costs 150,000 Param plc produces a range of products, two of which are Product X and Product Y. The following information relate to these two products. X Y Material costs per unit 5 8 Labour cost per unit 8 12 Number of process set-ups 150 210 Number of purchase orders issued 500 300 Number of customer orders 1,000 800 Machine hours per unit 3 2 Production (units) 10,000 6,000 Inspection takes place after each process set-up. The cost drivers which have been identified for the factory are: Quality control Process set-ups Purchasing Order processing Occupancy costs 450 inspections 450 set-ups 1,000 purchase orders 2,000 customer orders 75,000 machine hours Calculate the cost per unit for Products X and Y using: (i) (ii) existing overhead absorption rate per machine hour an activity-based costing approach. MANAGERIAL ACCOUNTING (AH) 21
ACTIVITY-BASED COSTING (ABC) Solutions Question 1 (a) (i) Total machine hours: Alpha 4 180 = 720 Beta 3 150 = 450 Gamma 2 120 = 240 Delta 3 180 = 540 = 1950 Total overheads = 48,750 48,750 Machine hour absorption rate = 1,950 = 25 (ii) Cost per unit Alpha Beta Gamma Delta Direct material 46 58 35 70 Direct labour 21 14 7 14 Production overhead 100 75 50 75 167 147 92 159 (b) Cost Driver Driver Cost per transactions driver Machine Dept 24,540 m/c hours 1950 12.58 Set-up 6,300 Runs 21 300 Receiving 7,200 Requisitions 120 60 Inspection 3,150 Runs 21 150 Despatch 7,560 Orders 63 120 22 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) Overheads cost per unit Alpha Beta Gamma Delta Set-up 1800 = 10 180 1500 = 10 150 1200 = 10 120 1800 = 10 180 Receiving 1800 = 10 180 1800 = 12 150 1800 = 15 120 1800 = 10 180 Inspection 900 = 5 180 750 = 5 150 600 = 5 120 900 = 5 180 1800 = 12 150 Despatch 2160 1440 = 12 = 12 180 120 Machine 4 12.58 3 12.58 2 12.58 3 12.58 Dept = 50.32 = 37.74 = 25.16 = 37.74 2160 = 12 180 Total cost per unit Alpha Beta Gamma Delta Materials 46.00 58.00 35.00 70.00 Labour 21.00 14.00 7.00 14.00 Set-up 10.00 10.00 10.00 10.00 Receiving 10.00 12.00 15.00 10.00 Inspection 5.00 5.00 5.00 5.00 Despatch 12.00 12.00 12.00 12.00 Machine Dept 50.32 37.74 25.16 37.74 154.32 148.74 109.16 158.74 MANAGERIAL ACCOUNTING (AH) 23
ACTIVITY-BASED COSTING (ABC) Question 2 (a) Direct labour hours: P 4,000 0.2 = 800 Q 3,000 0.5 = 1,500 R 1,600 1.0 = 1,600 3,900 Overhead absorption rates: Material receipt Power Material handling 31,200 = 8 per labour hour 3,900 39,000 = 10 per labour hour 3,900 27,300 = 7 per labour hour 3,900 Overhead cost per unit P Q R Material receipt 8 0.2 8 0.5 8 1 = 1.60 = 4 = 8 Power 10 0.2 10 0.5 10 1 = 2 = 5 = 10 Material handling 7 0.2 7 0.5 7 1 = 1.40 = 3.50 = 7 Total cost per unit P Q R Direct material 6.00 5.00 9.00 Direct labour 1.60 4.00 8.00 Material receipt costs 1.60 4.00 8.00 Power costs 2.00 5.00 10.00 Material handling 1.40 3.50 7.00 12.60 21.50 42.00 24 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) (b) ABC absorption rates Material receipt Power Material handling 31,200 = 503.23 per batch 62 39,000 = 1.08 per operation 36,200 (W1) 27,300 = 0.70 per kg 38,800 (W2) W1 (4,000 6) + (3,000 3) + (1,600 2) = 36,200 W2 (4,000 4) + (3,000 6) + (1,600 3) = 38,800 Overhead costs per unit P Q R Material receipts 503.23 20 503.23 10 503.23 10 4,000 3,000 1,600 = 2.52 = 1.68 = 10.06 Power 1.08 6 1.08 3 1.08 2 = 6.48 = 3.24 = 2.16 Material handling 0.70 4 0.70 6 0.70 3 = 2.80 = 4.20 = 2.10 Total cost per unit P Q R Direct material 6.00 5.00 9.00 Direct labour 1.60 4.00 8.00 Material receipt costs 2.52 1.68 10.06 Power costs 6.48 3.24 2.16 Material handling costs 2.80 4.20 2.10 19.40 18.12 31.32 MANAGERIAL ACCOUNTING (AH) 25
ACTIVITY-BASED COSTING (ABC) Question 3 (a) Number of machine hours = D 1,500 3 = 4,500 = E 2,500 2 = 5,000 = F 14,000 6 = 84,000 = 93,500 Overhead absorption rate 935,000 = 93,500 = 10 per machine hour Cost per unit D E F Material 18 10 20 Labour 8 24 16 Overhead 30 20 60 56 54 96 (b) Total number of set-ups = 90 + 138 + 576 = 804 327,250 Absorption rate per set-up = 804 = 407.03 per set-up Total number of issues = 16 + 28 + 116 = 160 Absorption rate per issue 187,000 = 160 = 1,168.75 Absorption rate per machine hour 140,250 = 93,500 = 1.50 Total number of inspections = 180 + 216 + 804 = 1,200 Absorption rate per inspection 280,500 = 1,200 = 233.75 26 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) Overheads per unit D E F Set-up Issue 90 407.03 138 407.03 576 407.03 1,500 2,500 14,000 = 24.42 = 22.47 = 16.75 16 1,168.75 28 1,168.75 116 1,168.75 1,500 2,500 14,000 = 12.47 = 13.09 = 9.68 Machining 3 1.50 2 1.50 6 1.50 = 4.50 = 3 = 9 Inspection 180 233.75 216 233.75 804 233.75 1,500 2,500 1,400 = 28.05 = 20.20 = 13.42 Total cost per unit D E F Material 18.00 10.00 20.00 Labour 8.00 24.00 16.00 Set-up costs 24.42 22.47 16.75 Handling costs 12.47 13.09 9.68 Machine costs 4.50 3.00 9.00 Inspection costs 28.05 20.20 13.42 95.44 92.76 84.85 MANAGERIAL ACCOUNTING (AH) 27
ACTIVITY-BASED COSTING (ABC) Question 4 (a) Total labour hours = P 4 15,000 = 60,000 Q 6 10,000 = 60,000 R 3 4,000 = 12,000 132,000 Total overheads = 1,834,000 Total absorption rate 1,834,000 132,000 = 13.89 Cost per unit P Q R Direct material 20.00 15.00 10.00 Direct labour 40.00 60.00 30.00 Production overheads 55.56 83.34 41.67 115.56 158.34 81.67 (b) Cost driver absorption rates Machining 684,000 114,000 = 6.00 per machine hour Set-up costs 60,000 (6 + 14 + 40) = 1,000 per production run Receiving costs 240,000 (12 + 28 + 80) = 2,000 per receipt Packing costs 300,000 (30 + 20 + 50) = 3,000 per order delivered Engineering costs 450,000 (45 + 30 + 75) = 3,000 per production order 28 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) Overhead cost per unit P Q R Machining 6.00 4 6.00 3 6.00 6 = 24.00 = 18.00 = 36.00 Set-up costs Receiving costs Packing costs Engineering costs 6 1,000 14 1,000 40 1,000 15,000 10,000 4,000 = 0.40 = 1.40 = 10 12 2,000 28 2,000 80 2,000 15,000 10,000 4,000 = 1.60 = 5.60 = 40 30 3,000 20 3,000 50 3,000 15,000 10,000 4,000 = 6 = 6 = 37.50 45 3,000 30 3,000 75 3,000 15,000 10,000 4,000 = 9 = 9 = 56.25 Total cost per unit P Q R Direct material 20.00 15.00 10.00 Direct labour 40.00 60.00 30.00 Machining 24.00 18.00 36.00 Set-up 0.40 1.40 10.00 Receiving 1.60 5.60 40.00 Packing 6.00 6.00 37.50 Engineering 9.00 9.00 56.25 101.00 115.00 219.75 MANAGERIAL ACCOUNTING (AH) 29
ACTIVITY-BASED COSTING (ABC) Question 5 (i) Total Factory Overheads = 90,000 135,000 105,000 120,000 150,000 600,000 Total machine hours = 75,000 Absorption rate 600,000 75,000 = 8 per machine hour Cost per unit X Y Material 5.00 8.00 Labour 8.00 12.00 Overheads 24.00 16.00 37.00 36.00 (ii) Cost Driver Absorption Rates Quality control 90,000 450 = 200 per inspection Process set-up 135,000 450 = 300 per set-up Purchasing 105,000 1,000 = 105 per order Order processing 120,000 2,000 = 60 per order Occupancy costs 150,000 75,000 = 2 per machine hour 30 MANAGERIAL ACCOUNTING (AH)
ACTIVITY-BASED COSTING (ABC) Overhead cost per unit X Y Quality control Process set-up Purchasing Order processing 150 200 210 200 10,000 6,000 = 3 = 7 150 300 210 300 10,000 6,000 = 4.50 = 10.50 500 105 300 105 10,000 6,000 = 5.25 = 5.25 1,000 60 800 60 10,000 6,000 = 6 = 8 Occupancy 6 4 Cost per unit X Y Material 5.00 8.00 Labour 8.00 12.00 Quality control 3.00 7.00 Set-up 4.50 10.50 Purchasing 5.25 5.25 Order processing 6.00 8.00 Occupancy 6.00 4.00 37.75 54.75 MANAGERIAL ACCOUNTING (AH) 31
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SECTION 2 MULTI-PRODUCT BREAK-EVEN ANALYSIS Multi-Product Break-Even Analysis You will recall from your studies of Break-Even Analysis in Higher Accounting that the basis of this technique was the ability to classify all costs in an enterprise as either fixed or variable. That is not to say that all costs are either totally fixed or totally variable. Indeed there will be very few costs in the long run which could be said to fall into either of these categories. However, the assumption that is made is that all costs will be made up of a variable component and a fixed component, and that these can be separated. Thus we could add all the variable components together to arrive at a total variable cost per unit, and all the fixed components to arrive at total fixed costs, e.g. if we consider a cost like machine maintenance it can be argued that there would be a minimum amount of maintenance required even if production was zero. That then would constitute the fixed component of machine maintenance. Then, of course, as output builds up the machines will be subject to more wear and tear and breakdowns, and thus require more and more maintenance. This would constitute the variable component of machine maintenance. However, in your past studies the behaviour of costs (i.e. how costs change as output changes) was kept relatively simple (e.g. direct costs like material and wages were often assumed to be perfectly variable and costs like rent assumed to be perfectly fixed). In fact there were a number of assumptions made in break-even analysis which had the effect of keeping things relatively simple, e.g. the relationship between sales revenue and volume was based on the assumption that the selling price was constant at all levels of output and variable costs per unit were also assumed to stay constant. As far as this section of notes is concerned there was one further assumption which simplified matters and which we are now going to relax, i.e. we assumed that we were dealing with a single product model or perhaps, if there were more than one product, we assumed a constant sales mix. Therefore what we are now going to consider is the effect of several products on the calculations of break-even and profit and loss and the effect of changes in product or sales mix. MANAGERIAL ACCOUNTING (AH) 33
MULTI-PRODUCT BREAK-EVEN ANALYSIS Basic Concepts of Break-Even Analysis It is perhaps worth revising the basic relationships which Break-Even Analysis depends on. As already stated the starting point is Total Costs = Fixed Costs + Variable Costs Since, by definition, fixed costs have no relationship with output/sales no attempt is made to arrive at a total cost per unit. The next step is to find what is left over out of sales revenue once the variable costs have been met. This is called the contribution. Contribution = Sales Variable Costs It is so called because it is the contribution towards paying the fixed costs. If there is sufficient contribution to pay the fixed costs and have something left over then that will be profit (since all costs have now been met). If there is insufficient contribution to cover the fixed costs then a loss will be made (since the total costs have exceeded sales revenue). In between these two situations there must be a point where there is just sufficient contribution to pay the fixed costs and thus neither a profit nor a loss is made. This is known as Break-Even Point and is where Contribution = Fixed Costs Remember as we said above Contribution Fixed Costs = Profit (if positive) = Loss (if negative) The key to calculating the profit or loss in any situation is therefore contribution, and profit/loss can only be found by two steps, i.e. find contribution by comparing sales and variable costs deduct fixed costs from contribution to determine profit or loss. 34 MANAGERIAL ACCOUNTING (AH)
MULTI-PRODUCT BREAK-EVEN ANALYSIS Break-Even Point is important, because it marks the output level where a business moves from loss into profit; therefore there is an important formula which allows us to calculate it, i.e. Break-Even Point (units) = Fixed Costs Contribution per unit To convert this into Break-Even Sales we only need to multiply the break-even units by the selling price per unit. Break-Even Point ( ) = B/E units Selling Price per unit There is one other relationship which is important in break-even analysis and that is the relationship between contribution and sales value. This is calculated as contribution/sales and is sometimes referred to as the Profit/Volume Ratio, although it can be referred to simply as the contribution/sales ratio. The important thing about this ratio is that it will remain constant at all levels of output. This is because all the constituent parts of the ratio are by definition variable, i.e. sales, variable costs and consequently contribution. It must be remembered, however, that this ratio will only remain constant as long as the basic assumptions mentioned earlier hold true, i.e. a constant selling price per unit and a constant variable cost per unit. The advantage of this ratio is that once calculated you can apply it at any level of output and thus determine the contribution earned from a particular level of sales or the sales necessary for a particular level of contribution and hence profit. MANAGERIAL ACCOUNTING (AH) 35
MULTI-PRODUCT BREAK-EVEN ANALYSIS Multi-Product Break-Even The problem with calculating the break-even point for a business with more than one product is that another variable has been added, i.e. the product mix. Product mix means the relative percentage or share of total sales which each product represents. If each product earns a different contribution per unit then any change in the relative volume of sales of each product will cause difficulties. The way round this is to calculate a weighted average contribution per unit to apply when calculating the break-even point. Example CMA plc produce a range of three products to which the following details relate: Product Basic Special Deluxe Selling Price p.u. 205 250 350 Variable Costs p.u. 130 145 200 Fixed costs for CMA plc total 600,000 Let s take each product in turn and calculate what the break-even point would be if only that product were produced and sold. Basic Contribution per unit = 205 130 = 75 Break-Even Point (units) = 600,000 75 = 8,000 36 MANAGERIAL ACCOUNTING (AH)
MULTI-PRODUCT BREAK-EVEN ANALYSIS Special Contribution per unit = 250 145 = 105 Break-Even Point (units) = 600,000 105 = 5,715 (approx.) Deluxe Contribution per unit = 350 200 = 150 Break-Even Point (units) = 600,000 150 = 4,000 The two extreme outcomes for break-even are 8,000 units if all sales were the basic model and 4,000 units if all sales were deluxe. Therefore any sales mix will be bound to produce a break-even point which lies somewhere between these two levels. Given a sales mix the break-even point can be found using the familiar formula but using a weighted average contribution per unit. Using the figures from the above example let s calculate the break-even point if sales were split evenly between the three products. Weighted Average Contribution per unit = (1/3 75) + (1/3 105) + (1/3 150) = 25 + 35 + 50 = 110 Break-Even Point (units) = 600,000 110 = 5454.5 = 5455 MANAGERIAL ACCOUNTING (AH) 37
MULTI-PRODUCT BREAK-EVEN ANALYSIS We can prove that this is correct by working out the relevant figures. Basic Special Deluxe Sales (units) 1,818 1,818 1,818 Sales ( ) 372,690 454,500 636,300 Variable Costs 236,340 263,610 363,600 Contribution 136,350 190,890 272,700 Total Contribution 599,940 Fixed Costs 600,000 60 (caused by rounding units) Now let s see what happens when the sales mix changes. Suppose the product mix is 3:2:1 for Basic/Special/Deluxe. Total sales are then represented by Basic 3/6 = 1/2 Special 2/6 = 1/3 Deluxe 1/6 Weighted Average Contribution per unit = (1/2 75) + (1/3 105) + (1/6 150) = 37.50 + 35 + 25 = 97.50 Break-Even Point (units) = 600,000 97.50 = 6154 (nearest unit) The answer is greater than the previous answer and that makes sense because we have moved to a situation where we are selling most of the product which has the lowest contribution per unit and we are selling fewest of the one with the highest contribution per unit. 38 MANAGERIAL ACCOUNTING (AH)
MULTI-PRODUCT BREAK-EVEN ANALYSIS Once again we can prove that this is the correct answer by multiplying out the figures. Total Units = 6,154 Split as follows: Basic 3077 (1/2) Special 2051 (1/3) Deluxe 1026 (1/6) Basic Special Deluxe Sales ( ) 630,785 512,750 359,100 Variable Costs 400,010 297,395 205,200 Contribution 230,775 215,355 153,900 Total Contribution 600,030 Fixed Costs 600,000 30 (due to rounding) This approach can then be used to answer the typical range of questions which you associate with basic break-even problems, i.e. calculating the level of sales required to earn a specified profit. For example, using the sales mix of 3:2:1 above calculate the sales in units of each product which would produce a profit of 100,000. Remember in marginal or break-even problems there is no direct connection between units and profit, and therefore we must convert profit into contribution. Contribution = Fixed Costs + Profit = 600,000 + 100,000 = 700,000 Total No. of Units Required = 700,000 97.50 = 7,180 (approx) Units of Basic = 1/2 7,180 = 3,590 Units of Special = 1/3 7,180 = 2,393 Units of Deluxe = 1/6 7,180 = 1,197 MANAGERIAL ACCOUNTING (AH) 39
MULTI-PRODUCT BREAK-EVEN ANALYSIS Let s just prove that this is the correct solution. Basic Special Deluxe Sales ( ) 735,950 598,250 418,950 Variable Costs 466,700 346,985 239,400 Contribution 269,250 251,265 179,550 Total Contribution 700,065 Less: Fixed Costs 600,000 Profit 100,065 (due to rounding) If we now consider the opposite type of problem: How much profit will be made from sales of 9,000 units, also assuming a ratio of 3:2:1 between sales of the three products? Once again we must convert the units into contribution before we can calculate profit. Contribution from 9,000 units = 9,000 97.50 = 877,500 Less: Fixed Costs 600,000 Profit 277,500 Once again we can prove the result: Sales Mix Basic 1/2 9,000 = 4,500 Special 1/3 9,000 = 3,000 Deluxe 1/6 9,000 = 1,500 Basic Special Deluxe Sales ( ) 922,500 750,000 525,000 Variable Costs 585,000 435,000 300,000 Contribution 337,500 315,000 225,000 Total Contribution 877,500 Fixed Costs 600,000 277,500 Here are some questions to try. 40 MANAGERIAL ACCOUNTING (AH)
MULTI-PRODUCT BREAK-EVEN ANALYSIS Question 1 Clear Picture Ltd produce two models of television sets, Brilliant and Super Bright to which the following details relate for the current year. Brilliant Super Bright Selling price per set 250 350 Variable cost per set 125 190 Current sales (units) 5,000 2,500 Fixed costs 600,000 (a) (b) (c) (d) (e) Calculate the profit which Clear Picture would earn from the above situation. Calculate the total number of sets which require to be sold to break even if the above sales mix applies. Prepare a detailed Profit Statement to show the full figures for each product at break-even point. What would the break-even point be if the sales mix changed to three Brilliant sets for every Super Bright set? Explain why the increase/decrease in break-even point was predictable. MANAGERIAL ACCOUNTING (AH) 41
MULTI-PRODUCT BREAK-EVEN ANALYSIS Question 2 MPV plc manufactures and sells three products with the following selling prices and variable costs: Basic Superior Supreme Unit selling price 3.00 3.75 5.00 Unit variable cost 2.10 1.50 3.25 Current sales (units) 500,000 230,000 190,000 Existing fixed costs amount to 1,000,000. (a) (b) Calculate the total number of units MPV plc will require to sell in order to break even if the current sales mix persists. Prepare a Profit Statement showing the relevant figures for the three products to prove your answer to (a). 42 MANAGERIAL ACCOUNTING (AH)
MULTI-PRODUCT BREAK-EVEN ANALYSIS Question 3 Easylearn Ltd provide expert tutoring on a range of subjects. Next year s budget shows the following expected figures: Accounting Maths English French Expected hours of work 2,500 3,000 3,500 1,000 Charge per hour 40 50 45 35 Variable cost per hour 10 15 9 10 Fixed costs for the year are expected to be 198,600. (a) (b) (c) (d) Calculate the total number of hours Easylearn Ltd will have to work to break even, assuming the above mix of tutoring hours. Calculate the contribution from each subject and in total at breakeven point. Using the same mix as above prepare a Profit Statement for Easylearn plc to earn a profit of 100,000. The actual hours provided during the year turned out to be: Accounting 1,500 Maths 1,000 English 4,500 French 3,000 Calculate the break-even number of hours. MANAGERIAL ACCOUNTING (AH) 43
MULTI-PRODUCT BREAK-EVEN ANALYSIS Solutions Question 1 (a) Brilliant Super Bright Contribution p.u. 125 160 Total Contribution 5,000 125 2,500 160 = 625,000 = 400,000 Total Contribution for company 1,025,000 less: Fixed Costs 600,000 Profit 425,000 (b) Sales (units) Brilliant 5,000 67% Super Bright 2,500 33% 7,500 100% Weighted Average Contribution p.u. = ( 125 67%) + ( 160 33%) = 83.75 + 52.80 = 136.55 B/E Point (units) = 600,000 136.55 = 4,394 (nearest unit) (c) Brilliant Super Bright Sales (units) 4394 67% 4394 33% 2944 1450 Profit Statement for Year Brilliant Super Bright Sales 736,000 507,500 Variable Costs 368,000 275,500 Contribution 368,000 232,000 Total Contribution 600,000 less: Fixed Costs 600,000 44 MANAGERIAL ACCOUNTING (AH)
MULTI-PRODUCT BREAK-EVEN ANALYSIS (d) Weighted Average Contribution p.u. = ( 125 75%) + ( 160 25%) = 93.75 + 40 = 133.75 B/E point (units) = 600,000 133.75 = 4,486 (e) Since they were selling more of the product with the lower contribution per unit, it was inevitable that the break-even point would increase. MANAGERIAL ACCOUNTING (AH) 45
MULTI-PRODUCT BREAK-EVEN ANALYSIS Question 2 (a) Sales (units) Basic 500,000 0.5435 or 54.35% Superior 230,000 0.25 or 25% Supreme 190,000 0.2065 or 20.65% 920,000 1.0 100% Contribution per unit Basic = 0.90 Superior = 2.25 Supreme = 1.75 Weighted Average Contribution p.u. = ( 0.90 0.5435) + ( 2.25 0.25) + ( 1.75 0.2065) = 48.915p + 56.25p + 36.138p = 141.303p B/E point (units) = 1,000,000 1.413 (b) Total Sales (units) = 707,714 = 707,714 Basic = 707,714 0.5435 = 384,643 Superior = 707,714 0.25 = 176,928 Supreme = 707,714 0.2065 = 146,143 MPV Profit Statement Basic Superior Supreme Total Sales 1,153,929 663,480 730,715 2,548,124 Variable Costs 807,750 265,392 474,965 1,548,107 Contribution 346,179 398,088 255,750 1,000,017 Fixed Costs 1,000,000 17 46 MANAGERIAL ACCOUNTING (AH)
MULTI-PRODUCT BREAK-EVEN ANALYSIS Question 3 (a) Tutoring hours: Accounting 2,500 25% Maths 3,000 30% English 3,500 35% French 1,000 10% 10,000 100% Contribution per hour Accounting 30 Maths 35 English 36 French 25 Weighted Average Contribution per hour = ( 30 25%) + ( 35 30%) + ( 36 35%) + ( 25 10%) = 7.50 + 10.50 + 12.60 + 2.50 = 33.10 B/E Point (hours) = 198,600 33.10 = 6,000 (b) Accounting Maths English French Total Hours of 1,500 1,800 2,100 600 6,000 Tutoring Contribution 1,500 1,800 2,100 600 30 35 36 25 45,000 63,000 75,600 15,000 198,600 MANAGERIAL ACCOUNTING (AH) 47
MULTI-PRODUCT BREAK-EVEN ANALYSIS (c) Contribution required = 198,600 + 100,000 = 298,600 Number of hours required = 298,600 33.10 = 9,021 (nearest hour) Hours per subject: Accounting 25% 2,255 Maths 30% 2,706 English 35% 3,158 French 10% 902 Profit Statement for Easylearn Ltd Accounting Maths English French Total Sales 90,200 135,300 142,110 31,570 399,180 Variable Costs 22,550 40,590 28,422 9,020 100,582 Contribution 67,650 94,710 113,688 22,550 298,598 less: Fixed Costs 198,600 Profit 99,998 (d) Accounting 1,500 15% Maths 1,000 10% English 4,500 45% French 3,000 30% 10,000 100% Weighted Average Contribution per unit = (15% 30) + (10% 35) + (45% 36) + (30% 25) = 4.50 + 3.50 + 16.20 + 7.50 = 31.70 B/E Point (hours) = 198,600 31.70 = 6,265 48 MANAGERIAL ACCOUNTING (AH)
SECTION 3 CONTRACT COSTING STATEMENTS Contract Costing Statements A long-term contract is defined as: A contract entered into for the design, manufacture or construction of a single substantial asset or the provision of a service where the time taken to complete the contract is such that the contract activity falls into different accounting periods. So a contract is really an example of job costing with the following important features: it usually takes a long time to complete it is usually completed at a particular site which is not the contractor s workplace. Therefore contracts are common in most types of building and construction work, civil engineering, shipbuilding, etc. These contracts pose a particular problem for the accountant, i.e. when should any profit on the contract be recognised in the accounts? The problem arises because there is a conflict between two fundamental accounting concepts or principles, i.e. matching and prudence. The matching or accruals concept states that income and expenditure should be matched against one another and placed in the accounting period to which they relate. Clearly in the case of long-term contracts the costs and indeed the revenues will overlap more than one accounting period. Because a contractor cannot wait until the end of a contract before he receives any income from it, the work is valued at regular intervals by architects who certify the value of the work at selling price. When this is compared with the costs incurred to date it may well indicate a profit on the contract. However, the prudence concept states that profits should not be anticipated and therefore recording profit on an incomplete contract could be construed as breaching that concept. MANAGERIAL ACCOUNTING (AH) 49
CONTRACT COSTING STATEMENTS As with many problems where basic principles conflict, the resolution of the problem is something of a compromise. It would clearly be unacceptable only to recognise contract profit at the end of the contract. This would mean that in any accounting period the profits would simply relate to those contracts which had finished during the period, irrespective of the length of period of the contracts. It seems that recognition of profit on a contract would be acceptable as long as the concept of prudence is not ignored. Statement of Standard Accounting Practice Number 9 (SSAP 9) gives guidance on this matter. It states that profits should only be recognised on a contract when its outcome can be assessed with reasonable certainty. The profit to be included should be calculated prudently and should reflect the amount of work completed at the accounting date. On the other hand if losses are anticipated they must be recognised in full. The standard does not give unequivocal guidance on a formula to be applied in recognising profit on a contract, and several methods have been developed which meet the underlying principles outlined above. One approach is to determine the expected profit at the conclusion of the contract and recognise a proportion of this figure based on the percentage completion of the contract at the appropriate date. 50 MANAGERIAL ACCOUNTING (AH)
CONTRACT COSTING STATEMENTS Consider the following example: At 31 December Year 4 the figures relating to an incomplete contract are as follows: Costs to date Estimated costs to complete Value of certified work Contract price 3m 1m 4m 5m We can calculate the expected outcome of the contract as follows: Cost of work completed 3m Add: estimated costs to complete 1m estimated total costs 4m contract price 5m estimated profit 1m Profit Recognised = = Estimated Profit Value of Certified Work Contract Price 1m 4m 5m = 800,000 However, if a contract is not close to completion the forecast of expected profits may be deemed to be too unreliable to adopt as a basis for profit recognition. In these circumstances the fraction may be based on the notional profit at that point in the life of the contract rather than on the estimated profit at the end of the contract, i.e. Profit recognised = Work Certified Notional Contract Price Profit What is important is that whichever formula is used takes into account the degree of completion of the contract, which both of the formulae above do. MANAGERIAL ACCOUNTING (AH) 51
CONTRACT COSTING STATEMENTS Preparing Contract Accounts Example A builder is currently working on two major contracts, both of which are incomplete at the end of his financial year on 31st March Year 7. The details of the contracts are as follows: Contract A Contract B 000s 000s Opening Balances at 1st April Year 6 Completed Work 1,620 Materials on Site 80 Plant & Machinery (written down value) 300 Wages Accrued 20 Costs Incurred During Year to 31st March Year 7 Materials Delivered to Site 340 880 Wages Paid 180 400 Salaries 60 160 Value of Plant Delivered 800 140 Head Office/Establishment Charges Apportioned 40 80 Closing Balances at 31st March Year 7 Materials on Site 80 Value of Plant on Site 600 80 Wages Accrued 20 40 Other Details Value of Work Certified at year end 800 3,200 Contract Price 1,200 5,800 Profit is recognised using the following formula: Work Certified Contract Price Notional Profit Prepare accounts for each of the contracts showing clearly the calculations of any profit to be taken for the period. 52 MANAGERIAL ACCOUNTING (AH)
CONTRACT COSTING STATEMENTS Solution Contract A a/c Materials 340 Balances c/d material 80 Wages Paid 180 plant 600 add: accrued 20 200 Cost of contract to date 758 Salaries 60 Plant & Machinery 800 Head Office costs 38 1,438 1,438 Cost of Contract 758 Work Certified 800 Profit & Loss a/c (Profit Taken) 28 Profit not Taken 12 800 800 Balances b/d: material 80 Balances b/d wages 20 plant 600 Working Notional Profit 800 42 Profit Recognised = 1,200 = 28 = Value of Work Certified less cost of contract to date = 800 758 = 42 The first step is to charge or debit the Contract a/c with all the costs incurred during the year to date, including any accruals, e.g. in this case wages accrued. However, not all of these costs have been used up in the course of the year so any remaining unused, i.e. material and plant and machinery are carried down as balances to start the next period. This allows the cost of the contract to date to be calculated as the sum of the debit entries less the credit balances being carried forward. The working for the notional profit and the part of it which is going to be recognised can now be done, using whichever formula the question suggests. The profit taken is then debited to the account as it will go to the credit of the Profit & Loss a/c. MANAGERIAL ACCOUNTING (AH) 53
CONTRACT COSTING STATEMENTS Contract B a/c Balances b/d Balance b/d: Wages 20 Completed Work 1,620 Balances c/d: Plant 80 Material 80 Cost of Contract to date 3,600 Plant & Machinery 300 Materials Delivered 880 Wages Paid 400 add accrued 40 440 Salaries 160 Plant & Machinery 140 Head Office Costs 80 3,700 3,700 Cost of Contract 3,600 Work Certified 3,200 Profit & Loss (Loss written off) 400 3,600 3,600 Balances b/d: plant 80 Balances b/d wages 40 There are a number of differences to be accounted for with Contract B. Firstly, this is a contract which was already under way at the start of the year and therefore has opening balances which must be entered in the account to start with. Thereafter the procedure is the same, but when we attempt to calculate the notional profit we discover that in fact the contract is showing a loss at this point in time. When that happens we have to write off the whole of the loss (there is no division into part recognised and part not recognised) to comply with the prudence concept. The above question illustrated a number of basic principles of accounting for long-term contracts: how to deal with opening balances how to calculate notional profit how to apply formulae for recognising profit how to treat anticipated losses. The following questions give you the opportunity to test your understanding of these principles. Some of the questions are based on previous Higher Accounting or Higher Accounting and Finance paper questions. 54 MANAGERIAL ACCOUNTING (AH)
CONTRACT COSTING STATEMENTS Question 1 (based on Higher Paper II 1997 Q7) JBC plc, a construction company, undertook a 2-year contract with Factory Outlets Ltd for a fixed price of 1m. Work began in September of Year 5 and on 1 January Year 6 the following information was available. Direct materials on site 10,000 Plant at cost on site 90,000 At 31 December Year 6 the following information was available. Direct materials sent to site 350,000 Materials requisitioned from stores 5,000 Materials returned to stores 2,000 Direct wages paid 337,000 Direct expenses 20,000 Sub-contracting costs 28,000 Architect s fees 2,000 Insurance 1,000 Hire of special equipment 6,000 Plant maintenance 2,000 Value of plant on site at 31 Dec Year 6 78,000 Value of work certified by architect 850,000 Cost of work not yet certified at 31 Dec Year 6 15,000 Direct wages due at 31 Dec Year 6 3,000 Direct materials on site at 31 Dec Year 6 3,000 Overheads are charged at 10% of Direct Wages cost. JBC plc recognises profit using the formula Notional Profit Work Certified Contract Price Prepare the Contract Account at 31 December Year 6 showing clearly the profit recognised. MANAGERIAL ACCOUNTING (AH) 55
CONTRACT COSTING STATEMENTS Question 2 (based on Higher 1993 Paper II Q2) Appin Builders plc started work on a 3-year contract on 1 April Year 2 at a contract price of 5m. On 31 March Year 3 the following information was available. 000s Plant sent to site 75 Materials sent to site 375 Materials delivered from store 50 Sub-contracting costs 48 Direct wages 250 Direct expenses 85 Hire of scaffolding 20 Work certified by architect 1,000 Cost of work not yet certified 150 Value of plant at 31 March Year 3 50 Material unused on site at 31 March Year 3 23 Accrued wages 10 Overheads are recognised at 10% of Direct Material costs (including subcontract costs). Appin Builders plc recognise profit using the formula Notional Profit Work Certified Contract Price Prepare the Contract Account for year ended 31 March Year 3. 56 MANAGERIAL ACCOUNTING (AH)