Performance Management · May 2021

a. Concept of linear programming and usefulness Linear programming is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) subject to a number of limiting factors (constraints). A linear programming problem involves maximising or minimising a linear function (the objective function) subject to linear constraints. Both the constraints and the “best outcome” are represented as linear relationships. What constitutes the best outcome depends on the objective. The equation constructed to represent the best outcome is known as the objective function. Uses of linear programming (LP)

• Budgeting: In preparing budget, one of the first steps is the identification of the key (limiting) factor. When there is more than one limiting factor, LP can be used to identify the most profitable use of resources.

• Capital budgeting: When we have multi-period capital rationing, LP can be used to optimally allocate the available funds among the competing projects.

• Transfer pricing: In a divisionalised organisation, LP can be used to compute optimal transfer price between divisions when the supplying division does not have sufficient capacity to met all the demands placed upon it.

• Calculating relevant costs: The relevant cost of a scarce resource is calculated as acquisition cost of the resource plus opportunity cost. When more than one scarce resource exist, LP can be used to establish the opportunity cost (Shadow price).

• Maximum payment for the supply of additional scarce resources: If labour is an effective limiting factor, for example, the maximum overtime premium to pay per additional hour is the shadow price which can be determined using LP.

• Control: LP is also useful in the analysis of variances. For example, adverse material usage variances can be indication of material wastage. Such variances 68 should be valued at the standard cost of the material plus the opportunity cost of the loss of one scarce unit of material. LP can be used to determine the opportunity cost.

b. Computation of unit selling price and associated unit profit of the two products. Biggis N Smallis N Material 250 150 Labour costs: Machine time 60 30 Processing 40 50 Overhead cost 30 40 Total costs 380 270 Profit per unit 76 54 Selling price per unit 456 324

c. ADVICE ON THE OUTPUT TO BE PRODUCED TO MAXIMISE TOTAL PROFIT STEP 1 –DETERMINATION OF LIMITING FACTOR Materials needed to produce 200,000 units of Biggis & 100,000 units of Smallis BIGGIS 5kg x 200,000 1,000,000 SMALLIS 3kg x 100,000 300,000 Total Required 1,300,000 Available Material 1,800,000 Conclusion: Materials are not limiting factor since available resources exceed resources needed to meet production levels. Machine time needed to produce 200,000 units of Biggis and 100,000 units of Smallis. 69 BIGGIS 4hrs x 200,000 800,000 SMALLIS 2hrs x 100,000 200,000 Total Required 1,000,000 Available Hours 800,000 Conclusion: Machine time is a limiting factor since hours available are less than the hours needed to meet production levels. Other processing time needed to produce 200,00 units of Biggs and 100,000 units of smallis: BIGGIS 4hrs x 200,000 800,000 SMALLIS 5hrs x 100,000 500,000 Total Required 1,300,000 0 Available Hours 1,400,000 Conclusion: Other processing time is not a limiting factor since hours available exceeds hours needed to meet production levels. STEP 2 – DETERMINATION OF PRIORITY OF PRODUCTION PLAN Biggis Smallis N N Selling price 456 324 Total variable costs (350) (230) Contribution per unit 106 94 Machine time per unit 4 2 Contribution per machine time 26.5 47 Ranking 2nd 1st PRODUCT UNITS HOURS USED HOURS LEFT SMALLIS 100,000 200,000 600,000 BIGGIS 150,000 600,000 - 70 Comment Hence, the optimal production plan for NTAMS Manufacturing Company Ltd is to produce 100,000 units of Smallis and 150,000 units of Biggis.

(d) SHADOW PRICE MEANING The shadow cost of a binding constraint is the amount by which the objective function decreases (or increases) as a result of availability of one unit less or more of the scarce resource. The solutions to the dual problem of the primal problem give the shadow costs (prices), hence the alternative term dual costs (prices). USEFULNESS OF SHADOW PRICES

• Can be used to determine the relevant cost of a scarce resource

• Useful in setting transfer price

• Useful in setting transfer price

• It assists in determining opportunity cost

• Can be used in allocating funds to projects when there is multi-period capital rationing. The major limitation of shadow price is that it is valid for a limited range of output. For example, if labour hour is the limiting factor, the shadow price will tend to zero as more labour hours are supplied. 71 CALCULATION OF SHADOW PRICE OF THE CONSTRAINTS Shadow price only exists for binding resources – hence shadow price will only exist for machine time. If one (1) additional machine time is available, total machine time will be 800,001 Total units of Biggis to be produced wil l be 150,000.25 units (600,001/4) New Total contribution will be (100,000 x 94) + (150,000.25 x 106) = 25,300,026.50 Previous total contribution was (100,000 x 94) + (150,000 x 106) = 25,300,000 Increase in contribution = 25,300,026.50 – 25,300,000 = 26.50 Alternative solution Candidates may reduce the available machine time by 1 hour. If one machine hour is reduced Total units of Biggis =149,999.75 units N New contribution (100,000 x 94 + 149,999.75 x 106) = 25, 299,973.5 Old contribution 25,300,000 Shadow price (reduction in contribution) (26.50) Shadow price = N26.50k

ei) NPV (Discount Factor 15%) = 2.283 Total contribution = 25,300,000 (2.283) = 57,759,900 Total Outflow = 45,000,000 = 45,000.000 NPV = N12,759,000 Yes, the project’s NPV is positive and therefore worthwhile.

ii) If a discount factor = 35% Total contribution = 25.300,000 x 1.696 = N42,908,800 Total Outflow = N 45,000,000 NPV at 35% = (N2,091,200) IRR = a + ( BA

- A) (b – a) 72 a = Positive NPV discount rate A = Positive NPV b = Negative NPV discount rate B = Negative NPV = 15% + ( 200,091,2000,759,12 000,759,12 \+ ) (35% – 15%) = 15% + ( 000,759,12 100,851,14 ) (20%) = 15% + 17.18% = 32.18%

Examiner’s report The question tests students’ understanding of resource allocation using contribution per limiting factor. It was attempted by the majority of the candidates being a compulsory question. The performance was below average. The major pitfall was the lack of understanding in the subject area and the conditions that must be satisfied before the linear programming is applied. Candidates are advised to read the ICAN study text when preparing for future examination of the Institute.

Marking guide Mark Total a. Definition of linear programming 1 Explanation of linear programming 1 Usefulness (3 points at 1 mark per point) 3 5 b. Selling Price (20 ticks at ¼ mark per tick) 5 c. Advice on the optimal output 10 d. Shadow Price/usefulness/limitation 5 Shadow price computations 7 12 e. Investment analysis - NPV 4 Calculation of IRR 4 8 40 73

SECTION B

(a) Materials supply is a limiting factor for forecast 1, but not for forecast 2. Forecast 1 Product A Product B Product C ₦ ₦ ₦ Sales price per unit 10.00 20.00 30.00 Variable cost per unit 6.50 11.00 18.10 Contribution 3.50 9.00 11.90 Contribution per kg of material 0.88 1.29 0.85 Ranking 2nd 1st 3rd Optimal production plan for forecast 1 Units Contribution kg of material ₦ Product B 800 5,600 7,200 Product A 500 2,000 1,750 Product C 1,030 14,420 12,257 Total contribution 22,020 21,207 Optimal Production Plan for forecast 2 Product A Product B Product C Total ₦per unit ₦ per unit ₦ per unit Sales price 15.00 25.00 40.00 Variable-cost 6.50 11.00 18.10 Contribution 8.50 14.00 21.90 Sales volume (units) 350 700 1,000 Total contribution ₦2,975 ₦9,800 ₦21,900 ₦34,675 74 Recommendation: Forecast 2 should be adopted for the budget period. It produces a contribution of ₦34,675 which is ₦13,468 higher than the contribution for forecast 1.

(b) REPORT To: The Managing Director From: The Finance Manager Subject: Budget Preparation Process Date: 5 May 2021

1. INTRODUCTION In line with the request of the management of our company, PQR Plc (“PQR” or “the Company”) kindly see below the detailed discussion on some of the key issues in the budget preparation process.

2. PRINCIPAL BUDGET FACTOR The principal budget factor or limiting factor or key budget factor is a factor, which at any time is an overriding planning limitation on the activities of the organisation. Examples of principal budget factors include: staffing limitations, scarcity of materials and other logistics, limited financial resources, low sales demand, limited storage facilities, etc.

3. BUDGET MANUAL The budget manual sets out the budget guidelines which are budgeting instructions, that the Budget Committee gives to guide departmental heads involved in the preparation of the budget so that they follow a particular goal, objective, technique, trend or method of estimating the income and expenditure variables.

4. ROLE OF THE BUDGET COMMITTEE The Budget Committee is made up of members of senior management that oversees all budgetary matters. A typical budget committee includes the chief executive officer, heads of strategic business units and the chief finance officer. The committee sets or approves the overall budget goals for the organisation, and its major business units, 75 directs and coordinates budget preparation, approves the final budget, monitors operations as the year unfolds, and reviews the operating results at the end of the period. The budget committee also approves major revisions of the budget during the period. This committee usually consists of sectional or departmental managers and is usually serviced by the Budget Officer who normally is the finance officer. Apart from the above, the functions of the committee may include the following: ➢ Determine budget policy guidelines and selecting budget policies compatible with organisational goals and objectives; ➢ Establishing the budget timetable; ➢ Review budget estimates submitted by sectional heads; ➢ Facilitate the co-ordination of the budgets; ➢ Suggest amendments to budgets and revising budget estimates when necessary; ➢ Approve budgets after amendments; ➢ Facilitate the generation of budgetary control reports; ➢ Analysing budget reports and recommending changes; ➢ Examine variances, recommend investigation of variances and recommend solutions to remedy off-standard performance; and ➢ Advise top management on all matters concerning the budget.

Examiner’s report The question examines candidates on optimal mix of production and some concepts associated with the budgeting process. Majority of the candidates attempted the question, the performance was average. The main pitfall is inability of the students to identify the quantity of the limiting factor. Candidates are encouraged to read the Institute’s study text when preparing for the examination of the Institute.

Marking guide Mark Total a. Forecast to be Adopted/Computation 11 b. i) Principal budget factor 3 ii) Budget manual 3 iii) Role of budget committee 3 9 20 76

a) Year Quarter Trend point Sales trend (cartons) x y = a + bx 2019 3 13 10,472.33 + (82.67 × 13) = 11,547 2019 4 14 10,472.33 + (82.67 × 14) = 11,630 2020 1 15 10,472.33 + (82.67 × 15) = 11,712 2020 2 16 10,472.33 + (82.67 × 16) = 11,795 The seasonally adjusted forecasts are therefore as follows: Year Quarter Seasonally adjusted forecast sales (cartons) 2019 3 11,547 × 1.06 = 12,240 2019 4 11,630 × 0.91 = 10,583 2020 1 11,712 × 1.05 = 12,298 2020 2 11,795 × 0.98 = 11,559

b) We need to calculate the regression line of the last five periods' observations. This line is y = a + bx where b = n xy− x y n x2− x 2 and a = yn − 𝑏 x n So b = 5 × 4,442.15 − (40 × 555.1) 5 × 330 − 40 × 40 = 6.75 50 = 0.135 a = 555.1 5 − 0.135 × 40 5 = 111.02 − 1.08 = 109.94 We need to multiply the a and b values back up by 100 to compensate for the fact that the y values were scaled down by 100 before the sigma calculations were carried out. So the regression line is y = 10,994 + 13.5x 77 Year Quarter Trend point Sales trend (cartons) x y = a + bx 2019 3 13 10,994 + (13.5 × 13) = 11,169.5 2019 4 14 10,994 + (13.5 × 14) = 11,183.0 2020 1 15 10,994 +(13.5 × 15) = 11,196.5 2020 2 16 10,994 + (13.5 × 16) = 11,210.0 The seasonally adjusted forecasts are therefore as follows: Year Quarter Seasonally adjusted forecast sales (cartons) 2019 3 11,169.5 × 1.06 = 11,840 2019 4 11,183.0 × 0.91 = 10,177 2020 1 11,196.5 × 1.05 = 11,756 2020 2 11,210.0 × 0.98 = 10,986

c) One common method of deciding on which forecasting basis produces the better result is to compare the coefficients of determination. With ten periods' observations we are told that r2 = 0.535. With five periods' observations we have to calculate the coefficient of determination from the equation given in the tables provided. r2 = n xy − x y 2 n x2 − x 2 n 𝑦2 − ( 𝑦)2 = 5 × 4,442.15 − 40 × 555.1 2 5 × 330 − 40 × 40 5 × 61,627.4 − (555.1 × 555.1) = 6.752 50 × 0.99 = 0.92 Prima facie the forecasting method, using five periods' observations is much better than the other using ten periods, since the coefficient of determination of the former is 0.92 compared with 0.535 for the latter. We can explain 92% of the variations in sales by the passage of time using the former method, but can explain only 53.5% of the variations in sales using the latter method. 78

Examiner’s report The question tests candidates’ knowledge of regression analysis in forecasting. Few candidates attempted the question, the performance was average. The major pitfall of the candidates was inability to apply seasonal variation of the trend to the forecast. Candidates are encouraged to read the Institute’s study text when preparing for future examination of the Institute.

Marking guide Mark Total a. Forecast of 4 Quarters using 10-period observation 8 b. Forecast of 4 Quarters using 5-period observation 8 c. Commenting of better of forecast:

- Coefficient of determination formulae 1 - Substituting of figures into the formulae 1 - Comparation of two forecast figures 1 - Decision 1 4 20

ADRAC COMMUNITY SCHOOL

a. REDRAFTING THE BUDGET FOR THE YEAR ENDED 30 JUNE 2020 BUDGETED INCOME N’000 Pupils Rate/Pupil N Pupils registered at the beginning of school year 720 21,000 15, 120 Average Expected Number of New Joiners 51 18,000 918 16,038 79 BUDGETED EXPENDITURE Actual cost for the year Ended 30-June-2019 Budget Cost for the year Ended 30-June-2020 N’000 N’000 Repairs and Maintenance Note 1 600 3% 618 Salary Note 2 11,880 2% 12,019 Improvement of canteen Note 3 1,300 1,255 13,892 Budgeted Surplus/(Deficit) 2,146

Note 1: Repairs & maintenance 600,000 (1.03) = 618,000

Note 2: Salaries (12,400,000 – 520,000) (1 + 0.02 x 7/12) = 12,019,000

Note 3: Improvement of canteen Estimated cost Pro Expected cost 1,450,000 0.7 1,015,000 800,000 0.3 240,000 1,255,000

(b) Advantages of Incremental Budgeting – Incremental budgeting is very easy to prepare. This makes it possible for a person without any accounting training to build a budget. – Incremental budgeting is also very quick to comprehend compared to other budgeting methods. – The information required to complete it is also usually readily available Disadvantages of Incremental Budgeting – There is no incentive to eliminate wasteful or unnecessary spending from the budget; – It encourages more waste (or budget slack) because managers will try to spend up to their budget limit so that budget for next financial year will not reduce. – It increases allocated cost irrespective of performance. 80 Inflationary Adjustment

(c) STEPS IN PREPARING ZERO-BASED BUDGET Zero-based Budget is prepared as follows:

(i) A decision must be taken to provide for a minimum level of operation. This means deciding for each basic operation whether or not to perform the operation. (ii) Having decided on a basic level of operations, a basic expenditure budget can be prepared. (iii) The next step is to consider each incremental decision package and decide whether additional operation is justified. An incremental decision package is justified if the expected benefits exceed the estimated costs.

(d) EXTENT TO WHICH ZERO-BASED BUDGET CAN BE USED BY ADRAC TO IMPROVE BUDGETING PROCESS

i. It can be used to help lower costs by avoiding blanket increases or decreases to a prior period's budget. ii. It can be used to help in efficient allocation of resources (department-wise) as it does not look at the historical numbers but looks at the actual numbers iii. It leads to the identification of opportunities and more cost- effective ways of doing things by removing all the unproductive or redundant activities. iv. Since every line item is to be justified, zero-based budget overcomes the weakness of incremental budgeting of budget inflation. v. It also improves coordination and communication within the department and motivates employees by involving them in decision- making.

Examiner’s report The question tests candidates’ understanding of Incremental Budget and Zero Based Budget. Majority of the candidates attempted the question. Candidates performance was above average. The candidates are advised to read the Institute’s study text when preparing for the Institute’s examination in future. 81

Marking guide Mark Total a. Redrafted budget 6 b. i) Advantages (Any 2 at 1 mark) 2

ii) Disadvantages (Any 2 at 1 mark) 2 4 c. 3 steps at 2 marks 6 d. Extent of use of ZBB by Adrac (Any 2 points at 2 marks each) 4 20

a) Unit contribution ₦13,000 – (8,000 + 500) = ₦4,500 Unit loss when surplus sold ₦8,500 – 5,000 = ₦3,500 Unit penalty when demand not satisfied ₦2,000 per outfit not sold Probability of sales levels Sales Probability 1,100 0.3 1,200 0.4 1,300 0.2 1,400 0.1 Contribution calculations (1,100 units purchased) Demand contribution ₦ 1,100 1,100 × ₦4,500 = 4,950,000 1,200 1,100 × ₦4,500 – 100 × ₦2,000 = 4,750,000 1,300 1,100 × ₦4,500 – 200 × ₦2,000 = 4,550,000 1,400 1,100 × ₦4,500 – 300 × ₦2,000 = 4,350,000 (1,200 units purchased) Demand Contribution ₦ 1,100 1,100 × ₦4,500 – 100 × ₦3,500 = 4,600,000 1,200 1,200 × ₦4,500 = 5,400,000 1,300 1,200 × ₦4,500 – 100 × ₦2,000 = 5,200,000 1,400 1,200 × ₦4,500 – 200 × ₦2,000 = 5,000,000 82 (1,300 units purchased) Demand Contribution ₦ 1,100 1,100 × ₦4,500 – 200 × ₦3,500 = 4,250,000 1,200 1,200 × ₦4,500 – 100 × ₦3,500 = 5,050,000 1,300 1,300 × ₦4,500 = 5,850,000 1,400 1,300 × ₦4,500 – 100 × ₦2,000 = 5,650,000 (1,400 units purchased) Demand Contribution ₦ 1,100 1,100 × ₦4,500 – 300 × ₦3,500 = 3,900,000 1,200 1,200 × ₦4,500 – 200 × ₦3,500 = 4,700,000 1,300 1,300 × ₦4,500 – 100 × ₦3,500 = 5,500,000 1,400 1,400 × ₦4,500 = 6,300,000 Summary of outcomes Probability Order quantity Demand 1,100 1,200 1,300 1,400 0.3 0.4 0.2 0.1 Application of probability on the Pay off Matrix State of Nature (Sales) Decision 0.3 0.4 0.2 0.1 Alternatives 1,100 1,200 1,300 1,400 Max 1100 1,485,000 1,900,000 910,000 435,000 1,900,000 1200 1,380,000 2,160,000 1,040,000 500,000 2,160,000 1300 1,275,000 2,020,000 1,170,000 565,000 2,020,000 1400 1,170,000 1,880,000 1,100,000 630,000 1,880,000 :. On the basis of the expected contribution the number of outfits to order is 1,200 units.

Note: The order/receipt costs of ₦80,000 are constant throughout and therefore have been ignored. Expected contribution ₦000 1,100 4,950,000 4,750,000 4,550,000 4,350,000 4,730 1,200 4,600,000 5,400,000 5,200,000 5,000,000 5,080 1,300 4,250,000 5,050,000 5,850,000 5,650,000 5,030 1,400 3,900,000 4,700,000 5,500,000 6,300,000 4,780 83

b) The basic EOQ model assumes a known demand per period e.g., per year and the aim is then to find how often, and therefore how much, to order at a time so as to minimise total costs, each order arriving when the stock level is zero so that there are no ’lost sales’ and no surplus stock. (It has to be said that the basic EOQ model is rarely, if ever applicable in this simple form in a real-life case, although refinements such as variable demand can be built into the model). By contrast, in the model calculated, demand is not known with certainty but is assumed to conform to the probability distribution given. Since the whole of the season’s stock has to be ordered in a single batch at the start of the season, both overstocking and under stocking are possible, with resultant loss of profit contribution.

Examiner’s report The question tests the candidates’ understanding of decision making under uncertainty. Few students attempted the question and performance was below average. The major pitfall was lack of understanding in identifying possible scenarios for decision making. Candidates are advised to study the Institute’s text for future Institute’s study examination.

Marking guide Mark Total a. i) Number of outfits to maximise profits (32 ticks at ½ mark) 16 ii) Decision 1 17 b. Compare models 1½ Contrast models 1½ 3 20

CHUKWUKAH NIGERIA LIMITED

(a) Full budgeted production cost per unit using absorption costing Product Jel Jet Jal Total Budgeted annual production (units) 25,000 20,000 27,600 Labour hours per unit 2·5 3 2 Total labour hours 62,500 60,000 55,200 177,700 Overhead absorption rate = N6,887,000/177,700 = N38·76 per hour. 84 Product Jel Jet Jal N per unit N per unit N per unit Direct materials 250.00 280.00 220.00 Direct labour 300.00 360.00 240.00 Overhead (N38·76 x 2·5/3/2) 96.90 116.28 77.52 Full cost per unit 646.90 756.28 537.52

(b) Full budgeted production cost per unit using activity based costing Product Jel Jet Jal Total Budgeted annual production (units) 25,000 20,000 27,600 Batch size 500 800 400 Number of batches (i.e. set ups) 50 25 69 144 Number of purchase orders per batch 4 5 4 Total number of orders 200 125 276 601 Machine hours per unit 1·5 1·25 1·4 Total machine hours 37,500 25,000 38,640 101,140 Cost driver rates: Cost per machine set up N1,400,000/144 = N9,722.22 Cost per order N1,580,000/601 = N2,628.95 Machine running cost = ₦21,000,000/101140 = ₦20.76 General facility cost = 1,807,000/101140 = ₦17.87 Allocation of overheads to each product: Product Jel Jet Jal Total N N N N Machine set up costs 486,111 243,055 670,833 1,400,000 Material ordering costs 525,790 328,619 725,591 1,580,000 Machine running cost 778,624 519,082 802,294 2,100,000 General facility cost 669,987 446,658 690,355 1,807,000 Total 2,460,512 1,537,414 2,889,073 6,887,000 85 Quantity Produced 25,000 20,000 27,600 Overhead cost per unit N98.42 N76.87 N104.68 Allocation of overheads to each product Total cost per unit: N per unit N per unit N per unit Direct materials 250.00 280.00 220.00 Direct labour 300.00 360.00 240.00 Overhead 98.42 76.87 104.68 ABC cost per unit 648.42 716.87 564.68

c. The company prices product on the basis of cost plus pricing model. The application of ABC model will impact the selling price and sales volume of the products as follows: Jel: The demand is elastic. As a result of ABC model, cost will increase from N646.90 to N648.42 meaning increase in selling price and reduction in sales volume Jet: The demand is elastic. As a result pf ABC method, cost will decrease from N756.28 to N716.87 meaning that there will be a decrease in selling price and increase in sales volume. JAL: The demand is inelastic meaning change in price will not affect the quantity demanded. Hence, even though the cost increased from N537.52 to N564.68, selling price will increase but will not affect the sales volume.

Examiner’s report The question tests the candidates’ understanding of overhead apportionment using Traditional and Activity Based Costing Method. Majority attempted the question and the performance was average. The major pitfall was the determination of the number of batches involved. Candidates are encouraged to make use of the Institute’s text for future Institute’s examination. 86

Marking guide Mark Total a. Budgeted full cost per unit (12 ticks at ½ mark each tick) 6 b. Budgeted ABC full production cost per unit Cost driver rate (4 ticks at ½ mark each) 2 Production cost per unit (12 ticks at ½ mark each) 6 8 c. Impact of ABC on selling price/sales volume 6 20 87 THE INSTITUTE OF CHARTERED ACCOUNTANTS OF NIGERIA