Revenues, costs and the decision process

Transcription

1 CHAPTER 10 Revenues, costs and the decision process Teaching tips and points to stress Information and the decision process The relevance concept is the underlying theme of Chapter 10. Students find this chapter difficult because of the variety of different types of decisions that are based on relevant costs and revenues, and they have trouble applying the relevance concept to new situations. Try to assign a variety of homework problems with this chapter, and emphasise the importance of independently solving problems. Emphasise to students that there are two primary keys to analysing relevant cost/revenue decisions. The first key is to distinguish between relevant and irrelevant costs and revenues. The second key is to use a CM approach. Distinguishing between VC and FC spurs analysts to consider whether each variable and fixed cost is affected by the alternatives under consideration. The CM approach is most useful for short-run decisions because in the long run, fewer costs are fixed. (In the very long run, nothing is fixed.) Relevant costs meet two criteria: (1) future costs that (2) differ between alternatives. Actually, only the second criterion is necessary. Past costs are already incurred, so they cannot differ between future alternative choices. However, emphasising the first criterion helps students remember that past costs are always irrelevant (except to the extent that they facilitate predictions). An illustration of relevance: choosing output levels This section emphasises that the traditional CM approach is appropriate if (1) costs are either totally fixed or purely variable, and (2) the number of output units is the only cost driver. Current management accounting thought has restricted the number of situations to which these assumptions apply. A later section relaxes these assumptions, and illustrates an approach that can be used in conjunction with ABC and the hierarchy of costs described in Chapter 11. What is a one-time special order? Ask students, What if the customer asks for a special order, but then a year later requests a similar deal? What if customer A asks for a special order in January, customer B asks for one in March and customer C asks for one in June? The one-time special order concept is more ambiguous than students realise. If the company has chronic excess capacity, it may be better off downsizing than accepting a series of special orders that do not cover full costs. 147

2 The CM approach is appropriate in the short run. In the longer term, other more profitable opportunities may arise, so the company should not tie up its resources in marginally profitable products. Also, all costs must be covered in the long run. The company cannot survive by producing products that consistently sell for less than full cost. Warn students to be very careful with the total cost/unit that includes fixed costs (FC) per unit. Managers often misuse total cost/unit data for decisions where FC are not relevant. Managers may also mistakenly multiply the same total cost/unit by different numbers of units. They may not realise that the total cost/unit changes as the output level changes because FC are spread over different numbers of outputs. Telling students that total cost/unit figures are valid only at the assumed output levels may help get the point across. Special orders usually do not incur regular marketing costs because they usually do not go through normal channels. There may be special fixed (marketing) costs of obtaining the order if there is excess manufacturing OH. However, the special order could increase fixed manufacturing OH if it increases output to a higher relevant range, or if it requires special machinery, etc. Fixed manufacturing OH and marketing and distribution costs may or may not be relevant in special order decisions, depending on the specific situation. Outsourcing and make-or-buy decisions In the example in Chapter 10, even though the number of units remains the same, the total purchasing, receiving and set-up costs increase because the number of batches is doubled. This illustrates why reduction in set-up time is key as firms move to smallbatch production and JIT delivery systems. Opportunity costs, outsourcing and capacity constraints One general approach to outsourcing decisions is the following: Maximum we Incremental Opportunity cost would pay = cost + of insourcing (Outlay cost) This formula tells us how much we can pay the outside supplier and still make a profit as if we produced the number of units ourselves. We are willing to pay at least the incremental cost of insourcing (i.e. our outlay cost). If facilities would otherwise be idle, the opportunity cost of insourcing is zero, because there is nothing better to do with the plant. In the example, opportunity cost is not zero because the plant can be used to produce another product. The incremental outlay cost is 150,000 and opportunity costs are 25,000 (see Panel B of Exhibit 10.7). The maximum that should be paid to the outside supplier is 175,000/10,000 = per unit. 148

3 At least two factors help explain why some companies have had high stock levels. First, since the cost of capital tied up in stock is not reported by the accounting system, management may never see this information. Second, purchasing managers are frequently rewarded for favourable price variances, so they may be tempted to purchase large quantities to obtain a quantity discount. Irrelevance of past costs and equipment-replacement decisions The concept of sunk costs also applies to students personal lives. People who recognise the irrelevance of sunk costs tend to be more productive. For example, research has shown that students who start again on weak course assignments and academic staff who abandon research that is not progressing perform better than their peers who follow traditional advice to stick with it. Many managers like the old American adage, Use it up, wear it out, make it do or do without. They think that past costs are relevant. This problem often occurs in the context of rapid technology changes. Managers argue that they need to recoup their investment in the old technology before investing in a new technology. However, customers may not continue to buy products based on old technology. Managers should compare the expected net inflows from the new technology with the expected net inflows from the old technology. Appendix: linear programming The LP discussion in this appendix extends the notion, maximise CM/unit of scarce resource, advanced in the chapter in more complex settings with multiple constraints. The objective is to maximise the contribution margin (rather than the profit) per unit of the constraints. Fixed costs are irrelevant since they are assumed to remain the same regardless of the product mix. Such analysis is most appropriate in the short run where many costs are indeed fixed with respect to the number of units of output. The graphic approach illustrated in Exhibit is feasible with two products, three products would require a three-dimensional graph, etc. Stress that we use the graphic approach to help students develop an intuitive understanding of the basic concepts. In practice, the graphic solution is almost never used, since most LP problems involve numerous products and constraints. Companies use calculater software packages programmed to solve large LP problems. The discussion of the intuition underlying LP helps students understand why LP works. The basic point is that LP systematically analyses the exchange of a given CM per unit of scarce resource for some other contribution margin of scarce resource in order to find the optimal product mix (highest contribution margin or lowest cost). This section shows that large changes in contribution margin per unit of product may not affect the optimal product mix if there are no other nearby corner points. 149

4 Solutions to Chapter The five steps in the decision process outlined in Exhibit 10.1 of the text are: 1 Gathering information 2 Making predictions 3 Choosing an alternative 4 Implementing the decision 5 Evaluating performance 10.2 Relevant costs are those expected future costs that differ among alternative courses of action. Historical costs are irrelevant because they are past costs and therefore cannot differ among alternative future courses of action No. Relevant costs are defined as those expected future costs that differ among alternative courses of action. Thus, future costs that do not differ among the alternatives are irrelevant to deciding which alternative to choose Quantitative factors are outcomes that are measured in numerical terms. Some quantitative factors are financial that is, they can be easily expressed in financial terms. Direct materials is an example of a quantitative financial factor. Qualitative factors are factors that are not measured in numerical terms. An example is employee morale No. Some variable costs may not differ among the alternatives under consideration and hence will be irrelevant. Some fixed costs may differ among the alternatives and hence will be relevant No. Some of the total unit costs to manufacture a product may be fixed costs, and hence will not differ between the make and buy alternatives. These fixed costs are irrelevant to the make-or-buy decision. The key comparison is between purchase costs and the costs that will be saved if the company purchases the component parts from outside Opportunity cost is the contribution to income that is forgone (rejected) by not using a limited resource in its next-best alternative use. 150

5 10.8 Cost written off as depreciation is irrelevant when it pertains to a past cost. But the purchase cost of new equipment to be acquired in the future that will then be written off as depreciation is often relevant No. Managers tend to favour the alternative that makes their performance look best so they focus on the measures used in the performance-evaluation model. If the performance-evaluation model does not emphasise maximising operating income or minimising costs, managers are not likely to choose the alternative that maximises operating income or minimises costs The text outlines two methods of determining the optimal solution to an LP problem: 1 Trial-and-error solution approach. 2 Graphical solution approach. Most LP applications in practice use standard software packages that rely on the simplex method to calculate the optimal solution (20 25 min.) Relevant costs, contribution margin, product emphasis. 1 Cola Lemonade Punch Natural orange juice Selling price per case Deduct variable costs per case Contribution margin per case The argument fails to recognise that shelf space is the constraining factor. There are only 12 metres of front shelf space to be devoted to drinks. Consuelo should aim to get the highest daily contribution margin per metre of front shelf space: Cola Lemonade Punch Natural orange juice Contribution margin per case Sales (number of cases) per metre of shelf space per day Daily contribution per metre of front shelf space

6 3 The allocation that maximises the daily contribution from soft drink sales is: Daily contribution Metres of per metre of Total contribution shelf space front shelf space margin per day Cola Lemonade Natural orange juice Punch , The maximum of 6 metres of front shelf space will be devoted to Cola because it has the highest contribution margin per unit of the constraining factor. Four metres of front shelf space will be devoted to Lemonade, which has the second highest contribution margin per unit of the constraining factor. No more shelf space can be devoted to Lemonade since each of the remaining two products, Natural orange juice and Punch (that have the second lowest and lowest contribution margins per unit of the constraining factor) must each be given at least one metre of front shelf space (20 min.) Question from the Chartered Institute of Management Accountants, Stage 1, November a Deficiency in machine-hours for next period Product A Product B Product C Total Machine-hours required per unit = 6 = 4 = Maximum demand (units) 3,000 2,500 5,000 Total machine-hours to meet max. demand 18,000 10,000 35,000 63,000 Machine-hours available 50,000 Deficiency of machine-hours 13,

7 b Since the variable cost of making each product is less than the buy-in price, the company should make each product, rather than buy in, wherever possible. Product A Product B Product C ( ) ( ) ( ) Selling price per unit Variable cost per unit (154) (112) (178) Contribution per unit Machine-hours required per unit Contribution per machine-hour Order of production Therefore make: 2,500 units of Product B, using machine-hours of (4 2,500) 10,000 3,000 units of Product A, using machine-hours of (6 3,000) 18,000 28,000 Machine-hours left to make product C 22,000 50,000 Therefore, the company should make 3,142, i.e. 22,000 units of Product C. 7 Therefore, the company should only buy out 1,858 (5,000 3,142) units of product C in the period. c Profit for the next period Total Product A Product B Product C ( ) ( ) ( ) ( ) Contribution from items made: 46 3, , , , , ,532 Contribution from items bought in: Selling price 224 Variable cost ,858 44, , , , ,124 Fixed costs (300,000) Profit for the period 142,

8 10.14 (20 25 min.) Customer profitability, choosing customers. 1 Jours-Daim should not drop the Fourbe-Riz business as the following analysis shows. Loss in revenues from dropping Fourbe-Riz (80,000) Savings in costs: Variable costs 48,000 Fixed costs 20% 100,000 20,000 Total savings in costs 68,000 Effect on operating income (12,000) Jours-Daim would be worse off by 12,000 if it drops the Fourbe-Riz business. 2 If Jours-Daim accepts the additional business from Fourbe-Riz, it would take an additional 500 hours of machine time. If Jours-Daim accepts all of Fourbe-Riz s and Harpes-à-Gonds business for February, it would require 2,500 hours of machine time (1,500 hours for Harpes-à-Gonds and 1,000 hours for Fourbe-Riz). Jours-Daim has only 2,000 hours of machine capacity. It must therefore choose how much of the Harpes-à- Gonds or Fourbe-Riz business to accept. If Jours-Daim accepts any additional business from Fourbe-Riz, it must forgo some of Harpes-à-Gonds business. To maximise operating income, Jours-Daim should maximise contribution margin per unit of the constrained resource. (Fixed costs will remain unchanged at 100,000 whatever business Jours-Daim chooses to accept in February, and are therefore irrelevant.) The contribution margin per unit of the constrained resource for each customer in January is: Revenues Variable costs Contribution margin Harpes-à-Gonds 120,000 42,000 78,000 Fourbe-Riz 80,000 48,000 32,000 Contribution margin per machine hour 78,000 1,500 = 52 32, = 64 Since the 80,000 of additional Fourbe-Riz business in February is identical to jobs done in January, it will also have a contribution margin of 64 per machine-hour, which is greater than the contribution margin of 52 per machine hour from Harpes-à-Gonds. To maximise operating income, Jours-Daim should first allocate all the capacity needed to take the Fourbe-Riz business (1,000 machine-hours) and then allocate the remaining 1,000 (2,000 1,000) machine-hours to Harpes-à-Gonds. Jours-Daim s operating income in February would then be 16,000 as shown below, greater than the 10,000 operating income in January. 154

9 Contribution margin per machine hour Machine-hours to be worked Contribution margin Fixed costs Operating income Harpes-à- Gonds 52 1,000 52,000 Fourbe- Riz Total 64 1,000 64, , ,000 16,000 Alternatively, we could present Jours-Daim s operating income by taking two-thirds (1,000 1,500 machine-hours) of Harpes-à-Gonds January revenues and variable costs, and doubling (1, machine-hours) Fourbe-Riz s January revenues and variable costs. Revenues Variable costs Contribution margin Fixed costs Operating income Harpes-à- Gonds 80,000 28,000 52,000 Fourbe- Riz 160,000 96,000 64,000 Total 240, , , ,000 16,000 The problem indicated that Jours-Daim could choose to accept as much of the Harpes-à- Gonds and Fourbe-Riz business for February as it wants. However, some students may raise the question that Jours-Daim should think more strategically before deciding what to do. For example, how would Harpes-à-Gonds react to Jours-Daim s inability to satisfy its needs? Will Fourbe-Riz continue to give Jours-Daim 160,000 of business each month or is the additional 80,000 of business in February a special order? For example, if Fourbe-Riz s additional work in February is only a special order and Jours- Daim wants to maintain a long-term relationship with Harpes-à-Gonds, it may in fact prefer to turn down the additional Fourbe-Riz business. It may feel that the additional 6,000 in operating income in February is not worth jeopardising its long-term relationship with Harpes-à-Gonds. Other students may raise the possibility of Jours- Daim accepting all the Harpes-à-Gonds and Fourbe-Riz business for February if it can subcontract some of it to another reliable, high-quality printer. 155

10 10.15 (30 40 min.) Relevance of equipment costs. 1 a Statements of cash receipts and disbursements Receipts from operations: Sales Deduct disbursements: Other operating costs Operation of machine Purchase of old machine Purchase of new equipment Cash inflow from sale of old equipment Net cash inflow Year 1 150,000 (110,000) (15,000) (20,000)* 5,000 Keep Year 2, 3, 4 150,000 (110,000) (15,000) 25,000 Four years together Year 1 600,000 (440,000) iiiii i(60,000) iiiii(20,000) 80, ,000 iiiii(110,000) iiiii (9,000) iiiii (20,000) iiiii (24,000) 8,000 (5,000) Buy new machine Year 2, 3, 4 150,000 iiiii(110,000) iiiiiiii (9,000) 31,000 Four years together 600,000 (440,000) (36,000) (20,000) (24,000) 8,000 88,000 *Some students ignore this item because it is the same for each alternative. However, note that a statement for the entire year has been requested. Obviously, the 20,000 would affect Year 1 only under both the keep and buy alternatives. The difference is 8,000 for four years taken together. In particular, note that the 20,000 book value can be omitted from the comparison. Merely cross out the entire line; although the column totals are affected, the net difference is still 8,000. Note the motivational factors here. A manager may be reluctant to replace simply because the large loss on disposal severely harms profitability in Year 1. Nevertheless, the cumulative cash flow effects are beneficial to the company as a whole (assuming a world of no income taxes and no interest). 156

11 1 b Again, the difference is 8,000: Income statements Year 1, 2, 3, 4 Keep Four years together Year 1 Buy new machine Year 2, 3, 4 Four years together Sales Costs (excluding disposal): Other operating costs Depreciation Operating costs of machine Total costs (excluding disposal) Loss on disposal: Book value ( cost ) Proceeds ( revenue ) Loss on disposal Total costs Operating income 150, ,000 5,000 15, , ,000 20, , ,000 20,000 60,000 20, ,000 80, , ,000 6,000 9, ,000 20,000 (8,000) 12, ,000 13, , ,000 6,000 9, , ,000 25, , ,000 24,000 36, ,000 20,000* (8,000) 12, ,000 88,000 *As in requirement (1a), the 20,000 book value may be omitted from the comparison without changing the 8,000 difference. This adjustment would mean excluding the depreciation item of 5,000 per year (a cumulative effect of 20,000) under the keep alternative and excluding the book value item of 20,000 in the loss on disposal calculation under the buy alternative. 1 c The 20,000 purchase cost of the old equipment, the sales and the other costs are irrelevant because their amounts are common to both alternatives. 2 The net difference would be unaffected. Any number may be substituted for the original 20,000 figure without changing the final answer. Of course, the net cash outflows under both alternatives would be high. The Car Wash manager really blundered. However, keeping the old equipment will increase the cost of the blunder to the cumulative tune of 8,000 over the next four years. 3 Book value is irrelevant in decisions about the replacement of equipment, because it is a past (historical) cost. All past costs are down the drain. Nothing can change what has already been spent or what has already happened. The 20,000 has been spent. How it is subsequently accounted for is irrelevant. The analysis in requirement (1) clearly shows that we may completely ignore the 20,000 and still have a correct analysis. The only relevant items are those expected future items that will differ among alternatives. Despite the economic analysis shown here, many managers would keep the old machine rather than replace it. Why? Because in many organisations the income statements of requirement (2) would be a principal means of evaluating performance. Note that the first-year operating income would be higher under the keep alternative. The conventional accrual accounting model might motivate managers toward maximising their first-year reported operating income at the expense of long-run cumulative betterment for the organisation as a whole. This criticism is often made of the accrual accounting model. That is, the action favoured by the correct or best economic 157

12 decision model may not be taken, either because the performance-evaluation model is inconsistent with the decision model or because the focus is only on the short-run part of the performance-evaluation model (30 min.) Contribution approach, relevant costs. 1 Average one-way fare per passenger 500 Commission at 8% of Net cash to Air Calabria per ticket 460 Average number of passengers per flight 200 Revenues per flight ( ) 92,000 Food & beverage cost per flight ( ) 4,000 Total contribution from passengers 88,000 Fuel costs per flight 14,000 Contribution per flight 74,000 Fixed costs allocated to each flight: Lease costs 53,000 Baggage handling 7,000 Flight crew 4,000 64,000 Operating income per flight 10,000 2 If fare is Commission at 8% of Net cash per ticket Food and beverage cost per ticket Contribution per passenger Total contribution margin from passengers ( x 212) 89, All other costs are irrelevant On the basis of quantitative factors alone, Air Calabria should decrease its fare to 480 because reducing the fare gives Air Calabria a higher contribution margin from passengers ( 89, versus 88,000). 3 In evaluating whether Air Calabria should charter its plane to Cima-Rosa, we compare the charter alternative to the solution in requirement (2) because requirement (2) is preferred to requirement (1). Under requirement (2), Air Calabria gets 89, Deduct fuel costs 14, Total contribution per flight 75, Air Calabria gets 75,000 per flight from chartering the plane to Cima-Rosa. On the basis of quantitative financial factors Air Calabria is better off not chartering the plane and instead lowering its own fares. 158

13 Students who compare the 75,000 that Air Calabria earns from chartering its plane to the contribution from passengers in requirement (1) ( 74,000) will conclude that Air Calabria should charter the plane to Cima-Rosa. Strictly speaking, though, the correct answer must compare the charter fee of 75,000 to the 75, passenger contribution in requirement (2) since lowering the fare is certainly an alternative available to Air Calabria. Other qualitative factors that Air Calabria should consider in coming to a decision are: a The lower risk from chartering its plane relative to the uncertainties regarding the number of passengers it might get on its scheduled flights. b Chartering to Cima-Rosa means that Air Calabria would not have a regular schedule of flights each week. This arrangement could cause inconvenience to some of its passengers. c The stability of the relationship between Air Calabria and Cima-Rosa. If this is not a long-term arrangement, Air Calabria may lose current market share and not benefit from sustained charter revenues (30 min.) Optimal production plan, calculater manufacturer. 1 Let X = Units of printers and Y = Units of desktop computers Objective: Maximise total contribution margin of 200X + 100Y Constraints: For production line 1: 6X + 4Y < 24 For production line 2: 10X < 20 Sales of X and Y: X Y < 0 Negative production impossible: X > 0 Y > 0 2 Solution Exhibit presents a graphical summary of the relationships. The sales-mix constraint here is somewhat unusual. The X Y < 0 line is the one going upward at 45 angle from the origin. Using the trial-and-error method: Trial Corner (X; Y) Total contribution margin 1 (0; 0) 200(0) + 100(0) = 0 2 (2; 2) 200(2) + 100(2) = (2; 3) 200(2) + 100(3) = (0; 6) 200(0) + 100(6) = 600 The optimal solution that maximises operating income is two printers and three computers. 159

14 Solution Exhibit Graphic solution to find optimal mix, Fiordi-Ligio Srl (30 40 min.) Optimal sales mix for a retailer, sensitivity analysis. 1 Let G = floor space of grocery products carried D = floor space of dairy products carried The LP formula of the decision is: Maximise: 10G + 3D Subject to: G + D < 4,000 G > 1,000 D > Vier-und-Zwanzig may wish to maintain its reputation as a full-service food store carrying both grocery and dairy products. Customers may not be attracted if Vier-und- Zwanzig carries only the product line with the highest unit contribution margins. (Marketing and economics courses examine this issue under the label of interdependencies in the demand for products.) 160

15 3 Solution Exhibit presents the graphic solution. The optimal solution is 3,200 square metres of grocery products and 800 square metres of dairy products. The trial-and-error solution approach is: Trial Corner (G; D) TCM = 10G + 3D (1,000; 800) (1,000; 3,000) (3,200; 800) 10 (1,000) + 3 ( 800) = 12, (1,000) + 3 (3,000) = 1, (3,200) + 3 ( 800) = 34,400* * Optimal solution is G = 3,200 and D = The optimal mix determined in requirement (3) will not change if the contribution margins per square metre change to grocery products, 8 and dairy products, 5. To avoid cluttering the graphic solution in Solution Exhibit we demonstrate this using the trial-and-error solution approach. Trial Corner (G; D) TCM = 8G + 5D 1 (1,000; 800) 8 (1,000) + 5 ( 800) = 12,000 2 (1,000; 3,000) 8 (1,000) + 5 (3,000) = 23,000 3 (3,200; 800) 8 (3,200) + 5 ( 800) = 29,600* * Optimal solution is still G = 3,200 and D = 800. The student can also verify, by drawing lines parallel to the line through G = 500 and D = 800 (the equal contribution line for 4,000) that the furthest point where the equal contribution line intersects the feasible region is the point G = 3,200 and D =

16 Solution Exhibit Graphic solution to find optimal mix, Vier-und-Zwanzig (30 min.) Question from the Institute of Chartered Accountants in Ireland, Professional Examination 2, Management Accounting & Business Finance I, Summer 1996 Newsnow Ltd a Breakeven daily sales volume Breakeven volume = Fixed cost Contribution per unit Fixed costs = Occupancy costs + Depreciation = = 3000 Contribution per unit = Revenue Expense = = 0.06 Breakeven volume = 3000 / 0.06 = 50,

17 Daily sales volume of the Daily Oracle would need to be 50,000 copies to enable Newsnow Ltd to break even. Workings Total cost Volume Cost per unit Sales p Advertising revenue p Direct materials p Direct labour p Variable overheads p Distribution costs p b Margin of safety ratio = (60,000 50,000) 60,000 = 16.67% c Option Y is preferred as it offers the company a daily net profit of Option X results in a daily net loss of 260. Working Option X: Quality Paper Sales would decline by 10% = Expected sales 36,000 Revenue Sales 36,000 27p 9720 Advertising 36,000 12p Less Materials 36,000 9p 3240 Labour 36,000 12p 4320 Variable o/h 36,000 3p 1080 Distribution 36,000 6p 2160 Occupancy 2000 Depreciation Net Loss (260) 163

18 Workings Option Y: Freesheet Revenue Advertising 40,000 31p 124,000 Less Expenses Materials 40,000 9p Labour 40,000 8p Variable o/h 40,000 3p Distribution 40,000 10p 4000 Occupancy 2000 Depreciation ,000 Net Loss 1,000 d Breakeven point sales revenue = Fixed costs Profit volume ratio = Minimum daily revenue = 93,000 e Assumptions implicit in the Cost volume profit analysis All other variables remain constant. Total cost and total revenues are linear functions of output. A single product or constant sales mix. Complexity-related fixed costs do not change. Profits are calculated on a variable costing basis. The analysis applies to the relevant range only. Costs can be accurately divided into their fixed and variable elements (40 min.) Question from the Institute of Chartered Accountants in Ireland, Professional Examination 3, Management Accounting & Business Finance II, Summer a At present only 30,000 machine-hours are available per period, which allows the production of 20,000 PQR products: 164

19 P: 25 hours per 100 components or 0.25 hr per component Q: 50 hours per 100 components or 0.50 hr per component R: 75 hours per 100 components or 0.75 hr per component. This gives a total of 1.50 machine-hours to machine one unit of PQR. 30,000/1.50 = 20,000 units of PQR. To make 25% more product, this means 25,000 units of PQR, requiring: Hours to machine P: ,000 = 6,250 hours Hours to machine Q: ,000 = 12,500 hours Hours to machine R: ,000 = 18,750 hours Total hours required = 37,500 hours To decide on the component to be bought in, we establish the net advantage per scarce machine-hour of continuing to manufacture rather than buy in, rank the components and then pick the component which provides the smallest net advantage to the company, if it is manufactured rather than purchased. P Q R Cost of manufacture : Cost of purchase : Net saving on manufacture : Per scarce machine hour : 75/25 140/50 180/75 Ranking Therefore, R should be purchased. The plan should be: Make 25,000 PQR products as follows: Make 25,000 P requiring Make 25,000 Q requiring Make 15,000 R requiring Total machine-hrs. Used 6,250 machine-hrs 12,500 machine-hrs 18,750 machine-hrs 30,000 machine-hrs Buy in 10,000 R 165

20 b If the company is to produce 50% more, then it will produce 20,000 x 1.5 = 30,000 units. 30,000 units of PQR require 30,000 P requiring 7,500 machine-hrs. 30,000 Q requiring 15,000 machine-hrs 22,500 machine-hrs but the available machine-hours in-house is 30,000, so available for R 7,500 machine-hrs 10,000 units R 30,000 machine-hrs Therefore, we must buy in 20,000 units of component R. c Derivation of profit earned no components purchased: Without any units of R being purchased, we are constrained to just 30,000 machinehours and 20,000 units of PQR. The only assumption that needs to be made in the derivation of the profit earned is the amount of fixed overhead expenditure that is incurred. Given that the question states that no additional fixed overhead will be incurred in either Machining or Assembly, as a result of increases in production, then it may be assumed that 20,000 to 30,000 units of production of PQR, represents the relevant range and therefore we can look to the information given in the question for unit fixed cost and try to establish from there the level of fixed overhead in total that prevails over the relevant range. Note 1 Machining Department fixed overhead: The unit fixed costs are thus: P: 50/100 = 0.50 per unit Q: 100/100 = 1.00 per unit R: 150/100 = 1.50 per unit Unit fixed cost in Machining = 3.00 per set of components to make one unit of PQR. Assembly Department fixed overhead: The unit fixed costs for one batch of assembled PQR units = 100/100 = 1 per PQR unit. Any calculation which involves going from unit fixed costs to total fixed costs must always be undertaken with care, as the unit fixed cost figures are only true when associated with the denominator level from which they were derived, namely 100 units in this case. However, it would appear unreasonable that total fixed costs are thus: 166

21 Machining: = 300 Assembly: = 100 Total fixed costs 400 However, if these per unit fixed cost amounts could be related to a denominator of 20,000 units of PQR, we would get total fixed cost of: Machining: ,000 = 60,000 Assembly: ,000 = 20,000 For further reading on this area, see Horngren, C.T., Cost Accounting: A Managerial Emphasis, 8th Edn., ch. 2, pp Unit Variable Cost of making one unit of PQR: Machining: Variable cost of mfg. P 0.75 Q 1.25 R Assembly Unit mfg. variable cost 3.00 Total var. mfg. cost 6.50 Selling price So, unit CM 5.50 Therefore, with all components being manufactured, we can only produce 20,000 finished units of PQR: Total contribution ( ,000) = 110,000 Fixed cost Machining (Note 1) = 60,000 Fixed cost Assembly (Note 1) = 20,000 Expected net profit = 30,000 Derivation of profit earned when some of component R is purchased outside: Units of PQR being made = 30,

22 Sales revenue: 12 30, ,000 Variable cost of sales : 30, ,500 30, ,500 10, ,000 20, ,000 Total variable mfg. cost Machining 141,000 Total variable mfg. cost Assembly 30, ,000 Total variable manufacturing cost 231,000 Total contribution 129,000 Fixed cost: Machining 60,000 Assembly 20,000 Total fixed cost 80,000 Expected net profit 49,000 Note 1 As expected, the option of increasing production capacity by buying in some of component R results in a higher profit for the company, by 19,000, than if it had remained at the level of 20,000 units of PQR. Note 2 It is assumed that no non-manufacturing overhead cost, such as marketing or distribution expenditure, accrues under any of the situations considered in the question. Note 3 It is assumed that there are no stocks, neither opening nor closing stocks, for the period. Marginal costing income statements are also prepared, because of ease of preparation and because of the lack of information regarding the normal level of denominator activity for the fixed overhead rate. 168

23 10.22 (45 min.) Question from the Chartered Institute of Management Accountants in Ireland, Stage 2, Operational Cost Accounting (November 1998). a AZ Buses division Planned/total contribution and profit for the year ending 31 December 2002 Route W X Y Z Total Income Adult 140, , , ,280 Child 46,800 74,880 35,100 34,320 Total 187, , , ,600 Variable costs Fuel and repairs 24,570 21,060 25,740 22,230 Bus contribution 162, , , ,370 Specific fixed costs: Wages* 74,880 74,880 74,880 74,880 Vehicle fixed costs 4,000 4,000 4,000 4,000 Route contribution 83, , ,480 70, ,860 General admin. 300,000 Profit 297,860 * This item would also be viewed as a variable cost. b i Adult ( ) Child ( ) Existing revenue 45 (15 x 3.00) 15 (10 x 1.50) Revised revenue 45 (12 x 3.75) 12 (8 x 1.50) Net gain/(loss) nil (3) The contribution per return journey will fall by ii Each vehicle carries on average 25 passengers on the W route (the capacity is 30). If there is significant variability, occasionally over 30 potential passengers will require the service. By reducing the mean number of passengers carried to 20, the company would be able to satisfy demand. Alternatively, it may be possible to change to lower-cost, lower capacity buses via leasing, because of reduction in passenger numbers. Other factors may be relevant to the decision to increase price, e.g. reaction of potential competitors, loss of customer goodwill, increased focus on the quality of the service, etc. If this reduces the average bus loading it may be worth the 5% turnover loss. 169

24 c i Annual maintenance costs Staffing: Fitters 31,616 Supervisor 24,000 55,616 Material costs: Bus servicing (499,200km /4,000) x ,480 Bus safety checks (48 x 75) 3,600 Taxi servicing (192 x 100) 19,200 Taxi safety checks (36 x 75) 2,700 37,980 Total cost 93,596 ii Cost of maintenance division 93,596 Cost of new employee 20,000 Cost of retaining present facilities 113,596 Cost of buying in maintenance 90,000 Redundancy costs for fitters 15,808 Cost of buying in services 105,808 Cost of reduction from buying in services 7,788 On a one-year basis, a cash saving of 7,788 is made if the services are bought in. Following the period of redundancy payments, this would increase to an annual 23,596 ( 7, ,808). iii It may be more difficult to ensure quality of work, or the most appropriate scheduling of work if externally contracted. It may be advisable to consider where AZ Buses competitive strengths lie, and then subcontract out the services which are deemed least critical, or which it performs least well. Vehicle maintenance could also be set up as a profit centre, and made to compete with external competitors for the work of the AZ Transport Group (45 min.) Question from the Chartered Institute of Management Accounts in Ireland, Stage 2, Operational Cost Accounting (May 1999). a Product A B C D Contribution Unit machine-hours Contribution per machine-hour Ranking

25 Product Quantity Machine Contribution units hours C 250 1,000 5,750 B ,060 D ,024 2,000 10,834 Fixed costs 8,000* Profit 2,834 *1,000 labour hours x 8.00 per hour = 8,000 b i Sales shortfall units Unit contribution Additional cost per unit Revised unit contribution Net benefit ii D * A ,500 2,620 * 4.00 labour variable overhead per unit Variable cost of B 13 Cost of external purchase 20 Increase in cost 7 Reduction in contribution = 7 x 180 units = 1,260 Hours released = 540 Allocated as follows: Product D 8 units (x 5) 40 Product A 125 units (x 4) 500 Additional hours Additional contribution D A 500 2,000 2,176 B Contribution loss 1,260 Net benefit

26 REPORT To: From: Re: Marketing Director Management Accountant Expansion of capacity The financial outcomes of the two options are identified above. Working overtime (i) involves no additional fixed costs, and the significant increase in capacity results in additional profit. Option (ii) also results in a higher profit, but is less attractive because of the reduced unit contribution. Moreover, the capacity increase is only 64% (540/840 machine-hours). If the company is near capacity for labour hours, option (i) may not be realisable due to a reluctance of staff to work overtime. Option (ii) involves a loss of control, and may be less flexible than option (i). Since (i) offers the greater return for the company, it may be preferable and should be adopted to yield incremental profit of 2,620, which is 1,704 per week over the next best alternative (35 40 min.) Special-order decision. 1 Time spent on manufacturing bottles = 750,000 bottles 100 bottles per hour So 10,000 7,500 = 2,500 hours available for toys. = 7,500 hours 100,000 units The moulded plastic toy requires 40 = 2,500 hours, so Fri-Flask has enough capacity to accept the toys order. Additional income from accepting the order is: Revenue DKr ,000 Variable costs ,000 Contribution margin Fixed costs Additional income DKr300, ,000 60,000 20,000 DKr 40,000 So Fri-Flask should accept the order since it has enough excess capacity to make the 100,000 toys. 2 Time spent on manufacturing bottles = 850,000 = 8,500 hours 100 So 10,000 8,500 = 1,500 hours available for toys. From requirement (1) moulded plastic toy requires 2,500 hours and generates DKr40,000 in operating income. 172

27 So if the toy order is accepted, 1,000 hours (2,500 hours required 1,500 hours available) of bottle making will be forgone, equal to 100,000 bottles (100 bottles/hr 1,000 hrs.) Operating income from accepting DKr40,000 Forgone contribution margin (100,000 bottles x DKr0.30) 30,000 Increase in operating income DKr10,000 So Fri-Flask should accept the special order. 3 Without considering the fixed costs of the toy mould, the contribution per machine-hour of the constrained resource for bottles and the special toy are as follows: Bottles Toys Contribution margin per unit DKr0.30 DKr0.60 Multiplied by units made in 1 machine hour Contribution margin per machine hour DKr30 DKr24 This suggests that Fri-Flask should make as many bottles as it can rather than the special toys because bottles generate a higher contribution margin per machine-hour. So if Fri-Flask used the 1,500 hours available to it for making toys after using the 8,500 hours to make bottles, it would be able to make 1, = 60,000 toys and earn operating income of: Contribution margin 60,000 x DKr0.60 DKr36,000 Fixed mould costs 20,000 Increase in operating income DKr16,000 The contribution margin earned covers the fixed costs of the mould, so Fri-Flask should make 850,000 bottles and 60,000 toys. 4 Time spent on manufacturing bottles = 900, = 9,000 hours So 10,000 9,000 = 1,000 hours available for toys. So if the toy order is accepted, then 1,500 hours (2,500 hours required 1,000 hours available) of bottle capacity will be forgone = 150,000 bottles Contribution from accepting toy offer DKr40,000 Forgone profits on bottles 150,000 x DKr0.30 (45,000) Increase (decrease) in operating income DKr(5,000) So reject the special order. 5 As in requirement (3), Fri-Flask should first use the 9,000 hours to make bottles and then consider using the 1,000 hours available to it for making toys. It would be able to make 1,000 hours 40 = 40,000 toys and earn operating income of: 173

28 Contribution margin 40,000 x DKr0.60 DKr24,000 Fixed mould costs 20,000 Increase in operating income DKr 4,000 Fri-Flask should make 900,000 bottles and 40,000 toys. 6 As in requirements (3) and (5), Fri-Flask should first use 9,500 hours to make bottles and then consider using the 500 hours available to it for making toys. It would be able to make 500 hours 40 = 20,000 toys and earn operating income of Contribution margin 20,000 DKr0.60 DKr12,000 Fixed mould costs 20,000 Increase (decrease) in operating income DKr (8,000) So Fri-Flask should refuse to make any of the plastic toys. If it tried to make the toy product more profitable by making more toys, it would have to give up the plastic bottles. This trade-off is not worthwhile because Fri-Flask makes DKr24 per hour from the toys and would lose DKr30 per hour from the plastic bottles. 7 The subcontracting option is a good option because it nets Fri-Flask DKr0.20 per toy (DKr3.00 DKr2.80) without using up any of its limited capacity. So long as Fri-Flask is manufacturing in-house, it would prefer to first make bottles (contribution of DKr30 per hour) and then make toys (contribution of DKr24 per hour). As in requirement (5), Fri-Flask would make 900,000 bottles and be left with 1,000 hours available for toy making. It has two options at this stage (1) use 1,000 hours of available in-house capacity to make 40,000 toys and subcontract 60,000 toys outside or (2) subcontract all 100,000 toys from outside. 40,000 toys in-house 100,000 toys 60,000 toys subcontracted subcontracted Revenues (irrelevant) DKr300,000 DKr300,000 Costs Variable manufacturing costs (40,000 x DKr2.40) 96,000 Incremental fixed costs of mould 20,000 Subcontract costs (DKr2.80 x 60,000; 168,000 DKr2.80 x 100,000) 280,000 Total costs 284, ,000 Operating income DKr 16,000 DKr 20,000 So Fri-Flask should use 9,000 hours of its capacity to make 900,000 bottles, leave 1,000 hours capacity idle and subcontract out all the 100,000 toys. 174

29 A short-cut to solving this problem is to calculate when it is worthwhile for Fri-Flask to manufacture toys in-house rather than subcontracting them. Suppose number of toys manufactured is X, the cut-off point is obtained by solving: DKr20,000 + DKr2.40X = DKr2.80X fixed manufacturing costs variable manufacturing costs per unit subcontracting costs X = DKr20,000 = 50,000 toys DKr0.40 This means that if the internal manufacturing capacity is for less than 50,000 toys, it is cheaper to subcontract, whereas if the internal manufacturing capacity is for more than 50,000 toys, it is better to manufacture in-house. In our example, the internal manufacturing capacity is for 40,000 toys, so it is better to subcontract out entirely. 175