Chapter 11. Decision Making and Relevant Information Linear Programming as a Decision Facilitating Tool

Transcription

1 Chapter 11 Decision Making and Relevant Information Linear Programming as a Decision Facilitating Tool 1

2 Introduction This chapter explores cost accounting for decision facilitating purposes It focuses on specific decisions such as accepting or rejecting a one-time-only special order, insourcing or outsourcing products or services, and replacing or keeping equipment. Furthermore it introduces Linear Programming as a method to cope with multiple constraints A decision model is a formal method for making a choice, often involving quantitative and qualitative analysis. Cost accounting may provide input to decision models or act as a substitute for an explicit decision model. 2

3 Five-Step Decision Process 1 Gathering information 2 Making predictions (support by decision model) 3 Choosing an alternative 4 Implementing the decision 5 Evaluating performance Decision making requires relevant information, especially relevant costs. Not all cost data meet the requirement of decision relevance because cost accounting is a multipurpose activity. 3

4 The Meaning of Relevance Relevant costs and relevant revenues are expected future costs and revenues that differ among alternative courses of action. Historical costs are irrelevant to a decision but are used as a basis for predicting future costs. Sunk costs are past costs which are unavoidable. Differential income (net relevant income) is the difference in total operating income when choosing between two alternatives. Differential costs (net relevant costs) are the difference in total costs between two alternatives. 4

5 Quantitative and Qualitative Relevant Information Quantitative factors are outcomes that are measured in numerical terms: Financial Nonfinancial a one-dimensional objective is required to arrive at a preference order between alternatives a common approach is to optimize a financial objective under restrictions on nonfinancial performance measures Qualitative factors are outcomes that cannot be measured in numerical terms Aspiration levels for qualitative factors restrict the feasible set of alternatives 5

6 A Special Case: One-Time-Only Special Order Decision criterion: Accept the order if the revenue differential is greater than the cost differential. Accept the order if the contribution margin is positive But: Beware of aftereffects. Is it really an isolated one-time-only special order or does it change the situation for future business? Does it accustom sales people to accept prices below full cost? Once the order is accepted, better opportunities might arrive but capacity is now insufficient to deal with them: opportunity costs! 6

7 Short term production decisions Income = revenue cost Contribution Margin of a Marketable Product = (variable) revenue variable costs Per unit Contribution Margin = contribution number of product units Rule 1: Do not offer products with a negative contribution margin to the market. 7

8 Constraints Mostly, a company is not free in its decision but faces constraints procurement constraints production constraints sales constraints Constraints might affect only single products (e.g. sales constraints) multiple products several products compete for scarce resources (e.g. procurement constraints) 8

9 Decision Problem Maximize the firm s profit max x ( p1 k1) x1 such that i sales constraints 0 x production constraints procurement constraints are kept satisfied ( p k ) x I i X i a j1 x 1 I I K a ji f x I Cap j 9

10 Example Product i = 1 i = 2 i = 3 Sales price Variable costs Contribution margin Sales constraint X i Input coefficient a Input coefficient a Machine j = 1 j = 2 Capacity

11 Special case 1: Only Sales Constraints Rule 2 Identify all products with a positive contribution margin For each selected product set the production level equal to the maximum quantity the market accepts 11

12 Special Case 2: Single Resource Constraint Example: Resource A raw material Resource B raw material Resource 3: Machine (limited capacity) a 1 a 2 Product 1 Product 2 one unit of product 1 uses a 1 units of the bottleneck taking one unit of the bottleneck resource away from product 2 decreases its output by 1/a 2 units production of an additional unit of product 1 prevents a 1 /a 2 units of product 2 from being produced 12

13 Which Products Should be Produced? If capacity is scarce (not all products can be produced up to the level of the sales constraints) Expansion of output level of product one should increase total contribution additional contribution per unit: (p 1 k 1 ) 1 loss of contribution from product 2: (p 2 k 2 ) a 1 /a 2 Rule: Prefer product 1 if a1 ( p1 k1) > ( p2 k2) p1 k1 p2 k2 or > a2 a a 1 2 Relative contribution margins (CM per machine hour) 13

14 Product-Mix Under a Single Capacity Constraint Which product(s) should be produced first? The product(s) with the highest contribution margin per unit of the constraining resource. Detailed rule (rule 3) Step 1: go for the product with the highest contribution margin per hour of capacity usage until sales constraint is binding or until capacity constraint is binding; if there is capacity left after step 1: delete product from candidate list Step 2: repeat step 1 on the remaining list until there is no capacity left 14

15 Example Bottleneck: Machine 1 Capacity = 1000 Product i = 1 i = 2 i = 3 Sales price Variable costs Contribution margin Sales constraint X i Input coefficient a Input coefficient a p1 k1 = 40, p2 k2 = 80 a 1 = 2, a 2 = 8 p a 1 k = = 20 p a 2 k = = 10 x x x = = = 300; 50; 0 Contribution: 16,000 Profit: 12,000 15

16 What if Bottleneck unknown? Solution using Excel 1. Enter the coefficient matrix a row for each restriction the last row for the per unit contribution margins Example the data for each product must form a column in the matrix 2. Provide a row for the variables (the production volumes) under the matrix 3. Enter a column right to the matrix with the formula Mmult(A;Mtrans(x)) (Usage column) where A denotes the matrix, and x the row of variables. 4. Enter the column of capacities 5. Then call the Solver and define the last cell of the usage column as the objective value add the restrictions Capacity, Nonnegativity, Sales and press solve 16

17 Another Example: Insourcing versus Outsourcing Outsourcing is the process of purchasing goods and services from outside vendors rather than producing goods or providing services within the organization, which is called insourcing. Decisions about whether to outsource or produce within the organization are often called make-or-buy decisions. The most important factors in the make-or-buy decision are quality, dependability of supplies, and costs. Should a firm manufacture the part or buy it from an outside supplier? The answer depends on the difference in expected future costs between the alternatives. 17

18 Opportunity Costs, Outsourcing, and Constraints Opportunity cost is the contribution to income that is forgone or rejected by not using a limited resource in its next best alternative use. The opportunity cost of holding inventory is the income forgone from tying up money in inventory and not investing it elsewhere. Carrying costs of inventory can be a significant opportunity cost and should be incorporated into decisions regarding lot purchase sizes for materials. Opportunity costs are not recorded in formal accounting records since they do not generate cash outlays. These costs also are not ordinarily incorporated into formal reports: ad hoc analyses required to estimate them 18

19 Again: Beware of the long-run consequences of your decision dependence on suppliers technological know-how may be lost information asymmetry may increase to the detriment of the buyer strategic orientation of outsourcing decisions: intended core competencies will not be outsourced even if this would be profitable from a pure accounting standpoint 19

20 Equipment-Replacement Decisions Assume The new machine is more efficient than the old machine. Revenues will be unaffected. Approach: 1. Calculate the present value C of all expenditures for the new machine if the machine will presumably replaced indefinitely: let C equal the present value of expenditures for the replacement chain for the optimal life time of the new machines 2. what is gained by postponing the replacement to the next period at which cost? gain: C occurs one period later; gain: interest rate (r) on C cost: the maintenance and operating cost c of the old machine for the current period Rule: replace if c is greater than rc. 20

21 Equipment-Replacement Decisions Irrelevance of Past Costs: The book value of existing equipment is irrelevant since it is neither a future cost nor does it differ among any alternatives (sunk costs never differ). The disposal price of old equipment and the purchase cost of new equipment are relevant costs and revenues because... they are future costs or revenues that differ between alternatives to be decided upon. 21

22 Decisions and Performance Evaluation In the real world would the manager replace the machine? An important factor in replacement decisions is the manager s perceptions of whether the decision model is consistent with how the manager s performance is judged. Managers often behave consistent with their short-run interests and favor the alternative that yields best performance measures in the short run. When conflicting decisions are generated, managers tend to favor the performance evaluation model. Top management faces a challenge that is, making sure that the performance evaluation model of subordinate managers is consistent with the decision model. 22

23 Multiple Constraints Activities may be characterized by output: e.g. products, services, (also for internal use) restricted due to commitments or for unrestricted sale, to be valued at sales prices input: of committed resources, restricted availability current inputs (unrestricted availability at purchase prices) activity level (determines both input and output quantities) Special case: linear activities output and input quantities vary linearly with the activity level 23

24 Linear Activity Analysis Activities are characterized by column vectors*) a j : component a ij represents the net production of the ith resource per unit of activity j = gross production gross consumption of resource i (per unit of the activity level) component a 0j represents contribution to gross profit per unit of the activity level; measurement in: [monetary units] a 0j = sales revenue cost of current inputs (per unit of the activity level) *) the first index is the row index, the second one is the column index. A dot in place of an index means a running index. So a j denotes a column vector while a i would denote a row vector. 24

25 Linear Activity Analysis, (cont d) Commitments and capacity limits are represented in a column vector a 0 Activity levels x j may be subject to an upper or lower bound: x j x j x j 0 (x j must always be nonnegative) Types of restrictions minimum output requirement: Σ j a ij x j a i0 in matrix notation*) : a i x a i0 a i x a i0 input restriction: input-output balance: a i x = 0 Both sides negative! *) x denotes the column vector of activity levels with components x j 25

26 Modeling specific activities Pure procurement activity for restricted resource i: a 0j < 0; a ij > 0; a lj = 0 (l i); x j x j input-output balance: a i x = 0 Pure selling activity for a product i produced in several alternative production activities a 0j >0; a ij <0; a lj = 0 (l i); x j x j input-output balance: a i x = 0 Storage activity: a ij = 1 in line i for the respective good this period a i+1,j = +1 in line i +1 for the same good next period 26

27 Example: Exercise 2-4, Kaplan/Atkinson: Advanced Management Accounting, 3 rd ed. p. 51 SHC produces chemicals for the paint industry. Chemical A is bought at $4/liter and processed in dept. 1 in batches of 150 liters. Each batch produces 100 liter of chemical B and 50 liters of C. B is sold for $15 per liter. C is used in dept. 2 in batches of 200 liters to produce 120 liters of D, 50 liters of E, and 30 liters of F. D is sold for $18 per liter, E is a waste product that can be given away at no cost, F is hazardous waste that has to be disposed of at a cost of $8 per liter. It can also be processed in dept. 3 in batches of 40 liters to produce 20 liters of C. No more than 1000 liters of C can be produced due to storage constraints. Sales limits: B: liters, D: liters. Labor requirements (hrs per batch): Dept. 1: 12, dept. 2: 18, dept. 3: labor hrs. available, paid at $15 per hour. Restrictions on the number of batches: Dept. 1: 700, dept. 2: 120, dept. 3: 70. Other variable costs: Dept. 1: $300, dept. 2: $825, dept. 3: $ 120 per batch. 27

28 Activities: production processes in departments j = 1,2,3; upper bounds on all production activity levels selling products B, D and F (j = 4,5,6) F at a negative price, upper bounds for B and D. no procurement activities need be modeled explicitly, since procurement is not restricted. Restrictions: input-output balances for all products upper bound for production of C (storage restriction) 28

29 Details of activities B 150 x x 1 x 4 B $15 50 x 1 C A $4 20 x 3 40 x x 2 30 x x 2 D F x 5 D $18 F $ -8 x 6 E $0 x j := no. of batches in dept. j (j = 1,...,3) := no. of liters of resp. product to be sold (j = 4,...,6) 29

30 A $4 B 150 x x 1 x 4 B $15 50 x 1 C 20 x 3 40 x 3 F $ -8 x x 2 30 x x 2 F E $0 x 5 D D $18 Input-output balances B: (i = 1) : 100 x 1 = x 4 C: (i = 2) : 50 x x x 2 D: (i = 3) : 120 x 2 = x 5 E: not relevant F: (i = 4) : 40 x 3 + x 6 = 30 x 2 Sales restrictions: B: x 4 40,000 D: x 5 15,000 Capacity restrictions: vats: x x x 3 70 labor hours: (i = 5): 12 x x x storage restriction C: (i = 2): 50 x x x

31 A $4 B 150 x x 1 x 4 B $15 Objective function 50 x 1 C 200 x 2 30 x x 2 20 x 3 40 x 3 F x 5 D D $18 for a spreadsheet solution see: ProductMix.xls at the course web site F $ -8 x 6 E $0 x 1 x 2 x 3 x 4 x 5 x 6 Revenue Material Labor other Σ Objective function: 1080 x x x x x 5 8 x 6 31

32 System design decisions Activities may be reengineered add the new version of the activity to the model the model will show then whether the new version is useful under given capacity restrictions New capacity can be introduced this will entail additional committed cost it is profitable if the optimal objective function value enhances more than this additional cost If reengineering or capacity enhancement requires investments then estimate the benefit for the future periods from the LP solution, calculate the present value and compare to the investment outlay 32

33 Bottlenecks The model shows the bottleneck(s) There may be short-run adaptation opportunities that may widen the bottleneck at an additional cost The Lagrange Multiplier (dual variable) for a bottleneck gives an estimate of the maximum allowable cost per unit of additional capacity 33

34 Quiz 1. Mikaelabelle Products sells product A at a selling price of $40 per unit. Mikaelabelle s cost per unit based on the full capacity of 500,000 units is as follows: Direct materials $ 6 Direct labor 3 Indirect manufacturing (60% of which is fixed) 10 $19 A one-time-only special order offering to buy 50,000 units was received from an overseas distributor. The only other costs that would be incurred on this order would be $4 per unit for shipping. Mikaelabelle has sufficient existing capacity to manufacture the additional units. In negotiating a price for the special order, Mikaelabelle should consider that the minimum selling price per unit should be a. $17. b. $19. c. $21. d. $23. 34

35 Quiz 2. Troy Instruments uses ten units of Part Number S1798 each month in the production of scientific equipment. The unit cost to manufacturing one unit of S1798 is presented below. Direct materials $ 4,000 Materials handling (10% of direct materials cost) 400 Direct manufacturing labor 6,000 Indirect manufacturing (200% of direct labor) 12,000 Total manufacturing cost $22,400 Materials handling represents the direct variable costs of the Receiving Department that are applied to direct materials and purchased components on the basis of their cost. This is a separate charge in addition to indirect manufacturing cost. Troy s annual indirect manufacturing cost budget is one-fourth variable and three-fourths fixed. Duncan Supply, one of Troy s reliable vendors, has offered to supply Part Number S1798 at a unit price of $17,000. If Troy purchases the S1798 units from Duncan, the capacity Troy used to manufacture these parts would be idle. Should Troy decide to purchase the parts from Duncan, the unit cost of S1798 would a. decrease by $3,700. b. decrease by $5,600. c. increase by $3,600. d. increase by $5,

36 Quiz 3. Troy Instruments uses ten units of Part Number S1798 each month in the production of scientific equipment. The unit cost to manufacturing one unit of S1798 is presented below. Direct materials $ 4,000 Materials handling (10% of direct materials cost) 400 Direct manufacturing labor 6,000 Indirect manufacturing (200% of direct labor) 12,000 Total manufacturing cost $22,400 Materials handling represents the direct variable costs of the Receiving Department that are applied to direct materials and purchased components on the basis of their cost. This is a separate charge in addition to indirect manufacturing cost. Troy s annual indirect manufacturing cost budget is one-fourth variable and three-fourths fixed. Duncan Supply, one of Troy s reliable vendors, has offered to supply Part Number S1798 at a unit price of $17,000. Assume that Troy Instruments does not wish to commit to a rental agreement to rent all idle capacity but could use idle capacity to manufacture another product that would contribute $60,000 per month. If Troy elects to manufacture S1798 in order to maintain quality control, Troy s opportunity cost is a. $(53,000). b. $7,000. c. $(24,000). d. $36,

37 Quiz 4. Which of the following is not a correct use of the term opportunity cost? a. Opportunity costs are considered period costs rather than inventoriable costs for accounting purposes. b. Opportunity costs must be considered by managers when making decisions c. Opportunity cost plus the incremental future revenues and costs equal the relevant revenues and costs of any alternative when capacity is constrained. d. The opportunity cost of holding inventory is the income forgone by tying up money in inventory and not investing it elsewhere. 37

38 Quiz 5. Nicholas, Inc., has provided the following unit data for review: Simple Product Advanced Product Selling price $22.75 $55.00 Variable cost Pounds of scarce raw material per unit 3 5 Which product, Simple or Advanced, is most profitable for Nicholas, Inc., to manufacture? a. Both in ratio of 3 : 5 b. Both in ratio of 5 : 8 c. Simple d. Advanced 38

39 Quiz 6. At December 31, 2005, Brown Co. had a machine with an original cost of $90,000, accumulated depreciation of $75,000, and an estimated salvage value of zero. On December 31, 2005, Brown was considering the purchase of a new machine having a five-year life, costing $150,000, and having an estimated salvage value of $30,000 at the end of five years. In its decision concerning the possible purchase of the machine, how much should Brown consider as sunk cost at December 31, 2005? a. $150,000 b. $120,000 c. $90,000 d. $15,000 39