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Cost ManagementMeasuring, Monitoring, and Motivating Performance
Chapter 4
Relevant Information for Decision Making
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 1
Chapter 4: Relevant Costs for Nonroutine
Operating Decisions
Learning objectives
•
•
•
•
•
•
Q1: What is the process for identifying and using relevant
information in decision making?
Q2: How is relevant quantitative and qualitative information
used in special order decisions?
Q3: How is relevant quantitative and qualitative information
used in keep or drop decisions?
Q4: How is relevant quantitative and qualitative information used in
outsourcing (make or buy) decisions?
Q5: How is relevant quantitative and qualitative information used in
product emphasis and constrained resource decisions?
Q6: What factors affect the quality of operating decisions?
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 2
Q1: Nonroutine Operating Decisions
• Routine operating decisions are those made on a
regular schedule. Examples include:
• annual budgets and resource allocation decisions
• monthly production planning
• weekly work scheduling issues
• Nonroutine operating decisions are not made on a
regular schedule. Examples include:
• accept or reject a customer’s special order
• keep or drop business segments
• insource or outsource a business activity
• constrained (scarce) resource allocation issues
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 3
Q1: Nonroutine Operating Decisions
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 4
Q1: Process for Making Nonroutine
Operating Decisions
1. Identify the type of decision to be made.
2. Identify the relevant quantitative analysis
technique(s).
3. Identify and analyze the qualitative factors.
4. Perform quantitative and/or qualitative analyses
5. Prioritize issues and arrive at a decision.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 5
Q1: Identify the Type of Decision
•
•
Special order decisions
•
determine the pricing
•
accept or reject a customer’s proposal for order quantity
and pricing
•
identify if there is sufficient available capacity
Keep or drop business segment decisions
•
•
examples of business segments include product lines,
divisions, services, geographic regions, or other distinct
segments of the business
eliminating segments with operating losses will not
always improve profits
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 6
Q1: Identify the Type of Decision
•
•
•
Outsourcing decisions
•
make or buy production components
•
perform business activities “in-house” or pay another
business to perform the activity
Constrained resource allocation decisions
•
determine which products (or business segments)
should receive allocations of scarce resources
•
examples include allocating scarce machine hours or
limited supplies of materials to products
Other decisions may use similar analyses
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 7
Q1: Identify and Apply the Relevant
Quantitative Analysis Technique(s)
•
•
Regression, CVP, and linear programming are
examples of quantitative analysis techniques.
Analysis techniques require input data.
•
Data for some input variables will be known and for
other input variables estimates will be required.
•
Many nonroutine decisions have a general
decision rule to apply to the data.
•
The results of the general rule need to be
interpreted.
•
The quality of the information used must be considered
when interpreting the results of the general rule.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 8
Q2-Q5 : Identify and Analyze Qualitative Factors
•
Qualitative information cannot easily be valued in
dollars.
•
•
•
can be difficult to identify
can be every bit as important as the quantitative
information
Examples of qualitative information that may be
relevant in some nonroutine decisions include:
•
quality of inputs available from a supplier
•
effects of decision on regular customers
•
effects of decision on employee morale
•
effects of production on the environment or the
community
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 9
Q1: Consider All Information and Make a Decision
•
Before making a decision:
•
Consider all quantitative and qualitative information.
• Judgment is required when interpreting the effects of
qualitative information.
•
Consider the quality of the information.
• Judgment is also required when user lower-quality
information.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 10
Q2: Special Order Decisions
•
•
A new customer (or an existing customer) may
sometimes request a special order with a lower
selling price per unit.
The general rule for special order decisions is:
•
•
accept the order if incremental revenues exceed
incremental costs,
subject to qualitative considerations.
Price >=
•
Relevant
Variable Costs +
Relevant
Fixed Costs +
Opportunity
Cost
If the special order replaces a portion of normal
operations, then the opportunity cost of accepting
the order must be included in incremental costs.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 11
Q2: Special Order Decisions
RobotBits, Inc. makes sensory input devices for robot manufacturers.
The normal selling price is $38.00 per unit. RobotBits was approached
by a large robot manufacturer, U.S. Robots, Inc. USR wants to buy
8,000 units at $24, and USR will pay the shipping costs. The per-unit
costs traceable to the product (based on normal capacity of 94,000
units) are listed below. Which costs are relevant to this decision?
yes$6.20 Relevant?
Direct materials
yes 8.00 Relevant?
Direct labor
Variable mfg. overhead yes 5.80 Relevant?
no 3.50 Relevant?
Fixed mfg. overhead
yes
Shipping/handling
no 2.50 Relevant?
Fixed administrative costs no 0.88 Relevant?
no 0.36 Relevant?
Fixed selling costs
$27.24
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
$20.00
Slide # 12
Q2: Special Order Decisions
Suppose that the capacity of RobotBits is 107,000 units and projected
sales to regular customers this year total 94,000 units. Does the
quantitative analysis suggest that the company should accept the
special order?
First determine if there is sufficient idle capacity to accept this
order without disrupting normal operations:
Projected sales to regular customers
Special order
94,000 units
8,000 units
102,000 units
RobotBits still has 5,000 units of idle capacity if the order is
accepted. Compare incremental revenue to incremental cost:
Incremental profit if accept special order =
($24 selling price – $20 relevant costs) x 8,000 units = $32,000
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 13
Q2: Qualitative Factors in
Special Order Decisions
What qualitative issues, in general, might RobotBits consider before
finalizing its decision?
• Will USR expect the same selling price per unit on future
orders?
• Will other regular customers be upset if they discover the
lower selling price to one of their competitors?
• Will employee productivity change with the increase in
production?
• Given the increase in production, will the incremental costs
remain as predicted for this special order?
• Are materials available from its supplier to meet the increase
in production?
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 14
Q2: Special Order Decisions and Capacity Issues
Suppose instead that the capacity of RobotBits is 100,000 units and
projected sales to regular customers this year totals 94,000 units.
Should the company accept the special order?
Here the company does not have enough idle
capacity to accept the order:
Projected sales to regular customers
Special order
94,000 units
8,000 units
102,000 units
If USR will not agree to a reduction of the order to 6,000
units, then the offer can only be accepted by denying sales
of 2,000 units to regular customers.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 15
Q2: Special Order Decisions and Capacity Issues
Suppose instead that the capacity of RobotBits is 100,000 units and
projected sales to regular customers this year total 94,000 units. Does
the quantitative analysis suggest that the company should accept the
special order?
Direct materials
Direct labor
Variable mfg. overhead
Fixed mfg. overhead
Shipping/handling
Fixed administrative costs
Fixed selling costs
$6.20
8.00
5.80
3.50
2.50
0.88
0.36
$27.24
Variable cost/unit for
regular sales = $22.50.
CM/unit on regular sales
= $38.00 – $22.50 = $15.50.
The opportunity cost of accepting this
order is the lost contribution margin
on 2,000 units of regular sales.
Incremental profit if accept special order =
$32,000 incremental profit under idle capacity – opportunity cost =
$32,000 – $15.50 x 2,000 = $1,000
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 16
Q2: Qualitative Factors in
Special Order Decisions
What additional qualitative issues, in this case of a capacity constraint,
might RobotBits consider before finalizing its decision?
• What will be the effect on the regular customer(s) that do not
receive their order(s) of 2,000 units?
• What is the effect on the company’s reputation of leaving
orders from regular customers of 2,000 units unfilled?
• Will any of the projected costs change if the company
operates at 100% capacity?
• Are there any methods to increase capacity? What effects do
these methods have on employees and on the community?
• Notice that the small incremental profit of $1,000 will probably
be outweighed by the qualitative considerations.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 17
Q3: Keep or Drop Decisions
•
Managers must determine whether to keep or
eliminate business segments that appear to be
unprofitable.
•
The general rule for keep or drop decisions is:
•
•
keep the business segment if its contribution margin
covers its avoidable fixed costs,
subject to qualitative considerations.
Drop if: Contribution < Relevant Margin Fixed Costs • + Opportunity Cost If the business segment’s elimination will affect continuing operations, the opportunity costs of its discontinuation must be included in the analysis. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 18 Q3: Keep or Drop Decisions Starz, Inc. has 3 divisions. The Gibson and Quaid Divisions have recently been operating at a loss. Management is considering the elimination of these divisions. Divisional income statements (in 1000s of dollars) are given below. According to the quantitative analysis, should Starz eliminate Gibson or Quaid or both? Revenues Variable costs Contribution margin Traceable fixed costs Division operating income Unallocated fixed costs Operating income Gibson Quaid Russell $390 $433 $837 247 335 472 143 98 365 166 114 175 ($23) ($16) $190 Breakdown of traceable fixed costs: Avoidable $154 Unavoidable 12 $166 © John Wiley & Sons, 2011 $96 18 $114 Total $1,660 1,054 606 455 151 81 $70 $139 36 $175 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 19 Q3: Keep or Drop Decisions Revenues Variable costs Contribution margin Traceable fixed costs Division operating income Unallocated fixed costs Operating income Gibson Quaid Russell $390 $433 $837 247 335 472 143 98 365 166 114 175 ($23) ($16) $190 Breakdown of traceable fixed costs: Avoidable $154 Unavoidable 12 $166 $96 18 $114 Total $1,660 1,054 606 455 151 81 $70 $139 36 $175 Contribution margin Avoidable fixed costs Effect on profit if keep Use the general rule to determine if Gibson and/or Quaid should be eliminated. Gibson Quaid $143 $98 154 96 ($11) $2 The general rule shows that we should keep Quaid and drop Gibson. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 20 Q3: Keep or Drop Decisions Revenues Variable costs Contribution margin Traceable fixed costs Division operating income Unallocated fixed costs Operating income Gibson Quaid Russell $390 $433 $837 247 335 472 143 98 365 166 114 175 ($23) ($16) $190 Breakdown of traceable fixed costs: Avoidable $154 Unavoidable 12 $166 $96 18 $114 Total $1,660 1,054 606 455 151 81 $70 $139 36 $175 Using the general rule is easier than recasting the income statements: Gibson Quaid Russell Total Revenues $390 $433 $837 $1,270 Variable costs 247 335 472 807 Contribution margin 143 98 365 $463 Traceable fixed costs 166 114 175 289 Division operating income ($23) ($16) $190 $174 Unallocated fixed costs 81 Gibson's unavoidable fixed costs 12 Operating income $81 Quaid & Russell only Profits increase by $11 when Gibson is eliminated. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 21 Q3: Keep or Drop Decisions Suppose that the Gibson & Quaid Divisions use the same supplier for a particular production input. If the Gibson Division is dropped, the decrease in purchases from this supplier means that Quaid will no longer receive volume discounts on this input. This will increase the costs of production for Quaid by $14,000 per year. In this scenario, should Starz still eliminate the Gibson Division? Effect on profit if drop Gibson before considering impact on Quaid's production costs Opportunity cost of eliminating Gibson Revised effect on profit if drop Gibson $11 (14) ($3) Profits decrease by $3 when Gibson is eliminated. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 22 Q3: Qualitative Factors in Keep or Drop Decisions What qualitative issues should Starz consider before finalizing its decision? • What will be the effect on the customers of Gibson if it is eliminated? What is the effect on the company’s reputation? • What will be the effect on the employees of Gibson? Can any of them be reassigned to other divisions? • What will be the effect on the community where Gibson is located if the decision is made to drop Gibson? • What will be the effect on the morale of the employees of the remaining divisions? © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 23 • Q4: Insource or Outsource (Make or Buy) Decisions Managers often must determine whether to • • • make or buy a production input keep a business activity in house or outsource the activity The general rule for make or buy decisions is: • • choose the alternative with the lowest relevant (incremental cost), subject to qualitative considerations If the decision will affect other aspects of operations, these costs (or lost revenues) must be included in the analysis. Outsource if: Cost to Outsource < Cost to Insource Where: © John Wiley & Sons, 2011 Cost to Relevant Relevant Opportunity Insource = FC + VC + Cost Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 24 Q4: Make or Buy Decisions Graham Co. currently of our main product manufactures a part called a gasker used in the manufacture of its main product. Graham makes and uses 60,000 gaskers per year. The production costs are detailed below. An outside supplier has offered to supply Graham 60,000 gaskers per year at $1.55 each. Fixed production costs of $30,000 associated with the gaskers are unavoidable. Should Graham make or buy the gaskers? The production costs per unit for manufacturing a gasker are: yes $0.65 Relevant? Direct materials yes 0.45 Relevant? Direct labor Variable manufacturing overhead yes 0.40 Relevant? no 0.50 Relevant? Fixed manufacturing overhead* $2.00 *$30,000/60,000 units = $0.50/unit $1.50 Advantage of “make” over “buy” = [$1.55 - $1.50] x 60,000 = $3,000 © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 25 Q4: Qualitative Factors in Make or Buy Decisions The quantitative analysis indicates that Graham should continue to make the component. What qualitative issues should Graham consider before finalizing its decision? • Is the quality of the manufactured component superior to the quality of the purchased component? • Will purchasing the component result in more timely availability of the component? • Would a relationship with the potential supplier benefit the company in any way? • Are there any worker productivity issues that affect this decision? © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 26 Q3: Make or Buy Decisions Suppose the potential supplier of the gasker offers Graham a discount for a different sub-unit required to manufacture Graham’s main product if Graham purchases 60,000 gaskers annually. This discount is expected to save Graham $15,000 per year. Should Graham consider purchasing the gaskers? Advantage of “make” over “buy” before considering discount (slide 23) $3,000 Discount Advantage of “buy” over “make” 15,000 $12,000 Profits increase by $12,000 when the gasker is purchased instead of manufactured. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 27 Q5: Constrained Resource (Product Emphasis) Decisions • Managers often face constraints such as • • production capacity constraints such as machine hours or limits on availability of material inputs limits on the quantities of outputs that customers demand • Managers need to determine which products should first be allocated the scarce resources. • The general rule for constrained resource allocation decisions with only one constraint is: • allocate scarce resources to products with the highest contribution margin per unit of the constrained resource, • subject to qualitative considerations. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 28 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Urban’s Umbrellas makes two types of patio umbrellas, regular and deluxe. Suppose there is unlimited customer demand for each product. The selling prices and variable costs of each product are listed below. Selling price per unit Variable cost per unit Contribution margin per unit Regular $40 20 $20 Deluxe $110 44 $ 66 Contribution margin ratio 50% 60% Required machine hours/unit 0.4 2.0 Urban has only 160,000 machine hours available per year. Write Urban’s machine hour constraint as an inequality. 0.4R + 2D  160,000 machine hours © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 29 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Suppose that Urban decides to make all Regular umbrellas. What is the total contribution margin? Recall that the CM/unit for R is $20. The machine hour constraint is: 0.4R + 2D  160,000 machine hours If D=0, this constraint becomes 0.4R  160,000 machine hours, or R  400,000 units Total contribution margin = $20*400,000 = $8 million Suppose that Urban decides to make all Deluxe umbrellas. What is the total contribution margin? Recall that the CM/unit for D is $66. If R=0, this constraint becomes 2D  160,000 machine hours, or D  80,000 units Total contribution margin = $66*80,000 = $5.28 million © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 30 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) If the choice is between all Ds or all Rs, then clearly making all Rs is better. But how do we know that some combination of Rs and Ds won’t yield an even higher contribution margin? make all Ds; get $5.28 million make all Rs; get $8 million In a one constraint problem, a combination of Rs and Ds will yield a contribution margin between $5.28 and $8 million. Therefore, Urban will only make one product, and clearly R is the best choice. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 31 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) The general rule for constrained resource decisions with one scarce resource is to first make only the product with the highest contribution margin per unit of the constrained resource. In Urban’s case, the sole scarce resource was machine hours, so Urban should make only the product with the highest contribution margin per machine hour. R: CM/mach hr = $20/0.4mach hrs = $50/mach hr D: CM/mach hr = $66/2mach hrs = $33/mach hr Notice that the total contribution margin from making all Rs is $50/mach hr x 160,000 machine hours to be used producing Rs = $8 million. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 32 Q5: Constrained Resource Decisions (Multiple Scarce Resources) • Usually managers face more than one constraint. • Multiple constraints are easiest to analyze using a quantitative analysis technique known as linear programming. • A problem formulated as a linear programming problem contains • an algebraic expression of the company’s goal, known as the objective function • • for example “maximize total contribution margin” or “minimize total costs” a list of the constraints written as inequalities © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 33 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) Suppose Urban also need 2 and 6 hours of direct labor per unit of R and D, respectively. There are only 120,000 direct labor hours available per year. Formulate this as a linear programming problem. Max 20R + 66D R,D subject to: 0.4R+2D  160,000 mach hr constraint 2R+6D  120,000 DL hr constraint nonnegativity constraints R0 (can’t make a negative D0 amount of R or D) objective function R, D are the choice variables constraints © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 34 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) Draw a graph showing the possible production plans for Urban. Every R, D ordered pair To determine this, graph the is a production plan. constraints as inequalities. But which ones are feasible, 0.4R+2D  160,000 mach hr constraint given the constraints? When D=0, R=400,000 D When R=0, D=80,000 2R+6D  120,000 DL hr constraint When D=0, R=60,000 When R=0, D=20,000 80,000 20,000 60,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 35 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) There are not enough machine hours or enough direct labor hours to produce this production plan. There are enough machine hours, but not enough direct labor hours, to produce this production plan. This production plan is feasible; there are enough machine hours and enough direct labor hours for this plan. D 80,000 The feasible set is the area where all the production constraints are satisfied. 20,000 60,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 36 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) The graph helped us realize an important aspect of this problem – we thought there were 2 constrained resources but in fact there is only one. For every feasible production plan, Urban will never run out of machine hours. D The machine hour constraint is non-binding, or slack, but the direct labor hour constraint is binding. 80,000 We are back to a one-scarceresource problem. 20,000 60,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 37 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Here direct labor hours is the sole scarce resource. We can use the general rule for one-constraint problems. R: CM/DL hr = $20/2DL hrs = $10/DL hr D: CM/DL hr = $66/6DL hrs = $11/DL hr D Urban should make all deluxe umbrellas. 80,000 Optimal plan is R=0, D=20,000. Total contribution margin = $66 x 20,000 = $1,320,000 20,000 60,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 38 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) Suppose Urban has been able to train a new workforce and now there are 600,000 direct labor hours available per year. Formulate this as a linear programming problem, graph it, and find the feasible set. Max 20R + 66D R,D subject to: 0.4R+2D  160,000 mach hr constraint 2R+6D  600,000 DL hr constraint R0 D0 The formulation of the problem is the same as before; the only change is that the right hand side (RHS) of the DL hour constraint is larger. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 39 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) The machine hour constraint is the same as before. 0.4R+2D  160,000 mach hr constraint D 100,000 2R+6D  600,000 DL hr constraint When D=0, R=300,000 When R=0, D=100,000 80,000 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 40 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) There are not enough machine hours or enough direct labor hours for this production plan. There are enough direct labor hours, but not enough machine hours, for this production plan. There are enough machine hours, but not enough direct labor hours, for this production plan. D 100,000 This production plan is feasible; there are enough machine hours and enough direct labor hours for this plan. 80,000 The feasible set is the area where all the production constraints are satisfied. 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 41 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) How do we know which of the feasible plans is optimal? We can’t use the general rule for one-constraint problems. We can graph the total contribution margin line, because its slope will help us determine the optimal production plan. D 100,000 80,000 The objective “maximize total contribution margin” means that we . . . this would be the choose a production plan so that the optimal production plan. contribution margin is a large as possible, without leaving the feasible set. If the slope of the total contribution margin line is lower (in absolute value terms) than the slope of the machine hour constraint, then. . . 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 42 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) What if the slope of the total contribution margin line is higher (in absolute value terms) than the slope of the direct labor hour constraint? If the total CM line had this steep slope, . . D 100,000 . . then this would be the optimal production plan. 80,000 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 43 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) What if the slope of the total contribution margin line is between the slopes of the two constraints? If the total CM line had this slope, . . D 100,000 . . then this would be the optimal production plan. 80,000 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 44 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) The last 3 slides showed that the optimal production plan is always at a corner of the feasible set. This gives us an easy way to solve 2 product, 2 or more scarce resource problems. D 100,000 R=0, D=80,000 The total contribution margin here is 0 x $20 + 80,000 x $66 = $5,280,000. R=?, D=? Find the intersection of the 2 constraints. 80,000 R=300,000, D=0 The total contribution margin here is 300,000 x $20 + 0 x $66 = $6,000,000. 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 45 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) To find the intersection of the 2 constraints, use substitution or subtract one constraint from the other. multiply each side by 5 Total CM = $5,280,000. D 100,000 80,000 0.4R+2D = 160,000 2R+10D = 800,000 2R+6D = 600,000 2R+6D = 600,000 subtract 0R+4D = 200,000 D = 50,000 Total CM = $20 x 150,000 + 2R+6(50,000) = 600,000 $66 x 50,000 = $6,300,000. 2R = 300,000 R = 150,000 Total CM = $6,000,000. 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 46 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) By checking the total contribution margin at each corner of the feasible set (ignoring the origin), we can see that the optimal production plan is R=150,000, D=50,000. Total CM = $5,280,000. D 100,000 80,000 Knowing how to graph and solve 2 product, 2 scarce resource problems is good for understanding the nature of a linear programming problem (but difficult in more complex problems). Total CM = $6,300,000. 50,000 Total CM = $6,000,000. 150,000 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 47 Q5: Qualitative Factors in Scarce Resource Allocation Decisions The quantitative analysis indicates that Urban should produce 150,000 regular umbrellas and 50,000 deluxe umbrellas. What qualitative issues should Urban consider before finalizing its decision? • The assumption that customer demand is unlimited is unlikely; can this be investigated further? • Are there any long-term strategic implications of minimizing production of the deluxe umbrellas? • What would be the effects of attempting to relax the machine hour or DL hour constraints? • Are there any worker productivity issues that affect this decision? © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 48 Q5: Constrained Resource Decisions (Multiple Products; Multiple Constraints) • Problems with multiple products, one scarce resource, and one constraint on customer demand for each product are easy to solve. • The general rule is to make the product with the highest contribution margin per unit of the scarce resource: – until its customer demand is satisfied – then move to the product with the next highest contribution margin per unit of the scarce resource, etc. • Problems with multiple products and multiple scarce resources are too cumbersome to solve by hand – Excel solver is a useful tool here. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 49 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Urban’s Umbrellas makes two types of patio umbrellas, regular and deluxe. Suppose customer demand for regular umbrellas is 300,000 units and for deluxe umbrellas customer demand is limited to 60,000. Urban has only 160,000 machine hours available per year. What is his optimal production plan? How much would he pay (above his normal costs) for an extra machine hour? Selling price per unit Variable cost per unit Contribution margin per unit Regular $40 20 $20 Deluxe $110 44 $ 66 Required machine hours/unit 0.4 2.0 CM/machine hour $50 $33 Urban should first concentrate on making Rs. He can make enough to satisfy customer demand for Rs: 300,000 Rs x 0.4 mach hr/R = 120,000 mach hrs. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 50 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Selling price per unit Variable cost per unit Contribution margin per unit Regular $40 20 $20 Deluxe $110 44 $ 66 Required machine hours/unit 0.4 2.0 CM/machine hour $50 $33 The 40,000 remaining hours will make 20,000 Ds. The optimal plan is 300,000 Rs and 20,000 Ds. The CM/mach hr shows how much Urban would be willing to pay, above his normal costs, for an additional machine hour. Here Urban will be producing Ds when he runs out of machine hours so he’d be willing to pay up to $33 for an additional machine hour. If customer demand for Rs exceeded 400,000 units, Urban would be willing to pay up to an additional $50 for a machine hour. If customer demand for Rs and Ds could be satisfied with the 160,000 available machine hours, then Urban would not be willing to pay anything to acquire an additional machine hour. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 51 Q5: Constrained Resource Decisions Using Excel Solver To obtain the solver dialog box, choose “Solver” from the Tools pull-down menu. The “target cell” will contain the maximized value for the objective (or “target”) function. Choose “max” for the types of problems in this chapter. Add constraint formulas by clicking “add”. © John Wiley & Sons, 2011 Choose one cell for each choice variable (product). It’s helpful to “name” these cells. Click “solve” to obtain the next dialog box. Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 52 Q5: Constrained Resource Decisions Using Excel Solver Cell B2 was named “Regular” and cell C2 was named Deluxe. =20*Regular + 66*Deluxe =0.4*Regular+ 2*Deluxe =2*Regular+ 6*Deluxe =Regular (cell B2) =Deluxe (cell C2) Then click “solve” and choose all 3 reports. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 53 Q5: Excel Solver Answer Report Microsoft Excel 9.0 Answer Report Refer to the problem on Slide #50. Target Cell (Max) Original Cell Name Value 0 $B$3 Regular The total contribution margin for the optimal plan was $6.3 million. Final Value 6,300,000 The optimal production plan was 150,000 Rs and 50,000 Ds. Adjustable Cells Original Cell Name Value 0 $B$2 Regular 0 $C$2 Deluxe Final Value 150,000 50000 The machine and DL hour constraints are binding – the plan uses all available machine and DL hours. Constraints Cell Value Formula Status 600,000 $B$9=$C$11 Binding 50,000 $B$10 R>0
Not
150,000 $B$10>=$C$10 Binding
150,000
Cell
Name
$B$9 DL hr
© John Wiley & Sons, 2011
Slack
The nonnegativity
constraints for R and D
are not binding; the slack
is 50,000 and 150,000
units respectively.
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 54
Q5: Excel Solver Sensitivity Report
Microsoft Excel 9.0 Sensitivity Report
Refer to the problem on Slide #50.
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value
Cost Coefficient Increase Decrease
$B$2 Regular 150,000
0
20
2
6.8
$C$2 Deluxe
50000
0
66
34
6
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value
Price R.H. Side Increase Decrease
$B$9 DL hr
600,000
9
600000
200000
120000
$B$8 mach hr 160,000
8
160000
40000
40000
$B$11 D>0
50,000
0
0
50000
1E+30
$B$10 R>0
150,000
0
0
150000
1E+30
This shows
how much the
slope of the
total CM line
can change
before the
optimal
production
plan will
change.
The CM per unit for Regular can drop to $13.20 or increase to $22 (all else equal)
before the optimal plan will change. The CM per unit for Deluxe can drop to $60 or
increase to $100 (all else equal) before the optimal plan will change.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 55
Q5: Excel Solver Sensitivity Report
Microsoft Excel 9.0 Sensitivity Report
Refer to the problem on Slide #50.
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value
Cost Coefficient Increase Decrease
$B$2 Regular 150,000
0
20
2
6.8
$C$2 Deluxe
50000
0
66
34
6
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value
Price R.H. Side Increase Decrease
$B$9 DL hr
600,000 8.50
600000
200000
120000
$B$8 mach hr 160,000 7.50
160000
40000
40000
$B$11 D>0
50,000 0.00
0
50000
1E+30
$B$10 R>0
150,000 0.00
0
150000
1E+30
This shows
how much the
RHS of each
constraint can
change
before the
shadow price
will change.
The available DL hours could decrease to 480,000 or increase to 800,000 (all
else equal) before the shadow price for DL would change. The available
machine hours could decrease to 120,000 or increase to 200,000 (all else
equal) before the shadow price for machine hours would change.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 56
Q5: Excel Solver Sensitivity Report
Microsoft Excel 9.0 Sensitivity Report
Refer to the problem on Slide #50.
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value
Cost Coefficient Increase Decrease
$B$2 Regular 150,000
0
20
2
6.8
$C$2 Deluxe
50000
0
66
34
6
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value
Price R.H. Side Increase Decrease
$B$9 DL hr
600,000 8.50
600000
200000
120000
$B$8 mach hr 160,000 7.50
160000
40000
40000
$B$11 D>0
50,000 0.00
0
50000
1E+30
$B$10 R>0
150,000 0.00
0
150000
1E+30
The shadow
price shows
how much a
one unit
increase in
the RHS of a
constraint will
improve the
total
contribution
margin.
Urban would be willing to pay up to $8.50 to obtain one more DL hour and up
to $7.50 to obtain one more machine hour.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 57
Q7: Impacts to Quality of
Nonroutine Operating Decisions
• The quality of the information used in nonroutine
operating decisions must be assessed.
• There may be more information quality issues (and more
uncertainty) in nonroutine decisions because of the
irregularity of the decisions.
• Three aspects of the quality of information
available can affect decision quality.
• Business risk (changes in economic condition, consumer
demand, regulation, competitors, etc.)
• Information timeliness
• Assumptions in the quantitative and qualitative analyses
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 58
Q7: Impacts to Quality of
Nonroutine Operating Decisions
• Short term decision must align to company’s overall
strategic plans
• Must watch for decision maker bias
– Predisposition for specific outcome
– Preference for one type of analysis without considering
other options
• Opportunity costs are often overlooked
• Performing sensitivity analysis can help assess and
minimize business risk
• Established control system incentives (performance
bonuses, etc.) can encourage sub-obtimal decision
making
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 59
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