Transcript Strategic Transfer Pricing, Absorption Costing and

Chapter 11
Decision making
and Relevant Information
Linear Programming as a
decision facilitating tool
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Introduction
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This chapter explores the decision-making
process.
It focuses on specific decisions such as
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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.
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Five-Step Decision Process
Gathering information
2 Making predictions
3 Choosing an alternative
4 Implementing the decision
5 Evaluating performance
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The Meaning of Relevance
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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.
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Quantitative and Qualitative Relevant
Information
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Quantitative factors are outcomes that are measured
in numerical terms:
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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
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Aspiration levels for qualitative factors restrict the feasible
set of alternatives
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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.
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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!
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Short term production decisions
Income
= revenue - cost
Contribution of a Product
= (variable) revenue - variable costs
Contribution Margin
= contribution  number of product units
Rule 1: Do not produce products with a negative
contribution margin.
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Constraints
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Mostly, a company is not free in its decision but
faces constraints
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procurement constraints
production constraints
sales constraints
Constraints might affect
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only single products (e.g. sales constraints)
multiple products
several products compete for scarce resources
(e.g. procurement constraints)
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The formal decision problem
Maximize the firm‘s profit
maxxi ( p1 - k1 ) x1  ... ( pI - kI ) xI - K f
such that
 sales
constraints
 production constraints
 procurement constraints
0  xi  X i
a j1x1 ... a jI xI  Capj
are kept satisfied
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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
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Example
Product
i=1 i=2 i=3
Sales price
200 480 1.100
Variable costs
160 400 1.170
Contribution
40
80
-70
margin
Sales constraint Xi 300 200 600
Input coefficient a1
2
8
5
Input coefficient a2
9
4
1
Machine
Capacity
j=1 j=2
2.500 3.700
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Special case 2:
a single resource constraint
Example:
Resource A
raw material
Resource B
raw material
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Resource 3:
Machine
(limited
capacity)
a1
Product 1
a2
Product 2
Problem: production of an additional unit of product 1
makes production of a1/ a2 units of product 2 impossible
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When should you expand
production 1?
Expansion should increase total contribution
 additional contribution
(p1 - k1) ·1
- loss of contribution
(p2 - k2) · a1/a2
Rule:
a1
p1 - k1 p2 - k2
( p1 - k1 )  ( p2 - k2 ) 
or

a2
a
a
1
2
„Relative contribution margins“
(CM per machine hour)
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Product-Mix Decisions Under
Capacity Constraints
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
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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
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Example
Machine
Capacity
1
2
1.000 3.700
Product
i=1 i=2 i=3
Sales price
200 480 1.100
Variable costs
160 400 1.170
Contribution
40
80
-70
margin
Sales constraint Xi 300 200
600
Input coefficient a1
2
8
5
Input coefficient a2
9
4
1
p1 - k1  40, p2 - k2  80
a1  2, a2  8
p1 - k1 40
 20
a1
2
p2 - k 2 80
  10
a2
8
x1 300;
x2 50;
x3 0
Contribution: 16,000
Profit: 12,000
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Insourcing versus Outsourcing
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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.
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Opportunity Costs, Outsourcing, and Constraints
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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.
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Opportunity Costs, Outsourcing, and Constraints
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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
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Make-or-Buy Decisions
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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.
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Again: Beware of the long-run consequences of
your decision
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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
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Equipment-Replacement Decisions
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Assume
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1.
Approach:
Calculate the present value C of all expenditures for
the new machine
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if the machine will presumably replaced indefinitely: let C
equal the present value of expenditures for the replacemnet
chain
what is gained by postponing the replacement to
the next period at which cost?
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The new machine is more efficient than the old machine.
Revenues will be unaffected.
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 only if c becomes greater than rC.
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Equipment-Replacement Decisions
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Irrelevance of Past Costs:
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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.
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Decisions and Performance Evaluation
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In the real world would the manager replace the
machine?
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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.
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Multiple Constraints
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Activities may be characterized by
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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
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output and input quantities vary linearly with the activity level
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Linear Activity Analysis
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Activities are characterized by column vectors*) a•j:
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component aij
 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)
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component a0j
 represents contribution to gross profit per unit of the activity level;
measurement in: [monetary units]
 a0j = 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 ai• would denote a row vector.
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Linear Activity Analysis, (cont’d)
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Commitments and capacity limits are represented in a
column vector a•0
Activity levels xj may be subject to an upper or lower
bound: xj  xj  xj  0 (xj must always be nonnegative)
Types of restrictions
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minimum output requirement:
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in matrix notation*) :
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input restriction:
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input-output balance:
Sj aij xj  ai0
ai• x  ai0
ai• x  ai0
ai• x = 0
Both sides
negative!
*) x denotes the column vector of activity levels with components xj
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Modeling specific activities
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Pure procurement activity for restricted resource i:
a0j < 0; aij > 0; alj = 0 (l  i); xj  xj
input-output balance: ai• x = 0
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Pure selling activity for a product i produced in
several alternative production activities
a0j > 0; aij < 0; alj = 0 (l  i); xj  xj
input-output balance: ai• x = 0
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Storage activity:
aij = - 1 in line i for the respective good this period
ai+1,j = +1 in line i +1 for the same good next period
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Example: Exercise 2-4, Kaplan/Atkinson: Advanced Management
Accounting, 3rd 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: 40000 liters, D: 15000 liters.
 Labor requirements (hrs per batch): Dept. 1: 12, dept. 2: 18, dept. 3: 15.
8000 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.
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Activities:
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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:
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input-output balances for all products
upper bound for production of C (storage restriction)
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A $4
150 x1
Details of activities
B
100 x1
50 x1
C
x4
200 x2
30 x2
F
20 x3
B $15
40 x3
120 x2
D
x5
D $18
F $ -8
x6
E $0
xj := no. of batches in dept. j (j = 1,...,3)
:= no. of liters of resp. product to be sold (j = 4,...,6)
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A $4
150 x1
B
100 x1
50 x1
C
x4
200 x2
30 x2
F
20 x3
B $15
40 x3
Input-output balances
B: (i = 1) : 100 x1
C: (i = 2) : 50 x1 + 20 x3
D: (i = 3) : 120 x2
E: not relevant
F: (i = 4) : 40 x3 + x6
120 x2
D
x5
D $18
F $ -8
x6
=
x4
 200 x2
=
x5
= 30 x2
E $0
x4  40,000
x5  15,000
Sales restrictions:
B:
D:
Capacity restrictions:
vats:
labor hours: (i = 5):
storage restriction C: (i = 2):
x1  700
x2  120
x3  70
12 x1 + 18 x2 + 15 x3  8000
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50 x1 + 20 x3 – 200 x2  1000
A $4
150 x1
B
100 x1
50 x1
C
x4
Objective function
200 x2
30 x2
F
20 x3
B $15
40 x3
120 x2
for a spreadsheet solution see:
ProductMix.xls at the course
web site
D
x5
D $18
F $ -8
x6
Revenue
Material
Labor
other
S
E $0
x1
x2
x3
-4·150
-15·12
-300
-
-15·18
-825
-
-15·15
-120
-
x4
15
x5
18
x6
-8
15
18
-8
Objective function:
- x- x2- xxx- x6
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System design decisions
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Activities may be reengineered
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New capacity can be introduced
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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
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
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Bottlenecks
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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
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CCs for chapter 11

11-19 (5%)
same as in 11th ed.
 11-21 (5%)
 11-29 (5%) new in 12th ed.
 11-31 (5%) (=11.11-30)
 11-23 (3%) (same as in 11th ed.
 11-33 (8%)(=11.11-32)
 11-25 (5%)
 11-35 (8%)
same as in 11th ed.
 11-27 (5%)
 11-41 (similar in 11th ed.)
Excel solution, with calculation of opportunity cost
values for the capacities (15%)
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