Chapter 3: CVP Analysis

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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.

• If the special order replaces a portion of normal
  operations, then the opportunity cost of
  accepting the order must be included in
  incremental costs.

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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.

• If the business segments elimination will affect
  continuing operations, the opportunity costs of
  its discontinuation must be included in the
  analysis.

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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.

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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.

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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 companys goal,
  known as the objective function

• for example maximize total contribution margin
  or minimize total costs

• a list of the constraints written as inequalities

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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.

subject to
mach hr constraint
0.4R2D ? 160,000
2R6D ? 120,000
DL hr constraint
R ? 0
D ? 0
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Constrained Resource Decisions(Two Products Two
Scarce Resources)
In order to provide a more extensive
example, assume that the direct labor hours are
limited to 600,000 hours. All other information
is unchanged from earlier.
subject to
mach hr constraint
0.4R2D ? 160,000
2R6D ? 600,000
DL hr constraint
R ? 0
D ? 0
Graph these relationships,putting Product D On
the vertical axis.
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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).The following example will show how a
dedicated software program, LINDO, allows the
solution of more realistic problems. In addition,
the program permits us to evaluate the
sensitivity of our solutions to variations in the
estimated costs, resource constraints, and other
information that is used in formulating the
product mix problem.
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Relaxing a constraint impact on optimal product
mix (one product increases, the other decreases,
because the constraints have negative slopes).
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2
1
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H
Market size
60
Material
Plt45
2P1Hlt60
Assume that you are able to acquire additional
labor at a premium price. How much labor would
you be willing to hire, and how much of a price
premium would you be willing to pay? What would
be your new product mix and total contribution
margin?
Hlt60-2(P)
40
(P15, H30)
30
OI90H120P-2,700 H(2,700OI)/90 -(120/90)P
Skilled labor 2P3Hlt120
Hlt40-2/3(P)
H30-(120/90)(P)
30
45
60
22.5
P
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H
Market size
60
Material
Plt45
2P1Hlt60
Assume that you are able to purchase
additional material at a premium price. How
much would you be willing to purchase, and how
much of a price premium would you be willing to
pay? What would be your new product mix and total
contribution margin?
Hlt60-2(P)
40
(P15, H30)
30
OI90H120P-2,700 H(2,700OI)/90 -(120/90)P
Skilled labor 2P3Hlt120
Hlt40-2/3(P)
H30-(120/90)(P)
30
45
60
22.5
P
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Shifts in the profit line as the product on the
horizontal axis becomes less profitable.
3
2
1
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H
Market size
60
Material
Plt45
2P1Hlt60
Assume that your product contribution
margins have been estimated statistically, and
you need to evaluate the impact of estimation
errors. By what amount could the contribution of
product H be different, before the optimum
product mix shown here would be less than
optimal?
Hlt60-2(P)
40
(P15, H30)
30
OI90H120P-2,700 H(2,700OI)/90 -(120/90)P
Skilled labor 2P3Hlt120
Hlt40-2/3(P)
H30-(120/90)(P)
30
45
60
22.5
P
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H
Market size
60
Material
Plt45
2P1Hlt60
Assume that your product contribution
margins have been estimated statistically, and
you need to evaluate the impact of estimation
errors. By what amount could the contribution of
product P be different, before the optimum
product mix shown here would be less than
optimal?
Hlt60-2(P)
40
(P15, H30)
30
OI90H120P-2,700 H(2,700OI)/90 -(120/90)P
Skilled labor 2P3Hlt120
Hlt40-2/3(P)
H30-(120/90)(P)
30
45
60
22.5
P
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Cost of prediction error
Our earlier evaluation of the sensitivity of the
optimal product mix to mis-estimates of the unit
contribution margins indicates that for product
H, the initial solution remains optimal as long
as the unit contribution remains between 80 and
200 per unit. Assume that the actual unit
contribution margin for product H is 70 per
unit. What has been the cost of the estimation
error, if the company produced the product mix
that was indicated by your earlier solution?
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Linear programming problems generally entail
many more activities (e.g. products) and
constraints than the simple example that we have
just reviewed. Many dedicated programs are
available for the solution of larger-scale
and more realistic decisions. A very friendly
(easy-to-use) program available at UMass is
LINDO. The following slides illustrate the
formulation and solution of our example problem
using LINDO. Note that In addition to solving for
the optimal product mix, the available output
includes extensive sensitivity analysis that
permits you to evaluate the potential impacts
of errors in the management accounting
measurements that are imbedded in the formulation
of the problem.
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Formulating and solving a Product-mix problem
using LINDO