Ch 04 Rel Costs LP Spring 2011 Rev

This chapter applies your knowledge

of cost and revenue behavior,

obtained in the previous chapters, to

a variety of operating decisions. The

framework for such decisions

includes the following fundamental

concepts:

Differential costs and revenues:

The costs and revenues that are relevant

to a specific decision are those that differ

as a consequence of the decision. You

have seen this concept earlier, in

deciding among alternative cost

functions.

Sunk costs:

The irrecoverable costs incurred in

the past are usually not relevant in

making decisions that affect future

costs and revenues. In some cases,

sunk costs may be relevant if they

affect the way that managers’

performance is measured.

Opportunity costs:

Opportunity costs represent the benefits

foregone from alternative uses of resources.

A rational decision maker attempts to

minimize opportunity losses, which is the

same as maximizing profits.

Information accuracy:

A central issue in the use of estimated costs

and revenues is the amount of error in the

estimates that will cause the manager to make

a costly mistake. This issue is usually

described as the “sensitivity” of a decision to

changes in estimates or assumptions.

.

Avoid arbitrary allocations

of costs and benefits (e.g.

joint cost allocations).

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,

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

• subject to qualitative considerations.

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?


Direct materials $6.20Direct labor 8.00Variable mfg. overhead 5.80Fixed mfg. overhead 3.50Shipping/handling 2.50Fixed administrative costs 0.88Fixed selling costs 0.36

$27.24

Relevant?yes$20.00

Relevant?yesRelevant?yesRelevant?noRelevant?Relevant?noRelevant?no

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 94,000 unitsSpecial order 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

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?

Special Order Decisions and Capacity Issues

Here the company does not have enough idle capacity to accept the order:

Projected sales to regular customers 94,000 unitsSpecial order 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.

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?


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.

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 =

Direct materials $6.20Direct labor 8.00Variable mfg. overhead 5.80Fixed mfg. overhead 3.50Shipping/handling 2.50Fixed administrative costs 0.88Fixed selling costs 0.36

$27.24

Variable cost/unit for regular sales = $22.50.

$32,000 - $15.50 x 2,000 = $1,000

Alternative calculation: Revenues: Increase, special order sales, 8,000 units @24 $192,000 Decrease, lost regular sales, 2,000 units @38 ( 76,000) Costs: Increase, 6,000 units @ $20 (120,000) Decrease, shipping costs saved, $2.50 per unit 5,000 Net effect (benefit) $ 1,000


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,

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


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?


Gibson Quaid Russell TotalRevenues $390 $433 $837 $1,660 Variable costs 247 335 472 1,054Contribution margin 143 98 365 606Traceable fixed costs 166 114 175 455Division operating income ($23) ($16) $190 151

81$70

Avoidable $154 $96 $139 Unavoidable 12 18 36

$166 $114 $175

Unallocated fixed costsOperating income

Breakdown of traceable fixed costs:



81$70


$166 $114 $175



Use the general rule to determine if Gibson and/or Quaid should

be eliminated.

Use the general rule to determine if Gibson and/or Quaid should

be eliminated.

The general rule shows that we should keep Quaid and drop Gibson.

Gibson QuaidContribution margin $143 $98 Avoidable fixed costs 154 96Effect on profit if keep ($11) $2


81$70


$166 $114 $175




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

81

Gibson's unavoidable fixed costs 12

$81

Unallocated fixed costs

Operating income

Quaid & Russell

only

Profits increase by $11 when Gibson is eliminated.

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?


$11Opportunity cost of eliminating Gibson (14)

($3)Revised effect on profit if drop Gibson

Effect on profit if drop Gibson before considering impact on Quaid's production costs

Profits decrease by $3 when Gibson is eliminated.




$11Opportunity cost of eliminating Gibson (14)

($3)Revised effect on profit if drop Gibson

Effect on profit if drop Gibson before considering impact on Quaid's production costs

Profits decrease by $3 when Gibson is eliminated.


Question: In this case, should Gibson and Quaid both be dropped? Are they truly independent divisions?

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),

• If the decision will affect other aspects of operations, these costs (or lost revenues) must be included in the analysis.


Graham Co. currently 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?

Advantage of “make” over “buy” = [$1.55 - $1.50] x 60,000 = $3,000

The production costs per unit for manufacturing a gasker are:Direct materials $0.65Direct labor 0.45Variable manufacturing overhead 0.40Fixed manufacturing overhead* 0.50

$2.00*$30,000/60,000 units = $0.50/unit

Relevant?Relevant?yesRelevant?yes

Relevant?no

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?

Make or Buy Decisions

Profits increase by $12,000 when the gasker is purchased instead of manufactured.

Advantage of “make” over “buy”before considering discount $3,000

Discount 15,000

Advantage of “buy” over “make” $12,000

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

• 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,


• Managers need to determine which products should first be allocated the scarce resources.

• Usually managers face more than one constraint.

• an algebraic expression of the company’s goal, known as the objective function

• a list of the constraints written as inequalities

• Multiple constraints are easiest to analyze using a quantitative analysis technique known as linear programming.

Constrained Resource Decisions(Multiple Scarce Resources)

• A problem formulated as a linear programming problem contains

• for example “maximize total contribution margin” or “minimize total costs”

Urbane Co. produces two lines of hiking boots, Regular (Product R) and Deluxe (Product D). Pertinent information is shown below.

Required: Recast the information given above in a linear programming format, including (a) the objective function, assuming that the firm aims to maximize its total contribution margin, and (b) the set of constraints.

Product R Product D Sales price per unit $ 90 $ 161 Variable cost per unit $ 70 $ 95 Contribution margin per unit $ 20 $ 66 Machine time per unit (total available is 160,000 hours per period)

0.4 hours

2.0 hours

Labor time per unit (total available is 600,000 hours per period)

2.0 hours

6.0 hours

Constrained Resource Decisions(Multiple Scarce Resources)

Max OI = 20R + 66D - F

.4R+2D 160,000

2R+6D 600,000

subject to:

mach hr constraint

DLH constraint

Constrained Resource Decisions(Two Products; Two Scarce Resources)

Graph these relationships,putting Product DOn the vertical axis.


0.4 hours

2.0 hours


2.0 hours

6.0 hours

100,000

80,000

400,000300,000R

D

0.4R+2D 160,000Machine hr constraint

2R+6D 600,000 Direct labor hr constraint



0.4 hours

2.0 hours


2.0 hours

6.0 hours

100,000

80,000

400,000300,000R

D


There are not enough machine hours or enough direct labor hours for this production plan.

This production plan is feasible; there are enough machine hours and enough

direct labor hours for this plan.

The feasible set is the area where all the production constraints are satisfied.

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.

100,000

80,000

400,000300,000R

D


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.

The objective “maximize total contribution margin” means that we choose a production plan so that the

contribution margin is a large as possible, without leaving the feasible

set.

If the iso-profit line is very shallow. . . this would be the optimal production

plan.

100,000

80,000

400,000300,000R

D


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 iso-profit line is very steep. .

then this would be the optimal

production plan.

100,000

80,000

400,000300,000R

D


What if the slope of the total contribution margin line is between the slopes of the two constraints?

. . then this would be the optimal

production plan.

100,000

80,000

400,000300,000R

D


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.

R=0, D=80,000The total contribution margin here is

0 x $20 + 80,000 x $66 = $5,280,000.

R=300,000, D=0The total contribution margin here is

300,000 x $20 + 0 x $66 = $6,000,000.

R=?, D=?Find the intersection of the 2 constraints.

100,000

80,000

400,000300,000R

D


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.

Total CM = $6,000,000.

Total CM = $6,300,000.

150,000

50,000

100,000

80,000

400,000300,000R

D

0.4R+2D 160,000mach hr constraint

2R+6D 600,000 DL hr constraint


Suppose that additional machine hoursare available at a premium price. •How many additional hours could be used?•What would be the resulting product mix?•What would be the resulting total contribution margin? •What would be the “shadow price” per machine hour?

100,000

80,000

400,000300,000R

D

0.4R+2D 160,000mach hr constraint

2R+6D 600,000 DL hr constraint


Suppose that additional labor hoursare available at a premium price. •How many additional hours could be used?•What would be the resulting product mix?•What would be the resulting total contribution margin? •What would be the “shadow price” per labor hour?


Assume that the firm is considering production of a third product, Product G, that uses the same types of labor and equipment as do Products R and D. Each unit of Product G requires two machine hours and three labor hours, and incurs variable costs of $60 per unit. Assuming that these two resources are constrained as shown in the previous slides, what is the minimum sales price per unit required for Product G?


Assume that the firm is considering production of a third product, Product G, that uses the same types of labor and equipment as do Products R and D. Each unit of Product G requires two machine hours and three labor hours, and incurs variable costs of $60 per unit. Assuming that these two resources are constrained as shown in the previous slides, what is the minimum sales price per unit required for Product G?

Approach: The sales price of Product G must cover its variable costs of production, and also the opportunity costs (or “shadow prices) of the scarce resources (labor and machine time) required for its production. Minimum sales price = variable costs + opportunity costs.

Handout 4(a):Special Order

Decisions

R o tu n d a , In c . m a k e s m u ff in fa n s fo r d e s k to p c o m p u te rs . T h e n o rm a l s e llin g p r ic e is $ 4 5 .0 0 p e r u n it. R o tu n d a w a s a p p ro a c h e d b y a la rg e c o m p u te r m a n u fa c tu re r, U p d ra ft, In c . U p d ra ft w a n ts to b u y 1 0 ,0 0 0 u n its a t $ 3 2 , a n d w ill p a y th e s h ip p in g c o s ts . T h e p e r -u n it c o s ts tra c e a b le to th e p ro d u c t (b a s e d o n e x p e c te d o u tp u t o f 1 0 0 ,0 0 0 u n its ) a re lis te d b e lo w . W h ic h c o s ts a re re le v a n t to th is d e c is io n ?

D ire c t m a te r ia ls $ 8 .0 0D ire c t la b o r 1 2 .0 0V a ria b le m fg . o ve rh e a d 9 .0 0F ixe d m fg . o ve rh e a d 3 .5 0S h ip p in g /h a n d lin g 3 .0 0F ixe d a d m in is tra t ive c o s ts 2 .0 0F ixe d s e llin g c o s ts 1 .0 0

$ 3 8 .5 0

The direct m aterials, direct labor and variable overhead are relevant. The per-unit total variable cost is $29 ($8 + 12 + 9 = $29)

R o tu nd a , In c . m a ke s m u ffin fa n s fo r d esk to p co m p u te rs . T h e n o rm a l se llin g p r ice is $ 4 5 .0 0 pe r u n it. R o tu n d a w a s a p p ro ach e d b y a la rg e com p u te r m a n u fa c tu re r, U p d ra ft, In c . U p d ra ft w a n ts to bu y 1 0 ,00 0 u n its a t $3 2 , a n d w ill p ay th e sh ip p in g co s ts . T h e p e r -u n it co s ts tra ce a b le to th e p ro d u c t (b a se d o n ex p e c te d o u tp u t o f 1 0 0 ,0 0 0 u n its ) a re lis te d b e lo w . W h ich co s ts a re re le v a n t to th is d ec is io n ?

D ire c t m a te ria ls $ 8 .0 0D ire c t la b o r 1 2 .0 0Va ria b le m fg . o ve rh e a d 9 .0 0F ixe d m fg . o ve rh e a d 3 .5 0S h ip p in g /h a n d lin g 3 .0 0F ixe d a d m in is tra t ive c o s ts 2 .0 0F ixe d s e llin g c o s ts 1 .0 0

$ 3 8 .5 0

R e q u ire d : 1 . S u p p ose th a t th e ca p a c ity o f R o tu n d a is 1 2 0 ,0 0 0 u n its a n d p ro je c te d

sa le s to re gu la r cu s tom e rs th is ye a r to ta l 1 0 0 ,0 0 0 u n its . D o e s th e q u a n tita tiv e a n a lys is su g g e s t th a t th e co m p a n y sh o u ld a cce p t th e sp e c ia l o rde r?

The direct materials, direct labor and variable overhead are relevant. The per-unit total variable cost is $29 ($8 + 12 + 9 = $29)

E a ch u n it so ld to U p d ra ft w ill in crea se R o tu n d a ’s p ro fi ts b y $ 3 ( $ 3 2 sa les p rice less $ 2 9 va ria b le u n it co st) , fo r a to ta l in crea se in p ro fi ts o f $ 3 0 ,0 0 0 ( $ 3 x 1 0 ,0 0 0 u n its) .

R o tu n d a , In c . m a k e s m u f f in f a n s fo r d e s k to p c o m p u te r s . T h e n o r m a l s e l l in g p r ic e is $ 4 5 .0 0 p e r u n it . R o tu n d a w a s a p p r o a c h e d b y a la r g e c o m p u te r m a n u fa c tu r e r , U p d r a f t , In c . U p d r a f t w a n ts to b u y 1 0 ,0 0 0 u n its a t $ 3 2 , a n d w i l l p a y th e s h ip p in g c o s ts . T h e p e r - u n i t c o s ts t r a c e a b le to th e p r o d u c t ( b a s e d o n e x p e c te d o u tp u t o f 1 0 0 ,0 0 0 u n i ts ) a r e l is te d b e lo w . W h ic h c o s ts a r e r e le v a n t to th is d e c is io n ?

D ir e c t m a t e r ia ls $ 8 . 0 0D ir e c t la b o r 1 2 . 0 0V a r ia b le m fg . o v e r h e a d 9 . 0 0F ixe d m fg . o v e r h e a d 3 . 5 0S h ip p in g / h a n d l in g 3 . 0 0F ixe d a d m in is t r a t iv e c o s t s 2 . 0 0F ixe d s e l l in g c o s t s 1 . 0 0

$ 3 8 . 5 0

R e q u ir e d : 1 . S u p p o s e th a t th e c a p a c ity o f R o tu n d a is 1 2 0 ,0 0 0 u n i ts a n d p r o je c te d

s a le s to r e g u la r c u s to m e r s th is y e a r to ta l 1 0 0 ,0 0 0 u n i ts . D o e s th e q u a n t i ta t iv e a n a ly s is s u g g e s t th a t th e c o m p a n y s h o u ld a c c e p t th e s p e c ia l o r d e r ?

T h e d irec t m a te ria ls , d irec t la b o r a n d v a ria b le o v e rh e a d a re re lev a n t. T h e p e r- u n it to ta l v a ria b le co st is $ 2 9 ( $ 8 + 1 2 + 9 = $ 2 9 )

2. Suppose instead that the capacity of Rotunda is 105,000 units and projected sales to regular customers this year total 100,000 units. Does the quantitative analysis suggest that the company should accept the special order? If not, what is the minimum price per unit that Rotunda could accept for an order of 10,000 units, without a reduction in profits?


In this case, acceptance of the special order (in full) would displace regular sales of 5,000 units and cause a decrease in total contribution margin of $35,000: Benefit from special order if no capacity constraint: $30,000 Reduction in profits from loss of 5,000 regular sales with a per-unit contribution of $13 ($45 –32): ($65,000) Net: ($35,000)


In this case, acceptance of the special order (in full) would displace regular sales of 5,000 units and cause a decrease in total contribution margin of $35,000: Benefit from special order if no capacity constraint: $30,000 Reduction in profits from loss of 5,000 regular sales with a per-unit contribution of $13 ($45 –32): ($65,000) Net: ($35,000) Alternative calculation: Revenues: Increase, special order sales,10,000 units $320,000 Decrease, lost regular sales, 5,000 units (225,000) Costs: Increase, 5,000 units @ $29 (145,000) Decrease, shipping costs saved, $3 per unit 15,000 Net effect (loss) ($35,000) Note that if the special order revenues could be increased by a total of $35,000, or by $3.50 per unit, Rotunda would be equally profitable with or without the special order.

Handout 4(b):Drop or Keep

Business Segment

Handout 4(b) Drop or keep a business segment

Clock, Inc. has 3 divisions. The Hickory and Dickory Divisions have recently been operating at a loss. Management is considering the elimination of these divisions. Divisional income statements are given below. According to the quantitative analysis, should Clock eliminate Hickory or Dickory or both?

Hickory Dickory Dock TotalRevenues $500 $600 $900 $2,000 Variable costs 320 460 500 1,280Contribution margin 180 140 400 720Traceable fixed costs 240 170 200 610Division operating income ($60) ($30) $200 $110

50$60


$240 $170 $200



Handout 4(b) Drop or keep a business segment

Clock, Inc. has 3 divisions. The Hickory and Dickory Divisions have recently been operating at a loss. Management is considering the elimination of these divisions. Divisional income statements are given below. According to the quantitative analysis, should Clock eliminate Hickory or Dickory or both?


50$60


$240 $170 $200



Hickory’s avoidable fixed costs exceed the division’s contribution margin, so profits will increase by $20,000 if this division is dropped. Dickory’s contribution margin exceeds its avoidable fixed costs, so the division should be retained. Note that after Hickory is dropped, the division’s unavoidable fixed costs will continue, and will be included in Clock’s unallocated fixed costs.

Suppose that the Hickory and Dickory Divisions use the same supplier for a particular production input. If the Hickory Division is dropped, the decrease in purchases from this supplier means that Dickory will no longer receive volume discounts on this input. This will increase the costs of production for Dickory by $32,000 per year. In this scenario, should Clock still eliminate the Hickory Division?

Suppose that the Hickory and Dickory Divisions use the same supplier for a particular production input. If the Hickory Division is dropped, the decrease in purchases from this supplier means that Dickory will no longer receive volume discounts on this input. This will increase the costs of production for Dickory by $32,000 per year. In this scenario, should Clock still eliminate the Hickory Division?

Hickory should be retained because the increase in production cost of $32,000 exceeds the $20,000 gain from shutting down the division.


50$60


$240 $170 $200



Handout 4(c):Multi-Product

Profit Maximization

Two products, one constraint: Arcane Products provides the following revenue and cost information for its two

products, Product P and Product H:

Product P Product H Sales price $200 $170 Variable cost $ 80 $ 80 Contribution margin $120 $ 90 Material per unit 2 lbs. 1 lb.

Total material pounds available: 60 lbs. Total fixed manufacturing costs: $ 2,700

Questions:

1. Write out the profit-volume equation for Arcane Products.

OI = 120P + 90H – 2,700

1. Solve the profit-volume equation for Product H.

H = (2,700 + OI) / 90 – (120 / 90) P

2. Draw a graph of this equation (with units of Product H on the vertical axis).

Determine the optimum production level for Products P and H.

H earns the highest return per material pound used, therefore the company

should produce 60 units of H and zero P.

Slope = -120/90

(2700 + OI) / 90 H

P



1. Determine the value (opportunity cost, or “shadow price”) of material per

pound. $ 90

2. Write out the materials constraint as a linear equation (in this case, as a <

inequality). Solve the constraint equation for product H.

2P + 1H < 60; H < 60 – 2P

3. Include a line to represent the materials constraint on the graph prepared in

question 3 above.

Slope = -120/90

(2700 + OI) / 90

P

H

Slope = -2



1. Holding the price of Product H constant, by what amount would the sales price of Product P

have to change in order for the firm to be indifferent between production of products P and H?





Variable cost of P plus opportunity cost of the two pounds of material removed from H:

$260 (VC of $80 + 2 x $90)






$260 (VC of $80 + 2 x $90)

2. Holding the price of Product P constant, by what amount would the sales price of Product H







$260 (VC of $80 + 2 x $90)



Variable cost of H plus opportunity cost of the pound of material removed from P: $140

(VC of $80 + $60)






$260 (VC of $80 + 2 x $90)




(VC of $80 + $60)

3. Holding the prices of products P and H constant, assume that a third product, Product T, may

also be produced in the same facility as Products H and P. Product T has variable production

costs of $ 50 per unit, and requires 1.5 pounds of material. What is the minimum required sales

price per unit of Product T, in order not to reduce the firm’s total profit?






$260 (VC of $80 + 2 x $90)




(VC of $80 + $60)

3. Holding the prices of products P and H constant, assume that a third product, Product T, may

also be produced in the same facility as Products H and P. Product T has variable production

costs of $ 50 per unit, and requires 1.5 pounds of material. What is the minimum required sales

price per unit of Product T, in order not to reduce the firm’s total profit?

Variable cost of T plus opportunity cost of the 1.5 pounds of material removed from H:

$185 (VC of $50 + 1.5 x $90)



Two products, multiple constraints: In addition to the information above, you now learn that Arcane Products uses skilled

labor in its products. The skilled labor is in short supply, and a maximum of 120 hours is

available in each period. Each unit of Product P requires two hours, and each unit of

Product H requires three hours, of skilled labor. In addition, the maximum amount of

Product P that can be sold is 45 units per period.

Questions:

1. Write out the skilled labor constraint as a linear equation (in this case, as a <

inequality). 2P + 3H < 120

2. Include a line to represent the skilled labor constraint on the graph prepared above.

(See below)

3. Include a line to represent the market size constraint on the graph prepared above.

(See below)

4. Determine the optimum production level for Products P and H.

H

P

H=30-(120/90)(P)

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

P<45 Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

P<45

Skilled labor2P+3H<120

Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

H<40-2/3(P)

P<45


Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

H<40-2/3(P)

P<45


Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

H<40-2/3(P)

P<45 Material

2P+1H<60


Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

H<60-2(P)

H<40-2/3(P)

P<45 Material

2P+1H<60


Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

H<60-2(P)

H<40-2/3(P)

P<45 Material

2P+1H<60


Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

30

22.5

H=30-(120/90)(P)

H<60-2(P)

H<40-2/3(P)

P<45 Material

2P+1H<60

Skilled labor 2P+3H<120

Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

H

P

60

30 45

40

60

(P=15, H=30)30

22.5

H=30-(120/90)(P)

H<60-2(P)

H<40-2/3(P)

P<45 Material

2P+1H<60


Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

Relaxing a constraint: impact on optimal product mix (one product increases, the other decreases, because the constraints have negative slopes).

1


2

1


2

3

1

H

P

60

30 45

40

60

(P=15, H=30)30

22.5

H=30-(120/90)(P)

H<60-2(P)

H<40-2/3(P)

P<45 Material

2P+1H<60


Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

Assume that you are able to acquire additional labor at a premium price. How much laborwould you be willing to hire, and how muchof a price premium would you be willing to pay?What would be your new product mix and total contribution margin?

Shifts in the profit line as the product on the horizontal axis becomes less profitable.

1


12


12

3

H

P

60

30 45

40

60

(P=15, H=30)30

22.5

H=30-(120/90)(P)

H<60-2(P)

H<40-2/3(P)

P<45 Material

2P+1H<60


Market size

OI=90H+120P-2,700

H=(2,700+OI)/90

-(120/90)P

Assume that your product contribution marginshave been estimated statistically, and you need to evaluate the impact of estimation errors. Bywhat amount could the contribution of productH be different, before the optimum product mix shown here would be less than optimal?

Linear programming problems generally entail many more activities (e.g. products) and constraints than the simpleexample that we have just reviewed. Many dedicated programs are available for the solution of larger-scale andmore 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 thatIn addition to solving for the optimal product mix, the available output includes extensive sensitivity analysisthat permits you to evaluate the potential impacts oferrors in the management accounting measurements thatare imbedded in the formulation of the problem.

max

120p+90h

st

2p+1h<60

2p+3h<120

p<45

end

Formulation of a product mix problem in LINDO:

MaterialLaborMarket

MaterialLaborMarket

Handout 4(d):Relevant CostsMultiple-choice

items

1. Gandy Company has 5,000 obsolete desk lamps that are carried in inventory at a manufacturing cost of $50,000. If the lamps are reworked for $20,000, they could be sold for $35,000. Alternatively, the lamps could be sold for $8,000 for scrap. In a decision model analyzing these alternatives, the sunk cost would be: A. $8,000 B. $15,000 C. $20,000 D. $50,000

1. Gandy Company has 5,000 obsolete desk lamps that are carried in inventory at a manufacturing cost of $50,000. If the lamps are reworked for $20,000, they could be sold for $35,000. Alternatively, the lamps could be sold for $8,000 for scrap. In a decision model analyzing these alternatives, the sunk cost would be: A. $8,000 B. $15,000 C. $20,000 D. $50,000

Additional questions: If the lamps are sold for scrap, what is the opportunity cost? What is the opportunity loss?

2. Hodge Inc. has some material that originally cost $74,600. The material has a scrap value of $57,400 as is, but if reworked at a cost of $1,500, it could be sold for $54,400. What would be the incremental effect on the company's overall profit of reworking and selling the material rather than selling it as is as scrap? A. -$79,100 B. -$21,700 C. -$4,500 D. $52,900

2. Hodge Inc. has some material that originally cost $74,600. The material has a scrap value of $57,400 as is, but if reworked at a cost of $1,500, it could be sold for $54,400. What would be the incremental effect on the company's overall profit of reworking and selling the material rather than selling it as is as scrap? A. -$79,100 B. -$21,700 C. -$4,500 D. $52,900

The net realizable value from rework is $52,900 ($54,400 - $1,500). This is $4,500 below the proceeds from scrap sale ($57,400 - $52,900 = $4,500).

3. Rice Corporation currently operates two divisions which had operating results last year as follows:

Since the Troy Division also sustained an operating loss in the prior year, Rice's president is considering the elimination of this division. Troy Division's traceable fixed costs could be avoided if the division were eliminated. The total common corporate costs would be unaffected by the decision. If the Troy Division had been eliminated at the beginning of last year, Rice Corporation's operating income for last year would have been: A. $15,000 higher B. $30,000 lower C. $45,000 lower D. $60,000 higher

3. Rice Corporation currently operates two divisions which had operating results last year as follows:

Since the Troy Division also sustained an operating loss in the prior year, Rice's president is considering the elimination of this division. Troy Division's traceable fixed costs could be avoided if the division were eliminated. The total common corporate costs would be unaffected by the decision. If the Troy Division had been eliminated at the beginning of last year, Rice Corporation's operating income for last year would have been: A. $15,000 higher B. $30,000 lower C. $45,000 lower D. $60,000 higher

Dropping the Troy Division would reduce contribution margin by $100,000 and fixed costs by $70,000 for a net decrease in operating income of $30,000.

4. Beaver Company (a multi-product firm) produces 5,000 units of Product X each year. Each unit of Product X sells for $8 and has a contribution margin of $5. If Product X is discontinued, $18,000 of fixed overhead would be eliminated. As a result of discontinuing Product X, the company's overall operating income would: A. decrease by $25,000 B. increase by $43,000 C. decrease by $7,000 D. increase by $7,000

4. Beaver Company (a multi-product firm) produces 5,000 units of Product X each year. Each unit of Product X sells for $8 and has a contribution margin of $5. If Product X is discontinued, $18,000 of fixed overhead would be eliminated. As a result of discontinuing Product X, the company's overall operating income would: A. decrease by $25,000 B. increase by $43,000 C. decrease by $7,000 D. increase by $7,000

Dropping Product X would decrease contribution margin by $25,000 and reduce fixed costs by $18,000, for a net income decrease of $7,000.

5. Milli Company plans to discontinue a division that generates a total contribution margin of $20,000 per year. Fixed overhead associated with this division is $50,000, of which $5,000 cannot be eliminated. The effect of this discontinuance on Milli's operating income would be an increase of: A. $5,000 B. $20,000 C. $25,000 D. $30,000

5. Milli Company plans to discontinue a division that generates a total contribution margin of $20,000 per year. Fixed overhead associated with this division is $50,000, of which $5,000 cannot be eliminated. The effect of this discontinuance on Milli's operating income would be an increase of: A. $5,000 B. $20,000 C. $25,000 D. $30,000

Closing the division would reduce contribution margin by $20,000 and reduce fixed costs by $45,000, for a total increase of $25,000 in operating income.

6. Supler Company produces a part used in the manufacture of one of its products. The unit product cost is $18, computed as follows:

An outside supplier has offered to provide the annual requirement of 4,000 of the parts for only $14 each. It is estimated that 60 percent of the fixed overhead cost above could be eliminated if the parts are purchased from the outside supplier. Based on these data, the per-unit dollar advantage or disadvantage of purchasing from the outside supplier would be: A. $1 disadvantage B. $1 advantage C. $2 advantage D. $4 disadvantage

6. Supler Company produces a part used in the manufacture of one of its products. The unit product cost is $18, computed as follows:

An outside supplier has offered to provide the annual requirement of 4,000 of the parts for only $14 each. It is estimated that 60 percent of the fixed overhead cost above could be eliminated if the parts are purchased from the outside supplier. Based on these data, the per-unit dollar advantage or disadvantage of purchasing from the outside supplier would be: A. $1 disadvantage B. $1 advantage C. $2 advantage D. $4 disadvantage

Purchasing from the outside supplier at $14 per unit would avoid costs per unit of $16 ($13 variable unit costs and $3 avoidable fixed costs.

7. Holden Company produces three products, with costs and selling prices as follows:

A particular machine is a bottleneck. On that machine, 3 machine hours are required to produce each unit of Product A, 1 hour is required to produce each unit of Product B, and 2 hours are required to produce each unit of Product C. In which order should it produce its products? A. C, A, B B. A, C, B C. B, C, A D. The order of production doesn't matter.

7. Holden Company produces three products, with costs and selling prices as follows:

A particular machine is a bottleneck. On that machine, 3 machine hours are required to produce each unit of Product A, 1 hour is required to produce each unit of Product B, and 2 hours are required to produce each unit of Product C. In which order should it produce its products? A. C, A, B B. A, C, B C. B, C, A D. The order of production doesn't matter.

The products should be produced in the order of their contribution per machine hour.The contribution per machine hour is $4 for Product A, $5 for Product B and $4.50 for Product C. The ordering should be B, C and A.

Ch 04 Rel Costs LP Spring 2011 Rev

Documents

incremental costs

opportunity costs

relevant costs x

sunk costs

differential costs

irrecoverable costs

future costs

shipping costs