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ACCA F5

Performance Management (PM)

业绩管理

ACCA Lecturer: Kimberley Gong

Copyright © ACCAspace.comACCAspace 中国ACCA特许公认会计师教育平台 2

1

2

What are limiting factors?

One limiting factor/Multi-limiting factor

Content of chapter 8

3 Shadow prices

4 Lecture example


Limiting factor analysis

What are limiting factors?

A limiting factor is any factor that is in scarce supply

and that stops the organisation from expanding its

activities further. Examples:

Demand

Materials

Labour

Machine hours

Money



One limiting factor

Usual objective is to maximise profit

Fixed costs are unaffected in short term

Maximise contribution



One limiting factor-key factor analysis

1. Identify the scarce resource.

2. Calculate the contribution per unit for each

product.

3. Calculate the contribution per unit of the scarce

resource for each product.

4. Rank the products in order of the result from 3.

5. Allocate the resources using this ranking.


Lecture example 1

Cotton ltd produces three products P1, P2, P3. The

maximum machine hours per week and labor hours

are 1000hours and 900 hours. What is the optimal

production plan?

Selling prince 250 240 200

Variable cost 130 130 100

Fixed cost 80 80 80

Profit 40 30 20

Demand per week

60 60 60

Machine hour per unit

12 10 5

Labour hour per unit

6 5 4


Lecture example 1

Step1 : Total machine hrs needs

60 * ( 12 + 10 + 5 ) = 1620 > 1000 hrs

Total labour hours needs

60 * ( 6 + 5 + 4 ) = 900

MACHINE HOURS IS LIMITED RESOURCES

Step2 : contribution per unit =

P1 P2 P3

120 110 100

120/12=10 11 20

3 2 1

ContributionContribution/hrs

Rank


Lecture example 1

1st : P3 = 60*5 = 300 hrs

2nd : P2 = 60*10 = 600 hrs

3rd : P1(B) = 1000 – 900 = 100 hrs

100/12 = 8 , 8*12 = 96 hrs



Multi-limiting factor---linear programming analysis

A) Define the variables (x, y)

B) Define and formulate the objective

C) Formulate the constraints

D) Draw a graph identifying the feasible region

E) Draw ISO contribution line to Solve the optimal

production plan

F) Answer the question


Lecture example 2

Soft company makes 2 products in 3 departments.

Details are shown below:

Formulate a linear program and find the optimal

production plan.

Product A Hours per unit

Product B Hours per unit

Availablehours

Department X 10 15 18000

Department Y 5 15 12000

Department Z 15 8 15000

Contribution per unit

8 12


Lecture example 2

Step 1 : Identify X = the optimal number of product A

Y = the optimal number of product B

Step 2 : Identify ISO contribution line is to max 8X + 12Y

Step 3 : constraints

10X + 15 Y <=18000

5X + 15Y <= 12000

15X + 8Y <= 15000

X , Y >= 0


Lecture example 2

Step 4 : feasible area

15X + 8Y = 150005X + 15Y = 12000

10X + 15Y = 18000

8X + 12 Y


Lecture example 2

Step 5 : X = 697 , Y = 567



Slack/Surplus

Slack: Resource actually used<Resource available.

Surplus: Actual outcome>minimal requirement



Shadow prices

A shadow price or (dual price) is:

The additional contribution generated from one

additional unit of limiting factor.

The opportunity cost of not having the use of one

extra unit.

The maximum extra amount that should be paid

for one additional unit of scarce resource.


Lecture example 3

WX manufactures two products A and B. Both

products pass through two production

departments, mixing and shaping. The company’s

objective is to maximise contribution to fixed costs.

Product A is sold for $1.5/unit while product B is

priced at $2/unit. There is unlimited demand for A

but demand for B is limited to 13, 000 units per

annum. The machine hours of each department are

restricted to 2400 per annum.


Lecture example 3

Required: Calculate the shadow price of one hour of

machine time in Shaping department

Machine hours required Variable cost per unit

Mixing Shaping

Product A 0.06hrs 0.04hrs $1.3

Product B 0.08hrs 0.12hrs $1.7


Lecture example 3

Step 1 : X = A , Y = B

Step 2 : max 0.2X + 0.3Y

Step 3 : constraints

0.06X + 0.08Y <= 2400

0.04X + 0.12Y <= 2400

Y <= 13000

X , Y >= 0


Lecture example 3

Y = 13000

0.06X + 0.08Y = 2400 0.04X + 0.12Y = 2400


Lecture example 3

Step 5 : X = 24000 , Y = 12000

X1 = 23986 , Y1 = 12015

Additional contribution = 8400 – 8401.7 = 1.7



Implications of shadow price

Management can use shadow prices to measure

the maximum premium that they would be

willing to pay for one more unit of the scarce

resource.

It is possible for management to negotiate a

lower shadow price than calculation.

After a certain point there will be little point in

buying more of the scarce resource as any non-

critical constraints will become critical.

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