ACCA F2 Management Accounting - 2010 - Study text - Emile Woolf Publishing
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Chapter 14: Relevant costs
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with the previous diagram showing the relevant cost of materials. They are the
same!)
Is the machine
in regular use?
Relevant cost = current
replacement cost
Relevant cost =
Opportunity cost.
Opportunity cost = the
hi
g
her of:
Net disposal value
/
scrap value
Net benefit from
alternative use
Yes No
Note on terminology for non-current assets
If you have already studied financial accounting (financial reporting) you will be
familiar with non-current assets, depreciation of non-current assets and net book
value. If you are not familiar with financial accounting yet, the following brief
explanation might be useful.
A non-current asset is held for a number of years. The cost of a non-current asset
is ‘written off’ as an expense in the income statement over its expected useful
life.
There is a annual notional charge in the income statement for the use of an asset.
This is a depreciation charge. For example, if a non-current asset has a life of
four years and costs $40,000, there might be an annual depreciation charge for
the asset of $10,000 each year for four years.
The net book value of a non-current asset is its original cost (assuming that it is
not-re-valued at any time) less the accumulated depreciation to date. The asset
above that cost $40,000 would therefore have a net book value of $30,000 after
one year, $20,000 after two years, $10,000 after three years and $0 at the end of
the fourth year.
The points to note about depreciation and net book value, for the purpose of
relevant costing, are that:
Depreciation charges are a notional annual charge: they do not represent cash
flows
Net book value is a notional value of an asset: it has no economic or ‘cash flow’
significance.
Depreciation and net book value should always be ignored when identifying the
relevant costs of non-current assets.
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Example
A machine was purchased eight years ago for $20,000 and is depreciated at the rate
of $2,000 per year. The net book value of the machine is $4,000 and its net disposal
value is $3,000. A similar machine would cost $45,000 today.
The machine is not due to be replace for another two years, but as it has developed a
fault which cannot be repaired, the company must replace the machine
immediately.
Required
What is the relevant cost of the machine?
Answer
The machine is obviously in regular use. The relevant cost of the machine is
therefore its replacement cost, $45,000.
Note the following points.
The purchase price of $20,000 is not a relevant cost. It is a sunk cost that was
incurred in the past.
Net book values are not relevant costs. They do not represent cash flows or
disposal values. In this example the NBV of $4,000 is not a relevant cost.
The net disposal value of $3,000 is only relevant if the machine will not be
replaced and has no alternative use.
Example
A company has an item of equipment that originally cost $50,000. It would now cost
$60,000 to replace. Its current carrying amount (net book value) is $20,000 and it is
being depreciated by $10,000 each year.
The company does not use the equipment any more, and does not foresee any
further use for it. Another company, not a competitor, has offered to buy the
equipment for $12,000.
What is the relevant cost of the equipment?
Answer
The asset has no other use and would not be replaced if it is disposed of. The
options are to sell the equipment and earn $12,000 or not to sell it and earn nothing.
The relevant cost is $12,000.
Chapter 14: Relevant costs
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Example
A company has an item of equipment that originally cost $30,000. Its net book value
is now $12,000. It could be used now on a three-month contract. If it is not used for
the contract it would be sold off, and the net disposal proceeds would be $4,000.
After use on the contract, the equipment would no longer have any sale value, and
it would have to be dismantled and disposed of at a cost of $2,000.
What is the relevant cost of the equipment?
Answer
The asset has no other use and will not be replaced. If the contract is undertaken, the
company will lose the opportunity to sell the equipment for $4,000. In addition, it
would have to pay disposal costs of $2,000 at the end of the three months. The total
relevant cost is therefore $4,000 + $2,000 = $6,000.
(The net book value is totally irrelevant.)
2.5 Using relevant costs
Relevant costs are used in accounting for decision-making. The costs and revenues
that are taken into consideration when evaluating the effect of a decision must be
the costs and revenues that are relevant to that decision. Non-relevant costs and
revenues must be ignored when evaluating a decision.
The examination syllabus does not cover the use of relevant costs for specific
decision-making problems, but you will come across these in your future studies of
accounting.
Practice multiple choice questions
1 A company is considering whether to undertake a job for a customer. The job would
require 1,800 kilos of a material that is used regularly in production. The company
already holds 1,200 kilos of the material in inventory, which cost $7,200 last month.
The supplier has recently announced a price increase of 5% for the material.
What is the total relevant cost of the material for the contract?
A $3,780
B $7,560
C $10,980
D $11,340 (2 marks)
2 A company is considering a contract that would require 120 hours of skilled labour.
The skilled labour is paid $24 per hour and all skilled employees are fully employed
manufacturing a product to which the following data relates:
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$ $
Selling price
75
Less: Variable costs
Skilled labour 36
Other variable costs 15
51
Contribution per unit
24
No other supply of skilled labour is available.
What is the total relevant cost of the labour for the contract?
A $1,920
B $2,880
C $4,800
D $6,000
(2 marks)
3 A company would need 800kg of material D for a contract it is considering. It
already has 600 kg of the material held in inventory. These materials were
purchased last month, but since then the supplier has increased the purchase price
by 6% to $53. The company uses material D regularly in normal production.
What is the total relevant cost for the contract of raw material D?
A $40,492
B $40,600
C $42,400
D $44,944
(2 marks)
4 A company owns a machine that has a current net book value of $2,700. It has not
been used for several months, but it could now be used on a job for a customer
which would last for up to six months. If the machine is not used for this job, it will
be sold immediately to earn net income of $2,900. After using the machine for the
contract, it would have no further use or value, and it would have to be disposed of
at a cost of $500.
What is the total relevant cost of the machine for the contract?
A $2,400
B $2,700
C $2,900
D $3,400
(2 marks)
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Paper F2
Management Accounting
CHAPTER
15
Limiting factors and
linear programming
Contents
1 Limitingfactordecisions:singlelimitingfactor
2 Limitingfactordecisions:linearprogramming
3 Linearprogramming:graphicalsolution
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Limiting factor decisions: single limiting factor
Definition of a limiting factor
Deciding whether there is a limiting factor
Maximising profit when there is a single limiting factor
Budgeting with one limiting factor
1 Limiting factor decisions: single limiting factor
1.1 Definition of a limiting factor
It is normally assumed in budgeting that a company can produce as many units of
its products (or services) that are necessary to meet the available sales demand.
Sales demand is therefore normally the factor that sets a limit on the volume of sales
in each period.
Sometimes, however, there could be a shortage of a key production resource, such
as an item of direct materials, or skilled labour, or machine capacity. In these
circumstances, the limiting factor setting a limit to the volume of sales and profit in
a particular period is the availability of the scarce resource.
It is assumed in this chapter that an entity makes and sells more than one different
product. When there is a limiting factor, the problem is therefore to decide how
many of each different product to make and sell in order to maximise profits.
1.2 Deciding whether there is a limiting factor
A limiting factor needs to be identified when the budget is prepared. The existence
of a limiting factor can be established by comparing:
the amount of each resource required to produce the quantities of products in
the budget, and
the total amount of the resource that will be available.
Example
A company makes three products, A, B and C, using the same direct labour work
force and the same machines to make all the products. Budgeted data for the
company is as follows.
Product X Product Y Product Z
Budgeted production (units) 30,000 24,000 18,000
Time required per unit minutes minutes minutes
Direct labour time (minutes) 15 20 40
Machine time (minutes 10 15 30
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The company expects to have 26,000 direct labour hours and 21,000 machine hours
available in the period.
Required
Is either direct labour time or machine time a limiting factor?
Answer
We need to compare the time required for production and the time available
Labour time Machine
time
Time required hours
hours
Product X 7,500
5,000
Product Y 8,000
6,000
Product Z 12,000
9,000
Total time required 27,500
20,000
Time available 26,000
21,000
Surplus/(shortfall) (1,500)
1,000
Direct labour time is a limiting factor but machine time is not a limiting factor.
1.3 Maximising profit when there is a single limiting factor
Limiting factor analysis uses the same principles as CVP analysis and relevant
costing, although it is normally sufficient to use the concepts of simple CVP
analysis.
When there is just one limiting factor (other than sales demand), total profit will be
maximised in a period by maximising the total contribution earned with the
available scarce resources.
The objective should be to maximise total contribution.
This will be achieved by maximising the contribution in total from the scarce
resource.
Products should therefore be ranked in order or priority for manufacture and
sale.
The priority ranking should be according to the contribution earned by each
product (or service) for each unit of the scarce resource that the product uses.
The products or services should be produced and sold in this order of priority,
up to the expected sales demand for each product.
The planned output and sales should be decided by working down through the
priority list until all the units of the limiting factor have been used.
In other words, in order to maximise profit, the aim should be to maximise the
contribution for each unit of limiting factor used.
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Example
A company makes four products, A, B, C and D, using the same direct labour work
force on all the products. Budgeted data for the company is as follows.
Product A
B
C D
Annual sales demand (units) 4,000
5,000
8,000 4,000
$
$
$ $
Direct materials cost 3.0
6.0
5.0 6.0
Direct labour cost 6.0
12.0
3.0 9.0
Variable overhead 2.0
4.0
1.0 3.0
Fixed overhead 3.0
6.0
2.0 4.0
Full cost 14.0
28.0
11.0 22.0
Sales price 15.5
29.0
11.5 27.0
Profit per unit 1.5
1.0
0.5 5.0
Direct labour is paid $12 per hour. However, only 6,000 direct labour hours are
available during the year.
Required
Identify the quantities of production and sales of each product that would maximise
annual profit.
Answer
The products should be ranked in order of priority according to the contribution
that they make per direct labour hour.
A
B
C D
$
$
$ $
Sales price per unit 15.5
29.0
11.5 27.0
Variable cost per unit 11.0
22.0
9.0 18.0
Contribution per unit 4.5
7.0
2.5 9.0
Direct labour hours perunit 0.5
1.0
0.25 0.75
Contribution per direct labour hour 9.0
7.0
10.0 12.0
Priority for making and selling 3
rd
4
th
2
nd
1
st
The products should be made and sold in the order D, C, A and then B, up to the
volume of sales demand for each product and until all the available direct labour
hours (limiting factor resources) are used up.
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Profit-maximising budget
Product
Sales units
Direct labour
hours
Contribution
per unit
Total
contribution
$ $
D (1
st
) 4,000 3,000
9.0 36,000
C (2
nd
) 8,000 2,000
2.5 20,000
A (3
rd
) 2,000 (balance) 1,000
4.5 9,000
6,000
65,000
1.4 Budgeting with one limiting factor
You might not be told by an examination question that a limiting factor exists,
although you might be told that there is a restricted supply of certain resources. You
might be expected to identify the limiting factor by calculating the budgeted
availability of each resource and the amount of the resource that is needed to meet
the available sales demand.
Example
A company manufactures and sells two products, Product X and Product Y. The two
products are manufactured on the same machines. There are two types of machine,
and the time required to make each unit of product is as follows:
Product X Product Y
Machine type 1 10 minutes per unit 6 minutes per unit
Machine type 2 5 minutes per unit 12 minutes per unit
Sales demand each year is for 12,000 units of Product X and 15,000 units of Product Y.
The contribution per unit is $7 for Product X and $5 for Product Y.
There is a limit to machine capacity, however, and in each year there are only 3,000
hours of Machine 1 time available and 4,200 hours of Machine 2 time available.
Required
Recommend the quantities of Product X and Y that the company should make and
sell in order to maximise its annual profit.
Answer
The first step is to identify whether or not there is any limiting factor other than sales
demand. To do this we calculate the required machine time to manufacture units of
Product X and Y to meet the maximum sales demand. We then compare this
requirement for machine time with the actual time available.
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Machine type 1
Machine type 2
hours
hours
Time required
To make 12,000 units of Product X 2,000
1,000
To make 15,000 units of Product Y 1,500
3,000
Hours needed to meet sales demand 3,500
4,000
Hours available 3,000
4,200
Shortfall (500)
-
Machine type 1 is a limiting factor, but Machine type 2 is not. To maximise
contribution and profit, we should therefore give priority to the product that gives
the higher contribution per Machine type 1 hour.
Product X Product Y
Contribution per unit $7 $5
Machine type 1 time per unit 10 minutes 6 minutes
Contribution per hour (Machine type 1)
$42 $50
Priority for making and selling 2
nd
1
st
Profit-maximising budget
Product
Sales
units
Machine
type 1 hours
Contribution
per unit
Total
contribution
$ $
Y (1
st
) 15,000
1,500
5.0 75,000
X (2
nd
) - balance 9,000
1,500
7.0 63,000
3,000
138,000
Exercise 1
A company makes four products, W, X, Y and Z, using the same single item of direct
material in the manufacture of all the products. Budgeted data for the company is as
follows.
Product W
X
Y Z
Annual sales demand (units) 4,000
4,000
6,000 3,000
$
$
$ $
Direct materials cost 5.0
4.0
8.00 6.00
Direct labour cost 4.0
6.0
3.00 5.00
Variable overhead 1.0
1.5
0.75 1.25
Fixed overhead 8.0
12.0
6.00 10.00
Full cost 18.0
23.5
17.75 22.25
Sales price 50.0
31.5
59.75 54.25
Profit per unit 32.0
8.0
42.00 32.00
Due to restricted supply, only $78,000 of direct materials will be available during the
year.