ba2 fundamentals of management accounting · costing systems i – absorption and marginal costing...
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Costing systems I – Absorption and Marginal costing
66
1. Costing systems
So let's set the scene! You are at your friend’s house sitting on the sofa, when
they come back from the kitchen with a can of the latest energy drink. As
they open it and take a sip you look at the price label still stuck to the can
which reads £1.99. You think to yourself 'so they sell it for £1.99 but I bet it
costs them less than a penny to make!'
I'm sure we've all had this thought about a product at some point!
“That's easy!” you might think. “Isn't the cost of something just however much
we paid for it?”
No, not usually!
The actual price paid is not as obvious as you might think.
Imagine you own a business building toy cars and this week you finished
building two new models: Car A and Car B.
The parts for Car A cost £200.
The parts for Car B cost £2,000.
Both have a selling price of £3,000.
On the surface, it appears that Car A is far more profitable than Car B. By
the looks of things you might even consider specialising in producing
Car A and forgetting about Car B altogether.
But what if Car A took five days to build and Car B only took an hour? What if
you needed to hire three different specialists just to assist in the building of
Car A? What if Car A needs £20,000 worth of special machinery to build?
What if you needed to pay rent for a new factory just to manufacture Car A? In
light of this information, what is real cost of Car A and Car B?
As you can see, costing is not always a simple exercise. Accurately costing
products is important because if you don’t know the cost of your product,
there’s no way to know whether it’s profitable.
To overcome this problem, corporations use costing systems. Costing
systems take costs and accurately allocate them to outputs. This allows
corporations to determine the actual costs of producing each product
and give them a better indication of each unit’s profitability. Helping
them make effective decisions.
Costing systems I – Absorption and Marginal costing
67
2. Absorption/Full costing
One of the costing systems used by companies to accurately assess
the cost of a product is absorption costing (also known as full costing.)
Traditional absorption costing is an accounting method used to
determine the full production cost per unit – hence it's other name!
The full production cost includes:
• Direct costs or prime costs such as the cost of materials (e.g. nuts
and bolts) and labour (e.g. the wages of our factory workers).
• Indirect costs known as production overheads (e.g. electricity or new
machinery).
Going back to our toy car example, to calculate the full production cost of a
unit, it's obvious that we need to add the costs of the parts (materials) and the
salary we pay the factory worker to build our product, these are our direct
costs. However, looking at the bigger picture, these are not the only things we
have to pay for to make toy cars. We cannot ignore our indirect costs such
as rent and new machinery. For these indirect costs then, we need a
method to fairly allocate them to the production side.
Our company makes more than one product (like most companies do)
so it would be inaccurate to say that all of the indirect costs are due to
the production of one particular product. This could lead this product's
selling price being set too high and another products selling price too low. It
would also be incorrect to split the costs equally over our production units
(e.g. half for car A, half for car B) because one product may require a much
more intensive and costly process.
The following section on the absorption costing system will show you how to accurately calculate the cost of these overheads and allocate them to
particular cost centres based on relevant information. The definition of a
cost centre is a part of an organisation which can have particular costs
charged to it. For example the salaries of the staff in the admin division can be
charged to the admin cost centre.
As you read through, remember our goal in this process is to end up with an
accurate overhead cost per unit.
Costing systems I – Absorption and Marginal costing
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Step 1 – Overhead allocation
The first stage of correctly apportioning overhead costs to cost units is to collect together overhead costs into relevant cost centres and categories.
Let's take an example of a pie shop business. The business has four main
cost centres: Preparation, Baking, Purchasing and Admin. Two of these are
production cost centres which are directly related to making the pies. The
other two are service cost centres which are more related to supporting the
production.
The overhead costs directly related to these cost centres are recorded and
grouped together. Let's say they are as follows:
Directly allocated costs:
£
Preparation 60,000
Baking 30,000
Purchasing 50,000
Admin 10,000
We may also have overheads that relate to the business as a whole and
which cannot be specifically allocated to a particular cost centre. For
example, electricity will be used in all areas of the business including
powering the ovens in the baking department or the lighting in the admin
department etc. In this case these general overheads are:
General overheads:
£
Rent 100,000
Machine maintenance 50,000
Water 20,000
Electricity 60,000
Heating 40,000
Step 2 – Apportioning general overheads to cost centres
Remember the aim of absorption costing is to calculate the full cost of a unit of production, so in order to relate an overhead to a cost unit accurately
we want to end up with all overheads in the production cost centres as
these most closely relate to the production of units. It will then be much
easier to relate the costs back to the cost of producing each unit. The process
of sharing overhead costs between production departments is called
apportionment.
Step 2 takes our general overheads and apportions them to cost centres.
To do this, we must decide what is the fairest way to spread our overheads
into cost centres.
Costing systems I – Absorption and Marginal costing
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Let's start with rent. Rent is most closely related to floor space – the higher
the floor space the higher the rent.
Here's some information that will help us to do this:
Preparation Baking Purchasing Admin
Floor space (m²) 300 200 400 100
Original machine cost £ 50,000 100,000 30,000 20,000
Similarly we can apportion water, electricity and heating by floor space, whereas machine maintenance should be apportioned by the original cost of
the machine as that is a fairer basis of spreading those costs.
We now need to work out exactly how much of each overhead should be
apportioned to each cost centre. We’ll start by calculating the proportion of
floor space used by each cost centre. As you can see our business has a total
of 1000m² worth of space and each cost centre utilises a different amount.
Using the table above we can work out the floor space proportions for each
cost centre by taking the amount used by the department and dividing by our
total of 1000m², then multiplying by 100. For example, the percentage that
the preparation department uses is 300m²/1000m² x 100 = 30%. We've
worked out the rest in the following table:
Preparation Baking Purchasing Admin
Floor space (m²) 300 200 400 100
Percentage of total floor space 30% 20% 40% 10%
Knowing these percentages, we can now calculate the amount of rent, water,
electricity and heating to attribute to each cost centre:
Preparation Baking Purchasing Admin
(30%) (20%) (40%) (10%)
Rent (£100,000) 30,000 20,000 40,000 10,000
Water (£20,000) 6,000 4,000 8,000 2,000
Electricity (£60,000) 18,000 12,000 24,000 6,000
Heating (£40,000) 12,000 8,000 16,000 4,000
Total 66,000 44,000 88,000 22,000
We can now do the same for the cost of the machines. The original cost of
all machines was £200,000, so we can divide the individual machine cost for
each department by this total. We can then create the following table:
Costing systems I – Absorption and Marginal costing
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Preparation Baking Purchasing Admin
Original machine cost 50,000 100,000 30,000 20,000
Percentage of total
machine cost 25% 50% 15% 10%
Our machine maintenance overhead cost was £50,000. So using the
percentages above, we can find out how much the maintenance costs in each
department. For example, the majority of expensive machinery is found in the
baking department (50%), so 50% of the total machine maintenance can be
apportioned there.
Preparation
(25%)
Bakin
g
(50%
)
Purchasing
(15%)
Admin
(10%)
Machine maintenance
(£50,000) 12,500 25,000 7,500 5,000
With this information we can now find the total apportioned overhead cost of
each cost centre:
Preparation Baking Purchasing Admin
£ £ £ £
Allocated Costs 60,000 30,000 50,000 10,000
Apportioned Costs:
Rent
30,000
20,000
40,000
10,000
Machine Maintenance 12,500 25,000 7,500 5,000
Water 6,000 4,000 8,000 2,000
Electricity 18,000 12,000 24,000 6,000
Heating 12,000 8,000 16,000 4,000
Total
138,500
99,000
145,500
37,000
Step 3 - Re-apportionment of service cost centres into
production costs centres
So, we have attributed our overhead costs to the various cost centres that
make up our business. However, it's difficult to directly absorb service
costs into direct production cost units. After all – how much administration
cost, for example, should relate to each unit – very difficult to say.
The way we overcome this problem is to re-apportion the service costs
Costing systems I – Absorption and Marginal costing
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proportionately between the two production cost centres.
Costing systems I – Absorption and Marginal costing
72
The following data shows the extent of work carried out by a particular service
cost centre for the production side:
Service cost centre
Preparation Baking Purchasing Admin
Purchasing 45% 35% / 20%
Admin 25% 65% 10% /
We can use these percentages to take the costs out of the purchasing and
administration departments and instead put them into preparation and
baking where they can be directly related to the units produced.
There are three main methods of re-apportioning service cost centres, each
with their own characteristics:
• The Direct Method
• The Step Method
• The Reciprocal Method
The Direct method
This is the simplest and quickest method of apportioning service costs
into production. Here we ignore any services carried out by service cost
centres on behalf of each other (inter-cost centre service).
In our case this would mean disregarding the 20% of work purchasing did for
admin and the 10% of work the admin did for purchasing.
Preparation Baking Purchasing Admin
£ £ £ £
Apportioned costs 138,500 99,000 145,500 37,000
Service cost centre
*Purchasing (45:35:20)
81,844
63,656
(145,500)
/
**Admin 10,278 26,722 / (37,000)
230,622 189,378 / /
In this case the 45, 35, 20 split would instead become a 45:35 ratio for the
purchasing costs, being absorbed exclusively into the production cost
centres.
*The 45 and 35 now form a ratio rather than a percentage so need to be
calculated differently:
Costing systems I – Absorption and Marginal costing
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45 + 35 = 80
Preparation
45 x 145,500
80
= 81,844
Baking
35 x 145,500
80
= 63,656
** The same goes for the admin costs;
25 + 65 = 90
Preparation
25 x 37,000
90
= 10,278
Baking
65 x 37,000
90
= 26,722
As you can see, these service costs are removed as they are absorbed by
production costs leaving us with grand totals of 0 in each of the service cost
centre columns.
Costing systems I – Absorption and Marginal costing
74
The Step method
In the step method we firstly distribute the costs of one service centre
department, then the next and so on until all service centres have been
covered. This time we do not ignore the work service centres do for each
other. Let's see how this works:
Let’s start with the purchasing cost centre. We can see that it is to be
distributed using a 45, 35 and 20 split, giving us:
Preparation = 145,500 x 45% = 65,475
Baking = 145,500 x 35% = 50,925
Admin = 145,500 x 20% = 29,100
Preparation Baking Purchasing Admin
£ £ £ £
Apportioned costs 138,500 99,000 145,500 37,000
Service cost centre
purchasing (45:35:20)
65,475
50,925
(145,500)
29,100
203,975 149,925 0 66,100
The admin cost centre can now be absorbed into preparation and baking
using the (25:65) ratio (ignoring the 10% related to the purchasing):
Preparation
25 x 66,100
90
= 18,361
Baking
65 x 66,100
90
= 47,739
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Chapter 4 Costing systems I – Absorption and Marginal costing
Preparation
£
Baking Purchasing Admin
£ £ £
Apportioned costs 203,975 149,925 0 66,100
Admin (25:65) 18,361 47,739 / (66,100)
222,336 197,664 0 0
The weakness of the step method is that in this second step we ignored the
10% of work done by admin for purchasing giving us a good, but not
completely accurate final result. It is however, more straight forward than
our final method; let's have a look at that!
The Reciprocal method
Our last method is the longest and most complicated, but also the most
accurate! The reciprocal method is the best method to use if there are lots of
service cost centres that have all contributed to each other to some extent,
under this method all inter-service work is fully recognised and catered
for.
The reciprocal method works by apportioning costs out as intended to each
cost centre, the next cost centre in turn apportions its costs out as
intended, this carries on until there is nothing left to apportion from any
service cost centre, perhaps this table will demonstrate this more
effectively:
Preparation Baking Purchasing Admin
Apportioned costs
£
138,500
£
99,000
£
145,500
£
37,000
Service cost centre
Purchasing (45:35:20) 65,475 50,925 (145,500) 29,100
66,100
Admin (25:65:10) 16,525 42,965 6,610 (66,100)
As you can see, this time we apportioned the admin costs as intended (25,
65, 10) which made a difference to the amounts that were added onto
preparation and baking.
But there's a problem – it also added cost back to the purchasing column
which had been emptied during the previous step, but it now has a number in
it so we must repeat the apportionment out of purchasing again. We now
continue in this fashion until all service costs have been completely
absorbed and exhausted, like so:
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Chapter 4 Costing systems I – Absorption and Marginal costing
Preparation
£
Baking Purchasing Admin
£ £ £
Apportioned costs 138,500 99,000 145,500 37,000
Service cost centre
Purchasing (45:35:20)
65,475
50,925
(145,500)
29,100
66,100
Admin (25:65:10) 16,525 42,965 6,610 (66,100)
6,610
Purchasing (45:35:20) 2,975 2,313 (6,610) 1,322
1,322
Admin (25:65:10) 330 860 132 (1,322)
132
Purchasing (45:35:20) 60 46 (132) 26
26
Admin (25:65:10) 6 17 3 (26)
3
Purchasing (45:35:20) 1 1 (3) 1
1
Admin (25:65:10) / 1 / (1)
223,872 196,128 / /
As you can see from the table above, by using the reciprocal method, we have
now apportioned the overhead costs from the service cost centres in full to
production cost centres
Step 4 – Apportioning overheads to cost unit production
We want to calculate the full cost of a unit of production and now that we know our overall overhead costs for each production cost centre we
can absorb it directly into production.
An assumption of absorption costing is that the higher the level
activity/volume produced, the higher the cost of that activity will be. This is
summarised by using what is known as the overhead absorption rate, or
OAR. The OAR is calculated by dividing the production overhead by the
activity level:
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Costing systems I – Absorption and Marginal costing
Production overhead
Activity level
= Overhead absorption rate
The basis of our activity level should be the one that most fairly reflects the
work in a particular department. For example, our baking department has the
most machines and uses the most machine hours, therefore it would be most
accurate to absorb the units of production by the number of machine hours.
Other suitable figures which we can base our absorption rate on include:
• Per unit produced
• Labour hours
• % of prime cost
Returning to our example, let us assume that the company chose the direct
method of re-apportionment and so has overheads of £230,622 and
£189,378 per our earlier working.
The following data has also been recorded regarding labour and machine
hours in those departments:
Preparation Baking
Overheads £230,622 £189,378
Labour hours 50,000 5,000
Machine hours 3,000 60,000
Units 100,000 100,000
So… how do we calculate the OAR for both the preparation and the
baking department?
We should choose the basis that most fairly reflects the work in a particular
department. We can see from the information that the preparation
department is a manual process with many more labour hours than machine
hours, whereas for the baking department it is machine hours that are the
focus of the work. As such it is fairest to use those as the basis for splitting
our overheads between units. We can now calculate our OAR:
Preparation
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Costing systems I – Absorption and Marginal costing
230,622
50,000
= £4.61 per labour hour
Overheads for the preparation department are absorbed a rate of £4.61 per
labour hour; for every labour hour worked on a particular pie in that
department we'll include £4.61 of overhead cost.
Baking
189,378
60,000
= £3.16 per machine hour
So, overheads for the baking department are absorbed a rate of £3.16 per
machine hour.
Let’s put this all together!
Our pie company makes a particular pie ‘the big one’ and the following costs
have been identified:
Direct materials (per unit) £6
Direct Labour hours per pie
- Preparation 1.5hrs
- Baking 0.5hrs
Direct machine hours per pie
- Preparation 0.5hrs
- Baking 3hrs
Labour paid at £7 an hour
So, first of all we need to calculate our direct labour costs. We know that
labour is paid at £7 an hour and that a pie takes 1.5 hours of labour time to
prepare and half an hour to bake. So we can work out our direct labour costs
like so:
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Costing systems I – Absorption and Marginal costing
(1.5 x £7) + (0.5 x £7) = 10.5 + 3.5 = £14
Now, we need to calculate our overheads, we know that baking overheads
for preparation are calculated by machine hours and preparation overheads
are calculated by labour hours:
Preparation overheads (labour hour basis):
1.5 labour hours x £4.61 per labour hour = £6.92
Baking overheads:
3 machine hours x £3.16 per machine hour = £9.48
Now that we have all the individual costs we can now calculate the total:
£
Direct material 6
Direct Labour 14
Preparation overheads 6.92
Baking overheads 9.48
Total: £36.40 per pie – An expensive pie!
Pre-determined overhead rates
The cost per unit is typically calculated at the start of the year for planning
purposes. As such the cost unit is often calculated using budgeted figures
and as such are called the pre-determined or budgeted OAR and is
calculated using the following formula:
Budgeted overhead
Budgeted activity level (e.g. number of units, or labour hours)
Let’s say that a cake shop had budgeted for 102,000 units and overheads of
£450,000 and they are going to use a per unit basis to absorb overheads.
450,000
102,000
= £4.41 per unit
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Costing systems I – Absorption and Marginal costing
As the year progresses it's that pre-determined OAR that is used in the
accounts throughout the year. We have to use this estimate during the year as
often actual overheads are not known until the year end.
By the end of the year a certain amount of overhead will have been included
in the accounts:
Actual activity (e.g. actual units or labour hours) x budgeted OAR
Let's say our shop actually produced just 100,000 cakes (2000 less than
expected).
100,000 x £4.41 = £441,000
This is the overhead absorbed.
At the end of the year a business will be able to calculate its true overhead
cost but this will be different from that included in the accounts during the
year.
So, if in the cake shop, actual overheads are £420,000 and from the above
calculation £441,000 was included during the year then too much as been
included and we say there is 'over absorption'.
Actual overheads incurred – Overhead absorbed = Under-or Over-
absorption
£420,000 - £440,100 = (£21,100)
£21,100 over absorbed!
At the end of the year the over-absorption is added to the accounts to get the
figure back to the right overhead figure.
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Costing systems I – Absorption and Marginal costing
Finally, we can sum up the steps in absorption costing in the following
diagram:
3. Marginal costing
Marginal costing is a much more simple costing method compared to
traditional absorption costing. Under marginal costing, fixed production costs
are not included in the cost of each unit of production and are instead treated
as 'period costs' which are written off in full against profit at the end of the
period.
You will recall that in absorption costing, we had “overheads” such as
rent, electricity and water and we found the cost of per unit (overhead
absorption rate) and added to the variable cost per unit to find the total
production cost per unit.
You don't need to worry about overheads when dealing with marginal costing.
Instead, we find what is known as the marginal cost:
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Costing systems I – Absorption and Marginal costing
Direct materials + direct labour + variable overheads per unit
Using this we can find the contribution per unit:
Selling price per unit – (direct materials + direct labour + variable
overheads per unit)
Under this system, each unit we produce and sell gives us some money
which will help to pay off our fixed costs. After we add up our total
contribution (contribution x total unit sales), we deduct our fixed costs to
find the profit.
We can think of the marginal cost as the extra cost that is incurred as a result
of producing one more unit. Conversely, we can say that it's the cost saved by
producing one less unit.
4. The use of costing information in pricing decisions
Marginal cost pricing
It can be difficult to decide on how much we should mark-up the marginal cost by because we don’t consider the fixed cost. There could be overheads
that are not covered in our cost that may mean we don’t break even or make
profit.
Marginal cost pricing is most useful in situations where the pricing decision is
a one-off. This is for short term decisions and should not be used for
routine production.
Absorption cost (full) pricing
As we have seen, the full cost of the unit can be found once we have allocated the absorbed overhead costs. This makes is a lot easier to decide
how much we must sell our product for to make a certain amount of profit.
If we wish to make £20,000 profit and each product has a full cost of £5, we
know that by selling 4,000 units at £10 we will reach this target. £20,000 of our
£10,000 revenue will cover the cost of producing 4,000 units at £5. The
remaining £20,000 is profit.
5. Selling price methods
Profit mark-up
There are two methods that can be used to calculate selling prices, mark-up or
margin. Profit mark-up is the selling price of a product that is expressed as a
percentage of its total cost. A mark-up is added onto the total cost of
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Costing systems I – Absorption and Marginal costing
the product in order to cover the costs and make a profit. Can be used to price
the unit or the job.
Let’s say that this job has a total cost of £20,400. It is company policy to
mark-up the total cost by 15% in order to find the selling price of the job.
15% of £20,400 is £3,060.
The price given for the job to the customer is therefore £23,460 (Total cost
+ Mark-up).
The mark-up percentage can be calculated by diving the mark-up amount by
the product cost.
£3,060
£20,400
= 0.15.
Profit margin
The profit margin is calculated differently. Margin (also known as gross margin) refers to the percentage of revenue remaining after all costs have
been deducted. Here is the equation:
Profit margin =
Net income
Net sales (revenue)
The Net Income or net profit is found by deducting all of company's expenses
from the total revenue.
For example, let's imagine that a product sells for £100 and costs £80.
Profit margin =
Profit margin =
(£100 - £80)
£100
£20
£100
The margin is £20 and the margin percentage is 20%.
This figure of 20% represents the amount of every pound of sales that the
company keeps as profit.