Activity Based Costing
Worked Example

The following information provides details of the costs, volume and transaction cost drivers for a period in respect of XYZ Ltd:

  Products  
  A B C Total
Sales and production (units) 90,000 30,000 15,000 135,000
Raw materials usage (units) 10 7 14 1,320,000
Direct materials cost (£) 30 40 15 4,125,000
Direct labour hours 2.5 3 1.5 337,500
Machine hours 5 3 7.5 652,500
Direct labour cost (£) 20 30 10 2,850,000
Number of production runs 5 10 50 65
Number of deliveries 18 7 50 75
Number of receipts 50 70 700 820
Number of production orders 45 25 60 130

Overhead costs £
Set up 75,000
Machines 1,000,000
Receiving 900,000
Packing 650,000
Engineering 750,000
Total 3,375,000

You are required to

(a) calculate the total costs for each product if all overhead costs are absorbed on a labour hour basis;
(b) calculate the total costs for each product, using activity based costing;
(c) calculate and list the unit product costs from your figures in (a) and (b) above to show the differences between them and to comment briefly on any conclusions which may be drawn which could have pricing and profit implications.

Solution to the worked example

There is more extensive treatment of Activity Based Costing in my book

Cost and Management Accounting (1996)
Prentice Hall
ISBN 0-13-205923-1

We will be working through these data three times. Firstly to see how traditional cost accounting methods might deal with them; secondly to look at the multiple volume based overhead method; and, finally, to look at the ABC method itself. Of the three approaches we will be looking at, only ABC will be using all of the data in any great detail. This is consistent with the general nature of the traditional method, and the only slightly more advanced multiple volume method.

Traditional direct labour hours basis

The direct labour hour rate is £10, calculated by dividing the total overheads by the total number of direct labour hours:

total overheads
total number of direct labour hours
 
3,375,000
337,500
 
£10 per dlh

Since we are using the direct labour hour rate method for the absorption of all overheads, the product costs per unit must be:

  A B C
Direct Materials 30 40 15
Direct Labour 20 30 10
Overheads 30 15 15
Total Product Cost 25 30 40

The overheads recovered are, of course:

Direct labour hour rate x number of direct labour hours per product

For product A, for example, the calculation is:

£10 per dlh x 2.5 dlh = £25

Multiple volume based allocation method

The multiple volume allocation method is an advance on the traditional allocation method in that it does make some allowance for activities to influence the absorption of overheads. In this example, we have two absorption rates to apply here: the receiving department overhead rate, and the "other" overhead rate

The reasoning here is that the organisation we are simulating is using a two rate basis of apportioning overheads: firstly, a material handling overhead rate is used to assign overhead to a separate cost centre and then charge it to production on the basis of the number of receipts; secondly all of the other overheads are assigned using a general machine hour rate on the basis that the number of machine hours far exceeds the number of labour hours.

Notice here, the rate we are using to assign the materials handling overheads is based on the number of receipts of materials into a department. The reason we are using this rate is that the activity of receiving dominates the reason for the existence of the overhead. Drury uses an overhead rate expressed as a percentage of direct materials cost. This is not a rate to be recommended particularly since tying the assignment of an overhead to the cost of a material is not realistic. As we know, merely because a material is expensive does not mean that its attendant overheads will vary in proportion to it.

The receiving overhead rate is

Total receiving overheads
Total number of receipts
 
£900,000
820
 
£1,097.56 per receipt

Using this rate as a constant allows us to evaluate the product overhead apportionments:
overheads per receipt x receipts per product group

For product A:

£1,097.56 per receipt x 50 receipts

£54,878

  Product
  A B C
Receiving overheads apportionment £54,787.0 £76,829.3 £768,292.7

We then divide these product apportionments by the number of units made for each product, to derive the cost per unit for receiving goods. The calculations here give the following results:

  Product
  A B C
Receiving cost per unit £0.60976 £2.5610 £51.2195

Notice, when compared with Drury's method of using the overhead rate as a percentage of direct materials cost, the version presented here gives a radically different result. Had we applied Drury's method, the product receiving cost per unit would have been:

Overhead absorption rate:

£900,000 x 100 = 21.82%

= £4,125,000

Applying this rate to each product's material costs gives:

Product
A B C
£6.55 8.73 3.27

The method we have used applies the full spirit of ABC by identifying and using fully the ABC approach. The other overhead rate, the Machine Hour Rate, is £3.79. This is calculated by dividing the total other overheads by the number of machine hours applied, or worked. In this case:

£3,375,000 – 900,000 = £3.79103
652,000 machine hours  

When multiplied by the number of machine hours per product, this then gives us the cost per unit for other overheads. For example, in the case of product A, the calculation is:

£3.79103 x 5 machine hours per unit = £18.9655

Once all the calculations have been completed, the product cost analysis per unit of each product is:

  Product
  A B C
Direct materials 30.0000 40.0000 15.0000
Direct labour 20.0000 30.0000 10.0000
Materials overheads 0.6098 2.5610 51.2195
Other overheads 18.9655 11.3793 28.4483
Total Product cost £69.5753 83.9403 104.6678

ABC method

As we said above, to apply the ABC method, we need to identify cost drivers for two stages:

1 cost drivers tracing the costs of inputs into cost pools; and
2 cost drivers tracing the cost pools into product costs

The workings that follow illustrate clearly how such cost drivers work through the ABC system in these two stages: an initial overhead rate or amount being further subdivided according the needs of the situation.

workings:

The calculations for each of the rates to be used are:

The machine hour rate is the only rate that is what we might call a traditional rate. All of the other rates we are about to use involve a two stage process. We will see the elements of these two stages as we get to them.

machine hour overhead rate

£1,000,000 = £1.5326
652,500 machine hours  

This rate is used as normal.

For the set up costs, we first devise a rate to tell us the cost per set up: total set up overheads divided by the number of set ups: in this case, this is

£75,000 = £1,153.85
65 production runs  

We will return to this rate shortly.

All of the other rates are calculated similarly. Hence they will be presented now without further comment.

Receiving rate £900,000 = £1,097.56
  820 receipts  


Packing rate £650,000 = £8,666.67
  75 deliveries  


Engineering rate £750,000 = £5,769.23
  130 production orders  

All of this information can now be put together into a cost per unit statement as follows.

The final stage in the whole ABC procedure, as far as product cost determination is concerned is to find out the costs per unit. The cost per unit statement follows, and then we will work through the calculations.

Unit costs A B C
  £ £ £
Direct materials 30.0000 40.0000 15.000
Direct labour 20.000 30.000 10.000
Machine overheads 7.6628 4.5977 11.4943
Set up costs 0.0641 0.3846 3.8462
Receiving costs 0.6098 2.5610 51.2195
Packing costs 1.7333 2.0222 28.8889
Engineering costs 2.8846 4.8077 23.0769
Total Costs £62.9546 £84.3732 £143.5257

workings:

Machine overheads are found by multiplying the machine hour rate by the number of machine hours per product per unit:

machine hour rate £1.5326 x

machine hours 5 3 7.5
gives £7.6628 4.5977 11.4943

The set up costs rate we have already is the rate per machine set up, the cost per unit is calculated by multiplying the rate per set up by the number of set up per product and then dividing the results by the total number of units per product:

Set up cost per set up £1153.85 x

No of set ups 5 10 50
gives £0.0010 0.0059 0.0592

Set up cost per set up £1,153.85 x

No of set ups 5 10 50
gives £5,769.25 11,538.50 57,692.50

these values are then divided by the number of units per product to give us the cost per unit:

  £0.0641 0.3846 3.8462

The receiving, packing and engineering costs are all calculated in the same way as the set up costs. There is no need to repeat these calculations, but check that they are understood.
Summarising each of these methods now we can see the impact of the different methods on product costs, Assuming that the ABC method is really more effective than the traditional approach, product A shows a cost difference of £42.1085 per unit.

Summary 1: Total costs per unit using each of the three methods
  Product
  A B C
DLH 75.0000 100.0000 40.0000
Mult 69.5753 83.9403 104.6678
ABC 62.9546 84.3732 143.5257

Summary 2: Overheads per unit using each of the three methods
  Product
  A B C
DLH 25.0000 30.0000 15.0000
Mult 19.5753 13.9403 79.6678
ABC 12.9546 14.3732 118.5257

Summary 3: Overheads as a percentage of total costs
  Product
  A B C
DLH 33.33% 30.00% 37.50%
Mult 28.14% 16.61% 76.11%
ABC 20.58% 17.04% 82.58%

© Duncan Williamson