Cost allocations
Outline
The issues that are discussed in this chapter are:
1. Allocation of service department costs to profit centers
a. Direct Method
b. Step Down Method
c. Reciprocal Method (actually, this is not covered, but I will cover
it in class).
2. Joint product allocations
a. Physical units
b. Relative Sales Value
c. Net Realizable Value
Service department cost allocation
Company direct costs and indirect costs are allocated to service
departments and production departments. Then, service department costs
are allocated to production departments. We will focus on this last link and
look at three ways to do it: the direct method, the step method (the method
most recommended by the book), and the reciprocal method.
Before moving on, I should note that there are additional situations that
relate to this type of allocation process other than “production”
departments. It could be ANY situation where you have profit centers and
cost centers (departments that are evaluated on profit and departments
that are evaluated on only costs).
It is important to know all 3 methods for different reasons. Most
companies use the direct method. It is simplest. With the direct method
you look at your service department costs and the proportion of that service
department’s benefits that are USED by the different production
departments. Then allocate the service department’s costs using those
proportions. This actually is not all that bad. The ONLY problem is when
one or more of your service departments has a large amount of its service
used by another service department. In that case, allocating based upon the
relatively small proportions that are used by the production departments
creates a distortion in the cost usage.
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The step method attempts to mitigate this potential distortion by allocating
out the service department that uses the supplies the largest amount of its
costs to other service departments first, then the service department that
supplies the next largest amount of its costs to other service deparments is
allocated next, and so on. There is still a chance for distortion, but it is
much decreased.
The reciprocal method is actually the most accurate. It uses linear algebra
to perfectly allocate all service department costs to other service
departments. Then these costs are allocated to the production departments
using a variation of the direct method. I actually find this method far
superior to the step method, because the step method is confusing to me.
And, of course, it is more accurate. This method is not demonstrated in the
text (I don’t think).
To illustrate these allocation methods consider the following example.
The Riverside Clinic has three service departments: Patient Records,
Personnel, and Administration and Accounting. The clinic has two “direct
care” departments (profit centers): Orthopedics and Internal Medicine.
Each service department services direct care departments - but they also
service each other.
Suppose the service departments have the following direct costs:
Department
Patient
Records
Personnel
Administrative
and Accounting
Total
Variable
Cost
Fixed
Cost
Total
Cost
$24,000
15,000
$76,000
45,000
$100,000
60,000
47,500
142,500
190,000
$86,500
$263,500
$350,000
Suppose that Patient Records costs are allocated on the basis of the number
of patients. Of course, Personnel and Administrative and Accounting have no
patients so that is not allocated to other service departments. Orthopedics
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has 30 patients and Internal Medicine has 50 patients. Suppose next that
Personnel is allocated on the basis of the number of employees. Patient
Records has 10 employees, Administrative and Accounting has 10 employees,
Orthopedics has 10 employees, and Internal medicine has 20 employees. We
NEVER allocate from a department to itself, so it does not matter how many
employees are in Personnel. Finally, Administrative and Accounting costs are
allocated based upon the total direct costs of the other departments
(assume that the costs in the table above are all direct costs). Orthopedics
has direct costs of $500,000 and Internal Medicine has direct costs of
$300,000.
Now, on to allocating costs…
The Direct Method
The following table summarizes the costs and percentages of usage for all
service and “production” centers:
Provider of Service
User of
Service
Patient Records
Service
Personnel
Departments
Administrative and
Accounting
Direct care Orthopedics
Departments Internal Medicine
Total
Administrative
Patient
and
Records Personnel Accounting
0.0%
20.0%
10.4%
100,000
0.0%
0.0%
6.3%
60,000
0.0%
20.0%
0.0%
190,000
37.5%
20.0%
52.1%
500,000
62.5%
40.0%
31.3%
300,000
100%
100%
100%
1,150,000
You should be able to reconstruct the table above using the information
provided in the narrative in the preceding section.
So, using the direct method, Patient records has a cost of $100,000. Of
that cost, 37.5% ($37,500) is allocated to Orthopedics and 62.5%
($62,500) is allocated to Internal Medicine. Personnel is a bit trickier since
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40% of Personnel costs go to other service departments. We ignore that
usage under the direct method. We focus only on the percentage going to
Production departments (60%). 1/3 of that (20% ÷ 60%) goes to
Orthopedics = $60,000 * 1/3 = $20,000 and 2/3 goes to Internal Medicine
($40,000). Finally, the Administrative and Accounting costs of $190,000
are allocated to Orthopedics and Internal Medicine in a 5/8 to 3/8 ratio.
Therefore Orthopedics is allocated $118,750 of these costs and Internal
Medicine is allocated $71,250 of the costs.
Step-Down Method
First, find the service department that provides the largest percentage of
its service to other service departments. That would be Personnel (40%).
Allocate Personnel costs to all other departments based upon their
percentages of use (including service departments). Their costs were:
$60,000. This allocation is shown in the table below:
User of
Service
Cost
Personnel Allocation
60,000
Patient Records
Service
Personnel
Departments Administrative and
Accounting
Direct care Orthopedics
Departments Internal Medicine
Total
20.0%
12,000
0.0%
-
20.0%
12,000
20.0%
12,000
40.0%
24,000
100%
60,000
Now, Patient Records has a cost of $112,000 and Administrative and
Accounting has costs of $202,000. Since Patient Records does not provide
any service to the other service departments, the second service
department to allocate is Administrative and Accounting. They provide
10.4% of their services to Patient Records. Note that we do not care about
the 6.3% that they provide to Personnel because Personnel has been
allocated out and they cannot be allocated again. We are done with
Personnel.
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The allocation of Administrative and Accounting is shown in the following
table:
User of
Service
Administrative
and
Accounting
202,000
Patient Records
11.1%
22,444
Service
Personnel
Departments Administrative and
Accounting
-
Direct care Orthopedics
Departments Internal Medicine
Total
55.6%
112,222
33.3%
67,333
100%
202,000
Now, Patient Records has a cost of $112,000 + $23,111 or $135,111. These
costs will be allocated to the Direct Care Departments as shown in the
following table:
User of
Service
Patient
Records
134,444
Patient Records
Service
Personnel
Departments Administrative and
Accounting
Direct care Orthopedics
Departments Internal Medicine
Total
37.5%
50,417
62.5%
84,028
100%
134,444
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Reciprocal Method
Finally, we turn to the reciprocal method. First set up three equations
identifying the “costs” of each service department. For example, the
Patient Records costs are their direct costs ($100,000) plus their allocated
costs (.2 * Personnel + .104 * Administrative and Accounting). The following
three equations give us the service department allocations:
PR = 100,000 + .2*P + .104*AA
P = 60,000 + .063*AA
AA = 190,000 + .2*P
Solving these equations by first substituting 190,000 +2*P for AA in the
second equation yields P = $72,888, which implies that AA = $204,578.
Finally, PR = $135,854.
Now, we allocate these to the two Direct Care Departments using the
absolute percentages (not their relative percentages) of usage. In other
words, AA will be allocated to Orthopedics and Internal Medicine using
52.1% and 31.3%, NOT 5/8 and 3/8. The following table shows the
allocations of PR, P, and AA to Orthopedics and Internal Medicine:
Provider of Service
Costs
Administrative
Patient
and
Records
Personnel
Accounting
135,854
72,888
204,578
Percentage Used
Orthopedics
37.5%
20.0%
52.1%
Internal Medicine
62.5%
40.0%
31.3%
50,945
14,578
106,551
Costs Allocated
Orthopedics
Internal Medicine
84,909
29,155
63,931
135,854
43,733
170,482
(note that these do not total EXACTLY to $350,000 due to rounding)
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Computing total costs (direct and allocated)
Now, we will total the costs under the three methods and compare the
allocations to Orthopedics and Internal Medicine.
Consider the tables below:
Orthopedics
StepDirect
down
Reciprocal
Method
Method
Method
Direct Costs
500,000
500,000
500,000
Service Department Costs
176,250
174,639
172,074
676,250
674,639
672,074
Total Costs
Direct Costs
Service Department Costs
Total Costs
Internal Medicine
StepDirect
down
Reciprocal
Method
Method
Method
300,000 300,000 300,000
173,750
175,361
177,995
473,750
475,361
477,995
This ends the service department allocation section.
Joint Cost Allocations
Remember, earlier in the term, we talked about whether to sell at a split-off
point or to process further? Now we look at a different side of that same
issue.
We have a single pool of raw material that we take to some split-off point.
We have incurred costs to that point that we call joint costs. Then, we
divide the material into two (or more) products. We want to find the cost of
the products. How much of the joint costs do each product bear?
We have three methods: Physical units, Relative Sales Value, and Net
Realizable Value. We discuss each of these methods with respect to the
following example.
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We process Cocoa beans that cost $500 per ton. We incur additional
processing costs of $600 per ton to get them to the split-off point. At that
point, we have two recognizable products: 1,500 Lb of cocoa butter, which is
worth $750 on the intermediate market, and 500 Lb of cocoa powder, which
is worth $500 on the intermediate market. We can process the cocoa
butter further and obtain tanning cream. The tanning cream has a sales
value of $3,000, but requires $1,560 in additional processing costs. We can
process the cocoa powder into cocoa mix, with a sales value of $2,000, and
this requires additional processing costs of $800.
Physical units method
Using the physical units method, we take the ratio of Lb of cocoa butter to
cocoa powder (1,500 Lb to 500 Lb) and allocate the costs using that ratio.
Note first that it is unlikely a ton (2,000 Lb) would ever yield 1,500 Lb of
one and 500 Lb of the other – that really doesn’t matter. It is possible,
though, that you might not want to use this method for a couple of reasons.
First, one product may be very expensive per physical unit (e.g. diamonds).
Second, the measures may not be commensurate. One may be easily
physically measured whereas the other may not. On with the analysis…
The joint costs are $1,100 ($500 + $600). Using the Physical Units method,
¾*$1,100, or $825, would be allocated to cocoa butter and ¼*$1,100, or
$275, would be allocated to cocoa powder. That cost would then apply
whether or not the product were processed further. Why ¾ and ¼? Because
1,500 Lb is ¾ of the total 1,500 Lb + 500 Lb and 500 Lb is ¼.
Relative Sales Value
If the intermediate product has a market, you can use the relative sales
value. In this case, the sales value at split-off of cocoa butter is $750 and
the sales value at split-off of cocoa powder is $500. To use this method,
BOTH products must have a sales value at split-off.
The allocation to cocoa butter will be .6*$1,100 = $660 and the allocation to
cocoa powder will be .4*$1,100 = $440. The .6 is computed as:
.6 =
750
750 + 500
.
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Net Realizable Value
Net Realizable Value is the sales value (ultimately) less the additional costs
of processing. In this case, the Net Realizable Value of the cocoa butter is
$3,000 - $1,560 = $1,440 and the Net Realizable Value of the cocoa powder
is $2,000 - $800 = $1,200. Using these weights, the proportion of the joint
costs allocated to cocoa butter is:
1,440
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. The allocation to
1,440 + 1,200 11
cocoa butter is, then, $1,100 * 6/11 = $600 and the allocation to cocoa
powder is $500.
=
You should be able to compute the expected profit of the tanning cream and
the cocoa mix using any of these allocations.
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