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SOLUTION
1a.
Support Departments
Operating Departments
AS I S Govt. Corp.
Costs
$600,000
$2,400,000
Alloc. of AS costs
(0.25, 0.40, 0.35)
(861,538)
215,385
$ 344,615
$ 301,538
Alloc. of IS costs
(0.10, 0.30, 0.60)
261,538
(2,615,385)
784,616
1,569,231
$ 0
$ 0
$1,129,231
$1,870,769
Reciprocal Method Computation
AS = $600,000 + 0.10 IS
IS = $2,400,000 + 0.25AS
IS = $2,400,000 + 0.25 ($600,000 + 0.10 IS)
= $2,400,000 + $150,000 + 0.025 IS
0.975IS = $2,550,000
IS = $2,550,000 ÷ 0.975
= $2,615,385
AS = $600,000 + 0.10 ($2,615,385)
= $600,000 + $261,538
= $861,538
1b.
Support Departments
Operating Departments
AS I S Govt. Corp.
Costs
$600,000
$2,400,000
1st Allocation of AS
(0.25, 0.40, 0.35)
(600,000)
150,000
$ 240,000
$ 210,000
2,550,000
1st Allocation of IS
(0.10, 0.30, 0.60)
255,000
(2,550,000)
765,000
1,530,000
2nd Allocation of AS
(0.25, 0.40, 0.35)
(255,000)
63,750
102,000
89,250
2nd Allocation of IS
(0.10, 0.30, 0.60)
6,375
(63,750)
19,125
38,250
3rd Allocation of AS
(0.25, 0.40, 0.35)
(6,375)
1,594
2,550
2,231
3rd Allocation of IS
(0.10, 0.30, 0.60)
160
(1,594)
478
956
4th Allocation of AS
(0.25, 0.40, 0.35)
(160)
40
64
56
4th Allocation of IS
(0.10, 0.30, 0.60)
4
(40)
12
24
15-2
5th Allocation of AS
(0.25, 0.40, 0.35)
(4)
1
2
1
5th Allocation of IS
(0.10, 0.30, 0.60)
0
(1)
0
1
Total allocation
$ 0
$ 0
$1,129,231
$1,870,769
2.
Govt. Consulting
Corp. Consulting
a. Direct $1,120,000 $1,880,000
b. Step-Down (AS first) 1,090,000 1,910,000
c. Step-Down (IS first) 1,168,000 1,832,080
d. Reciprocal 1,129,231 1,870,769
The four methods differ in the level of support department cost allocation across support
departments. The level of reciprocal service by support departments is material. Administrative
Services supplies 25% of its services to Information Systems. Information Systems supplies 10% of
its services to Administrative Services. The Information Department has a budget of $2,400,000 that
is 400% higher than Administrative Services.
The reciprocal method recognizes all the interactions and is thus the most accurate. This is
especially clear from looking at the repeated iterations calculations.
15-21 (40 min.) Direct and step-down allocation.
E-books, an online book retailer, has two operating departments—corporate sales and consumer
sales—and two support departments—human resources and information systems. Each sales
department conducts merchandising and marketing operations independently. E-books uses
number of employees to allocate human resources costs and processing time to allocate
information systems costs. The following data are available for September 2013:
Required:
15-3
1. Allocate the support departments’ costs to the operating departments using the direct method.
2. Rank the support departments based on the percentage of their services provided to other
support departments. Use this ranking to allocate the support departments’ costs to the
operating departments based on the step-down method.
3. How could you have ranked the support departments differently?
SOLUTION
1.
Support Departments
Operating Departments
HR
Info. Systems
Corporate
Consumer
Total
Costs Incurred
$72,700
$234,400
$ 998,270
$489,860
$1,795,230
Alloc. of HR costs
(42/70, 28/70)
(72,700)
43,620
29,080
Alloc. of Info. Syst. costs
(1,920/3,520, 1,600/3,520)
______
(234,400)
127,855
106,545
________
$ 0
$ 0
$1,169,745
$625,485
$1,795,230
2. Rank on percentage of services rendered to other support departments.
Step 1: HR provides 23.077% of its services to information systems:
212842
21
++
=
91
21
= 23.077%
This 23.077% of $72,700 HR department costs is $16,777.
Step 2: Information systems provides 8.333% of its services to HR:
320600,1920,1
320
++
=
840,3
320
= 8.333%
This 8.333% of $234,400 information systems department costs is $19,533.
Support Departments
Operating Departments
HR
Info. Systems
Corporate
Consumer
Total
Costs Incurred
$72,700
$234,400
$ 998,270
$489,860
$1,795,23
0
Alloc. of HR costs
(21/91, 42/91, 28/91)
(72,700)
16,777
33,554
22,369
$ 0
251,177
Alloc. of Info. Syst. costs
(1,920/3,520, 1,600/3,520)
(251,177)
137,006
114,171
$ 0
$1,168,830
$626,400
$1,795,23
0
3. An alternative ranking is based on the dollar amount of services rendered to other support
departments. Using numbers from requirement 2, this approach would use the following sequence:
15-4
Step 1: Allocate Information Systems first ($19533 provided to HR).
Step 2: Allocate HR second ($16777 provided to Information Systems).
15-22 (30 min.) Reciprocal cost allocation (continuation of 15-21).
Consider E-books again. The controller of E-books reads a widely used textbook that states that
“the reciprocal method is conceptually the most defensible.” He seeks your assistance.
Required:
1. Describe the key features of the reciprocal method.
2. Allocate the support departments’ costs (human resources and information systems) to the two
operating departments using the reciprocal method.
3. In the case presented in this exercise, which method (direct, step-down, or reciprocal) would
you recommend? Why?
SOLUTION
1. The reciprocal allocation method explicitly includes the mutual services provided among
all support departments. Interdepartmental relationships are fully incorporated into the support
department cost allocations.
2. HR = $72,700 + 0.08333 IS
IS = $234,400 + 0.23077 HR
HR = $72,700 + [0.08333($234,400 + 0.23077 HR)]
= $72,700 + [$19,532.55 + 0.01923 HR]
0.98077 HR = $92,232.55
HR = $92,232.55 0.98077
= $94,041
15-5
IS = $234,400 + (0.23077 $94,041)
= $256,102
Support Depts.
Operating Depts.
HR
Info. Systems
Corporate
Consumer
Total
Costs Incurred
$72,700
$234,400
$ 998,270
$489,860
$1,795,230
Alloc. of HR costs
(21/91, 42/91, 28/91)
(94,041)
21,702
43,404
28,935
Alloc. of Info. Syst. costs
(320/3,840, 1,920/3,840,
1,600/3,840)
21,341
(256,102)
128,051
106,710
_________
$ 0
$ 0
$1,169,725
$625,505
$1,795,230
Solution Exhibit 15-22 presents the reciprocal method using repeated iterations.
SOLUTION EXHIBIT 15-22
Reciprocal Method of Allocating Support Department Costs for September 2012 at
E-books Using Repeated Iterations
Support Departments
Operating Departments
Human
Resources
Information
Systems
Corporate
Sales
Consumer
Sales
Total
Budgeted manufacturing overhead costs
before any interdepartmental cost allocation
$72,700
$234,400
$998,270
$489,860
$1,795,230
1st Allocation of HR
(72,700)
16,777
33,554
22,369
(21/91, 42/91, 28/91)a
251,177
1st Allocation of Information Systems
(320/3,840, 1,920/3,840, 1,600/3,840)b
20,931
(251,177)
125,589
104,657
2nd Allocation of HR
(21/91, 42/91, 28/91)a
(20,931)
4,830
9,661
6,440
2nd Allocation of Information Systems
(320/3,840, 1,920/3,840, 1,600/3,840)b
402
(4,830)
2,415
2,013
3rd Allocation of HR
(21/91, 42/91, 28/91)a
(402)
93
185
124
3rd Allocation of Information Systems
(320/3,840, 1,920/3,840, 1,600/3,840)b
8
(93)
46
39
4th Allocation of HR
(21/91, 42/91, 28/91)a
(8)
2
4
2
4th Allocation of Information Systems:
(320/3,840, 1,920/3,840, 1,600/3,840)b
0
(2)
1
1
_________
Total budgeted manufacturing overhead
of operating departments
$ 0
$ 0
$1,169,725
$625,505
$1,795,230
Total accounts allocated and reallocated (the numbers in parentheses in first two columns)
HR $72,700 + $20,931 + $402 + $8 = $ 94,041
Information Systems $251,177 + $4,830 + $93 + $2 = $256,102
aBase is (21 + 42 + 28) or 91 employees
bBase is (320 + 1,920 + 1,600) or 3,840 minutes
3. The reciprocal method is more accurate than the direct and step-down methods when there
are reciprocal relationships among support departments.
A summary of the alternatives is:
Corporate Sales
Consumer Sales
Direct method
$1,169,745
$625,485
Step-down method (HR first)
1,168,830
626,400
Reciprocal method
1,169,725
625,505
The reciprocal method is the preferred method although, for September 2013, the numbers do not
appear materially different across the alternatives.
SOLUTION EXHIBIT 15-22
Reciprocal Method of Allocating Support Department Costs for September 2012 at
E-books Using Repeated Iterations
Support Departments
Operating Departments
Human
Resources
Information
Systems
Corporate
Sales
Consumer
Sales
Total
Budgeted manufacturing overhead costs
before any interdepartmental cost allocation
$72,700
$234,400
$998,270
$489,860
$1,795,230
1st Allocation of HR
(72,700)
16,777
33,554
22,369
(21/91, 42/91, 28/91)a
251,177
1st Allocation of Information Systems
(320/3,840, 1,920/3,840, 1,600/3,840)b
20,931
(251,177)
125,589
104,657
2nd Allocation of HR
(21/91, 42/91, 28/91)a
(20,931)
4,830
9,661
6,440
2nd Allocation of Information Systems
(320/3,840, 1,920/3,840, 1,600/3,840)b
402
(4,830)
2,415
2,013
3rd Allocation of HR
(21/91, 42/91, 28/91)a
(402)
93
185
124
3rd Allocation of Information Systems
(320/3,840, 1,920/3,840, 1,600/3,840)b
8
(93)
46
39
4th Allocation of HR
(21/91, 42/91, 28/91)a
(8)
2
4
2
4th Allocation of Information Systems:
(320/3,840, 1,920/3,840, 1,600/3,840)b
0
(2)
1
1
_________
Total budgeted manufacturing overhead
of operating departments
$ 0
$ 0
$1,169,725
$625,505
$1,795,230
Total accounts allocated and reallocated (the numbers in parentheses in first two columns)
HR $72,700 + $20,931 + $402 + $8 = $ 94,041
Information Systems $251,177 + $4,830 + $93 + $2 = $256,102
aBase is (21 + 42 + 28) or 91 employees
bBase is (320 + 1,920 + 1,600) or 3,840 minutes
3. The reciprocal method is more accurate than the direct and step-down methods when there
are reciprocal relationships among support departments.
A summary of the alternatives is:
Corporate Sales
Consumer Sales
Direct method
$1,169,745
$625,485
Step-down method (HR first)
1,168,830
626,400
Reciprocal method
1,169,725
625,505
The reciprocal method is the preferred method although, for September 2013, the numbers do not
appear materially different across the alternatives.
15-23 (20−25 min.) Allocation of common costs.
Evan and Brett are students at Berkeley College. They share an apartment that is owned by Brett.
Brett is considering subscribing to an Internet provider that has the following packages available:
Evan spends most of his time on the Internet (“everything can be found online now”). Brett prefers
to spend his time talking on the phone rather than using the Internet (“going online is a waste of
time”). They agree that the purchase of the $90 total package is a “win–win” situation.
Required:
1. Allocate the $90 between Evan and Brett using (a) the stand-alone cost-allocation method, (b)
the incremental cost-allocation method, and (c) the Shapley value method.
2. Which method would you recommend they use and why?
SOLUTION
1. Three methods of allocating the $90 are:
Evan
Brett
Stand-alone
Incremental (Brett primary)
Incremental (Evan primary)
Shapley value
$67.50
65.00
75.00
70.00
$22.50
25.00
15.00
20.00
a. Stand-alone cost allocation method.
Evan:
$75
$75 + $25
$90 =
3
4
$90 = $67.50
Brett:
$25
$75 + $25
$90 =
1
4
$90 = $22.50
b. Incremental cost allocation method.
Assume Brett (the owner) is the primary user and Evan is the incremental user:
User
Costs
Allocated
Cumulative Costs
Allocated
Brett
Evan
Total
$25
65 ($90 – $25)
$90
$25
$90
This method may generate some dispute over the ranking. Notice that Evan pays only $65
despite his prime interest in the more expensive Internet access package. Brett could make the
argument that if Evan were ranked first he would have to pay $75 because he is the major Internet
user. Then, Brett would only have to pay $15!
Assume Evan is the primary user and Brett is the incremental user:
User
Costs
Allocated
Cumulative Costs
Allocated
Evan
Brett
Total
$75
15 ($90 – $75)
$90
$75
$90
c. Shapley value (average over costs allocated as the primary and incremental user).
User
Costs
Allocated
Evan
Brett
($65 + $75)
2 = $70
($25 + $15)
2 = $20
15-9
2. The Shapley value approach is recommended. It is fairer than the incremental method
because it avoids considering one user as the primary user and allocating more of the common
costs to that user. It also avoids disputes about who is the primary user. It allocates costs in a
manner that is close to the costs allocated under the stand-alone method but takes a more
comprehensive view of the common cost allocation problem by considering primary and
incremental users that the stand-alone method ignores.
More generally, other criteria to guide common cost allocations include the following:
a. Cause and effect. It is not possible to trace individual causes (either Internet access or
phone services) to individual effects (uses by Evan or Brett). The $90 total package is
a bundled product.
b. Benefits received. There are various ways of operationalizing the benefits received:
(i) Monthly service charge for their prime interest––Internet access for Evan ($75),
and phone services for Brett ($25). This measure captures the services available to
each person.
(ii) Actual usage by each person. This would involve keeping a record of usage by each
person and then allocating the $90 on a percent usage time basis. This measure
captures the services actually used by each person, but it may prove burdensome,
and it would be subject to honest reporting by Evan and Brett.
c. Ability to pay. This criterion requires that Evan and Brett agree upon their relative
ability to pay.
d. Fairness or equity. This criterion is relatively nebulous. One approach would be to split
the $90 using the Shapely value or the stand-alone method.
15-24 (20 min.) Allocation of common costs.
Barbara Richardson, a self-employed consultant near Sacramento, received an invitation to visit a
prospective client in Baltimore. A few days later, she received an invitation to make a presentation
to a prospective client in Chicago. She decided to combine her visits, traveling from Sacramento
to Baltimore, Baltimore to Chicago, and Chicago to Sacramento.
Richardson received offers for her consulting services from both companies. Upon her return,
she decided to accept the engagement in Chicago. She is puzzled over how to allocate her travel
costs between the two clients. She has collected the following data for regular round-trip fares with
no stopovers:
15-10
Richardson paid $1,200 for her three-leg flight (Sacramento–Baltimore, Baltimore–Chicago,
Chicago–Sacramento). In addition, she paid $30 each way for limousines from her home to
Sacramento Airport and back when she returned.
Required:
1. How should Richardson allocate the $1,600 airfare between the clients in Baltimore and
Chicago using (a) the stand-alone cost-allocation method, (b) the incremental cost-allocation
method, and (c) the Shapley value method?
2. Which method would you recommend Richardson use and why?
3. How should Richardson allocate the $60 limousine charges between the clients in Baltimore
and Chicago?
