Question

PhoenixPartners provides management consulting services to government and corporate clients. Phoenix has two support departments—administrative services​(AS)...

PhoenixPartners provides management consulting services to government and corporate clients. Phoenix has two support departments—administrative services​(AS) and information systems​(IS)—and two operating departments—government consulting​ (GOVT) and corporate consulting​ (CORP). For the first quarter of 2017​, Phoenix's cost records indicate the​ following:

SUPPORT

OPERATING

AS

IS

GOVT

CORP

Total

Budgeted overhead costs before any interdepartment cost allocations

$600,000

$2,400,000

$8,756,000

$12,452,000

$24,208,000

Support work supplied by AS (budgeted head count)

0

25%

40%

35%

100%

Support work supplied by IS (budgeted computer time)

10%

0

30%

60%

100%

Requirement 1a. Allocate the two support​ departments' costs to the two operating departments using the reciprocal method.

​First, determine the linear equations for each support department.

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Phoenix
Reciprocal Method AS IS GOVT CORP Total
Support work supplied by AS 0.00% 25.00% 40.00% 35.00% 100.00%
Support work supplied by IS 10.00% 0.00% 30.00% 60.00% 100.00%
Department cost    600,000.00 2,400,000.00 8,756,000.00 12,452,000.00 24,208,000.00
Let cost of AS is $ X and IS $ Y
So, X= 600000+ 10% of Y Equation 1
Y= 2400000+ 25% of X Equation 2
Or, X= 600000+ 0.10Y
Y= 2400000+ 0.25X
Substituting the value of X in equation 2:
Y = 2400000 + 0.25(600,000 + 0.10Y)
Y = 2400000 + 150000+.0025Y
Y – 0.025Y = 2400000+150,000
0.975Y = 2,550,000
Y = 2,550,000/0.975
Y = $ 2,615,385
Substituting the value of Y in equation 1:
So, X= 600000+ .010Y
So, X= 600000+ 0.10*2615385
So, X= 600000+ 261538
X= $ 861,538
Allocation Summary AS IS GOVT CORP Total
Support work supplied by AS                     -   25.00% 40.00% 35.00% 100.00%
Support work supplied by IS 10.00%                        -   30.00% 60.00% 100.00%
Department cost    600,000.00 2,400,000.00 8,756,000.00 12,452,000.00 24,208,000.00
Allocation
S 1 (861,538.00)       215,385.00       344,615.00         301,538.00                          -  
S 2    261,538.00 (2,615,385.00)       784,616.00      1,569,231.00                          -  
Cost after allocation                     -                          -   9,885,231.00 14,322,769.00 24,208,000.00
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