{"id":671,"date":"2015-10-24T16:05:03","date_gmt":"2015-10-24T16:05:03","guid":{"rendered":"https:\/\/courses.candelalearning.com\/managacct2x10xmaster\/?post_type=chapter&p=671"},"modified":"2015-11-10T18:41:25","modified_gmt":"2015-11-10T18:41:25","slug":"reciprocal-method-of-allocation","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-managacct\/chapter\/reciprocal-method-of-allocation\/","title":{"raw":"Reciprocal Method of Allocation","rendered":"Reciprocal Method of Allocation"},"content":{"raw":"The final method, is the reciprocal method.\u00a0 Although it is the most accurate, it is also the most complicated.\u00a0 In the reciprocal method, the relationship between the service departments is recognized.\u00a0 This means service department costs are allocated to and from the other service departments.\r\n\r\nhttps:\/\/youtu.be\/NB0zsaPC4MI\r\n\r\nWe can break the process up into 3 steps so we can make sense of the process.\u00a0 To demonstrate, we will use the same basic data:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nService Dept\u00a0\u00a0<\/strong><\/td>\r\nOperating Dept\u00a0\u00a0<\/strong><\/td>\r\n<\/tr>\r\n
<\/td>\r\nMaintenance<\/strong><\/td>\r\nAdministration<\/strong><\/td>\r\n1<\/strong><\/td>\r\n2<\/strong><\/td>\r\n<\/tr>\r\n
Costs<\/td>\r\n$8,000<\/td>\r\n$4,000<\/td>\r\n$32,000<\/td>\r\n$36,000<\/td>\r\n<\/tr>\r\n
Machine-hours used<\/td>\r\n1,000<\/td>\r\n2,000<\/td>\r\n1,500<\/td>\r\n2,500<\/td>\r\n<\/tr>\r\n
Number of Employees<\/td>\r\n100<\/td>\r\n200<\/td>\r\n250<\/td>\r\n150<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nStep 1:\u00a0 Determine allocation bases<\/strong>\r\n\r\nJust like you would for direct or step,we need to calculate the allocation base EXCEPT the only thing you are excluding is the department cost you are trying to allocate -- ALL other departments are included.\u00a0 We can calculate the allocation base amount for each service department as follows:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nMaintenance Dept\u00a0<\/strong><\/td>\r\n\u00a0<\/strong><\/td>\r\nAdministration Dept\u00a0\u00a0<\/strong><\/td>\r\n<\/tr>\r\n
<\/td>\r\nMach Hrs<\/strong><\/td>\r\n% of Total<\/strong><\/td>\r\n\u00a0<\/strong><\/td>\r\nEmployees<\/strong><\/td>\r\n% of Total<\/strong><\/td>\r\n\u00a0<\/strong><\/td>\r\n<\/tr>\r\n
Maintenance<\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -<\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -<\/td>\r\n<\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 100<\/td>\r\n20.00%<\/td>\r\n(100\/500)<\/em><\/span><\/td>\r\n<\/tr>\r\n
Administration<\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2,000<\/td>\r\n2\/6**<\/td>\r\n(2,000\/6,000)<\/span><\/em><\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 -<\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 -<\/td>\r\n\u00a0<\/em><\/span><\/td>\r\n<\/tr>\r\n
Dept 1<\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1,500<\/td>\r\n25%<\/td>\r\n(1,500\/6,000)<\/span><\/em><\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 250<\/td>\r\n50.00%<\/td>\r\n(250\/500)<\/em><\/span><\/td>\r\n<\/tr>\r\n
Dept 2<\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2,500<\/span><\/td>\r\n2.5\/6**<\/span><\/td>\r\n(2,500\/6,000)<\/span><\/em><\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 150<\/span><\/td>\r\n30.00%<\/span><\/td>\r\n(150\/500)<\/em><\/span><\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6,000<\/td>\r\n100%<\/td>\r\n<\/td>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 500<\/td>\r\n100.00%<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n**since these numbers do not come out evenly, we keep them in the fraction form and only round the final answer to the nearest dollar.\r\n\r\nStep 2:\u00a0 \u00a0Setup the formulas.\u00a0<\/strong>\r\n\r\nSince maintenance costs are allocated to administration and administration cost is allocated to maintenance -- things get interesting.\u00a0 You will need to determine the TOTAL cost being allocated to both the Administration and Maintenance Departments first.\r\n\r\n(a) Total Maintenance cost = Maintenance department cost + cost allocated to maintenance from administration.\r\n\r\n(b) Total Administration cost = Administration department cost + cost allocated to administration from maintenance.\r\n\r\nWe will work with the administration cost formula in (b) first:\r\n\r\nTotal Administration cost = Administration department cost + cost allocated to administration from maintenance.\u00a0 From step 1, we know the cost allocation to administration from maintenance is (2\/6 x total maintenance cost).\u00a0 We still do not know what total maintenance cost but we can plug in this new formula.\r\n\r\nTotal Administration cost = $ 4,000 administration department cost + (2\/6 x total maintenance cost)\r\n\r\nWe can insert the formula from (a) for total maintenance cost into the total administration cost formula (b) as follows:\r\n\r\nTotal Administration cost = $4,000 admin department cost + [2\/6 x (Maintenance department cost + cost allocated to maintenance from administration) ]\r\n\r\nWe can see from step 1 that administration cost is allocated to maintenance as total administration cost x 20%.\u00a0 Adding this to our formula, we now have:\r\n\r\nTotal Administration cost = $4,000 admin department cost + [2\/6 x ($8,000 Maintenance department cost + (total admin cost x 20%) ) ]\r\n\r\nUsing algebra, we can assign Total Administration Cost a variable of A giving the formula:\r\n\r\nA = 4,000 + [ 2\/6 x ($8,000 + 0.20)A]\r\n\r\nA = 4,000 + (2\/6 x 8,000) + (2\/6 x 0.20A)\r\n\r\nA = 4,000 + 2,666.67 + 0.067A -- rounded<\/em>\r\n\r\nA = 6,666.67 + 0.067A\r\n\r\n1.0A - 0.067A = 6,666.67\r\n\r\n0.933A = 6,666.67\r\n\r\nA or total administration cost = $7,145 rounded\r\n\r\nTotal maintenance cost can be calculated as $8,000 department cost + $1,429 (7,145 x 20%) allocated from administration for a total of $9,429.\r\n\r\nStep 3:\u00a0 Show cost allocations<\/strong>\r\n\r\nNow that you have the TOTAL Cost of Maintenance and Personnel, it is time to allocate it using the Total Cost amounts from Step 2 and the percents from Step 1.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nService Dept\u00a0\u00a0<\/strong><\/td>\r\nOperating Dept\u00a0\u00a0<\/strong><\/td>\r\n<\/tr>\r\n
<\/td>\r\nMaintenance<\/strong><\/td>\r\nAdministration<\/strong><\/td>\r\n1<\/strong><\/td>\r\n2<\/strong><\/td>\r\n<\/tr>\r\n
Costs<\/td>\r\n$8,000<\/td>\r\n$4,000<\/td>\r\n$32,000<\/td>\r\n$36,000<\/td>\r\n<\/tr>\r\n
Maintenance costs allocated<\/td>\r\n-9,429<\/td>\r\n3,143<\/td>\r\n2,357<\/td>\r\n3,929<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n(9,429 x 2\/6)<\/span><\/em><\/td>\r\n(9,429 x 25%)<\/span><\/em><\/td>\r\n(,9429 x 2.5\/6)<\/span><\/em><\/td>\r\n<\/tr>\r\n
Administration costs allocated<\/td>\r\n1,429<\/span><\/td>\r\n-7,145<\/span><\/td>\r\n3,572.50<\/span><\/td>\r\n2,143.50<\/span><\/td>\r\n<\/tr>\r\n
<\/td>\r\n(7,145 x 20%)<\/span><\/em><\/td>\r\n\u00a0<\/span><\/em><\/td>\r\n(7,145 x 50%)<\/span><\/em><\/td>\r\n(7,145 x 30%)<\/span><\/em><\/td>\r\n<\/tr>\r\n
Total costs<\/td>\r\n$0<\/td>\r\n($2)**<\/td>\r\n$37,930<\/td>\r\n$42,073<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n** difference due to rounding in calculations.\r\n\r\n ","rendered":"

The final method, is the reciprocal method.\u00a0 Although it is the most accurate, it is also the most complicated.\u00a0 In the reciprocal method, the relationship between the service departments is recognized.\u00a0 This means service department costs are allocated to and from the other service departments.<\/p>\n

https:\/\/youtu.be\/NB0zsaPC4MI<\/p>\n

We can break the process up into 3 steps so we can make sense of the process.\u00a0 To demonstrate, we will use the same basic data:<\/p>\n\n\n\n\n\n\n\n
<\/td>\nService Dept\u00a0\u00a0<\/strong><\/td>\nOperating Dept\u00a0\u00a0<\/strong><\/td>\n<\/tr>\n
<\/td>\nMaintenance<\/strong><\/td>\nAdministration<\/strong><\/td>\n1<\/strong><\/td>\n2<\/strong><\/td>\n<\/tr>\n
Costs<\/td>\n$8,000<\/td>\n$4,000<\/td>\n$32,000<\/td>\n$36,000<\/td>\n<\/tr>\n
Machine-hours used<\/td>\n1,000<\/td>\n2,000<\/td>\n1,500<\/td>\n2,500<\/td>\n<\/tr>\n
Number of Employees<\/td>\n100<\/td>\n200<\/td>\n250<\/td>\n150<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Step 1:\u00a0 Determine allocation bases<\/strong><\/p>\n

Just like you would for direct or step,we need to calculate the allocation base EXCEPT the only thing you are excluding is the department cost you are trying to allocate — ALL other departments are included.\u00a0 We can calculate the allocation base amount for each service department as follows:<\/p>\n\n\n\n\n\n\n\n\n\n
<\/td>\nMaintenance Dept\u00a0<\/strong><\/td>\n\u00a0<\/strong><\/td>\nAdministration Dept\u00a0\u00a0<\/strong><\/td>\n<\/tr>\n
<\/td>\nMach Hrs<\/strong><\/td>\n% of Total<\/strong><\/td>\n\u00a0<\/strong><\/td>\nEmployees<\/strong><\/td>\n% of Total<\/strong><\/td>\n\u00a0<\/strong><\/td>\n<\/tr>\n
Maintenance<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 –<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 –<\/td>\n<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 100<\/td>\n20.00%<\/td>\n(100\/500)<\/em><\/span><\/td>\n<\/tr>\n
Administration<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2,000<\/td>\n2\/6**<\/td>\n(2,000\/6,000)<\/span><\/em><\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 –<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 –<\/td>\n\u00a0<\/em><\/span><\/td>\n<\/tr>\n
Dept 1<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1,500<\/td>\n25%<\/td>\n(1,500\/6,000)<\/span><\/em><\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 250<\/td>\n50.00%<\/td>\n(250\/500)<\/em><\/span><\/td>\n<\/tr>\n
Dept 2<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2,500<\/span><\/td>\n2.5\/6**<\/span><\/td>\n(2,500\/6,000)<\/span><\/em><\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 150<\/span><\/td>\n30.00%<\/span><\/td>\n(150\/500)<\/em><\/span><\/td>\n<\/tr>\n
Total<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6,000<\/td>\n100%<\/td>\n<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 500<\/td>\n100.00%<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

**since these numbers do not come out evenly, we keep them in the fraction form and only round the final answer to the nearest dollar.<\/p>\n

Step 2:\u00a0 \u00a0Setup the formulas.\u00a0<\/strong><\/p>\n

Since maintenance costs are allocated to administration and administration cost is allocated to maintenance — things get interesting.\u00a0 You will need to determine the TOTAL cost being allocated to both the Administration and Maintenance Departments first.<\/p>\n

(a) Total Maintenance cost = Maintenance department cost + cost allocated to maintenance from administration.<\/p>\n

(b) Total Administration cost = Administration department cost + cost allocated to administration from maintenance.<\/p>\n

We will work with the administration cost formula in (b) first:<\/p>\n

Total Administration cost = Administration department cost + cost allocated to administration from maintenance.\u00a0 From step 1, we know the cost allocation to administration from maintenance is (2\/6 x total maintenance cost).\u00a0 We still do not know what total maintenance cost but we can plug in this new formula.<\/p>\n

Total Administration cost = $ 4,000 administration department cost + (2\/6 x total maintenance cost)<\/p>\n

We can insert the formula from (a) for total maintenance cost into the total administration cost formula (b) as follows:<\/p>\n

Total Administration cost = $4,000 admin department cost + [2\/6 x (Maintenance department cost + cost allocated to maintenance from administration) ]<\/p>\n

We can see from step 1 that administration cost is allocated to maintenance as total administration cost x 20%.\u00a0 Adding this to our formula, we now have:<\/p>\n

Total Administration cost = $4,000 admin department cost + [2\/6 x ($8,000 Maintenance department cost + (total admin cost x 20%) ) ]<\/p>\n

Using algebra, we can assign Total Administration Cost a variable of A giving the formula:<\/p>\n

A = 4,000 + [ 2\/6 x ($8,000 + 0.20)A]<\/p>\n

A = 4,000 + (2\/6 x 8,000) + (2\/6 x 0.20A)<\/p>\n

A = 4,000 + 2,666.67 + 0.067A — rounded<\/em><\/p>\n

A = 6,666.67 + 0.067A<\/p>\n

1.0A – 0.067A = 6,666.67<\/p>\n

0.933A = 6,666.67<\/p>\n

A or total administration cost = $7,145 rounded<\/p>\n

Total maintenance cost can be calculated as $8,000 department cost + $1,429 (7,145 x 20%) allocated from administration for a total of $9,429.<\/p>\n

Step 3:\u00a0 Show cost allocations<\/strong><\/p>\n

Now that you have the TOTAL Cost of Maintenance and Personnel, it is time to allocate it using the Total Cost amounts from Step 2 and the percents from Step 1.<\/p>\n\n\n\n\n\n\n\n\n\n\n
<\/td>\nService Dept\u00a0\u00a0<\/strong><\/td>\nOperating Dept\u00a0\u00a0<\/strong><\/td>\n<\/tr>\n
<\/td>\nMaintenance<\/strong><\/td>\nAdministration<\/strong><\/td>\n1<\/strong><\/td>\n2<\/strong><\/td>\n<\/tr>\n
Costs<\/td>\n$8,000<\/td>\n$4,000<\/td>\n$32,000<\/td>\n$36,000<\/td>\n<\/tr>\n
Maintenance costs allocated<\/td>\n-9,429<\/td>\n3,143<\/td>\n2,357<\/td>\n3,929<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n(9,429 x 2\/6)<\/span><\/em><\/td>\n(9,429 x 25%)<\/span><\/em><\/td>\n(,9429 x 2.5\/6)<\/span><\/em><\/td>\n<\/tr>\n
Administration costs allocated<\/td>\n1,429<\/span><\/td>\n-7,145<\/span><\/td>\n3,572.50<\/span><\/td>\n2,143.50<\/span><\/td>\n<\/tr>\n
<\/td>\n(7,145 x 20%)<\/span><\/em><\/td>\n\u00a0<\/span><\/em><\/td>\n(7,145 x 50%)<\/span><\/em><\/td>\n(7,145 x 30%)<\/span><\/em><\/td>\n<\/tr>\n
Total costs<\/td>\n$0<\/td>\n($2)**<\/td>\n$37,930<\/td>\n$42,073<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

** difference due to rounding in calculations.<\/p>\n

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