The equation for the reciprocal method is a simple linear equation of the form:
Cost = Total direct cost + Allocated cost
This is meant to actually measure the interactions between departments, so that the cost of any one department is paid for by the other departments that "use" it. Consider the IT Dept and the Sales Dept as an example. Let us say that in the past quarter, the IT Dept incurred costs of 100,000 and the Sales Dept 150,000. But let us consider that the Sales and IT departments interact with one another, thus are responsible for some of the cost of the other department:
Cost of Sales, S= 150,000 + 0.25IT, where IT=some proportion of the IT Dept's cost.
Cost of IT, IT= 100,000 + .5S, where as above, S is some cost of IT using Sales.
Substitute either equation into the other. Below I've chosen to substitute IT into Sales, but you could have replaced the S in the IT formula above. Either which way works just fine.
S = 150,000 + 0.25(100,000 + .5S)
S = 150,000 + 25,000 + 0.125S
S = 175,000 + 0.125S
S - 0.125 = 175,000
0.875S = 175000
S = 200,000
And that's it! All that remains is to use the variable you solved for in the other equation :)
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