Cost allocations of service departments

Bear with me. I'm studying. This is fairly complex, and I am having a hard time. I think that if I make notes about it here, it will become more clear to me. So here I go.

Allocation Methods

My text contains a table, which reads as follows:

	Service Department		Operating Department
	Hospital Administration	Custodial Services	Laboratory	Daily Patient Care	Total
Departmental costs before allocation	$360,000	$90,000	$261,000	$689,000	$1,400,000
Employee hours	12,000	6,000	18,000	30,000	66,000
Space occupied- square matres	1,000	20	500	4,500	6,020

There are three methods of allocation, being direct, step, and reciprocal.

Direct Method

The direct method is the most simple of the three. The information provided for the direct method indicates that "Hospital Administration costs will be allocated on the basis of employee-hours and Custodial Services costs will be allocated on the basis of square metres occupied". The direct method ignores services provided to other service departments, and allocates all costs to operating departments.

So, using the direct method, one would take the hospital administration charge of $360,000 and allocate it among the employee hours in the laboratory and daily patient care departments. There are a total of 48,000 hours in these two departments (18,000 in laboratory and 30,000 in daily patient care); therefore, 18/48 of the $360,000 would be allocated to the laboratory department and 30/48 to the daily patient care department, for totals of $135,000 and $225,000, respectively. Similarly, the custodial services charge of $90,000 would be allocated among the space occupied in the laboratory and daily patient care departments. There are a total of 5,000 square metres in these two departments (500 in laboratory and 4,500 in daily patient care); therefore, 5/50 of the $90,000 would be allocated to the laboratory department and 45/50 to the daily patient care department, for totals of $9,000 and $81,000 respectively.

The method is obviously fairly inaccurate. No portion of the custodial services costs will be allocated to hospital administration, nor would any portion of hospital administration be allocated to custodial services, despite the fact that it is apparent from the table above that the departments each provide services to one another.

Step Method

The step method is a little bit more complex than the direct method, but it is also slightly more accurate. Allocations are done in a series of sequential steps, starting with "the service department that provides the greatest amount of service to other departments". In this manner, costs are allocated between service departments, but only to a point. We are told to assume that the hospital administration costs will be allocated first.

So, using the step method, one would begin with the hospital administration costs of $360,000 and allocate it among the custodial services, laboratory and daily patient care departments. There are a total of 54,000 hours in these three departments (6,000 in custodial services, 18,000 in laboratory and 30,000 in daily patient care); therefore, 6/54 of the $360,000 would be allocated to the custodial services department, 18/54 to the laboratory department, and 30/54 to the daily patient care department, for totals of $40,000, $120,000 and $200,000, respectively. Next, the custodial services charges will be allocated. Custodial charges now include $40,000 of hospital administration charges, which have been allocated. Total custodial charges are now $130,000 ($90,000 + $40,000), which would be allocated among the space occupied in the laboratory and daily patient care departments. There are a total of 5,000 square metres in these two departments (500 in laboratory and 4,500 in daily patient care); therefore, 5/50 of the $130,000 would be allocated to the laboratory department and 45/50 to the daily patient care department, for totals of $13,000 and $117,000 respectively.

While the step method is more accurate than the direct method, it still is not the most accurate method available, because costs of custodial services are not allocated to the hospital administration department, who uses custodial services. But the step method is more cost effective than the more accurate reciprocal method, and so many companies use the step method.

Reciprocal Method

The reciprocal method is the most accurate of the three methods, but also the most complex. It uses "simultaneous linear equations" to arrive at a more precise allocation. The reciprocal method isn't often used because its complexity makes it more costly than the other systems, and its results are usually not significantly different from the step method. Use of computer programs is making its implementation a bit less costly.

Now here's where it gets dicey!

*Note: HA is hospital administration costs to be allocated; CS is custodial services costs to be allocated. The two equations follow.

HA=360,000+1/6CS

(The 1/6 figure is arrived at by taking the square metres from the hospital adminsitration department and dividing it by the total square metres found in the hospital, laboratory and daily patient care departments: 1,000/6,000=1/6)

CS=90,000+1/9HA

(The 1/9 fiture is arrived at by taking the employee hours from the custodial services department and dividing it by the total employee hours found in the custodial services, laboratory and daily patient care departments: 6,000/54,000=1/9)

To solve the equations, HA and CS need to be on the same sides. So the equations become:

-360,000=-HA+1/6CS
-90,000=1/9HA-CS

The two equations need to be added together. But in order to solve the problem, only one variable can exist once the equations are added together. Ergo, one of the variables must equal zero after the equations are added together. We will solve for CS first. In order to make HA zero, the second equation needs to be multiplied by 9 so that HA will not need to be multiplied by 1/9 any longer. Ergo, the two equations will become:

-360,000=-HA+1/6CS
-810,000=HA-9CS

(Note: if solving for HA first, the first equation would be multiplied by 6, and the second equation would be left alone:
-2,160,000=-6HA+CS
-90,000=1/9HA-CS)

Once the two equations are added together, we find that:
-1,170,000=-8(5/6)CS
CS=-1,170,000/-8(5/6)
CS=$132,453 (rounded to the nearest dollar).

(Note: if solving for HA first:
-2,250,000=-5(8/9)HA
HA=-2,250,000/-5(8/9)
HA=$382,076 (rounded to the nearest dollar)).

Now that we know one variable, we can solve for the other using the first equations indicated. For example, following the main calculation, we know that CS=$132,453. Therefore:

HA=360,000+1/6(132,453)=$382,076 (rounded to the nearest dollar).

(Note: If using the alternative calculations provided throughout, we know that HA=$382,076. Therefore:
CS=90,000+1/9(382,076)=$132,453 (rounded to the nearest dollar)).

Now that we know the amounts that need to be allocated, we can proceed to allocate the costs from hospital administration and custodial services to the various departments. We use the same fractions as in the step method (6/54, 18/54, 30/54) to allocate the hospital administration costs of $382,076 to the other three departments. To allocate custodial services costs of $132,453, we now must include the square metres in hospital administration into the calculation. Custodial services will be allocated among the three other departments using the following fractions: 10/60, 5/60, 45/60.

Of course, I still find it a bit confusing that the full costs of the service departments are allocated out to different departments. Service departments use resources for their own purposes too. I don't know why the hospital administration department is not allocated an amount for its 12,000 employee hours, nor do I understand why the custodial services department is not allocated costs for its 20 square metres of space.

An Epiphany: The goal is to eventually assign all of the service department costs to operating departments and then to assign all of the operating department costs to products and services. Therefore, all of the service department costs have to be allocated to the operating departments; no portion of the service department costs are treated as organization-sustaining activities because, according to page 739 of my text, "the costs that they incur are generally viewed as being part of the cost of the final product or service".

The three methods of cost allocation are ways of getting service department costs to the correct operating departments. And a service department doesn't attribute a portion of its costs to its own work because, if it did so, products and services would ultimately be undervalued.

Okay then. Clear as mud? Well, too bad. I now understand it, and it doesn't much matter if you do, since you are not taking the exam.