Anchor Corporation has two service departments, Personnel and Engineering, and two operating departments. The costs of the Personnel Department are allocated to other departments on the basis of the number of employees in the departments. Departments and number of employees are as follows: Costs in the Personnel Department total $765,000 per year.Suppose the company uses the step-down method and Personnel Department costs are allocated first. The amount of the Personnel Department cost allocated to the Engineering Department would be closest to:

A) $85,000
B) $0
C) $90,000
D) $102,000

Since the Personnel Department costs are allocated first using the step-down method, we need to allocate these costs to the two operating departments before allocating costs from the Engineering Department (since Engineering is also a service department).

To do this, we need to use the allocated costs from the Personnel Department for each department. Using the table given, we can see that the number of employees in the Personnel Department is 40 (20+20), and the Engineering Department has 60 employees.

So, the portion of Personnel Department costs allocated to Engineering would be:

(60/100) x $765,000 = $459,000

Now, we can allocate the Engineering Department costs to the operating department. The total costs of the Engineering Department are not given, so we can't use the reciprocal method to allocate costs. Instead, we need to use another method such as the simultaneous equations method or the algebraic method.

Assuming the Engineering Department costs are x, and the Personnel Department costs allocated to Operating Department 1 (OD1) and Operating Department 2 (OD2) are y and z respectively, we can set up two equations:

x = 0.5y + 0.6z (since Engineering is allocated 50% to OD1 and 60% to OD2)

y + z = $459,000 (total Personnel costs allocated to Engineering)

Solving these equations simultaneously, we get:

y = $153,000

z = $255,000

So, the portion of Engineering Department costs allocated to OD1 would be:

0.5 x $153,000 = $76,500

And the portion allocated to OD2 would be:

0.6 x $255,000 = $153,000

Therefore, the total costs allocated to the Engineering Department are:

x + $76,500 + $153,000 = $765,000

Solving for x, we get:

x = $535,500

Therefore, the amount of Personnel Department cost allocated to the Engineering Department would be:

$459,000 - $535,500 = -$76,500

Since this is a negative number, it means that the Engineering Department actually covers more than its fair share of the Personnel Department costs, and does not receive any allocation of Personnel Department costs.

The closest choice to this answer is C, $90,000, which is allocated assuming Engineering pays 60% of Personnel Department and would be correct if we were using the direct method instead of the step-down method. However, using the step-down method, the correct answer is B, $0.