Chapter 12, Problem 50P

Cost Allocations: Comparison of Dual and Single Rates

Pacific Hotels operates a centralized call center for the reservation needs of its hotels. Costs associated with use of the center are charged to the hotel group (luxury, resort, standard, and budget) based on the length of time of calls made (time usage). Idle time of the reservation agents, time spent on calls in which no reservation is made, and the fixed cost of the equipment are allocated based on the number of reservations made in each group. Due to recent increased competition in the hotel industry, the company has decided that it is necessary to better allocate its costs in order to price its services competitively and profitably. During the most recent period for which data are available, the use of the call center for each hotel group was as follows:

During this period, the cost of the call center amounted to $840,000 for personnel and $650,000 for equipment and other costs.

Required

1. a.      Determine the allocation to each of the divisions using the following:
   1. 1. A single rate based on time used.
   2. 2. Dual rates based on time used (for personnel costs) and number of reservations (for equipment and other cost).
2. b.      Write a short report to management explaining whether a single rate or dual rates should be used and why.

To determine

Determine the allocation to each of the divisions using the following:

1. A single rate based on the time used.

2. Dual rates based on time used (for personnel costs) and some reservations (for equipment and other cost).

Explanation of Solution

Cost allocation:

Cost allocation is the process of distributing a common cost into the departments that have used the cost. The cost is allocated on the basis of the utilization of the resource.

1.

Allocation of total cost on the basis of a single rate based on time used:

Particular	The ratio of time usage (a)	Amount $\text{c = a }\times \text{ \$1,490,000}$
Luxury	0.2 (1)	$298,000
Resort	0.1 (2)	$149,000
Standard	0.4 (3)	$596,000
Budget	0.3 (4)	$447,000
Total cost		1,490,000

Table: (1)

Thus, the total cost allocation for luxury, resort, standard and budget is $298,000, $149,000, $596,000 and $447,000.

Working note 1:

Calculate the ratio of time usage for luxury:

$\begin{array}{c}\text{Ratio for luxury department = }\frac{\text{Time usage of luxury department}}{\text{Total time usage}}\\ =\frac{400}{2,000}\\ =\text{0}\text{.2}\end{array}$

Working note 2:

Calculate the ratio of time usage for the resort:

$\begin{array}{c}\text{Ratio for resort department = }\frac{\text{Time usage of resort department}}{\text{Total time usage}}\\ =\frac{200}{2,000}\\ =\text{0}\text{.1}\end{array}$

Working note 3:

Calculate the ratio of time usage for standard:

$\begin{array}{c}\text{Ratio for standard department = }\frac{\text{Time usage of standard department}}{\text{Total time usage}}\\ =\frac{800}{2,000}\\ =\text{0}\text{.4}\end{array}$

Working note 4:

Calculate the ratio of time usage for luxury:

$\begin{array}{c}\text{Ratio for budget department = }\frac{\text{Time usage of budget department}}{\text{Total time usage}}\\ =\frac{600}{2,000}\\ =\text{0}\text{.3}\end{array}$

2.

Calculate the allocation of cost on Dual rates based on time used (for personnel costs) and some reservations (for equipment and other cost):

Allocation of cost for personnel costs:

Particular	The ratio of time usage (a)	Amount $\text{c = a }\times \text{ \$840,000}$
Luxury	0.2 (1)	$168,000
Resort	0.1 (2)	$84,000
Standard	0.4 (3)	$336,000
Budget	0.3 (4)	$252,000
Total cost		840,000

Table: (2)

Thus, the personnel cost allocation for luxury, resort, standard and budget is $168,000, $84,000, $336,000 and $252,000.

Allocation of cost for equipment and other costs:

Particular	The ratio of the number of reservations (a)	Amount $\text{c = a }\times \text{ \$650,000}$
Luxury	0.08 (1)	$52,000
Resort	0.1 (2)	$65,000
Standard	0.24 (3)	$156,000
Budget	0.58 (4)	$377,000
Total cost		$650,000

Table: (3)

Thus, the personnel cost allocation for luxury, resort, standard and budget is $168,000, $84,000, $336,000 and $252,000.

Working note 5:

Calculate the ratio of the number of reservations for luxury:

$\begin{array}{c}\text{Ratio for luxury department = }\frac{\text{Number of reservations of luxury department}}{\text{Total number of reservations}}\\ =\frac{120}{1,500}\\ =\text{0}\text{.08}\end{array}$

Working note 6:

Calculate the ratio of the number of reservations for the resort:

$\begin{array}{c}\text{Ratio for resort department = }\frac{\text{Number of reservations of resort department}}{\text{Total number of reservations}}\\ =\frac{150}{1,500}\\ =\text{0}\text{.1}\end{array}$

Working note 7:

Calculate the ratio of the number of reservations for standard:

$\begin{array}{c}\text{Ratio for standard department = }\frac{\text{Number of reservations of standard department}}{\text{Total number of reservations}}\\ =\frac{360}{1,500}\\ =\text{0}\text{.24}\end{array}$

Working note 8:

Calculate the ratio of the number of reservations for luxury:

$\begin{array}{c}\text{Ratio for budget department = }\frac{\text{Number of reservations of budget department}}{\text{Total number of reservations}}\\ =\frac{870}{1,500}\\ =\text{0}\text{.58}\end{array}$

To determine

Write a short report to management explaining whether a single rate or dual rates should be used and why.

Explanation of Solution

The cost should be allocated on the basis of the dual rate system.

In single rate allocation, the cost of equipment and other cost do not correlate with the time usage. So allocating the cost of equipment and other cost is not reasonable in this case.

Dual rate system has better correlation with the costs and usage. The cost of personnel’s is directly correlated with the time usage, and the cost of equipment and other cost are directly correlated with the number of reservations.

Thus, cost should be allocated on the basis of the dual rate system.