Chapter 5, Problem 68P

a.

To determine

Use the high-low method to estimate the fixed and variable portions of store costs based on employees.

Explanation of Solution

High-low cost method:

High-low cost method helps in separating the fixed and variable cost from the total cost. It is calculated by comparing the highest and lowest level of activities and the cost of these activities.

Show the cost equation of fixed and variable cost with the overhead cost:

$\begin{array}{c}\text{Store cost = Fixed cost + Variable cost}\\ \text{= }\left(\text{\$91}\right)\text{ (1) + (\$94}\text{.82(2) }\times \text{ Number of employees)}\end{array}$

Thus, the cost equation is: $\text{Store cost = \$232 + (\$94}\text{.82 }\times \text{ Number of employees)}$.

Working note 1:

Calculate the fixed cost:

$\begin{array}{c}\text{Fixed cost = Total cost - Variable cost}\\ \text{= \$5029 - \$5,120 (3)}\\ =\text{ (\$91)}\end{array}$

Calculate the highest and lowest activity:

Particular	Employees	Cost
Highest activity	54	$5,029
Lowest activity	26	$2,374

Table: (1)

Working note 2:

Calculate the variable cost (unit) with the help of high-low cost method:

$\begin{array}{c}\text{Variable cost = }\frac{\mathrm{Co}\text{st of highest activity }-\text{ Cost of lowest activity}}{\text{Highest activity units }-\text{ Lowest activity units}}\\ =\frac{\$5,029-\text{ \$2,374}}{\text{54 }-26}\\ =\text{ \$94}\text{.82}\end{array}$

Working note 3:

Calculate the variable cost ($) with the help of high-low cost method:

$\begin{array}{c}\text{Variable cost (\$) = Number of employees}\times \text{ Rate per unit}\\ \text{= 54 }\times \text{ \$94}\text{.82(2)}\\ \text{= \$5,120}\end{array}$

b.

To determine

Use the results of your high-low analysis to estimate the cost for a store with 30 employees.

Explanation of Solution

Total cost of store:

Total cost of the store includes the fixed and variable cost of the production. It is calculated by the cost equation.

Estimate the cost for the store:

$\begin{array}{c}\text{Store cost = \$232 + (\$8 }\times \text{ number of employees)}\\ \text{= (\$232) + (94}\text{.82 }\times \text{ 30)}\\ \text{= \$2,753}\end{array}$

Thus, the estimated cost for the store is $2,753.

c.

To determine

Prepare a scatter graph between store cost and employees.

Explanation of Solution

Scatter graph:

Scatter graph shows the relationship between the cost and the activity. It shows the cost at various level of activity. It helps in finding the outlier in the data. So the management can eliminate it to make more effective decisions.

Prepare the scatter graph for store cost and employee:

The scatter plot represents number of employees on the horizontal axis and the store cost on the vertical axis. The points on the scatter plot do not seem to form the linear pattern and there is not a healthy relationship as well.

d.

To determine

Prepare an estimate of the cost of a store with 30 employees using the results from a simple regression of store cost on employees.

Answer to Problem 68P

The store cost is $2,930.

Explanation of Solution

Cost equation:

Cost equation is a mathematical representation of the cost estimation at various level of activity. It is used by defining the fixed cost and variable cost per unit and then the variable cost per unit is multiplied by the given variable to calculate the relative cost.

$\begin{array}{c}\text{Store cost = (}\$162.9)+103.1\times \text{ Employees}\\ \text{= (}\$162.9)+103.1\times \text{ 30}\\ \text{= \$2,930}\end{array}$

Thus, the store cost is $2,930.

e.

To determine

Prepare an estimate of the cost of a store with revenues of $2.5 million and 30 employees using the results of a multiple regression of store costs on store revenues and employees.

Explanation of Solution

Multiple regressions:

Multiple regressions use two or more activities (variables) to establish the relationship between cost and activities:

$\begin{array}{c}\text{Store cost = (}\$204.2)+\text{ (}0.01)\times \text{ Revenues + 105}\text{.5 }\times \text{ Employees}\\ \text{= (}\$204.2)+(0.01)\times 2,500+105.5\times 30\\ =\text{ \$2,935}\text{.8}\end{array}$

Thus, the store cost is $2,935.8.

f.

To determine

Comment on the results of the regression analyses in parts d and e.

Explanation of Solution

Regression analysis:

Regression analysis is used to show the relationship between the cost and the activity. It is used to estimate the cost at various level of activity.

The most important step in the calculation of regression analysis is to establish a logical relationship between the cost and the activity. The activity (independent variable) is placed on the right-hand-side and the cost (dependant variable) is placed on the left-hand-side of the graph.

Comment on the results of the regression analyses:

In case of simple and multiple regressions, the both of the coefficients are not very significant. But the both the R² are similar and significant. This kind of problem arises when two or more independent variables in a multiple regression analyses are related to each other.

In the given case, the number of employees and revenue are closely related.