Chapter 18, Problem 42P

1.

To determine

Discuss the benefits from segment reporting for an organization. Evaluate segment reporting with respect to variable-costing basis against absorption-costing.

Explanation of Solution

Segment reporting is beneficial for an organization because segmental reporting focuses on the profitability of each segment. Segment reporting aids in identifying the unprofitable segments that are lost in the overall profit of the company as a whole.

Segmental reporting is better when carried out on variable basis rather than an absorption costing because variable costing does not allow a manager to increase profits by producing for inventory.  Moreover, the contribution that a segment makes to earn profit can easily be identified in the variable-costing income statements. Under absorption costing, it is difficult to determine whether an unprofitable segment makes a contribution to profit or not.

2.

To determine

Determine the contribution margin, contribution margin volume, and sales mix variances.

Explanation of Solution

Contribution margin variance: Contribution margin variance reflects difference between the actual contribution margin and budgeted contribution margin. It is computed using the given formula:

$\text{Contribution margin variance}=\left(\begin{array}{l}\text{Actual total }\\ \text{contribution}\\ \text{ margin}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted total }\\ \text{contribution}\\ \text{ margin}\end{array}\right)$

Determine the contribution margin:

$\begin{array}{c}\text{Contribution margin variance}=\left(\begin{array}{l}\text{Actual total }\\ \text{contribution}\\ \text{ margin}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted total }\\ \text{contribution}\\ \text{ margin}\end{array}\right)\\ =\$1,493,000-\$1,241,000\\ =\$252,000\left(\text{Favorable}\right)\end{array}$

Contribution margin volume variance: Contribution margin volume variance reflects difference between the actual quantity sold and the budgeted quantity sold multiplied by the budgeted average unit contribution margin. It is computed using the given formula:

$\begin{array}{l}\text{Contribution margin }\\ \text{volume variance}\end{array}\}=\left[\left(\begin{array}{l}\text{Actual }\\ \text{quantity }\\ \text{sold}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted }\\ \text{quantity }\\ \text{sold}\end{array}\right)\times \left(\begin{array}{l}\text{Budgeted average unit}\\ \text{ contribution margin}\end{array}\right)\right]$

Determine the contribution margin volume variance:

Given, the actual units sold are 46,000 units $\left(12,000+4,000+30,000\right)$ and budgeted units sales are 50,000 units $\left(8,000+22,000+20,000\right)$.

$\begin{array}{c}\begin{array}{l}\text{Contribution margin }\\ \text{volume variance}\end{array}\}=\left[\left(\begin{array}{l}\text{Actual quantity }\\ \text{sold }\left(\text{in units}\right)\end{array}\right)-\left(\begin{array}{l}\text{Budgeted quantity}\\ \text{ sold}\left(\text{in units}\right)\end{array}\right)\times \left(\begin{array}{l}\text{Budgeted average unit}\\ \text{ contribution margin}\end{array}\right)\right]\\ =\left[\left(46,000\right)-\left(50,000\right)\right]\times \$24.82\\ =\$99,280\left(\text{Unfavorable}\right)\end{array}$

Working note 1: Calculate the budgeted average unit contribution margin:

$\begin{array}{c}\begin{array}{l}\text{Budgeted average unit}\\ \text{ contribution margin}\end{array}\}=\frac{\text{}\text{Total budgeted contribution margin}}{\text{Total budgeted sales units}}\\ =\frac{\$1,241,000}{50,000\text{ units}}\\ =\$24.82\text{ per unit}\end{array}$

Sales mix variance: The sales mix represents the part of total sales generated by each product. Sales mix variance is the summation of change in units for each product multiplied by the difference between the budgeted contribution margin and the budgeted average unit contribution margin. It is computed using the given formula:

$\begin{array}{c}\text{Sales mix variance}=\left[\begin{array}{l}\left\{\left(\text{Actual units of Product1 }\right)-\left(\text{Budgeted units of Product1}\right)\right\}\times \\ \left\{\left(\begin{array}{l}\text{Budgeted contribution}\\ \text{ margin of Product1}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average unit }\\ \text{contribution margin}\end{array}\right)\right\}\end{array}\right]\\ +\\ \left[\begin{array}{l}\left\{\left(\text{Actual units of Product 2 }\right)-\left(\text{Budgeted units of Product 2}\right)\right\}\times \\ \left\{\left(\begin{array}{l}\text{Budgeted contribution}\\ \text{ margin of Product 2}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average unit }\\ \text{contribution margin}\end{array}\right)\right\}\end{array}\right]\end{array}$

Determine the sales mix variance for upscale lighting data:

$\begin{array}{c}\begin{array}{l}\text{Sales mix variance for}\\ \text{ upscale lighting data}\end{array}\}=\left[\begin{array}{l}\left\{\left(\begin{array}{l}\text{Actual units of}\\ \text{ upscale lighting data}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted units of }\\ \text{upscale lighting data}\end{array}\right)\right\}\times \\ \left\{\left(\begin{array}{l}\text{Budgeted contribution margin }\\ \text{of upscale lighting data}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average unit }\\ \text{contribution margin}\end{array}\right)\right\}\end{array}\right]\\ =\left(12,000\text{ units}-8,000\text{ units}\right)\times \left(\$68.75-\$24.82\right)\\ =4,000\text{ units}\times \$43.93\\ =\$175,720\left(\text{Favorable}\right)\end{array}$

Determine the sales mix variance for mid-range lighting data:

$\begin{array}{c}\begin{array}{l}\text{Sales mix variance for}\\ \text{ mid}-\text{range lighting data}\end{array}\}=\left[\begin{array}{l}\left\{\left(\begin{array}{l}\text{Actual units of mid}\\ -\text{range lighting data}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted units of mid}\\ -\text{range lighting data}\end{array}\right)\right\}\times \\ \left\{\left(\begin{array}{l}\text{Budgeted contribution margin }\\ \text{of mid}-\text{range lighting data}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average unit }\\ \text{contribution margin}\end{array}\right)\right\}\end{array}\right]\\ =\left(4,000\text{ units}-22,000\text{ units}\right)\times \left(\$12.32-\$24.82\right)\\ =18,000\text{ units}\times \$12.5\\ =\$225,000\left(\text{Favorable}\right)\end{array}$

Determine the sales mix variance for timing device data:

$\begin{array}{c}\begin{array}{l}\text{Sales mix variance for}\\ \text{ timing device data}\end{array}\}=\left[\begin{array}{l}\left\{\left(\begin{array}{l}\text{Actual units of }\\ \text{timing device data}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted units of}\\ \text{ timing device data}\end{array}\right)\right\}\times \\ \left\{\left(\begin{array}{l}\text{Budgeted contribution margin }\\ \text{of timing device data}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average unit }\\ \text{contribution margin}\end{array}\right)\right\}\end{array}\right]\\ =\left(30,000\text{ units}-20,000\text{ units}\right)\times \left(\$21.00-\$24.82\right)\\ =10,000\text{ units}\times \left(\$3.82\right)\\ =\$38,200\left(\text{Unfavorable}\right)\end{array}$

Determine the sales mix variance:

$\begin{array}{c}\text{Sales mix variance}=\left(\begin{array}{l}\text{Sales mix for }\\ \text{upscale lighting data}\end{array}\right)+\left(\begin{array}{l}\text{Sales mix for mid-}\\ \text{scale lighting data}\end{array}\right)+\left(\begin{array}{l}\text{Sales mix for }\\ \text{timing device data}\end{array}\right)\\ =\$175,720+\$225,000-\$38,200\\ =\$362,520\left(\text{Favorable}\right)\end{array}$

3.

To determine

Describe the reasons behind the variances.

Explanation of Solution

Since, the actual contribution margin is higher than budgeted the contribution margin variance is favorable. This happened due to the change in sales mix. A higher percentage of sales were possible due to the higher contribution margin of upscale lights, and a lower percentage of sales happened due to the lower contribution margin of mid-range lights.

It is to be noted that fewer units (46,000) were sold than budgeted (50,000). Therefore, it is the sales mix change that led to the higher actual contribution margin.