Chapter 18, Problem 31P

Haysbert Company provides management services for apartments and rental units. In general, Haysbert packages its services into two groups: basic and complete. The basic package includes advertising vacant units, showing potential renters through them, and collecting monthly rent and remitting it to the owner. The complete package adds maintenance of units and bookkeeping to the basic package. Packages are priced on a per-rental unit basis. Actual results from last year are as follows:

Haysbert had budgeted the following amounts:

Required:

1. 1. Calculate the contribution margin variance.
2. 2. Calculate the contribution margin volume variance.
3. 3. Calculate the sales mix variance.

To determine

Compute the contribution margin variance.

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:

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

Compute the contribution margin variance:

Particulars	Basic	Complete	Total
Actual results:
Sales: $\text{Basic:}\left(\$85\times \text{2,000 units}\right)$ $\text{Complete:}\left(\$240\times 4\text{00 units}\right)$	$280,000	$120,000	$400,000
Less: Variable expenses: $\text{Basic:}\left(\$85\times \text{2,000 units}\right)$ $\text{Complete:}\left(\$240\times 4\text{00 units}\right)$	($170,000)	($96,000)	($226,000)
Actual Contribution margin	$110,000	$24,000	$134,000
Budgeted results:
Sales: $\text{Basic:}\left(\$85\times \text{1,950 units}\right)$ $\text{Complete:}\left(\$240\times 4\text{00 units}\right)$	$282,750	$133,400	$416,150
Less: Variable expenses: $\text{Basic:}\left(\$85\times \text{2,000 units}\right)$ $\text{Complete:}\left(\$240\times 4\text{00 units}\right)$	($175,500)	($111,320)	($286,820)
Budgeted Contribution margin	$107,250	$22,080	$129,030
Computation of variance
Actual Contribution margin (A)			$134,000
Budgeted Contribution margin (B)			$129,030
Contribution margin variance $\left(\text{A}\right)-\left(\text{B}\right)$			$4,670 (F)

Table (1)

Since, the actual contribution margin is more than the budgeted contribution margin; the contribution margin variance of $4,670 is favorable (F).

To determine

Compute the contribution margin volume variance.

Explanation of Solution

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:

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

Compute the contribution margin volume variance:

$\begin{array}{c}\begin{array}{l}\text{Contribution margin }\\ \text{volume variance}\end{array}\}=\left[\left(\begin{array}{l}\text{Actual quantity }\\ \text{sold }\left(\text{in units}\right)\end{array}\right)-\left(\begin{array}{l}\text{Budgeted quantity}\\ \text{ sold}\left(\text{in units}\right)\end{array}\right)\times \left(\begin{array}{l}\text{Budgeted average unit}\\ \text{ contribution margin}\end{array}\right)\right]\\ =\left[\left(2,000+400\right)-\left(1,950+460\right)\right]\times \$53.6639\\ =\left[2,400-2,410\right]\times \$53.6639\\ =\$536.64\left(\text{Unfavorable}\right)\end{array}$

Therefore, the contribution margin volume variance is $536.64(Unfavorable).

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

$\begin{array}{c}\begin{array}{l}\text{Budgeted average unit}\\ \text{ contribution margin}\end{array}\}=\frac{\text{Budgeted contribution margin}}{\text{Budgeted sales units}}\\ =\frac{\$129,330}{\left(1,950\text{ units}+460\text{ units}\right)}\\ =\frac{\$129,330}{2,410\text{ units}}\\ =\$53.6639\end{array}$

To determine

Compute the sales mix variance.

Explanation of Solution

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:

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

Compute the basic sales mix:

$\begin{array}{c}\text{ Basic Sales mix}=\left[\left\{\left(\begin{array}{l}\text{Actual }\\ \text{units}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted}\\ \text{ units}\end{array}\right)\right\}\times \left\{\left(\begin{array}{l}\text{Budgeted }\\ \text{contribution }\\ \text{margin}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average}\\ \text{ unit contribution}\\ \text{ margin}\end{array}\right)\right\}\right]\\ =\left[\left(2,000-1,950\right)\times \left(\$55.00-\$53.6639\right)\right]\\ =\$66.81\left(\text{Favorable}\right)\end{array}$

Compute the complete sales mix:

$\begin{array}{c}\text{ Complete Sales mix}=\left[\left\{\left(\begin{array}{l}\text{Actual }\\ \text{units}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted}\\ \text{ units}\end{array}\right)\right\}\times \left\{\left(\begin{array}{l}\text{Budgeted }\\ \text{contribution }\\ \text{margin}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average}\\ \text{ unit contribution}\\ \text{ margin}\end{array}\right)\right\}\right]\\ =\left[\left(400-460\right)\times \left(\$48.00-\$53.6639\right)\right]\\ =\$339.83\left(\text{Favorable}\right)\end{array}$

Compute the sales mix variance:

$\begin{array}{c}\text{Sales mix variance}=\left(\text{Basic mix variance}\right)+\left(\text{Complete mix variance}\right)\\ =\$66.81+\$393.83\\ =\$406.64\left(\text{Favorable}\right)\end{array}$