Chapter 18, Problem 33P

1.

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	Model 1	Model 2	Model 3	Total
Actual results:
Sales:	$141,700	$89,080	$32,810	$263,590
Less: Variable expenses	($49,050)	($44,540)	($13,510)	($10,7100)
Actual Contribution margin	$92,650	$44,540	$19,300	$156,490
Budgeted results:
Sales:	$135,000	$91,000	$30,000	$256,000
Less: Variable expenses:	($54,000)	($39,000)	($10,000)	($103,000)
Budgeted Contribution margin	$81,000	$52,000	$20,000	$153,000
Computation of variance
Actual Contribution margin (A)				$156,490
Budgeted Contribution margin (B)				$153,000
Contribution margin variance $\left(\text{A}\right)-\left(\text{B}\right)$				$3,490 (F)

Table (1)

Since, the actual contribution margin is more than the budgeted contribution margin; the contribution margin variance of $3,490 is favorable (F).

2.

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:

$\begin{array}{c}\begin{array}{l}\text{Contribution margin }\\ \text{volume variance}\end{array}\}=\left[\left(\begin{array}{l}\text{Actual quantity }\\ \text{sold }\left(\text{in units}\right)\end{array}\right)-\left(\begin{array}{l}\text{Budgeted quantity}\\ \text{ sold}\left(\text{in units}\right)\end{array}\right)\times \left(\begin{array}{l}\text{Budgeted average unit}\\ \text{ contribution margin}\end{array}\right)\right]\\ =\left[\left(2,700+1,300+1,000\right)-\left(2,725+1,310+965\right)\right]\times \$30.60\\ =\left[5,000-5,000\right]\times \$30.60\\ =\$0\end{array}$

Therefore, the contribution margin volume variance is $0.

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

$\begin{array}{c}\begin{array}{l}\text{Budgeted average unit}\\ \text{ contribution margin}\end{array}\}=\frac{\text{Budgeted contribution margin}}{\text{Budgeted sales units}}\\ =\frac{\$153,000}{5,000\text{ units}}\\ =\$30.60\end{array}$

3.

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 model 1 mix:

$\begin{array}{c}\text{Model 1 mix}=\left[\left\{\left(\begin{array}{l}\text{Actual }\\ \text{units}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted}\\ \text{ units}\end{array}\right)\right\}\times \left\{\left(\begin{array}{l}\text{Budgeted }\\ \text{contribution }\\ \text{margin}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average}\\ \text{ unit contribution}\\ \text{ margin}\end{array}\right)\right\}\right]\\ =\left[\left(2,725-2,700\right)\times \left(\$30-\$30.60\right)\right]\\ =25\times \left(\$0.60\right)\\ =\$15\left(\text{Unfavorable}\right)\end{array}$

Compute the model 2 mix:

$\begin{array}{c}\text{Model 2 mix}=\left[\left\{\left(\begin{array}{l}\text{Actual }\\ \text{units}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted}\\ \text{ units}\end{array}\right)\right\}\times \left\{\left(\begin{array}{l}\text{Budgeted }\\ \text{contribution }\\ \text{margin}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average}\\ \text{ unit contribution}\\ \text{ margin}\end{array}\right)\right\}\right]\\ =\left[\left(1,310-1,300\right)\times \left(\$40-\$30.60\right)\right]\\ =10\times \$9.40\\ =\$94\left(\text{Favorable}\right)\end{array}$

Compute the model 3 mix:

$\begin{array}{c}\text{Model 1 mix}=\left[\left\{\left(\begin{array}{l}\text{Actual }\\ \text{units}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted}\\ \text{ units}\end{array}\right)\right\}\times \left\{\left(\begin{array}{l}\text{Budgeted }\\ \text{contribution }\\ \text{margin}\end{array}\right)-\left(\begin{array}{l}\text{Budgeted average}\\ \text{ unit contribution}\\ \text{ margin}\end{array}\right)\right\}\right]\\ =\left[\left(965-1,000\right)\times \left(\$20-\$30.60\right)\right]\\ =35\times \left(\$10.60\right)\\ =\$371\left(\text{Favorable}\right)\end{array}$

Compute the sales mix variance:

$\begin{array}{c}\text{Sales mix variance}=\left(\begin{array}{l}\text{Model 1 }\\ \text{mix variance}\end{array}\right)+\left(\begin{array}{l}\text{Model 2 }\\ \text{mix variance}\end{array}\right)+\left(\begin{array}{l}\text{Model 3 }\\ \text{mix variance}\end{array}\right)\\ =\left(\$15\right)+\$94+\$371\\ =\$450\left(\text{Favorable}\right)\end{array}$

Thus, the sales mix variance is $450 (Favorable).