The calculation of sales mix contribution and sales quantity contribution variances was examined in the May 2011 P1 and P2 papers. Both examiners commented in their post-exam guides that the answers to these two questions were generally poor.
Let’s look at the relevant sections of the P1 question in detail to see how it should have been answered and where the common errors were made in both papers. Having completed a number of calculations in the first parts of this question, students had the data in table 1 available to calculate the sales mix contribution variance and the sales quantity contribution variance. |
TABLE 1 |
| Extracts from last year’s budget | Economy | Premium | Deluxe | | Sales (units) | 180,000 | 360,000 | 260,000 | | Selling price per unit ($) | 2.80 | 3.20 | 4.49 | | Direct material cost per unit ($) | 1.00 | 1.60 | 2.20 | | Direct labour cost per unit ($) | 0.50 | 0.50 | 0.50 | | Variable overhead cost per unit ($) | 0.65 | 0.65 | 0.65 | | | | | | | Actual results from last year | Economy | Premium | Deluxe | | Sales (units) | 186,000 | 396,000 | 278,000 |
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TABLE 2 |
| | Selling price per unit | Variable unit cost | Contribution per unit | Budgeted sales (units) | Total budgeted contribution | | Economy | $2.80 | $2.15 | $0.65 | 180,000 | $117,000 | | Premium | $3.20 | $2.75 | $0.45 | 360,000 | $162,000 | | Deluxe | $4.49 | $3.35 | $1.14 | 260,000 | $296,400 | | Total | | | | 800,000 | $575,400 |
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TABLE 3 |
| | Budgeted sales | % | Actual sales in standard mix (units) | | Economy | 180,000 units | 22.5 | 860,000 x 22.5% = 193,500 | | Premium | 360,000 units | 45.0 | 860,000 x 45.0% = 387,000 | | Deluxe | 260,000 units | 32.5 | 860,000 x 32.5% = 279,500 | | Total | 800,000 units | 100.0 | 860,000 |
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The sales mix contribution variance
This variance measures the change in the standard contribution caused by a difference in the mix of products actually sold from the budgeted mix of products. Some goods earn a higher contribution than others and, if proportionately fewer of these more profitable products are sold, the potential contribution that could be earned will be lower.
The P1 examiner commented that candidates often wrongly evaluated the variances by using selling price rather than contribution. But note the full titles of the two variances: both are referred to ascontribution variances and must therefore be evaluated using contribution rather than selling price. Remember that we are monitoring the change in contribution caused by a change in the mix or quantity of sales. Or, to be more precise, we’re monitoring the change in the standard contribution caused by a change in the mix or quantity of sales.
The original question also provided actual unit costs and selling prices for each product. A second common error committed by exam candidates was to use the actual contribution rather than the standard contribution to evaluate the variances. This is wrong because we are monitoring the potential extra contribution (or loss of contribution) caused by a change in the mix or quantity of sales. The fact that the selling prices or costs are different from standard is monitored by the selling price variance and the various cost variances.
The first step is to calculate the standard weighted-average contribution per unit of the products in the standard mix using table 2. So the standard weighted-average contribution per unit is $575,400 ÷ 800,000 = $0.71925. This is the average contribution per unit that should be earned if the products are sold in the standard mix.
Next we need to look at the contribution per unit earned from the individual products: Economy and Premium both earn a lower contribution than the average. If the mix of actual sales contains proportionately more of these products, the sales mix variance will be adverse. On the other hand, if proportionately more units of Deluxe are sold, the sales mix variance will be favourable.
We are not concerned here with whether more or fewer units were sold than the number budgeted, since this is monitored by the sales quantity variance. So we need to calculate how many units of each product would have been sold if the actual sales had been in the standard mix. The standard mix of the actual sales is based on the budget. For example, the total budgeted sales volume is 800,000 units, of which 180,000 units are Economy. So 22.5 per cent (180,000 ÷ 800,000) of sales units should be Economy and so on. See table 3 for the full workings.
Now we are able to compare the standard mix of sales with the actual mix and evaluate the difference in contribution using table 4.
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TABLE 4 |
| | Actual Sales (units) | Actual sales in standard mix (units) | Difference (units): A | Variance from weighted-average contribution per unit: B | Sales mix contribution variance A x B | | Economy | 186,000 | 193,500 | -7,500 | ($0.65 – $0.71925 = -$0.06925) | $519 favourable | | Premium | 396,000 | 387,000 | 9,000 | ($0.45 – $0.71925 = -$0.26925) | $2,423 adverse | | Deluxe | 278,000 | 279,500 | -1,500 | ($1.14 – $0.71925 = $0.42075) | $631 adverse | | Total | 860,000 | 860,000 | | | $2,535 adverse |
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TABLE 5 |
| | Actual Sales (units) | Actual sales in standard mix (units) | Difference (units): A | Standard contribution contribution per unit: B | Sales mix contribution variance A x B | | Economy | 186,000 | 193,500 | -7,500 | $0.65 | $4,875 adverse | | Premium | 396,000 | 387,000 | 9,000 | $0.45 | $4,050 favourable | | Deluxe | 278,000 | 279,500 | -1,500 | $1.14 | $1,710 adverse | | Total | 860,000 | 860,000 | | | $2,535 adverse |
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TABLE 6 |
| | Budgeted sales (units) | Actual sales in standard mix (units) | Difference (units): A | Standard contribution contribution per unit: B | Sales mix contribution variance A x B | | Economy | 180,000 | 193,500 | 13,500 | $0.65 | $8,775 favourable | | Premium | 360,000 | 387,000 | 27,000 | $0.45 | $12,150 favourable | | Deluxe | 260,000 | 279,500 | 19,500 | $1.14 | $22,230 favourable | | Total | 800,000 | 860,000 | | | $43,155 favourable |
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The examiner reported that many candidates incorrectly showed adverse variances as favourable and vice versa. If the workings are arranged as in table 4, a positive result will be a favourable variance and a negative one will be an adverse variance. But memorising column headings is a dangerous approach. It is much better to understand the calculations and thereby deduce whether a particular variance is adverse or favourable. For example, Economy earns a lower contribution per unit than the average. Because fewer units of Economy were in the actual mix, a favourable variance resulted. Similarly, Premium earns a lower contribution per unit than average, so a greater number of Premium units in the mix resulted in an adverse variance. Deluxe earns a higher unit contribution, but fewer units were in the mix than standard, so the variance was adverse.
An alternative method is available for calculating the total sales mix variance (see table 5, previous page). It uses the same analysis of the difference in the sales mix, but it evaluates the differences at the standard contribution per unit, rather than at the weighted-average contribution, for each product. You can see from the table that this approach results in the same total mix variance, but different variances for the individual products.
The method was acceptable in the May 2011 P1 and P2 papers for calculating the total sales mix variance. But CIMA’s official terminology recommends that you use the first method – ie, the one shown in table 4 – if you are required to analyse the mix variance for each product. This is because the alternative approach doesn’t give meaningful results for individual products. For example, the variance shown for Economy using this method is adverse. But, as we have seen earlier, if proportionately fewer units of Economy are sold, the fact that it earns a lower-than-average contribution means that the potential total contribution is increased. The favourable variance for Economy using the first method reflects this situation correctly.
The sales quantity contribution variance
This variance measures the potential change in the contribution that could be earned as the result of a change in the number of units sold compared with the budgeted amount. In this example, the actual total sales volume was higher than budgeted, so the quantity variance will be favourable.
The sales quantity contribution variance is therefore (860,000 budgeted units – 800,000 actual units) x $0.71925 = $43,155 favourable.
The quantity variance is evaluated using the average unit contribution in the standard mix, because the effect of any change in the mix has already been monitored by the mix variance.
An alternative approach to calculating the sales quantity variance (see table 6) produces the same total result, but it also provides the variances for the individual products. This method is equally acceptable in the exams and it shows the potentially favourable effect on the contribution of selling more units than budgeted of each product.
What the variances indicate
The two variances combined will show the effect on standard contribution of a change in the volume of sales compared with the budgeted amount. The favourable quantity variance shows that contribution was potentially $43,155 higher because more units were sold in total than budgeted. But these units were in a less profitable mix, so the $2,535 adverse mix variance offset this gain slightly.
Note that it is possible for an adverse mix variance to outweigh a favourable quantity variance. This would signal to the management that, even though the number of units sold was higher than budgeted, proportionately more of the less-profitable products were sold, resulting in a lower potential contribution. So selling more units does not always result in a higher profit than budgeted.
One last point is worth mentioning about this question and indeed all numerical exam questions: the P2 examiner reported that some students didn’t show a dollar sign before their calculated variances. This is such an easy way to ensure that you earn all of the marks available, so always remember to include currency signs for all monetary figures.
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