Sales variance scenario: multiple products

Scenario 2: multiple products

The following information is provided for products X and Y for the month of June:

	Product X, budgeted	Product Y, budgeted	Product X, actual	Product Y, actual
Sales volume (in units)	2,500	3,500	3,000	4,000
Selling price (in USD)	15	20	17	18

Calculate the following variances:

1. Total sales variance
2. Sales price variance
3. Sales volume variance
4. Sales mix variance
5. Sales quantity variance

Exam tip: When faced with a CMA exam problem with multiple products, the best way to calculate the variances is to do them separately for each product and then add them together for the total variance. This example illustrates how to use the different shorthand formulas in computing the variances.

2.1. Total sales variance

The general formula is:

$$\text{Total sales variance}=\text{Actual sales}-\text{Budgeted sales}$$

We need to calculate the summation of total sales variance for each product:

$$\begin{array}{rl}\text{Total sales variance product X}& =\text{Actual sales product X}-\text{Budgeted sales product X}\\ & =(3,000\times 17)-(2,500\times 15)\\ & =51,000-37,500\\ & =13,500(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Total sales variance product Y}& =\text{Actual sales product Y}-\text{Budgeted sales product Y}\\ & =(4,000\times 18)-(3,500\times 20)\\ & =72,000-70,000\\ & =2,000(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Total sales variance}& =\text{Total sales variance product X}+\text{Total sales variance product Y}\\ & =13,500(\text{F})+2,000(\text{F})\\ & =15,500(\text{F})\end{array}$$

The total sales variance is favorable because the total actual sales are greater than the budget.

Sign rule: Every formula in this chapter is written as actual − budget. For revenue, a positive result is favorable because it raises operating income, and a negative result is unfavorable because it lowers it. A variance is always reported as its absolute value followed by (F) or (U) - that’s why a result of −8,000 is written as 8,000 (U) rather than as a negative number. Also watch the inputs a problem gives you: some CMA questions replace the budgeted selling price (BSP) used below with budgeted contribution margin per unit instead.

2.2. Sales price variance

The general formula is:

$$\begin{array}{rl}\text{Sales price variance}& =(\text{Actual selling price}-\text{Budgeted selling price})\times \text{Actual sales quantity}\\ & =(\text{ASP}-\text{BSP})\times \text{ASQ}\end{array}$$

We need to calculate the summation of the sales price variances for each product:

$$\begin{array}{rl}\text{Sales price variance product X}& =(ASP-BSP)\times ASQ\\ & =(17-15)\times 3,000\\ & =2\times 3,000\\ & =6,000(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Sales price variance product Y}& =(ASP-BSP)\times ASQ\\ & =(18-20)\times 4,000\\ & =-2\times 4,000\\ & =8,000(\text{U})\end{array}$$

$$\begin{array}{rl}\text{Sales price variance}& =\text{Sales price variance product X}+\text{Sales price variance product Y}\\ & =6,000(\text{F})+8,000(\text{U})\\ & =2,000(\text{U})\end{array}$$

The sales price variance for Product X is favorable because the actual selling price is higher than budgeted, while it is unfavorable for Product Y because the actual selling price is lower than budgeted. Since the unfavorable variance of Product Y is higher than that of Product X, it results in a net unfavorable variance.

2.3. Sales volume variance

The general formula is:

$$\begin{array}{rl}\text{Sales volume variance}& =\text{(Actual sales quantity}-\text{Budgeted sales quantity})\times \text{Budgeted selling price}\\ & =(\text{ASQ}-\text{BSQ})\times \text{BSP}\end{array}$$

We need to calculate the summation of the sales volume variances for each product:

$$\begin{array}{rl}\text{Sales volume variance product X}& =(\text{ASQ}-\text{BSQ})\times \text{BSP}\\ & =(3,000-2,500)\times 15\\ & =500\times 15\\ & =7,500(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Sales volume variance product Y}& =(\text{ASQ}-\text{BSQ})\times \text{BSP}\\ & =(4,000-3,500)\times 20\\ & =500\times 20\\ & =10,000(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Sales volume variance}& =\text{Sales volume variance product X}+\text{Sales volume variance product Y}\\ & =7,500(\text{F})+10,000(\text{F})\\ & =17,500(\text{F})\end{array}$$

The sales volume variances for both Product X and Product Y are favorable because the actual units sold are higher than budgeted. This resulted in a total favorable variance.

You can see that the total of the sales price and sales volume variances adds up to the same $\text{total sales variance}$ we computed before: $2,000(\text{U})+17,500(\text{F})=15,500(\text{F})$.

In flexible-budget terms, the total sales variance is the static-budget variance; the sales price variance is the flexible-budget revenue variance, comparing actual revenue to revenue at budgeted prices for the units actually sold; and the sales volume variance captures the effect of selling a different number of units than planned.

Lastly, the $\text{Sales volume variance}$ can be split into the mix and quantity variances, the total of which should agree with the $17,500 favorable variance computed in this section.

Preparing the mix percentages

Before computing the mix and quantity variances, you need the actual mix percentage (AM) and the standard, or budgeted, mix percentage (SM) for each product. The sales mix variance isolates the effect of selling products in different proportions than planned, while the sales quantity variance isolates the effect of selling a different total number of units than planned - both measured at budgeted prices.

$$\begin{array}{rl}\text{AM \% product X}& =\frac{3,000}{3,000+4,000}=42.8571\%\\ \text{AM \% product Y}& =\frac{4,000}{3,000+4,000}=57.1429\%\\ \text{SM \% product X}& =\frac{2,500}{2,500+3,500}=41.6667\%\\ \text{SM \% product Y}& =\frac{3,500}{2,500+3,500}=58.3333\%\end{array}$$

2.4. Sales mix variance

The general formula is:

$$\text{Sales mix variance}=((\text{Total ASQ}\times \text{AM})-(\text{Total ASQ}\times \text{SM}))\times \text{BSP}$$

We need to calculate the summation of the sales mix variances for each product. Note that the actual sales quantity used here (Total ASQ) is the combined actual sales quantity of 7,000 units (Product X + Product Y) - not the per-product ASQ used in the sales price and sales volume variances above.

$$\begin{array}{rl}\text{Sales mix variance product X}& =((\text{Total ASQ}\times \text{AM})-(\text{Total ASQ}\times \text{SM}))\times \text{BSP}\\ & =((7,000\times 42.8571\%)-(7,000\times 41.6667\%))\times 15\\ & =(3,000-2,916.67)\times 15\\ & =83.33\times 15\\ & =1,250(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Sales mix variance product Y}& =((\text{Total ASQ}\times \text{AM})-(\text{Total ASQ}\times \text{SM}))\times \text{BSP}\\ & =((7,000\times 57.1429\%)-(7,000\times 58.3333\%))\times 20\\ & =(4,000-4,083.33)\times 20\\ & =-83.33\times 20\\ & =1,666.67(\text{U})\end{array}$$

$$\begin{array}{rl}\text{Sales mix variance}& =\text{Sales mix variance product X}+\text{Sales mix variance product Y}\\ & =1,250(\text{F})+1,666.67(\text{U})\\ & =416.67(\text{U})\end{array}$$

2.5. Sales quantity variance

The general formula is:

$$\text{Sales quantity variance}=((\text{Total ASQ}\times \text{SM})-(\text{Total BSQ}\times \text{SM}))\times \text{BSP}$$

We need to calculate the summation of the sales quantity variances for each product. Note that the budgeted sales quantity used here (Total BSQ) is the combined budgeted sales quantity of 6,000 units (Product X + Product Y) - not the per-product BSQ used in the sales volume variance above.

$$\begin{array}{rl}\text{Sales quantity variance product X}& =((\text{Total ASQ}\times \text{SM})-(\text{Total BSQ}\times \text{SM}))\times \text{BSP}\\ & =((7,000\times 41.6667\%)-(6,000\times 41.6667\%))\times 15\\ & =(2,916.67-2,500)\times 15\\ & =416.67\times 15\\ & =6,250(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Sales quantity variance product Y}& =((\text{Total ASQ}\times \text{SM})-(\text{Total BSQ}\times \text{SM}))\times \text{BSP}\\ & =((7,000\times 58.3333\%)-(6,000\times 58.3333\%))\times 20\\ & =(4,083.33-3,500)\times 20\\ & =583.33\times 20\\ & =11,666.67(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Sales quantity variance}& =\text{Sales quantity variance product X}+\text{Sales quantity variance product Y}\\ & =6,250(\text{F})+11,666.67(\text{F})\\ & =17,916.67(\text{F})\end{array}$$

From here, we can check that the sales volume variance we previously computed with a different approach is equal when we add up the sales mix and quantity variances:

$$\begin{array}{rl}\text{Sales volume variance}& =\text{Sales mix variance}+\text{Sales quantity variance}\\ & =416.67(\text{U})+17,916.67(\text{F})\\ & =17,500(\text{F})\end{array}$$

The 416.67 (U) mix variance reflects a shift in sales mix toward Product X, the lower-priced item at a budgeted $15 - Product X made up 42.86% of actual units sold versus a budgeted 41.67%. The 17,916.67 (F) quantity variance confirms that total units sold beat budget by 1,000 units (7,000 actual vs. 6,000 budgeted), a genuine volume win. Keep in mind, though, that Product Y’s 500-unit volume gain followed a $2 price cut (part of its 8,000 (U) price variance) - a favorable volume variance doesn’t always mean good news on its own; it’s worth checking whether it came at the cost of price.

2.6. Summary

We can summarize all the variance computed from 2.1 to 2.5 into the following illustration: