Materials cost variance scenario: Multiple DMs

Scenario 2: Multiple DMs

ChocoDelight Cookies produces gourmet chocolate chip cookies. The production process uses two types of direct materials: premium chocolate chips (Material A) and organic flour (Material B). The company’s production standards and actual results for a recent batch are outlined below.

To produce 1,000 cookies, the following usage and cost standards apply:

• Material A: 5 kilograms per 1,000 cookies at $10 per kilogram
• Material B: 8 kilograms per 1,000 cookies at $5 per kilogram

Actual results for the recent batch were 1,500 cookies were produced:

• Material A: 6 kilograms at $12 per kilogram
• Material B: 15 kilograms at $6 per kilogram

Calculate the direct materials variances:

1. Materials price variance
2. Materials usage variance
3. Materials mix variance
4. Materials yield variance
5. Materials cost variance

If you would like to check the over-all solution, you can skip to the Scenario summary section at the end of this page.

The 1,000-cookie figure is just the basis for the standard rates; all quantity variances use the standard quantity allowed for actual output of 1,500 cookies.

Sign convention: every variance below is computed as standard − actual. For a cost, a positive result is favorable (the actual cost came in lower, which raises operating income), and a negative result is unfavorable. We still label each answer (F) or (U), but the sign itself already tells you which one it is.

Scenario 2.1. Materials price variance

We need to get the total of the price variances of each direct material, using the factored form $(\text{SP}-\text{AP})\times \text{AQ}$.

$$\begin{array}{rl}\text{Materials price variance material A}& =(\text{SP}-\text{AP})\times \text{AQ}\\ & =(10-12)\times 6\\ & =-2\times 6\\ & =-12\text{, i.e., }12(\text{U})\end{array}$$

The variance is unfavorable because the actual price per unit of Material A ($12) is higher than standard price ($10). $\text{Actual quantity (AQ)}$ of Material A is already available at 6 kilograms and does not need further computations.

$$\begin{array}{rl}\text{Materials price variance material B}& =(\text{SP}-\text{AP})\times \text{AQ}\\ & =(5-6)\times 15\\ & =-1\times 15\\ & =-15\text{, i.e., }15(\text{U})\end{array}$$

The variance is unfavorable because the actual price per unit of Material B ($6) is higher than standard price ($5). $\text{Actual quantity (AQ)}$ of Material B is already available at 15 kilograms and does not need further computations.

$$\begin{array}{rl}\text{Materials price variance}& =\text{Materials price variance material A}+\text{Materials price variance material B}\\ & =12(\text{U})+15(\text{U})\\ & =27(\text{U})\end{array}$$

Scenario 2.2. Materials usage variance

The $\text{Standard quantity (SQ)}$ to be used here is not the one in the master budget but the standard quantity that would have been used by the actual production of 1,500 cookies. The following are the $\text{SQ}$ for both Material A and B:

$$\text{SQ material A}=5\text{ kg}\times (1,500\text{ cookies}/1,000\text{ cookies})=7.5\text{ kg}$$

$$\text{SQ material B}=8\text{ kg}\times (1,500\text{ cookies}/1,000\text{ cookies})=12\text{ kg}$$

$$\text{SQ}=\text{SQ material A}+\text{SQ material B}=19.5\text{ kg}$$

After the $\text{Standard quantity (SQ)}$ is determined, we need to get the total of the usage variances of each direct material, using the factored form $(\text{SQ}-\text{AQ})\times \text{SP}$.

$$\begin{array}{rl}\text{Materials usage variance material A}& =(\text{SQ}-\text{AQ})\times \text{SP}\\ & =(7.5-6)\times 10\\ & =1.5\times 10\\ & =15(\text{F})\end{array}$$

The variance is favorable because the actual Material A used by production (6 kg) is lower than standard (7.5 kg).

$$\begin{array}{rl}\text{Materials usage variance material B}& =(\text{SQ}-\text{AQ})\times \text{SP}\\ & =(12-15)\times 5\\ & =-3\times 5\\ & =-15\text{, i.e., }15(\text{U})\end{array}$$

The variance is unfavorable because the actual Material B used by production (15 kg) is higher than standard (12 kg).

$$\begin{array}{rl}\text{Materials usage variance}& =\text{Materials usage variance material A}+\text{Materials usage variance material B}\\ & =15(\text{F})+15(\text{U})\\ & =0\end{array}$$

The favorable usage variance of Material A was offset by the unfavorable variance of Material B. This total usage variance can be verified by the computation of the materials mix and materials yield variances, shown next.

Scenario 2.3. Materials mix variance

The materials mix variance measures the cost effect of blending the materials in different proportions than the standard mix, holding the actual total quantity of materials used constant.

When faced with such problems, candidates need to determine the inputs that will be needed in the computations of the variances. Most notably for mix variances, we need to determine the following for each material used in production:

• Standard mix (SM)
• Actual mix (AM)
• Actual materials used (AMU)

$\text{Standard mixes (SM)}$, the total of which should be 100%:

$$\text{SM material A}=5\text{ kg}/(5\text{ kg}+8\text{ kg})=38.46\%$$

$$\text{SM material B}=8\text{ kg}/(5\text{ kg}+8\text{ kg})=61.54\%$$

$\text{Actual mixes (AM)}$, the total of which should be 100%:

$$\text{AM material A}=6\text{ kg}/(6\text{ kg}+15\text{ kg})=28.57\%$$

$$\text{AM material B}=15\text{ kg}/(6\text{ kg}+15\text{ kg})=71.43\%$$

$\text{Actual materials used (AMU)}$ will be total of the actual of Material A (6 kg) and Material B (15 kg), or $21\text{ kg}$, used in producing the 1,500 cookies.

Once all the above are determined, we can calculate the variances separately for each direct material.

$$\begin{array}{rl}\text{Materials mix variance material A}& =((\text{AMU}\times \text{SM})-(\text{AMU}\times \text{AM}))\times \text{SP}\\ & =((21\times 38.46\%)-(21\times 28.57\%))\times 10\\ & =(8.08-6)\times 10\\ & =2.08\times 10\\ & =20.8(\text{F})\end{array}$$

The favorable variance of $20.8 indicates that less Material A was used than expected in the standard mix, resulting in cost savings.

$$\begin{array}{rl}\text{Materials mix variance material B}& =((\text{AMU}\times \text{SM})-(\text{AMU}\times \text{AM}))\times \text{SP}\\ & =((21\times 61.54\%)-(21\times 71.43\%))\times 5\\ & =(12.92-15)\times 5\\ & =-2.08\times 5\\ & =-10.4\text{, i.e., }10.4(\text{U})\end{array}$$

The unfavorable variance of $10.4 shows that more Material B was used than expected in the standard mix, leading to higher costs.

$$\begin{array}{rl}\text{Materials mix variance}& =\text{Materials mix variance material A}+\text{Materials mix variance material B}\\ & =20.8(\text{F})+10.4(\text{U})\\ & =10.4(\text{F})\end{array}$$

Scenario 2.4. Materials yield variance

The materials yield variance measures the cost effect of using a different total quantity of materials than the standard allows for actual output, holding the mix at the standard proportions.

We will use the same mixes ($\text{SM}$ and $\text{AM}$) computed before.

The $\text{Standard material used (SMU)}$ is the total $\text{Standard quantities (SQ)}$ for both materials: Material A (7.5 kg) + Material B (12 kg) = $19.5\text{ kg}$. Please refer to the materials usage variance for explanation of how this was determined.

$$\begin{array}{rl}\text{Materials yield variance material A}& =((\text{SMU}\times \text{SM})-(\text{AMU}\times \text{SM}))\times \text{SP}\\ & =((19.5\times 38.46\%)-(21\times 38.46\%))\times 10\\ & =(7.5-8.08)\times 10\\ & =-0.58\times 10\\ & =-5.8\text{, i.e., }5.8(\text{U})\end{array}$$

The unfavorable variance of $5.8 indicates that the overall production process required more input than expected, and Material A’s portion of the excess input increased costs.

$$\begin{array}{rl}\text{Materials yield variance material B}& =((\text{SMU}\times \text{SM})-(\text{AMU}\times \text{SM}))\times \text{SP}\\ & =((19.5\times 61.54\%)-(21\times 61.54\%))\times 5\\ & =(12-12.92)\times 5\\ & =-0.92\times 5\\ & =-4.6\text{, i.e., }4.6(\text{U})\end{array}$$

The unfavorable variance of $4.6 reflects that additional input was used in production, with Material B’s share contributing to higher costs.

$$\begin{array}{rl}\text{Materials yield variance}& =\text{Materials yield variance material A}+\text{Materials yield variance material B}\\ & =5.8(\text{U})+4.6(\text{U})\\ & =10.4(\text{U})\end{array}$$

We can also verify the Materials Usage Variance computed in 2.2:

$$\begin{array}{rl}\text{Materials usage variance}& =\text{Material mix variance}+\text{Material yield variance}\\ & =10.4(\text{F})+10.4(\text{U})\\ & =0\end{array}$$

Here’s what these totals mean: the mix shifted toward the cheaper flour (Material B, standard $5 per kilogram) and away from the pricier chocolate chips (Material A, standard $10 per kilogram), producing the $10.4 favorable mix variance. At the same time, total materials input (21 kg) came in above the 19.5 kg standard allowed for 1,500 cookies, producing the $10.4 unfavorable yield variance - the two exactly offset, which is why the usage variance nets to zero. That offset is worth noticing: it means the $27 unfavorable materials cost variance is driven entirely by price, not quantity. A likely explanation is a recipe or process deviation (using relatively more flour and less chocolate than the standard formula calls for) combined with higher purchase prices for both materials. Corrective actions worth investigating include renegotiating supplier prices and reinforcing adherence to the standard recipe on the production line. (These totals are rounded from unrounded mix percentages; the exact mix and yield variances are each about $10.38.)

Scenario 2.5. Direct material cost variance

The material cost variance can be computed by adding up the price and the usage variances:

$$\begin{array}{rl}\text{Material cost variance}& =\text{Material price variance}+\text{Material usage variance}\\ & =27(\text{U})+0\\ & =27(\text{U})\end{array}$$

Alternatively, we can also use the cost variances per type of DM and we should get the same answer:

$$\begin{array}{rl}\text{Material cost variance material A}& =(\text{SQ}\times \text{SP})-(\text{AQ}\times \text{AP})\\ & =(7.5\times 10)-(6\times 12)\\ & =75-72\\ & =3(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Material cost variance material B}& =(\text{SQ}\times \text{SP})-(\text{AQ}\times \text{AP})\\ & =(12\times 5)-(15\times 6)\\ & =60-90\\ & =-30\text{, i.e., }30(\text{U})\end{array}$$

$$\begin{array}{rl}\text{Material cost variance}& =\text{Material cost variance material A}+\text{Material cost variance material B}\\ & =3(\text{F})+30(\text{U})\\ & =27(\text{U})\end{array}$$

Scenario summary

The following illustration shows the summary of the variances for Scenario 2: