Labor cost variance scenario: Multiple DLs

Scenario 2: Multiple types of direct labor

ChocoDelight Cookies continues its operations with a focus on producing gourmet chocolate chip cookies. To assess production efficiency and cost management, the company now wants to analyze its direct labor performance. The production process involves two types of labor: skilled bakers (Labor A) and assistant bakers (Labor B). Below are the standards and actual data for a recent production batch.

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

• Labor A: 6 hours per 1,000 cookies at $20 per hour
• Labor B: 4 hours per 1,000 cookies at $10 per hour

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

• Labor A: 8 hours at $22 per hour
• Labor B: 8 hours at $12 per hour

Calculate the direct labor variances:

1. Labor rate variance
2. Labor efficiency variance
3. Labor mix variance
4. Labor yield variance
5. Labor 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 cookies is only the base the standards are expressed per. Variances are measured against the standard hours allowed for the actual output of 1,500 cookies.

All formulas on this page are written as standard minus actual. A positive result is favorable (it raises operating income), and a negative result is unfavorable; we show the dollar amount with an F or U label.

Scenario 2.1. Labor rate variance

We need to get the total of the rate variances of each type of direct labor.

$$\begin{array}{rl}\text{Labor rate variance labor A}& =(\text{SR}\times \text{AH})-(\text{AR}\times \text{AH})\\ & =(20\times 8)-(22\times 8)\\ & =160-176\\ & =16(\text{U})\end{array}$$

The unfavorable variance of $16 indicates that skilled bakers were paid $2 more per hour than the standard rate, increasing labor costs. Actual Hours (AH) of Labor A is already available at 8 hours and does not need further computations.

$$\begin{array}{rl}\text{Labor rate variance labor B}& =(SR\times AH)-(AR\times AH)\\ & =(10\times 8)-(12\times 8)\\ & =80-96\\ & =16(U)\end{array}$$

The unfavorable variance of $16 indicates that assistant bakers were also paid $2 more per hour than the standard rate.

$$\begin{array}{rl}\text{Labor rate variance}& =\text{Labor rate variance labor A}+\text{Labor rate variance labor B}\\ & =16(U)+16(U)\\ & =32(U)\end{array}$$

The total unfavorable variance of $32 reflects higher-than-expected hourly wages for both skilled and assistant bakers, leading to increased overall labor costs.

Scenario 2.2. Labor efficiency variance

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

$$\text{SH labor A}=6\text{ hours}\times (1,500\text{ cookies}÷1,000\text{ cookies})=9\text{ hours}$$

$$\text{SH labor B}=4\text{ hours}\times (1,500\text{ cookies}÷1,000\text{ cookies})=6\text{ hours}$$

We then need to get the total of the efficiency variances of each type of direct labor.

$$\begin{array}{rl}\text{Labor efficiency variance labor A}& =(\text{SR}\times \text{SH})-(\text{SR}\times \text{AH})\\ & =(20\times 9)-(20\times 8)\\ & =180-160\\ & =20(\text{F})\end{array}$$

The favorable variance of $20 shows that skilled bakers worked fewer hours than expected, saving costs.

$$\begin{array}{rl}\text{Labor efficiency variance labor B}& =(\text{SR}\times \text{SH})-(\text{SR}\times \text{AH})\\ & =(10\times 6)-(10\times 8)\\ & =60-80\\ & =20(\text{U})\end{array}$$

The unfavorable variance of $20 indicates that assistant bakers worked more hours than expected, increasing costs.

$$\begin{array}{rl}\text{Labor efficiency variance}& =\text{Labor efficiency variance labor A}+\text{Labor efficiency variance labor B}\\ & =20(\text{F})+20(\text{U})\\ & =0\end{array}$$

A $0 total efficiency variance does not mean hours were on target. Total actual hours (16) exceeded standard hours (15), but shifting toward cheaper assistant bakers saved exactly as much as the extra hour cost. The mix and yield variances below separate these two effects.

This total efficiency variance can be verified by the computation of the labor mix and labor yield variances which will be shown below.

Scenario 2.3. Labor mix variance

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 labor used in production:

• Standard mix (SM)
• Actual mix (AM)
• Actual hours used (AHU)

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

$$\text{SM labor A}=9\text{ hours}/(9\text{ hours}+6\text{ hours})=60\%$$

$$\text{SM labor B}=6\text{ hours}/(9\text{ hours}+6\text{ hours})=40\%$$

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

$$\text{AM labor A}=8\text{ hours}/(8\text{ hours}+8\text{ hours})=50\%$$

$$\text{AM labor B}=8\text{ hours}/(8\text{ hours}+8\text{ hours})=50\%$$

$\text{Actual hours used (AHU)}$ will be total of the actual hours of Labor A (8 hours) and Labor B (8 hours), or $16\text{ hours}$, used in producing the 1,500 cookies.

Once all the above are determined, we can continue calculating the variances for each type of direct labor.

$$\begin{array}{rl}\text{Labor mix variance labor A}& =((\text{AHU}\times \text{SM})-(\text{AHU}\times \text{AM}))\times \text{SR}\\ & =((16\times 60\%)-(16\times 50\%))\times 20\\ & =(9.6-8)\times 20\\ & =1.6\times 20\\ & =32(\text{F})\end{array}$$

The favorable variance of $32 indicates that fewer skilled baker hours were used compared to the standard mix, reducing labor costs for this category.

$$\begin{array}{rl}\text{Labor mix variance labor B}& =((\text{AHU}\times \text{SM})-(\text{AHU}\times \text{AM}))\times \text{SR}\\ & =((16\times 40\%)-(16\times 50\%))\times 10\\ & =(6.4-8)\times 10\\ & =-1.6\times 10\\ & =16(\text{U})\end{array}$$

The unfavorable variance of $16 reflects that more assistant baker hours were used than expected in the standard mix, increasing overall costs.

$$\begin{array}{rl}\text{Labor mix variance}& =\text{Labor mix variance labor A}+\text{Labor mix variance labor B}\\ & =32(\text{F})+16(\text{U})\\ & =16(\text{F})\end{array}$$

Scenario 2.4. Labor yield variance

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

The $\text{Standard hours used (SHU)}$ is the total $\text{Standard hours (SH)}$ for both labor types: Labor A (9 hours) + Labor B (6 hours) = $15\text{ hours}$. Please refer to the labor efficiency variance for explanation of how this was determined.

$$\begin{array}{rl}\text{Labor yield variance labor A}& =((\text{SHU}\times \text{SM})-(\text{AHU}\times \text{SM}))\times \text{SR}\\ & =((15\times 60\%)-(16\times 60\%))\times 20\\ & =(9-9.6)\times 20\\ & =-0.60\times 20\\ & =12(\text{U})\end{array}$$

The unfavorable variance of $12 indicates that the overall labor process required more hours than expected, increasing costs for skilled bakers.

$$\begin{array}{rl}\text{Labor yield variance labor B}& =((\text{SHU}\times \text{SM})-(\text{AHU}\times \text{SM}))\times \text{SR}\\ & =((15\times 40\%)-(16\times 40\%))\times 10\\ & =(6-6.4)\times 10\\ & =-0.40\times 10\\ & =4(\text{U})\end{array}$$

The unfavorable variance of $4 reflects that excess total hours also raised costs for assistant bakers.

$$\begin{array}{rl}\text{Labor yield variance}& =\text{Labor yield variance labor A}+\text{Labor yield variance labor B}\\ & =12(\text{U})+4(\text{U})\\ & =16(\text{U})\end{array}$$

The $16 unfavorable variance highlights inefficiencies in labor utilization, leading to higher-than-expected costs.

We can verify the labor efficiency variance below by adding the mix and yield variances:

$$\begin{array}{rl}\text{Labor efficiency variance}& =\text{Labor mix variance}+\text{Labor yield variance}\\ & =16(\text{F})+16(\text{U})\\ & =0\end{array}$$

Scenario 2.5. Direct labor cost variance

The labor cost variance can be computed by adding up the rate and the efficiency variances:

$$\begin{array}{rl}\text{Labor cost variance}& =\text{Labor rate variance}+\text{Labor efficiency variance}\\ & =32(\text{U})+0\\ & =32(\text{U})\end{array}$$

Alternatively:

$$\begin{array}{rl}\text{Labor cost variance labor A}& =(\text{SH}\times \text{SR})-(\text{AH}\times \text{AR})\\ & =(9\times 20)-(8\times 22)\\ & =180-176\\ & =4(\text{F})\end{array}$$

$$\begin{array}{rl}\text{Labor cost variance labor B}& =(\text{SH}\times \text{SR})-(\text{AH}\times \text{AR})\\ & =(6\times 10)-(8\times 12)\\ & =60-96\\ & =36(\text{U})\end{array}$$

$$\begin{array}{rl}\text{Labor cost variance}& =\text{Labor cost variance labor A}+\text{Labor cost variance labor B}\\ & =4(\text{F})+36(\text{U})\\ & =32(\text{U})\end{array}$$

Together, these variances point to two separate causes. The $16 F mix variance came from substituting assistant-baker hours for skilled-baker hours, and that same substitution is the likely cause of the extra hour behind the $16 U yield variance - the cheaper labor mix took longer to finish the batch. The $32 U rate variance is a separate issue: both labor types were paid above their standard rates, which calls for a review of wage rates or overtime pay rather than labor mix. Management should judge the staffing decision by its net effect on total cost, not by the favorable mix variance alone.

Scenario summary

The following table shows the summary of the labor variances for Scenario 2:

The illustration below is carried over from the materials-variance scenario and does not depict this labor scenario; use the table above for the labor figures.