Labor efficiency variances

Formulas and variable definitions for labor cost, rate, efficiency, mix, and yield variances. — Labor Variances Overview

The labor efficiency variance arises from the difference between the actual working hours and the standard working hours applied to the actual production. This variance is typically the responsibility of operations or production managers, as it reflects how efficiently labor hours are utilized during production. This variance is influenced by internal factors such as workflow processes, workforce productivity, employee training, and equipment availability. Unfavorable variances may result from inefficiencies like idle time, untrained staff, or machine downtime, while favorable variances indicate effective resource utilization. Since the variance is driven by operational efficiencies and processes, it is within the control of production teams to address and improve performance.

In terms of formula:

$Labor efficiency variance = Standard cost of standard hours for actual production - Standard cost of actual hours$

It can also be expressed in terms of the formulas:

$Labor efficiency variance = (SR \times SH) - (SR \times AH) = (SH - AH) \times SR$

Where:

$SR$ is the standard labor rate
$AH$ is the actual labor hours incurred in production
$SH$ is the standard labor hours that would have been incurred at the level of actual production achieved

Each formula here is standard minus actual, so a positive result is favorable (fewer cost dollars, which raises operating income) and a negative result is unfavorable; the same orientation applies to the mix and yield variances below.

Sidenote

Standard hours reflect actual output

This is where the approach differs from the master budget. In variance analysis, the term $Standard hours allowed for actual production (SH)$ means that the actual production level must be used, not the budgeted production level. The $SH$ represents the number of labor hours that should have been used for the actual output, based on the standard allowed per unit.

For example, assume the master budget planned for 100 units, with each unit requiring 3 standard labor hours (300 hours total). If actual production was 150 units and the company used only 400 actual labor hours, the correct $SH$ for variance purposes is 450 hours (150 units × 3 hours). Using the budgeted 300 hours would be incorrect, since it would not reflect the higher level of output achieved. Since $450 > 400$ , the labor efficiency variance here is favorable.

Watch out: a favorable labor efficiency variance isn’t automatically good news. Substituting skilled workers for unskilled ones can cut hours worked (favorable efficiency) while raising the labor rate variance from the previous section, since skilled labor costs more per hour - read the rate and efficiency variances together.

The labor efficiency variance can be further analyzed through its two subcategories:

labor mix variance
labor yield variance

Together, these subcategories provide deeper insights into whether variances arise from changes in the composition of the workforce or inefficiencies in labor utilization. The same mix/yield logic applies to service firms too, such as partner vs. associate hours at a CPA firm.

How to compute standard mix (SM) and actual mix (AM) for the mix & yield variances

For any type of mix and yield variances (direct materials, direct labor, etc.), the mix percentages are computed the same way.

Standard mix (SM) %
The standard mix represents the expected proportion of each input (such as materials or labor) in the total input required, based on established production standards. It is calculated by dividing the standard quantity of a specific input by the total standard quantity of all inputs. The standard mix percentages across all inputs must add up to 100%, reflecting the planned input composition.

$Standard mix (SM) % = \frac{Standard quantity of input}{Total standard quantity}$

Actual mix (AM) %
The actual mix represents the proportion of each input that was actually used in the production process. It is calculated by dividing the actual quantity of a specific input by the total actual quantity of all inputs. The actual mix percentages across all inputs must add up to 100%, showing the composition of resources consumed in practice.

$Actual mix (AM) % = \frac{Actual quantity of input}{Total actual quantity}$

Labor mix variance

This variance evaluates the cost impact of deviations in the proportions of different labor types (e.g., skilled vs. unskilled) used in production compared to the standard mix. This variance occurs when the actual labor mix differs from the planned mix, potentially leading to higher costs or productivity issues.

Expressed in formula:

$Labor mix variance = Standard cost of total actual hours used in standard proportion - Standard cost of total actual hours used in actual proportion$

It can also be expressed in terms of other formulas:

$Labor mix variance = ((Total actual hours used \times Standard mix) - (Total actual hours used \times Actual mix)) \times Standard rate = ((AHU \times SM) - (AHU \times AM)) \times SR = ((AHU \times SM) - AH_{i}) \times SR$

Where:

$SR$ is the standard labor rate per hour
$AHU$ is the total actual hours of direct labor used in production
$SM$ is the standard mix of direct labor expressed in %
$AM$ is the actual mix of direct labor expressed in %
$AH_{i}$ is the actual hours of labor used for that specific type of labor

It is good to note that $(AHU \times AM)$ is equal to $AH_{i}$ for that specific type of labor and there is no need to perform computations for this part of the formula. This is because when the $Actual mix (AM)$ is applied to total actual hours, it results in the actual hours ( $AH_{i}$ ) for that specific type of input.

The formulas above are computed for each type of labor used in production and added together to the total labor mix variance.

Labor yield variance

This variance measures the efficiency of overall labor usage by assessing whether the total labor hours worked resulted in the expected level of output. It reflects the effect of changes in labor yield on labor cost, indicating how effectively labor inputs are converted into finished products.

Expressed in formulas:

$Labor yield variance = Standard cost of total standard labor usage in standard proportion - Standard cost of total actual labor usage in standard proportion$

It can also be expressed in terms of other formulas:

$Labor yield variance = ((Total standard labor usage \times Standard mix) - (Total actual labor usage \times Standard mix)) \times Standard rate = ((SHU \times SM) - (AHU \times SM)) \times SR$

Where:

$SR$ is the standard rate of direct labor
$AHU$ is the total actual hours of direct labor used in production
$SHU$ is the total standard hours of direct labor expected to be worked in production based on actual units produced
$SM$ is the standard mix of direct labor expressed in %

The formulas above are computed for each type of direct labor used in production and added together to the total labor yield variance.

Sidenote

From efficiency to mix and yield variances

The mix and yield variances split the labor efficiency variance $(SH - AH) \times SR$ into two pieces, each still priced at $SR$ :

Mix: $SH$ becomes $AHU \times SM$ and $AH$ becomes $AHU \times AM$ (equal to $AH_{i}$ , the actual hours of that labor type) - holding total hours worked ( $AHU$ ) constant, this isolates the shift between the standard mix and the actual mix.
Yield: $SH$ becomes $SHU \times SM$ and $AH$ becomes $AHU \times SM$ - holding the mix ( $SM$ ) constant, this isolates the shift between standard hour usage and actual hour usage.

Mix and yield together add up to the efficiency variance

$Labor mix variance + Labor yield variance = Labor efficiency variance$

In each formula, $AHU \times SM$ , $AHU \times AM$ , and $SHU \times SM$ are total hours for the period allocated to one labor type, in standard or actual proportion - not hours “to produce one unit.”

Example: Mix and yield together equal the efficiency variance

A company uses skilled labor ( $$20$ /hour) and unskilled labor ( $$12$ /hour) in a 40%/60% standard mix. The standard hours allowed (SH) for actual production are 1,000 total: 400 skilled and 600 unskilled. The company actually worked 1,050 total hours (AHU), split 50/50: 525 skilled and 525 unskilled.

Skilled: mix variance $= (420 - 525) \times $20 = - $2, 100$ ; yield variance $= (400 - 420) \times $20 = - $400$ ; efficiency variance $= (400 - 525) \times $20 = - $2, 500$

Unskilled: mix variance $= (630 - 525) \times $12 = $1, 260$ ; yield variance $= (600 - 630) \times $12 = - $360$ ; efficiency variance $= (600 - 525) \times $12 = $900$

Answer: total mix variance $= - $840$ ; total yield variance $= - $760$ ; total efficiency variance $= - $1, 600$ . Since $- $840 + (- $760) = - $1, 600$ , the mix and yield variances sum to the efficiency variance. All three are unfavorable: the mix variance is unfavorable because the share of higher-cost skilled hours rose from 40% to 50%, calling for tighter crew scheduling, and the yield variance is unfavorable because 1,050 total hours were worked against 1,000 standard hours allowed, pointing to a need for additional training or process review.