Appendix Mix and Yield Variances for Substitutable Inputs

The Webb Company example illustrates how to calculate price and efficiency variances when there is a single form of each input: one direct material (cloth) and one type of direct labor. But what if managers have leeway in combining and substituting inputs? For example, Del Monte Foods can combine material inputs (such as pineapples, cherries, and grapes) in varying proportions for its cans of fruit cocktail. Within limits, these individual fruits are substitutable inputs in making the fruit cocktail.

We illustrate how the efficiency variance (see section Efficiency Variance) can be subdivided into variances that highlight the financial impact of input mix and input yield when inputs are substitutable. We focus on multiple direct manufacturing labor inputs and substitution among these inputs. The same approach can be used for substitutable direct materials inputs.

Mode Company also manufactures jackets but, unlike Webb, employs workers of different skill (or experience) levels. Workers are of Low, Medium, or High skill. Higher-skill workers focus on more complicated aspects of the jacket, such as adding darts and fancy seam lines. They are compensated accordingly. Mode’s production standards require 0.80 labor-hours to produce 1 jacket; 50% of the hours are budgeted to be Low skill, 30% Medium, and 20% High. The direct manufacturing labor inputs budgeted to produce 1 jacket are:

<p>A table shows direct manufacturing labor inputs budgeted to produce 1 jacket for Mode Company</p>

The table depicts direct manufacturing labor inputs budgeted to produce 1 jacket. The details of the table are as follows:

1. 0.40 (50 percent of 0.80) hours of low-skill workers at 12 dollars per hour: 4.80 dollars

2. 0.24 (30 percent of 0.80) hours of medium-skill workers at 20 dollars per hour: 4.80 dollars

3. 0.16 (20 percent of 0.80) hours of high-skill workers at 40 dollars per hour: 6.40 dollars

4. Total budgeted direct manufacturing labor cost of 1 jacket: 16.00 dollars

The budgeted $16 labor cost for a jacket that requires 0.80 labor hours, implies a weighted average labor rate of $20 per hour $($16 \div 0.80 hours) .$

In April 2020, Mode produced 10,000 jackets using 9,000 labor-hours as follows:

<p>A table shows April 2020 production for Mode Company</p>

The table depicts how Mode produced 10,000 jackets using 9,000 labor-hours. The details of the table are as follows:

1. 4,500 hours of low-skill workers at actual cost of 12 dollars per hour: 54,000 dollars

2. 3,150 hours of medium-skill workers at actual cost of 26 dollars per hour: 81,900 dollars

3. 1,350 hours of high-skill workers at actual cost of 46 dollars per hour: 62,100 dollars

4. 9,000 hours of direct manufacturing labor: 198,000 dollars

5. Budgeted cost of 8,000 direct manufacturing labor-hours at 20 dollars per hour: 160,000 dollars

6. Flexible-budget variance for direct manufacturing labor: 38,000 dollars U

The actual labor mix percentage is Low skill, $inline style 50 percent sign ? left parenthesis text 4,500 end text divided by text 9,000 end text right parenthesis$ ; Medium skill, $35 percent sign ? left parenthesis text 3,150 end text space divided by space text 9,000 end text right parenthesis$ ; and High skill, $1 5 percent sign space ? left parenthesis text 1,350 end text space space divided by space text 9,000 end text right parenthesis$ .

Direct Manufacturing Labor Price and Efficiency Variances

Exhibit 7-7 presents in columnar format the analysis of Mode’s flexible-budget variance for direct manufacturing labor. The labor price and efficiency variances are calculated separately for each category of direct manufacturing labor and then added together. The variance analysis prompts Webb to investigate the unfavorable price and efficiency variances in each category. Why did it pay more for certain types of labor and use more hours than it had budgeted? Were actual wage rates higher, in general, or could the personnel department have negotiated lower rates? Did the additional labor costs result from inefficiencies in processing?

The details of the variances are as follows:

1. Actual costs incurred: Actual input quantity times actual price
- Low: 4,500 times dollar 12 equals dollar 54,000
- Medium: 3,150 times dollar 26 equals dollar 81,900
- High: 1,350 times dollar 46 equals dollar 62,100
- Total: dollar 198,000
2. Actual input quantity times budgeted price
- Low: 4,500 times dollar 12 equals dollar 54,000
- Medium: 3,150 times dollar 20 equals dollar 63,000
- High: 1,350 times dollar 40 equals dollar 54,000
- Total: dollar 171,000
3. Flexible budget: Budgeted input quantity allowed for actual output times budgeted price
- Low: 4,000 times dollar 12 equals dollar 48,000
- Medium: 2,400 times dollar 20 equals dollar 48,000
- High: 1,600 times dollar 40 equals dollar 64,000
- Total: dollar 160,000
Level 3
- Price variance: dollar 27,000 that has unfavorable effect on operating income is the difference between above 1 and 2.
- Efficiency variance: dollar 11,000 that has unfavorable effect on operating income is the difference between above 2 and 3.
Level 2
- Flexible-budget variance: dollar 38,000 that has unfavorable effect on operating income is the difference between above 1 and 3.

Direct Manufacturing Labor Mix and Yield Variances

Managers sometimes have discretion to substitute one input for another. The manager of Mode’s operations has some leeway in combining Low-, Medium-, and High-skill workers without affecting the quality of the jackets. We assume that to maintain quality, mix percentages of each type of labor can only vary up to 5% from standard mix. For example, the percentage of Low-skill labor in the mix can vary between 45% and 55% $(50% \pm 5 %) .$ When inputs are substitutable, direct manufacturing labor efficiency improvement relative to budgeted costs can come from two sources: (1) using a cheaper mix to produce a given quantity of output, measured by the mix variance, and (2) using less input to achieve a given quantity of output, measured by the yield variance.

Holding actual total quantity of all direct manufacturing labor used constant, the total direct manufacturing labor mix variance is the difference between:

budgeted cost for actual mix of actual total quantity of direct manufacturing labor used and
budgeted cost of budgeted mix of actual total quantity of direct manufacturing labor used.

Holding budgeted input mix constant, the direct manufacturing labor yield variance is the difference between:

budgeted cost of direct manufacturing labor based on actual total quantity of direct manufacturing labor used and
flexible-budget cost of direct manufacturing labor based on budgeted total quantity of direct manufacturing labor allowed for actual output produced.

Exhibit 7-8 presents the direct manufacturing labor mix and yield variances for Mode Company. Note that column (1) in this exhibit is identical to column (2) in Exhibit 7-7, and column (3) is the same in both exhibits.

A table shows the direct manufacturing labor yield and mix variances for Mode Company for April 2020.

The details of the table are as follows:

1. Actual total quantity of all inputs used times Actual input mix times Budgeted price
- Low: 9,000 times 0.50 times dollar 12 equals dollar 54,000
- Medium: 9,000 times 0.35 times dollar 20 equals dollar 63,000
- High: 9,000 times 0.15 times dollar 40 equals dollar 54,000
- Total: dollar 171,000
2. Actual total quantity of all inputs used times Budgeted input mix times Budgeted price
- Low: 9,000 times 0.50 times dollar 12 equals dollar 54,000
- Medium: 9,000 times 0.30 times dollar 20 equals dollar 54,000
- High: 9,000 times 0.20 times dollar 40 equals dollar 72,000
- Total: dollar 180,000
3. Flexible Budget: Budgeted total quantity of all inputs allowed for actual output times Budgeted input mix times Budgeted price
- Low: 8,000 times 0.50 times dollar 12 equals dollar 48,000
- Medium: 8,000 times 0.30 times dollar 20 equals dollar 48,000
- High: 8,000 times 0.20 times dollar 40 equals dollar 64,000
- Total: dollar 160,000
Level 4
- Mix variance: dollar 9,000 that has favorable effect on operating income is the difference between above 1 and 2.
- Yield variance: dollar 20,000 that has unfavorable effect on operating income is the difference between above 2 and 3.
Level 3:
- Efficiency variance: dollar 11,000 that has unfavorable effect on operating income is the difference between above 1 and 3.

Direct Manufacturing Labor Mix Variance

The total direct manufacturing labor mix variance is the sum of the direct manufacturing labor mix variances for each input:

$\begin{array}{l} \begin{matrix} Direct \\ labor \\ mix variance \\ for each input \end{matrix} & = & \begin{matrix} Actual total \\ quantity of all \\ direct labor \\ inputs used \end{matrix} & \times & (\begin{matrix} \begin{matrix} Actual \\ direct labor \\ input mix \\ percentage \end{matrix} & - & \begin{matrix} Budgeted \\ direct labor \\ input mix \\ percentage \end{matrix} \end{matrix}) & \times & \begin{matrix} Budgeted \\ price of \\ direct labor \\ input \end{matrix} \end{array}$

The direct manufacturing labor mix variances are as follows:

<p>A table shows direct manufacturing labor mix variances</p>

The table depicts direct manufacturing labor mix variances. The details of the table are as follows:

1. Low

9,000 hours times the quantity 0.50 minus 0.50 times 12 dollars per hour

Equals

9,000 times 0.00 times 12 dollars per hour

Equals 0 dollars

2. Medium

9,000 hours times the quantity 0.35 minus 0.30 times 20 dollars per hour

Equals

9,000 times 0.05 times 20 dollars per hour

Equals 9,000 dollars U

3. High

9,000 hours times the quantity 0.15 minus 0.20 times 40 dollars per hour

Equals

9,000 times negative 0.05 times 40 dollars per hour

Equals 18,000 dollars F

4. Total direct manufacturing labor mix variance: 9,000 dollars F

The total direct manufacturing labor mix variance is favorable because, relative to the budgeted mix, Mode substitutes 5% of the cheaper Medium-skill labor for 5% of the more-expensive High-skill labor.

Direct Manufacturing Labor Yield Variance

The yield variance is the sum of the direct manufacturing labor yield variances for each input:

$\begin{matrix} Direct \\ labor \\ yield variance \\ for each input \end{matrix} = (\begin{matrix} Actual total \\ quantity of \\ all direct \\ labor \\ inputs used \end{matrix} - \begin{matrix} Budgeted total \\ quantity of all \\ direct labor \\ input allowed \\ for actual output \end{matrix}) \times \begin{matrix} Budgeted \\ direct labor \\ input mix \\ percentage \end{matrix} \times \begin{matrix} Budgeted \\ price of \\ direct labor \\ input \end{matrix}$

The direct manufacturing labor yield variances are as follows:

$\begin{array}{lcc} Low : (9,000 - 8,000) hours \times 0.50 \times $ 12 per hour = 1,000 \times 0.50 \times $ 12 & = & $ 6,000 U \\ Medium : (9,000 - 8,000) hours \times 0.30 \times $ 20 per hour = 1,000 \times 0.30 \times $ 20 & = & 6,000 U \\ High : (9,000 - 8,000) hours \times 0.20 \times $ 40 per hour = 1,000 \times 0.20 \times $ 40 & = & 8,000 U \end{array} \begin{array}{lcc} Total direct manufacturing labor mix variance & \underset{}{$ 20,000 U} \end{array}$

The total direct manufacturing labor yield variance is unfavorable because Mode used 9,000 hours of labor rather than the 8,000 hours that it should have used to produce 10,000 jackets. The budgeted cost per hour of labor in the budgeted mix is $20 per hour. The unfavorable yield variance represents the budgeted cost of using 1,000 more hours of direct manufacturing labor, $(9,000 - 8,000) hours \times $ 20 per hour = $ 20,000 U .$ Mode should investigate reasons for the unfavorable yield variance. For example, did substitution of cheaper Medium-skill for High-skill labor, which resulted in the favorable mix variance, also cause the unfavorable yield variance?

The direct manufacturing labor variances computed in Exhibits 7-7 and 7-8 can be summarized as follows:

A flowchart shows the summary of direct manufacturing labor variance computed in exhibits 7-7 and 7-8.

The details of the flowchart are as follows: Level 2: Flexible-budget direct labor variance of dollar 38,000 has unfavorable effect on operating income. Level 3: Flexible-budget direct labor variance splits into: Direct Labor Price Variance of dollar 27,000 has unfavorable effect on operating income and direct labor efficiency variance of dollar 11,000 has unfavorable effect on operating income. Level 4: Direct labor efficiency variance splits into: Direct labor mix variance of dollar 9,000 has favorable effect on operating income and direct labor yield variance of dollar 20,000 has unfavorable effect on operating income.

Appendix Mix and Yield Variances for Substitutable Inputs

Direct Manufacturing Labor Price and Efficiency Variances

Exhibit 7-7

Direct Manufacturing Labor Price and Efficiency Variances for Mode Company for April 2020^a

Direct Manufacturing Labor Mix and Yield Variances

Exhibit 7-8

Direct Manufacturing Labor Yield and Mix Variances for Mode Company for April 2020^a

Direct Manufacturing Labor Mix Variance

Direct Manufacturing Labor Yield Variance