## 7GP.1 Sales Variances

To be added at a future time.

## 7GP.2 Direct Labor Variances

### 7GP.2.E1

Young Company has actual direct labor wages of $5,000 (at an actual rate of $16 per hour). The firm’s standard quantity, given actual finished goods output, is 300 direct labor hours. The firm’s standard price is $14 per hour.

**Required**

What is the direct labor price variance?

#### Answer

AQ*AP – AQ*SP

or

AQ(AP-SP)

AQ = $5,000 / $16 per hour = 312.5 actual hours

AP = $16 per hour

SP = $14 per hour

312.5 * ($16 – $14) = $625 unfavorable direct labor price variance

This variance is unfavorable because the actual price is greater than the standard.

### 7GP.2.E2

Young Company has actual direct labor wages of $5,000 (at an actual rate of $16 per hour). The firm’s standard quantity, given actual finished goods output, is 300 direct labor hours. The firm’s standard price is $14 per hour.

**Required**

What is the direct labor quantity variance?

#### Answer

The direct labor quantity variance is given as follows.

AQ*SP – SQ*SP

or

SP(AQ-SQ)

AQ = $5,000 / $16 per hour = 312.5 actual hours

SQ = 300 hours

SP = $14 per hour

$14 * (312.5 – 300) = $175 unfavorable direct labor quantity variance

This variance is unfavorable

### 7GP.2.M1

Olde Company’s standard quantity is 2.5 direct labor hours per unit. Last year the company budgeted 12,000 finished goods units. The actual finished goods units produced were 10,000. The firm uses the standard price of $25 per direct labor hour. Actual direct labor was 30,000 units at $23.50 per direct labor hour.

**Required**

What is Olde Company’s direct labor price variance?

#### Answer

The price variance is given by the following equation.

AQ(AP-SP)

AQ = 30,000

AP = $23.50

SP = $25.00

30,000 * (25 – 23.50) = $45,000 favorable direct labor price variance

This variance is favorable because the actual price was lower than the standard price.

### 7GP.2.M2

Olde Company’s standard quantity is 2.5 direct labor hours per unit. Last year the company budgeted 12,000 finished goods units. The actual finished goods units produced were 10,000. The firm uses the standard price of $25 per direct labor hour. Actual direct labor was 30,000 units at $23.50 per direct labor hour.

**Required**

A) What is Olde Company’s direct labor quantity variance?

B) What is the journal entry to record Olde Company’s direct labor costs and variances?

#### Answer (A)

The direct labor quantity variance is given by the following equation. (Notice that SQ is based on the flexible budget, which is the standard per unit multiplied by actual finished goods units.)

SP(AQ-SQ)

SP = $25.00

AQ = 30,000

SQ = 2.5 per FG unit * 10,000 actual FG units = 25,000

25 * (30,000 – 25,000) = $125,000 unfavorable direct labor variance

This variance is unfavorable because the actual quantity is greater than the standard quantity.

#### Answer (B)

The credit (to Cash or Wages Payable) in this entry is the actual costs (30,000 * $23.50 = $705,000) because they frown on not recording your debts at their actual cost. The debit (to WIP) for the entry is at full standard (25,000 * $25 = $625,000) because a standard system typically values Cost Of Goods Sold (which is derived from WIP) at standard and separates out variances.

Also the entry includes the two variance values: favorable price variance of $45,000 and unfavorable quantity variance of $125,000. The favorable variance is a credit, and the unfavorable variance is a debit (variances are expense accounts that go up with a debit, and expenses going up is an unfavorable outcome).

Dr. WIP $625,000

Dr. Direct Labor Quantity Variance $125,000

Cr. Direct Labor Price Variance $45,000

Cr. Wages Payable $705,000

## 7GP.3 Direct Materials Variances

### 7GP.3.E1

The High Company purchases and uses 100,000 liters of a direct material at a price of $0.16 per liter. The company’s standard quantity for this direct material is 2 liters per finished goods unit (both budgeted and actual finished goods units are 52,000). The standard price for this direct material is $0.14 per liter.

**Required**

**(A)** What is High Company’s direct materials quantity variance?

**(B)** What is High Company’s direct materials price variance?

#### Answer (A)

This problem simplifies things for us: actual and budgeted FG units are the same, and actual quantity purchased is the same as actual quantity used. So we can simply apply the quantity variance equation.

SP * (AQ – SQ)

SP = 0.14

AQ = 100,000

SQ = 52,000 * 2 = 104,000

0.14 * (100,000 – 104,000) = $560 favorable DM quantity variance (written as an absolute value here)

This variance is favorable because actual quantity is less than standard quantity.

#### Answer (B)

Again, given the simplification this problem provides us we can simply apply the price variance equation.

AQ * (AP – SP)

AQ = 100,000

SP = 0.14

AP = 0.16

100,000 * (0.16 – 0.14) = $2,000

This variance is unfavorable because actual price used is higher than the standard price.

### 7GP.3.E2

Low, Inc.’s actual cost for 1,000,000 units of direct material is $90,000,000. It’s direct materials price variance is a $150,000 unfavorable variance.

**Required**

What is Low, Inc.’s standard price for direct materials?

#### Answer

This problem can be solved algebraically using the price variance equation.

Price variance = AQ * (AP – SP)

Since 1,000,000 units of DM cost $90,000,000, the actual price is $90 per unit

150,000 = 1,000,000 * (90 – SP)

1,000,000 * SP = 90,000,000 – 150,000

SP = 89,850,000 / 1,000,000 = $89.85 per DM unit.

In this chapter textbook, I haven’t been strict about assigning signs to variances based on their favorability (I find that it throws people off when they have to calculate revenue variances, since the signs for favorable and unfavorable variances reverse).

However, given the simplicity of the price equation, this just means is that we need to check the answer to ensure it makes sense. and SP of 89.85 does make sense, because an SP lower than the AP (of $90) would make the variance unfavorable. *If *this problem instead had a $150,000 *favorable price *variance, I could follow the same algebra shown above, even resulting in $89.85 as the tentative SP. When I double check to make sure this SP make sense for a favorable variance, I’d recognize that it doesn’t makes sense and have to make an adjustment.

Instead of going through all the algebra again, I can simply look at the difference between the AP and the SP I found (i.e. 90 – 89.85 = 0.15) and recognize that the correct SP has that same difference, but in the opposite direction: $0.15 higher than AP, rather than $0.15 lower than AP. Thus 90.15 is SP if the firm has a $150,000 favorable price variance.

### 7GP.3.M1

This period, Left, LLC purchases 1,000 pounds of direct materials at $15 per pound. The firm’s standard for this direct material is $13 per pound and 0.5 pounds per finished goods unit. During the period Left, LLC uses 900 pounds of direct materials in production to produce 1,600 finished goods units. In the firm’s budget, Left, LLC budgeted that it would produce 2,000 finished goods this period.

**Required**

**(A)** What is Left, LLC’s direct materials quantity variance?

**(B)** What is Left, LLC’s direct materials price variance?

#### Answer (A)

DM quantity variance is found using the following equation.

SP * (AQU – SQ),

For thus equation SQ is the standard quantity of the input at *actual *production volume (i.e. the flexible budget SQ). AQU is the actual quantity used.

SP = $13

AQU = 900

SQ = 1,600 * 0.5 = 800

13 * (900 – 800) = $1,300 unfavorable direct materials quantity variance (unfavorable because actual quantity used is more than the standard quantity).

#### Answer (B)

Price variance is found with the following equation, where AQP is the actual quantity purchased.

AQP * (AP – SP)

AQP = 1,000

AP = $15

SP = $13

1,000 * (15 – 13) = $2,000 unfavorable direct materials price variance (unfavorable because actual price is greater than the standard price).

### 7GP.3.M2

This period, Right, Inc. purchases 2,000 pounds of direct materials at $30 per pound. The firm’s standard for this direct material is $32 per pound and 0.5 pounds per finished goods unit. During the period Right, Inc. uses 1,800 pounds of direct materials in production to produce 3,800 finished goods units. In the firm’s budget, Right, Inc. budgeted that it would produce 3,500 finished goods this period.

**Required**

What are the journal entries Right, Inc. uses to record direct materials purchases and usage?

#### Answer

First we need to calculate the variances.

Price variance = AQP * (AP – SP)

2,000 * (30 – 32) = $4,000 favorable variance (actual price is lower than standard price)

Quantity variance = SP * (AQU – SQ)

32 * (1,800 – 1,900) = $3,200 favorable variance (actual quantity is lower than standard quantity)

Now, upon purchase of the direct materials, the firm will record the price variance, the liability to accounts payable (or the decrease in cash, if paid in cash), and the increase in raw materials inventory. The credit (to a liability or to cash) needs to be the actual cost (i.e. AQP * AP). The debit to raw materials inventory is actual quantity purchased, priced at the standard price (i.e. AQP * SP).

Because the price variance is favorable, we will credit and thus decrease the expense account called “Direct Materials Price Variance.”

Dr. Raw Materials (2,000 * 32) $64,000

Cr. Direct Materials Price Variance $4,000

Cr. Accounts Payable (2,000 * 30) $60,000

When direct materials are used in production, the firm records the quantity variance, the decrease to raw materials inventory, and the increase in value of work in process. The credit to raw materials inventory needs to be the actual quantity used, priced at the standard price (i.e. AQU * SP). The debit to work in process is at full standard (i.e. SQ * SP).

The SQ we need to use is the *flexible budget *SQ (meaning the standard quantity of DM units we’d expect at the actual FG units of production), not the SQ expected at the FG volume given in the static budget. If we were to mistakenly use the 3,500 FG units in the static budget to calculate our SQ and our quantity variance, then we’d be intermingling volume variance with quantity variance. Then, we wouldn’t know for sure if the management of DM units in production was good or bad because the variance we’d calculated might be higher or lower simply due to higher or lower FG unit volume rather than due to the actions of the manager overseeing production. We have to isolate production decisions by using the SQ from the flexible budget, which effectively already accounts for the difference in FG volume between the static budget and actuals.

So, the actual quantity used is 1,800 and the standard quantity is 1,900 (3,800 actual FG units * 0.5 standard DM units per FG unit = 1,900). This means we used fewer DM units than expected at that volume of actual FG production. This means the quantity variance will be favorable. Because the quantity variance is favorable, we will credit (thus decreasing) the expense account called “Direct Materials Quantity Variance.”

Dr. Work in Process (1,900 * 32) $60,800

Cr. Direct Materials Quantity Variance $3,200

Cr. Raw Materials (1,800 * 32) $57,600

## 7GP.4 Overhead Variances

### 7GP.4.E1

A firm applies variable overhead using a standard rate of $2 per machine hour. The firm expects 1,000 machine hours to be consumed per 100,000 finished goods units. The firm’s actual finished goods volume was 300,000 units.

The firm’s actual machine hour usage was 3,200 machine hours, for a total actual variable overhead cost of $6,100.

**Required**

What are the firm’s variable overhead price variance and variable overhead quantity variance?

#### Answer

Variable overhead variances are similar to direct labor variances, with the PDOH being equivalent to the wage rate of direct labor workers and the cost driver consumed being equivalent to direct labor hours. Sometimes the cost driver *is *direct labor hours.

VOH quantity variance = (AQ – SQ) * SP

AQ = 3,200 machine hours

SQ = 1,000 / 100,000 * 300,000 = 3,000

SP = $2 per machine hour

VOH quantity variance = (3,200 – 3,000) * 2 = $400 unfavorable (because actual is greater than standard)

VOH price variance = (AP – SP) * AQ

AP = $6,100 / 3,200 = $1.91 per machine hour (rounded)

SP = $2 per machine hour

AQ = 3,200 machine hours

VOH price variance = (1.91 – 2) * 3,200 = $288 favorable (because actual is less than standard)

### 7GP.4.M1

Last year a firm budgeted $100,000 in fixed overhead costs. The firm’s PDOH rate is $10 per direct labor hour, half of which is due to variable overhead. The firm’s actual direct labor hours were 18,000. The firm’s actual fixed overhead costs were $98,000.

**Required**

What are the firm’s fixed overhead volume variance and fixed overhead spending variance?

#### Answer

The three numbers being compared for fixed overhead variances are different than for all other cost variances. We need (1) applied fixed overhead, (2) static budget fixed overhead, and (3) actual fixed overhead. Note that the PDFOH rate is $5 per direct labor hour, i.e. half of the $10 overall PDOH.

Applied FOH: $5 * 18,000 = $90,000

Actual FOH: $98,000

Static Budget FOH: $100,000

FOH volume variance = Static Budget FOH – Applied FOH

FOH volume variance = 100,000 – 900,000 = 10,000 unfavorable (because static budget was higher than applied FOH cost, so the PDFOH underapplied fixed overhead and more cost has to be added to get to the static budget).

FOH spending variance = Actual FOH – Static Budget FOH

FOH spending variance = 98,000 – 100,000 = 2,000 favorable (because actual FOH was less than the budgeted FOH)

## 7GP.5 Mix and Yield Variances

### 7GP.5.M1

A firm has two direct material inputs: input alpha and input beta. These two inputs are substitutable. The firm generally expects each batch of 100 finished goods units to require 30 pounds of input alpha and 20 pound of input beta. Input alpha costs $4 per pound and input beta costs $3 per pound (these two are the actual *and *standard prices for the inputs).

The firm actually produces 10,000 finished goods units and uses 3,500 pounds of input alpha and 1,500 pounds of input beta.

**Required**

What is the firm’s mix variance for direct materials?

#### Answer

The two inputs’ standard prices differ, and the actual mix ratio (3.5:1.5) differed from the standard mix (3:2), so there will be a mix variance (if either of these two conditions doesn’t hold, then the mix variance is $0).

Input alpha:

Actual input quantity: 3,500 pounds

Standard input quantity: 3,000 pounds (i.e. 30/100 = x/10,000 => x = 3,000)

Standard price: $4 per pound

(3,500 – 3,000) * 4 = $2,000

This is an unfavorable variance: we bought more input alpha than we thought we would based on the standard mix

Input beta:

Actual input quantity: 1,500 pounds

Standard input quantity: 2,000 pounds (i.e. 20/100 = x/10,000 => x = 2,000)

Standard price: $3 per pound

(1,500 – 2,000) * 3 = ($1,500)

This is a favorable variance: we bought less input beta than we thought we would based on the standard mix.

The net of these two is $500 unfavorable variance. This makes sense, we over-used the more expensive of the two inputs (input alpha).

### 7GP.5.M2

A firm uses two substitutable inputs: input zeta and input omega.

- The standard mix is 1 units of input zeta for every 2 units of input omega
- This, mix (i.e. 1 input zeta and 2 input omega units), is the standard per batch, which produces three finished goods units.
- Input zeta costs $40 per unit and input omega costs $100 per unit.
- To produce 300 finished goods units, the firm actually uses 150 units of input zeta and 100 units of input omega.

**Required**

What is the firm’s yield variance for these inputs?

#### Answer

The mix variance will have already accounted for the two inputs’ very diverging actual mix compared to the sales mix. But we can use the actual mix to give us the *total actual input units*.

150 zeta units + 100 omega units = 250 input units

Given this number of input units, the there should be 250 finished goods units (3 FG units per 3 input units = 1 FG unit per input).

Actual yield: 300 FG units

Standard yield: 250 FG units

Standard price at standard mix: (1 zeta per batch * $40 per zeta + 2 omega per batch * $100 per omega) / 3 FG units per batch = $80 per FG unit at standard mix

(300 – 250) * $80 = $4,000

This is a favorable variance because the actual yield was greater than expected, given the number of total actual input units.