## 6GP.1 Equivalent Units – Weighted Average

### 6GP.1.E1

The firm Londres uses the

**Required**

What are the equivalent units in ending inventory with respect to direct materials and conversion costs?

#### Answer

Equivalent units are the number of units multiplied by their percent completion.

Direct materials equivalent units = 5,500 * 1.00 = 5,500 equivalent units

Conversion costs equivalent units = 5,500 * 0.40 = 2,200 equivalent units

### 6GP.1.M1

The firm Rondon uses the weighted average method of process costing. It had 5,000 units in beginning WIP inventory. These units were 50% complete with respect to direct materials and 75% complete with respect to conversion costs. The firm started 40,000 units this period and has 10,000 units in ending WIP inventory. Ending WIP units are 25% complete with respect to materials and 50% complete with respect to conversion costs.

**Required**

What are the total equivalent units with respect to direct materials and conversion costs?

#### Answer

Total equivalent units for the weighted average method are the sum of units completed and equivalent units in ending WIP (units completed are by definition 100% complete, therefore the raw number of units completed is equal to the equivalent units completed).

Units complete in this case can be algebraically solved for (or through a T-account).

5,000 BWIP units + 40,000 units started – 10,000 EWIP units = 35,000 units completed.

Total equivalent units: DM = 35,000 + (10,000 * 0.25) = 37,500 equivalent units

Total equivalent units: CC = 35,000 + (10,000 * 0.50) = 40,000 equivalent units

Ignore BWIP percent completion. The weighted average ignores work done at last period’s rates and redistributes BWIP costs across all units worked on this period through using this period’s rate.

The 37,500 TEU: DM and 40,000 TEU: CC would, respectively, go into the denominator of the DM cost per unit and denominator of the CC per unit rate calculations.

## 6GP.2 Equivalent Units – FIFO

### 6GP.2.E1

Use the same information as Problem 6GP.1.E1 for this problem, except assume Londres uses the FIFO method of process costing.

**Required**

What are the equivalent units in ending inventory with respect to direct materials and conversion costs?

#### Answer

Equivalent units in EWIP are the same for both the weighted average and FIFO methods. These two methods differ only on how BWIP is treated.

Direct materials equivalent units = 5,500 * 1.00 = 5,500 equivalent units

Conversion costs equivalent units = 5,500 * 0.40 = 2,200 equivalent units

### 6GP.2.M1

Use the same information as Problem 6GP.1.M1 for this problem, except assume Rondon uses the FIFO method of process costing.

**Required**

What are the total equivalent units with respect to direct materials and conversion costs?

#### Answer

Total equivalent units

As in 6GP.1.M1, units completed

TEU: DM = 35,000 + (10,000 * 0.25) – (5,000 * 0.50) = 35,000 equivalent units

TEU: CC = 35,000 + (10,000 * 0.50) – (5,000 * 0.75) = 36,250 equivalent units

These figures are the denominators for the eventual FIFO unit rate calculations.

## 6GP.3 Unit Rates – Weighted Average

### 6GP.3.E1

The firm Hapon uses the weighted average method for process costing. Hapon has two departments: the Starting Department and the Finishing Department. Direct materials are all added at the beginning of the production process in the Finishing Department. The Starting Department completed 100,000 units this period and has 3,500 units in ending inventory that are halfway through the production process.

This period, the Starting Department incurred $50,000 of direct materials costs, $30,000 of direct labor costs, and $30,000 of overhead costs. At the beginning of the period, the department had a $5,000 balance in beginning WIP cost, including $2,500 direct materials costs, $1,250 of direct labor costs, and $1,250 overhead costs.

**Required**

What are the per equivalent unit rates this period for direct materials and for conversion costs in Hapon’s Starting Department?

#### Answer

The numerators for this problem are simply the current period costs plus beginning WIP costs, summed separately by cost category (i.e. direct materials and conversion costs). Conversion costs include direct labor costs and overhead costs.

Total DM costs = $50,000 + $2,500 = $52,500

Total CC costs = $30,000 + $30,000 + $1,250 + $1,250 = $62,500

Total equivalent units, the denominator, are calculated as the sum of units completed and equivalent units in ending WIP. Again, we need to come up with two separate figures: one for direct materials and one for conversion costs. Direct materials are all added at the beginning of the process, so all units in ending WIP have all the direct materials work they are going to receive in the Starting Department.

TEU: DM = 100,000 + (3,500 * 1.00) = 103,500 equivalent units

TEU: CC = 100,000 + (3,500 * 0.50) = 101,750 equivalent units

Now the rates are simply the quotient of these two numbers (within each respective cost category: direct materials and conversion costs).

DM per equivalent unit = $52,500 / 103,500 = $0.507 per equivalent unit (rounded to tentch of a cent)

CC per equivalent unit = $62,500 / 101,750 = $0.614 per equivalent unit (rounded to tentch of a cent)

### 6GP.3.M1

Use the information in 6GP.3.E1. Assume Finishing Department has 1,000 units in BWIP, which amount to $1,200 in BWIP costs.

**Required**

Do we have enough information to determine the Finishing Department’s equivalent unit rate for transferred-in costs this period? If so, what is the rate? If not, what information do we need?

#### Answer

We ** do **have enough information to calculate the transferred-in cost rate. From problem 6GP.3.E1 we know the rates at which the Starting Department assigned costs to units ($0.507 per equivalent unit for DM and $0.614 per equivalent unit for CC) and we know how many units that department completed (100,000 units).

The product of these rates and the units completed by the Starting Department, w gives us the debit to WIP-Starting-Department to account for goods completed. The other side of this entry is the credit to WIP-Finishing-Department for transferred-in costs. Thus, this number, plus the $1,200 in BWIP costs is the numerator for the transferred-in cost rate.

The denominator is not hard to find. Total equivalent units for the weighted average method is units completed plus the equivalent units in EWIP. The Starting Department transferred over 100,000 units. That means 100,000 units started. BWIP is 1,000 units. Those 101,000 units are either completed by the end of the period or they are in EWIP.

We don’t need to know how many of the 101,000 units are completed or end up in EWIP, because transferred-in costs re always 100% complete. So the total equivalent units, regardless of how many units the Finishing Department completed, are 101,000 units. Thus the rate is [100,000 TI units * (0.507 DM rate + 0.614 CC rate) + 1,200 BWIP cost] / 101,000 equivalent units = $1.122 TI cost per equivalent unit.

## 6GP.4 Unit Rates FIFO

### 6GP.4.E1

The firm Thames uses the FIFO method of process costing. It has the following data for direct materials costs and equivalent units.

**March 1**: 2,000 units in WIP, 40% complete at $5,000 direct materials costs.**March 30**: 1,000 units in WIP, 60% complete.

The firm’s total equivalent units (as defined by FIFO) are 48,000 equivalent units. The firm incurs $336,000 of direct materials costs this period.

**Required**

What is the equivalent unit rate for direct materials costs in March?

#### Answer

FIFO only includes *the current period’s costs *in the numerator for equivalent unit cost rates. FIFO keeps BWIP costs attached to the equivalent units’ worth of work in BWIP.

(The weighted average method, in contrast, strips away the BWIP costs from BWIP equivalent units and, by including these costs in the equivalent unit rates calculations, reassigns those costs across *all *the equivalent units of work done this period.)

FIFO direct materials equivalent unit rate = $336,000 / 48,000 = $7 per equivalent unit.

### 6GP.4.M1

**Required**

What are Thames’s conversion costs per equivalent unit for March?

#### Answer

In the *this period*. In the denominator, we must take the sum of units completed and equivalent units in ending WIP less

45,000 + (1,000 * 0.5) – (2,000 * 0.25) = 45,000 equivalent units.

FIFO conversion cost equivalent unit rate = $500,000 / 45,000 = $11.11 per equivalent unit

## 6GP.5 Cost of Units Completed and of EWIP Units – Weighted Average

### 6GP.5.E1

A firm called Temuzu uses weighted average process costing. The firm has one department.

For this period, Temuzu calculates a direct materials rate of $15 per equivalent unit and a conversion cost rate of $20 per equivalent unit.

The firm began the period with 50,000 units in BWIP (50% complete with respect to direct materials and conversion costs), ended the period with 60,000 units in EWIP (75% complete with respect to direct materials and conversion costs), and started 550,000 units during the period.

**Required**

**(A)** What is this department’s EWIP balance?

**(B)** What is the cost of the units completed this period?

#### Answer (A)

For both weighted average and FIFO, the ending WIP balance is found by summing the EWIP direct materials, conversion costs, and transferred-in costs. These costs, in turn, are the product of the relevant rate and the relevant equivalent units.

In this problem there are no transferred-in costs, since this is the only department in the firm. Also, the problem is simplified by the fact that direct materials and conversion costs are completed uniformly (i.e. the percent complete for direct materials is equal to the percent complete for conversion costs).

Therefore, we simply have to find the product of each rate and the same EWIP equivalent unit number.

DM costs in EWIP = $15 DM rate * (60,000 EWIP units * 0.75 percent complete) = $675,000 direct materials cost in EWIP

CC costs in EWIP = $20 CC rate * (60,000 EWIP units * 0.75 percent complete) = $900,000 conversion costs in EWIP

EWIP balance = $675,000 + $900,000 = $1,575,000

Alternatively, since EWIP equivalent units for direct materials and conversion costs are the same (and only in this special case), we can sum the two rates ($15 + $20 = $35) and multiply the combined total cost rate by the equivalent units in EWIP.

$35 * 45,000 = $1,575,000

#### Answer (B)

Units completed = BWIP units + Units completed – EWIP units

[Note that the above equation refers to raw units, not equivalent units]

Units completed = 50,000 + 550,000 – 60,000 = 540,000

Like in question A, we just multiply the rates by units completed and sum the resulting products to get total cost of units completed.

Cost of units completed = $15 * 540,000 + $20 * 540,000 = $18,900,000

### 6GP.5.M1

The firm 5Rings2012 uses the weighted average method of process costing. This firm’s second department in the process has the following information from this period.

- Materials, including transferred in materials, are all added at the beginning of the process.
- 1,000 units in BWIP: 50% complete with respect to conversion costs, $650 in DM costs, $1,500 in CC, $2,125 in TI costs.
- 10,500 units started.
- $12,000 in DM costs this period. $25,000 in CC this period. $18,000 in TI costs this period.
- 1,500 units in EWIP: 40% complete with respect to conversion costs.

**Required**

**(A)** What is this department’s EWIP balance?

**(B)** What is the cost of the units completed and transferred out of the department this period?

#### Answer (A)

First we must calculate the rates (for weighted average, TEU = units completed + EWIP equivalent units).

NOTE: Units completed = 1,000 BWIP units + 10,500 units started – 1,500 EWIP units = 10,000 units completed

Rate = (BWIP costs + Current period costs) / TEU

DM Rate = (650 + 12,000) / (10,000 + 1,500 * 1.00) = $1.10 DM per EU

CC Rate = (1,500 + 25,000) / (10,000 + 1,500 * 0.40) = $2.50 CC per EU

TI Rate = (2,125 + 18,000) / (10,000 + 1,500 * 1.00) = $1.75 DM per EU

Then we sum the product of these rates and the relevant EWIP equivalent units number

$1.10 * (1,500 * 1.00) = $1,650

$2.50 * (1,500 * 0.40) = $1,500

$1.75 * (1,500 * 1.00) = $2,625

1,650 + 1,500 + 2,625 = $5,775 total EWIP cost

#### Answer (B)

In the weighted average method, we can use the rates from part A and multiply them by the units completed (i.e. 10,00 units) to get the costs of those units completed.

DM costs: $1.10 * 10,000 = $11,000

CC: $2.50 * 10,000 = $25,000

TI costs: $1.75 * 10,000 = $17,500

11,000 + 25,000 + 17,500 = $53,500 total costs of units completed

As a check, the sum of costs in EWIP and costs of units completed should equal the sum of BWIP and current period costs.

$5,775 EWIP costs + $53,500 units completed costs = $59,275

(650 + 1500 + 2125) BWIP costs + (12,000 + 25,000 + 18,000) current period costs = 59,275

## 6GP.6 Cost of Units Completed and of EWIP Units – FIFO

### 6GP.6.E1

Use the same information provided about Temuzu in problem 6GP.5.E1, but now assume Temuzu uses the FIFO method (assume the rates given are correct for FIFO now). Also, assume there are $1,800,000 in BWIP at the beginning of the period.

**Required**

**(A)** What is this department’s EWIP balance?

**(B)** What is the cost of the units completed this period?

#### Answer (A)

The procedure for applying costs to EWIP is the same under weighted average and FIFO: multiply the rates by the equivalent units in

DM costs in EWIP = $15 DM rate * (60,000 EWIP units * 0.75 percent complete) = $675,000 direct materials cost in EWIP

CC costs in EWIP = $20 CC rate * (60,000 EWIP units * 0.75 percent complete) = $900,000 conversion costs in EWIP

EWIP balance = $675,000 + $900,000 = $1,575,000

This is the same result as in 6GP.5.E1. However, that doesn’t mean FIFO’s and weighted average’s EWIP balances are always the same, even though I said that they follow the same procedure. Thats’s because the two methods almost always produce different cost per equivalent unit rates. There are two exceptions to this.

First, the two methods might have the same rates if there is no BWIP balance. In this case, the FIFO rate equation is mathermatically equivalent to the weighted average rate equation.

Second, if last period’s rates are exactly the same as this period’s then the rates will also be equal. It doesn’t matter that FIFO’s strictly segreges between last period’s work (in BWIP) and this period’s work (as expressed through the cost rates) and that weighted average does * not *thus segregate when the two rates are the same per equivalent unit.

Thus the answer to this problem is only the same as the answer to 6GP.5.E1 because I have artifically, for the sake of simplifying things, used the same cost per equivalent rates under both methods.

#### Answer (B)

Under FIFO, the rates do not include beginning WIP costs, so those costs ($1,800,000) have to be directly added to units completed. Also, the “units completed”

Units completed – BWIP equivalent units = Units completed*

540,000 – (50,000 * 0.5) = 515,000

($15 + $20) * 515,000 + $1,800,000 = $19,825,000

### 6GP.6.M1

Use the same information provided about 5Rings2012 in problem 6GP.5.M1, but now assume the firm uses the FIFO method.

**Required**

**(A)** What is this department’s EWIP balance?

**(B)** What is the cost of the units completed and transferred out of the department this period?

#### Answer (A)

FIFO rates calculations omits BWIP costs in the numerator and subtracts BWIP equivalent units from the denominator.

DM: 12,000 / (10,000 + 1,000 – 1,500) = $1.26 DM per equivalent unit

CC: 25,000 / (10,000 + 1,000 * 0.5 – 1,500 * 0.40) = $2.53 CC per equivalent unit

TI: 18,000 / (10,000 + 1,000 – 1,500) = $1.89 TI per equivalent unit

Applying these rates to the equivalent units in EWIP leads to the following EWIP balance.

$1.26 * 1,500 + $2.53 * 600 + $1.89 * 1,500 = $6,243 EWIP balance

#### Answer (B)

The cost of units completed is BWIP costs plus the product of the rates (calculated in part A) and a modified definition of units completed.

Units completed – BWIP equivalent units = Units completed*

DM: 10,000 – 1,000 = 9,000

CC: 10,000 – (1,000 * 0.50) = 9,500

TI: 10,000 – 1,000 = 9,000

$1.26 * 9,000 = $11,340

$2.53 * 9,500 = $24,035

$1.89 * 9,000 = $17,010

(650 + 1,500 + 2125) + (11,340 + 24,035 + 17,010) = $56,660