Chapter 6, Problem 70C

AKL Foundry manufactures metal components for different kinds of equipment used by the aerospace, commercial aircraft, medical equipment, and electronic industries. The company uses investment casting to produce the required components. Investment casting consists of creating, in wax, a replica of the final product and pouring a hard shell around it. After removing the wax, molten metal is poured into the resulting cavity. What remains after the shell is broken is the desired metal object ready to be put to its designated use.

Metal components pass through eight processes: gating, shell creating, foundry work, cutoff, grinding, finishing, welding, and strengthening. Gating creates the wax mold and clusters the wax pattern around a sprue (a hole through which the molten metal will be poured through the gates into the mold in the foundry process), which is joined and supported by gates (flow channels) to form a tree of patterns. In the shell-creating process, the wax molds are alternately dipped in a ceramic slurry and a fluidized bed of progressively coarser refractory grain until a sufficiently thick shell (or mold) completely encases the wax pattern. After drying, the mold is sent to the foundry process. Here, the wax is melted out of the mold, and the shell is fired, strengthened, and brought to the proper temperature. Molten metal is then poured into the dewaxed shell. Finally, the ceramic shell is removed, and the finished product is sent to the cutoff process, where the parts are separated from the tree by the use of a band saw. The parts are then sent to the grinding process, where the gates that allowed the molten metal to flow into the ceramic cavities are ground off using large abrasive grinders. In the finishing process, rough edges caused by the grinders are removed by small handheld pneumatic tools. Parts that are flawed at this point are sent to welding for corrective treatment. The last process uses heat to treat the parts to bring them to the desired strength.

In 20X1, the two partners who owned AKL Foundry decided to split up and divide the business. In dissolving their business relationship, they were faced with the problem of dividing the business assets equitably. Since the company had two plants—one in Arizona and one in New Mexico—a suggestion was made to split the business on the basis of geographic location. One partner would assume ownership of the plant in New Mexico, and the other would assume ownership of the plant in Arizona. However, this arrangement had one major complication: the amount of WIP inventory located in the Arizona plant.

The Arizona facilities had been in operation for more than a decade and were full of WIP. The New Mexico facility had been operational for only 2 years and had much smaller WIP inventories. The partner located in New Mexico argued that to disregard the unequal value of the WIP inventories would be grossly unfair.

Unfortunately, during the entire business history of AKL Foundry, WIP inventories had never been assigned any value. In computing the cost of goods sold each year, the company had followed the policy of adding depreciation to the out-of-pocket costs of direct labor, direct materials, and overhead. Accruals for the company are nearly nonexistent, and there are hardly ever any ending inventories of materials.

During 20X1, the Arizona plant had sales of $2,028,670. The cost of goods sold is itemized as follows:

Upon request, the owners of AKL provided the following supplementary information (percentages are cumulative):

Gating had 10,000 units in BWIP, 60% complete. Assume that all materials are added at the beginning of each process. During the year, 50,000 units were completed and transferred out. The ending inventory had 11,000 unfinished units, 60% complete.

Required:

1. 1. The partners of AKL want a reasonable estimate of the cost of WIP inventories. Using the gating department’s inventory as an example, prepare an estimate of the cost of the EWIP. What assumptions did you make? Did you use the FIFO or weighted average method? Why? (Note: Round unit cost to two decimal places.)
2. 2. Assume that the shell-creating process has 8,000 units in BWIP, 20% complete. During the year, 50,000 units were completed and transferred out. (Note: All 50,000 units were sold; no other units were sold.) The EWIP inventory had 8,000 units, 30% complete. Compute the value of the shell-creating department’s EWIP. What additional assumptions had to be made?

To determine

Provide an estimate of the ending WIP of gating process. Also, explain the method used to measure WIP and reason for such selection.

Explanation of Solution

Process Costing:

Process costing is a system in which an organization ascertains costs associated which specific processes undertaken within the company.

Step 1: Physical flow analysis:

Particulars	Units
Units to account for:
Units in beginning WIP	10,000
Add: Units started during the period1	51,000
Units to account for	61,000
Units accounted for:
Units completed and transferred	50,000
Add: Units in ending WIP	11,000
Units accounted for	61,000

Table (1)

Step 2: Computation of equivalent units:

Particulars	Material	Conversion
Units started and completed	40,000	40,000
Equivalent units of beginning WIP $\left(10,000\times 40\%\right)$		4,000
Equivalent units of ending WIP $\left(11,000\times 60\%\right)$	11,000	6,600
Equivalent units	51,000	50,600

Table (2)

Step 3: Computation of unit cost:

Particulars	Material ($)	Conversion ($)
Material cost $\left(23\%\times \$378,000\right)$	86,940
Labor cost $\left(\$530,300\times 35\%\right)$		185,605
Overhead cost $\left(\$643,518\times 35\%\right)$		225,231
Total cost	86,940	410,836
Equivalent units	51,000	50,600
Unit cost $\left(\frac{\text{Total}\text{cost}}{\text{Equivalent}\text{units}}\right)$	1.70	8.12

Table (3)

Step 4: Valuation of ending inventory:

Particulars	Amount ($)
Equivalent units of material $\left(11,000\times \$1.70\right)$	18,700
Equivalent units for conversion $\left(6,600\times \$8.12\right)$	53,592
Total value	72,292

Table (4)

FIFO method has been used since, costs associated with beginning inventory is to be removed from the equivalent units so that current period’s cost can be correctly allocated amongst the equivalent units for computation of unit cost.

Working Notes:

1. Computation of units started during the period:

$\begin{array}{c}\text{Units}\text{started}=\text{Units}\text{started}\text{and}\text{completed}+\text{Units}\text{in}\text{ending}\text{WIP}\\ =\left(\begin{array}{l}\text{Units}\text{completed}\text{and}\text{transferred}\\ -\text{Units}\text{in}\text{beginning}\text{WIP}\end{array}\right)+\text{Units}\text{in}\text{ending}\text{WIP}\\ =\left(50,000-10,000\right)+11,000\\ =51,000\end{array}$

To determine

Provide an estimate of the ending WIP of shell-creating process.

Explanation of Solution

Step 1: Physical flow analysis:

Particulars	Units
Units to account for:
Units in beginning WIP	8,000
Add: Units started during the period1	50,000
Units to account for	58,000
Units accounted for:
Units completed and transferred	50,000
Add: Units in ending WIP	8,000
Units accounted for	58,000

Table (5)

Step 2: Computation of equivalent units:

Particulars	Material	Conversion
Units started and completed	42,000	42,000
Equivalent units of beginning WIP $\left(8,000\times 80\%\right)$		6,400
Equivalent units of ending WIP $\left(8,000\times 30\%\right)$	8,000	2,400
Equivalent units	50,000	50,800

Table (6)

Step 3: Computation of unit cost:

Particulars	Material ($)	Conversion ($)
Material cost $\left(47\%\times \$378,000\right)$	177,660
Labor cost $\left(\$530,300\times 15\%\right)$		79,545
Overhead cost $\left(\$643,518\times 15\%\right)$		96,528
Total cost	177,660	176,073
Equivalent units	50,000	50,800
Unit cost $\left(\frac{\text{Total}\text{cost}}{\text{Equivalent}\text{units}}\right)$	3.55	3.47

Table (7)

Step 4: Valuation of ending inventory:

Particulars	Amount ($)
Equivalent units of material $\left(8,000\times \$3.55\right)$	28,400
Equivalent units for conversion $\left(2,400\times \$3.47\right)$	8,328
Transferred in $\left(8,000\times \$9.82\right)$	78,560
Total value	115,288

Table (8)

Working Notes:

1.

Computation of units started during the period:

$\begin{array}{c}\text{Units}\text{started}=\text{Units}\text{started}\text{and}\text{completed}+\text{Units}\text{in}\text{ending}\text{WIP}\\ =\left(\begin{array}{l}\text{Units}\text{completed}\text{and}\text{transferred}\\ -\text{Units}\text{in}\text{beginning}\text{WIP}\end{array}\right)+\text{Units}\text{in}\text{ending}\text{WIP}\\ =\left(50,000-8,000\right)+8,000\\ =50,000\end{array}$