Using the weighted-average method, compute equivalent units, cost per equivalent unit, ending WIP cost, and cost of units transferred out for Weston Products’ Grinding Department (May) given: beginning WIP 45,000 lb (materials $66,600, conversion $46,350; 100% materials, 30% conversion), started 337,000 lb, ending WIP 124,000 lb (100% materials, 70% conversion), May costs added materials $559,880 and conversion $350,170.

What you are trying to produce in a weighted-average process-costing problem

You need four things: (1) physical flow of units, (2) equivalent units (EUP) for materials and conversion, (3) cost per EUP using total costs (beginning WIP + costs added), and (4) assign total costs to ending WIP and to units transferred out.

1) Reconcile the physical flow of pounds

Pounds to account for:

• Beginning work in process (WIP): $45{,}000$
• Started in May: $337{,}000$

$$45{,}000 + 337{,}000 = 382{,}000 \text{ lb total}$$

Pounds accounted for:

• Ending WIP: $124{,}000$
• Transferred out to Mixing: $$382{,}000 - 124{,}000 = 258{,}000 \text{ lb}$$

2) Compute equivalent units of production (weighted-average)

Weighted-average treats all units completed this period as 100% complete for the current department, and it includes beginning WIP in the “units completed” figure.

Materials EUP

Materials are added at the start, so both completed units and ending WIP are 100% complete for materials.

$$\text{EUP (materials)} = 258{,}000 + 124{,}000(1.00) = 382{,}000$$

Conversion EUP

Completed units are 100% converted; ending WIP is 70% converted.

$$\text{EUP (conversion)} = 258{,}000 + 124{,}000(0.70) = 258{,}000 + 86{,}800 = 344{,}800$$

3) Compute cost per equivalent unit

Under weighted-average, use total costs to account for (beginning WIP costs + costs added in May).

Total costs to account for

Materials: $$66{,}600 + 559{,}880 = 626{,}480$$ Conversion: $$46{,}350 + 350{,}170 = 396{,}520$$

Cost per EUP

Materials: $$\$\text{ per EUP (materials)} = \frac{626{,}480}{382{,}000} = 1.64$$ Conversion: $$\$\text{ per EUP (conversion)} = \frac{396{,}520}{344{,}800} = 1.15$$

4) Assign costs to ending WIP and transferred out

Ending WIP cost

Materials in ending WIP: $$124{,}000 \times 1.64 = 203{,}360$$ Conversion in ending WIP (only 70% complete): $$86{,}800 \times 1.15 = 99{,}820$$ Total ending WIP: $$203{,}360 + 99{,}820 = 303{,}180$$

Cost of units transferred out

Transferred out (258,000 lb) are 100% for both cost categories:

Materials: $$258{,}000 \times 1.64 = 423{,}120$$ Conversion: $$258{,}000 \times 1.15 = 296{,}700$$ Total transferred out: $$423{,}120 + 296{,}700 = 719{,}820$$

Quick check (cost reconciliation)

$$303{,}180 + 719{,}820 = 1{,}023{,}000$$ Total costs to account for: $$626{,}480 + 396{,}520 = 1{,}023{,}000$$ They match, so the allocations are consistent.