Process costing

Cedar Ridge's Classic chairs are identical. It would be pointless to keep a separate cost sheet for each of the 7,000 chairs the line makes in a year, because every chair receives the same materials and the same work. Instead, the company accumulates costs by department for each period and divides by the number of units the department worked on. That is process costing, the system used by makers of chairs, paint, flour, cereal, pharmaceuticals, steel and electricity. The tricky part is that at the end of any period some units are only partly finished. This lesson introduces equivalent units to deal with partly finished units, works through the weighted-average method step by step, shows how costs are transferred between departments, compares the FIFO method briefly, and introduces spoilage. ACCT-222 covers FIFO, spoilage and joint products in depth.

How process costing differs from job costing

Process costing uses the same three cost elements and the same flow from raw materials to work in process to finished goods as job costing. Two things change. First, there is a separate work in process account for each processing department, and costs are accumulated by department, not by job. Second, unit costs are calculated by dividing each department's costs for the period by the units it produced, expressed as equivalent units. Cedar Ridge's chair line has two departments: Assembly, where boards are cut, shaped and assembled into chairs, and Finishing, where chairs are sanded, stained and lacquered. Chairs move from Assembly to Finishing, then to finished goods.

Equivalent units

Suppose Assembly worked on chairs during March and ended the month with 50 chairs that had all their wood but only 60 per cent of their assembly work done. Those 50 partly finished chairs represent the same amount of conversion effort as 30 fully assembled chairs. Equivalent units express partly completed work as the number of whole units that could have been completed with the same effort: equivalent units = physical units × percentage complete. Because materials and conversion are often added at different times, equivalent units are computed separately for each cost element. At Cedar Ridge, all hardwood is issued at the start of Assembly, so units in Assembly are always 100 per cent complete for materials. Conversion costs (direct labour and overhead) are added evenly through the process.

The weighted-average method in five steps

The weighted-average method combines the cost of the beginning work in process with the costs added during the period and spreads the total over all units worked on, as if the beginning units had been started this period. It is simple and widely used. The calculation follows five steps, summarized in a production cost report: (1) account for physical units; (2) compute equivalent units for each cost element; (3) total the costs to account for; (4) compute the cost per equivalent unit; and (5) assign costs to units completed and transferred out and to ending work in process.

# Weighted-average production cost report: Assembly, March (illustrative)
beg_units, started, end_units = 80, 600, 50
end_pct = {"materials": 1.00, "conversion": 0.60}
beg_cost = {"materials": 4_800, "conversion": 1_500}
added = {"materials": 36_000, "conversion": 30_180}

completed = beg_units + started - end_units
eu = {k: completed + end_units * pct for k, pct in end_pct.items()}
total_cost = {k: beg_cost[k] + added[k] for k in added}
per_eu = {k: total_cost[k] / eu[k] for k in eu}

transferred = completed * sum(per_eu.values())
ending = sum(end_units * end_pct[k] * per_eu[k] for k in per_eu)

print(f"Completed and transferred: {completed} chairs")
for k in eu:
    print(f"{k:<11} EU {eu[k]:>5.0f}  cost {total_cost[k]:>7,}  per EU ${per_eu[k]:.2f}")
print(f"Transferred out ${transferred:,.0f}; ending WIP ${ending:,.0f}; "
      f"total ${transferred + ending:,.0f}")

Completed and transferred: 630 chairs
materials   EU   680  cost  40,800  per EU $60.00
conversion  EU   660  cost  31,680  per EU $48.00
Transferred out $68,040; ending WIP $4,440; total $72,480

The program reproduces the hand calculation and makes it easy to test changes. For example, if ending work in process were only 20 per cent complete for conversion, conversion equivalent units would fall to 640 and the conversion cost per unit would rise to $49.50, shifting a little more cost to the chairs transferred out.

Transferred-in costs and the second department

When chairs move to Finishing, their Assembly cost moves with them as transferred-in cost. To Finishing, transferred-in cost behaves like a raw material added at the start of its process: every unit in Finishing is 100 per cent complete for transferred-in cost. Finishing then adds its own materials (stain and lacquer, which at Cedar Ridge are applied near the end of the process) and its own conversion costs. Finishing's production cost report therefore has three cost columns: transferred in, materials and conversion. The cost of the chairs Finishing completes carries all the costs from both departments.

# Finishing department, March: three cost elements (illustrative)
beg = {"units": 40, "transferred in": 4_310, "materials": 0, "conversion": 520}
received, end_units = 630, 30
end_pct = {"transferred in": 1.0, "materials": 0.0, "conversion": 0.5}   # lacquer added at end
added = {"transferred in": 68_040, "materials": 4_960, "conversion": 15_310}

completed = beg["units"] + received - end_units
total_unit_cost = 0
assigned_end = 0
for k in added:
    eu = completed + end_units * end_pct[k]
    cost = beg[k] + added[k]
    per = cost / eu
    total_unit_cost += per
    assigned_end += end_units * end_pct[k] * per
    print(f"{k:<15} EU {eu:>4.0f}  cost {cost:>7,}  per EU ${per:6.2f}")
print(f"Finished chairs: {completed} at ${total_unit_cost:.2f} = ${completed * total_unit_cost:,.0f}")
print(f"Ending WIP in Finishing: ${assigned_end:,.0f}")

transferred in  EU  670  cost  72,350  per EU $107.99
materials       EU  640  cost   4,960  per EU $  7.75
conversion      EU  655  cost  15,830  per EU $ 24.17
Finished chairs: 640 at $139.90 = $89,538
Ending WIP in Finishing: $3,602

Each finished Classic chair costs about $140 by the time it reaches the warehouse in March: about $108 from Assembly and about $32 of Finishing materials and conversion. That is close to the $132 manufacturing cost per chair the company uses in its plans, which includes fixed overhead at the normal volume of 7,200 chairs a year; March's figure is slightly higher because March production of 640 finished chairs is part of a seasonal pattern and the fixed overhead charged to the month is spread over fewer chairs. Managers comparing monthly unit costs should watch for exactly this kind of volume effect, which lesson 8 explores.

Journal entries in a process costing system

Overhead in process costing is still usually applied at a predetermined rate, by department, just as in job costing, and under- or overapplied overhead is cleared at year end in the same way (lesson 5).

The FIFO method in brief

The first-in, first-out (FIFO) method separates the work done on beginning inventory from the work done on units started this period. Equivalent units count only the work done this period: the work needed to finish the beginning units, plus the work on units started and completed, plus the work on ending work in process. Costs per equivalent unit use only the costs added this period, so they measure current-period performance without the influence of last period's costs. That makes FIFO better for evaluating this month's efficiency, at the price of more calculation.

# FIFO equivalent units and cost per EU for Assembly, March (illustrative)
beg_units, beg_pct_conv = 80, 0.40
started, end_units, end_pct_conv = 600, 50, 0.60
added = {"materials": 36_000, "conversion": 30_180}

started_completed = started - end_units
eu_mat = 0 * beg_units + started_completed + end_units           # materials already in beginning WIP
eu_conv = beg_units * (1 - beg_pct_conv) + started_completed + end_units * end_pct_conv
print(f"FIFO EU: materials {eu_mat:.0f}, conversion {eu_conv:.0f}")
print(f"FIFO cost per EU: materials ${added['materials'] / eu_mat:.2f}, "
      f"conversion ${added['conversion'] / eu_conv:.2f}")

FIFO EU: materials 600, conversion 628
FIFO cost per EU: materials $60.00, conversion $48.06

Under FIFO the materials cost per equivalent unit is $60 (the hardwood price did not change), but the conversion cost per equivalent unit is about $48.06, slightly higher than the weighted-average figure of $48, because beginning inventory carried conversion costs from February at a lower rate ($1,500 ÷ 32 equivalent units ≈ $46.88), which weighted average blends into the March figure. When prices and efficiency are stable, the two methods give nearly the same results. Both are acceptable for external reporting; companies choose based on the usefulness of the information and the cost of the calculation.

Spoilage in brief

Some units are inevitably damaged or rejected: a chair leg splits, a finish blisters. Normal spoilage is the amount expected under efficient operating conditions; its cost is treated as part of the cost of the good units, because it is an unavoidable cost of producing them. Abnormal spoilage is spoilage beyond what is expected; its cost is charged to a loss account in the period, because it should not inflate the cost of good units and managers need to see it. If Cedar Ridge expects 2 per cent of chairs to fail inspection and 5 per cent fail one month, the extra 3 per cent is abnormal and is reported separately. The detailed calculations belong to ACCT-222; the principle is that the accounting should make avoidable waste visible.