Introduction / Context:
Distributing indirect (overhead) costs to products or activities often uses a chosen base—commonly direct labour cost—through an overhead ratio (or rate). Knowing the correct relationship is essential for accurate unit costing, pricing, and bid preparation in construction and manufacturing settings.
Given Data / Assumptions:
- Overhead ratio is defined relative to direct labour cost (e.g., Overhead ratio = Total overhead / Total direct labour cost).
- Direct labour cost per unit is known from the estimate or job-costing records.
- We want the overhead component per unit produced or installed.
Concept / Approach:
When the allocation base is direct labour cost, overhead is applied proportionally. If OHR = Overhead / Direct labour, then overhead assigned to a unit with direct labour cost DL_u equals OHR * DL_u. Choosing a different base (e.g., machine hours, direct materials) would change the formula, but within this context the correct relationship uses direct labour cost per unit.
Step-by-Step Solution:
Define Overhead ratio: OHR = Overhead_total / Direct_labour_total.For a unit with direct labour cost DL_u, overhead_u = OHR * DL_u.Unit cost then becomes: Unit cost = Direct materials_u + DL_u + overhead_u (plus any equipment or subcontract items).
Verification / Alternative check:
Cross-check by summing across all units: Σoverhead_u = OHR * ΣDL_u = Overhead_total, confirming consistency of the allocation.
Why Other Options Are Wrong:
Prime cost base (materials + labour) would require an overhead ratio defined on prime cost, not labour only.Dividing by direct labour cost is dimensionally and conceptually incorrect.Using only materials as the base conflicts with the given labour-based overhead ratio.
Common Pitfalls:
Mixing bases (labour vs. materials) across jobs, causing distortions; failing to update OHR as productivity and burden rates change.
Final Answer:
Overhead cost per unit = Overhead ratio * Direct labour cost per unit
Discussion & Comments