8.4 Break-Even Analysis, Technical Capability Assessment & Costing Systems (Traditional, ABC & Standard Costs)

8.4 Break-Even Analysis, Technical Capability Assessment & Costing Systems

The specification lists break-even analysis, technical capability assessment, and ROR under engineering economics, and costing systems (activity-based costing, cost drivers, and guidelines for overhead, labor, and materials) as a separate topic. Rate of return is covered earlier in this chapter; this section covers the rest.

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1. Break-Even Analysis

With selling price $p$, variable cost $v$ per unit, and fixed cost $F$ per period:

$\text{Profit} = (p - v)Q - F, \qquad Q_{BE} = \frac{F}{p - v}$

• Unit contribution margin: $p - v$. Contribution margin ratio: $(p - v)/p$.
• Break-even revenue: $F / \text{CM ratio}$.
• Volume for a target profit $\Pi$: $Q = (F + \Pi)/(p - v)$.
• Margin of safety: $(\text{actual or planned sales} - \text{break-even sales}) / \text{actual or planned sales}$.
• Degree of operating leverage (DOL): total contribution margin ÷ operating profit. A 10% change in volume changes profit by about $\text{DOL} \times 10\%$.

Worked example: A part sells for $50, variable cost is $30, and annual fixed cost is $240,000.

• $Q_{BE} = 240{,}000 / 20 = 12{,}000$ units, or $600,000 of revenue.
• For a $60,000 profit: $Q = 300{,}000 / 20 = 15{,}000$ units.
• At planned sales of 16,000 units, the margin of safety is $(16{,}000 - 12{,}000)/16{,}000 = 25\%$.
• At 16,000 units, profit $= 320{,}000 - 240{,}000 = \text{\textdollar}80{,}000$, so $\text{DOL} = 320{,}000 / 80{,}000 = 4.0$. A 10% sales increase would raise profit by about 40%.

Make-or-Buy and Equipment Choice

The same idea gives the indifference volume between two options. Buying a part at $18 has no fixed cost. Making it costs $10 per unit plus $96,000 per year in tooling and overhead. The indifference volume is $96{,}000 / (18 - 10) = 12{,}000$ units. Above 12,000 units per year, making is cheaper, provided capacity, quality, and strategic factors also favor it.

Multiple products: use a weighted-average contribution margin based on the sales mix: $Q_{BE,\text{total}} = F / \sum (\text{mix share}_j \times CM_j)$.

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2. Technical Capability Assessment

Before comparing costs, confirm that each alternative can actually do the job. An option that fails a technical requirement is not cheap; it is infeasible.

A practical sequence:

1. Screen out options that fail any must-have requirement.
2. Score the remaining options on weighted wants if needed.
3. Compare the survivors economically with present worth, annual worth, or incremental ROR.

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3. Costing Systems

Elements of Product Cost

• Direct materials: materials traced to the product.
• Direct labor: labor traced to the product.
• Manufacturing overhead: everything else in the plant, such as indirect labor, supervision, utilities, depreciation, maintenance, and quality. Overhead cannot be traced directly, so it must be allocated.

Job order costing accumulates cost by job (custom work, job shops). Process costing accumulates cost by process step and spreads it over units (continuous and repetitive production).

Traditional Overhead Allocation

A predetermined overhead rate is set at the start of the period:

$\text{Overhead rate} = \frac{\text{Budgeted overhead}}{\text{Budgeted allocation base (direct labor hours, machine hours, or labor cost)}}$

A single plantwide rate based on labor hours was reasonable when labor was the main cost. In automated plants, overhead is driven by setups, engineering changes, and inspections rather than labor hours.

Activity-Based Costing (ABC)

1. Identify the main activities that consume overhead.
2. Collect overhead into activity cost pools.
3. Choose a cost driver for each pool, the measure that causes the cost (number of setups, inspections, purchase orders, or machine hours).
4. Compute an activity rate = pool cost ÷ total driver quantity.
5. Assign overhead to products by their driver usage.

Worked example: Plant overhead is $600,000.

Traditional: rate = $600,000 ÷ 10,000 DLH = $60 per DLH. S gets $480,000 ($48.00 per unit) and K gets $120,000 ($60.00 per unit).

ABC:

• S: $100(500) + 500(100) + 7{,}000(25) = 50{,}000 + 50{,}000 + 175{,}000 = \text{\textdollar}275{,}000$, or $27.50 per unit.
• K: $300(500) + 1{,}000(100) + 3{,}000(25) = 150{,}000 + 100{,}000 + 75{,}000 = \text{\textdollar}325{,}000$, or $162.50 per unit.

The labor-hour rate overcosted the high-volume standard product by $20.50 per unit and undercosted the custom product by $102.50 per unit. Pricing on traditional costs would chase away profitable standard business and underprice custom work.

Standard Costs and Variances

Standard costing sets expected prices and quantities, then explains differences:

Here $A$ means actual, $S$ means standard, $SQ$ and $SH$ are the standard quantity and hours allowed for the actual output, and a positive result is unfavorable.

Example: The standard for 1,000 units is 2 kg per unit at $5.00/kg and 0.5 labor hour per unit at $30/hr. Actual use was 2,100 kg bought at $5.20/kg and 520 hours paid at $29/hr.

• Material price: $(5.20 - 5.00)(2{,}100) = \text{\textdollar}420$ unfavorable.
• Material quantity: $(2{,}100 - 2{,}000)(5.00) = \text{\textdollar}500$ unfavorable.
• Labor rate: $(29 - 30)(520) = -\text{\textdollar}520$, which is favorable.
• Labor efficiency: $(520 - 500)(30) = \text{\textdollar}600$ unfavorable.

The efficiency and usage variances point the industrial engineer at the shop floor. The price and rate variances usually belong to purchasing and human resources.