Physical Quantity Method

The Physical Quantity Method allocates joint production costs to multiple products in proportion to their physical output—measured in tonnes, barrels, litres, or units—rather than their market value. It is the simplest allocation approach, though often the least economically defensible.

The straightforward logic

When crude oil is distilled into gasoline, diesel, heating oil, and bitumen, the refinery incurs a single large joint cost. One way to divide it is purely mechanical: measure how many barrels of each product emerge, and allocate the joint cost proportionally to those volumes.

If 1,000 barrels of crude yield 400 barrels of gasoline, 300 barrels of diesel, 200 barrels of heating oil, and 100 barrels of bitumen, the total is 1,000 barrels. A $500,000 joint processing cost is split as: gasoline receives $200,000 (40%), diesel receives $150,000 (30%), heating oil receives $100,000 (20%), and bitumen receives $50,000 (10%). No accounting judgment required.

The formula is simply:

Product Cost = [Joint Costs] × [Product Quantity ÷ Total Quantity]

Where quantity is measured in consistent physical units.

Why it is appealing (and why that appeal is limited)

The physical quantity method is transparent and audit-friendly. There is no estimation, no valuation, no assumptions about future prices. Anyone can verify the calculation by looking at production records. This makes it popular in regulated industries where cost allocation must be defensible and reproducible.

For commodity-like products with relatively stable price ratios—steel grades, petrol octane ratings, or flour types—the method can work adequately. But it breaks down when products have vastly different economic value. Assigning a tonne of prime beef the same per-unit cost as a tonne of offal ignores economic reality. A barrel of premium gasoline and a barrel of heavy fuel oil cost nearly the same to separate but sell for very different prices.

The method is most honest when used for products of genuinely similar value. Otherwise, it is a proxy—sometimes useful, often misleading.

Comparison with value-based methods

The relative-sales-value-method allocates by split-off market prices, recognizing that $1,000 of gasoline is more valuable than $1,000 of bitumen. The net-realizable-value-method goes further, deducting separable costs before allocation.

Physical quantity ignores both. It treats a barrel of low-margin fuel the same as a barrel of high-margin specialty product. In consequence, high-value products are systematically undercosted, and low-value products are overcosted. This distortion can lead to poor pricing and product-mix decisions.

A revealing example

A sawmill processes a log weighing 500 kg. The joint cutting and debarking cost $100. It yields:

• Dimensional lumber: 300 kg, sells for $2/kg = $600 market value
• Wood chips: 150 kg, sells for $0.10/kg = $15 market value
• Sawdust: 50 kg, sells for $0.05/kg = $2.50 market value

Physical quantity allocation:

• Lumber: $100 × (300 ÷ 500) = $60; unit cost = $0.20/kg; margin = $600 − $60 = $540
• Chips: $100 × (150 ÷ 500) = $30; unit cost = $0.20/kg; margin = $15 − $30 = −$15 (loss!)
• Sawdust: $100 × (50 ÷ 500) = $10; unit cost = $0.20/kg; margin = $2.50 − $10 = −$7.50 (loss!)

The method absurdly assigns the same per-kilogram cost to products selling at 20-fold or 40-fold differences. Wood chips and sawdust appear unprofitable even though they generate positive cash.

Relative sales value allocation (for comparison):

• Lumber: $100 × ($600 ÷ $617.50) = $97.11; margin = $600 − $97.11 = $502.89
• Chips: $100 × ($15 ÷ $617.50) = $2.43; margin = $15 − $2.43 = $12.57
• Sawdust: $100 × ($2.50 ÷ $617.50) = $0.41; margin = $2.50 − $0.41 = $2.09

Each product shows positive margin proportional to its value. The allocation makes economic sense.

When physical quantity is defensible

The method works best in two scenarios:

Homogeneous outputs: If products are essentially identical—different grades of the same material, or cuts from the same batch—physical quantity can approximate value-based allocation reasonably well.

Regulatory or administrative constraint: Some regulated utilities or non-profit entities are required by statute to use simple, objective allocation methods. Physical quantity is defensible in quasi-judicial settings precisely because it removes judgment.

Internal reporting where value ratios are stable: If a firm produces multiple varieties of the same product (say, three sizes of cans from a single production line) and prices those sizes consistently over time, physical quantity allocation can be a shortcut, provided margins don’t diverge unexpectedly.

The accounting treatment

Under Generally Accepted Accounting Principles, products allocated costs via physical quantity are carried on the balance-sheet at that allocated amount. If the allocation produces unrealistic unit costs (e.g., a negative margin product that is clearly profitable), auditors may challenge it as lacking economic substance.

The method is stable: unlike value-based methods, it is not sensitive to price fluctuations. A 10% swing in the price of gasoline does not retroactively alter the cost allocation to yesterday’s production. This can be an advantage for historical cost accounting, but it also means the allocations drift further from economic reality as prices change.

Why many firms abandon it

Most manufacturing firms that start with physical quantity migrate to value-based methods—usually relative-sales-value or net-realizable-value—as they grow more sophisticated. The reason is that physical quantity distorts profitability by product, leading to bad decisions.

A manager seeing that “sawdust loses $10 per tonne” may recommend shutting down that operation. But sawdust actually earns margin; the cost allocation is simply misleading. Value-based methods correct this bias.

Byproducts and scrap

For truly immaterial outputs—offcuts, trim, dust—many firms treat these as byproducts rather than joint products. The byproduct’s revenue is subtracted from total joint cost, rather than allocated a formal share. This sidesteps the absurdity of allocating $1 of joint cost to a byproduct worth $0.50.

Practical implementation

The method requires accurate measurement of physical quantities at split-off. In grain elevators, this is straightforward (scales are standard). In oil refineries, volume is measured in barrels. In sawmills, board feet. In chemical plants, tonnes or litres. Any uncertainty in measurement directly translates to allocation error.

Mixed units (some products weighed, others counted, others measured by volume) require a conversion standard. A ton of water is 1,000 litres; a cord of wood is roughly 4 cubic metres. These conversions introduce another point of estimation.

See also