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Allocation basis: value preserves the price order

Spread one bill over your shipment lines and read the landed unit cost on three bases. On a 6,000 bill the heavier line overtakes a dearer one under weight, while value keeps the price order.

One bill, three cost readings

Line 1 has a landed unit cost of 65.26 and line 2 has a cost of 48.83 under weight for this 6,000.00 bill, reversing their starting price order.

ValueWeightVolume
Landed unit cost under each allocation basisOne horizontal currency scale is shared by all numbered lines. Value uses a solid line, weight a dashed line and volume a dotted line. All plotted costs, rounded to cents, appear in the table below the figure. The shipment total remains 27,000.00 under every available basis.

Each numbered row shows the same item under three bases; the selected basis uses the accent marker

Horizontal
Landed cost per unit, same currency
Vertical
Line
Read every plotted cost
LineValueWeightVolume
156.5765.2651.27
259.1448.8364.18
33.864.183.91
same currency

Declared allocation basis

Edit the shipment lines
Line 1
Line 2
Line 3

The bill still reconciles

Goods value
21,000.00
Shipment total under every basis
27,000.00
Bill minus rounded allocations
0.00
Common value multiplier
1.285714

Allocations are exact fractions before display; rounding each to cents can leave this residual, which is not assigned to a line.

Where two unit costs meet

Line 1 and line 2
Exact crossing bill: 2540039\frac{25400}{39}
First whole cent above: 651.29

Only the bill varies; all line values stay fixed, and comparisons use exact fractions before rounding to cents.

Here is the maths

The proportional allocation

  1. Multiply quantity by the selected per-unit driver to get each line's driver.
  2. Divide the line driver by the shipment driver total, then multiply by the shared bill.
  3. Add the allocated amount per unit to the starting unit price.
di=qigi,D=∑jdjd_i=q_i g_i,\qquad D=\sum_j d_jdi=qigi,D=∑jdj\begin{gathered}d_i=q_i g_i, \\ D=\sum_j d_j\end{gathered}
Ai=SdiD,ci=pi+AiqiA_i=S\frac{d_i}{D},\qquad c_i=p_i+\frac{A_i}{q_i}Ai=SdiD,ci=pi+Aiqi\begin{gathered}A_i=S\frac{d_i}{D}, \\ c_i=p_i+\frac{A_i}{q_i}\end{gathered}
∑iAi=S\sum_i A_i=S

Under value, the common multiplier is positive, so every price comparison is preserved for a non-negative bill and a positive goods total.

ci=pi(1+S∑jqjpj)c_i=p_i\left(1+\frac{S}{\sum_j q_j p_j}\right)

Two unequal driver slopes meet at the bill solved below; a negative solution lies outside the bill domain and equal slopes do not cross.

S∗=(pj−pi)Dgi−gj,gi≠gjS^*=\frac{(p_j-p_i)D}{g_i-g_j},\qquad g_i\ne g_jS∗=(pj−pi)Dgi−gj,gi≠gj\begin{gathered}S^*=\frac{(p_j-p_i)D}{g_i-g_j}, \\ g_i\ne g_j\end{gathered}

With a 6,000.00 bill, the weight drivers total 2,540.0000 kg; line 1 carries 4,251.97 and reaches 65.26 per unit, while line 2 reaches 48.83. Their exact crossing is 2540039\frac{25400}{39}, between 651.28 and 651.29.

Source basis

The source is proportional cost allocation in management accounting, with typed invoice and packing-list quantities. These three bases are declared comparisons; no valuation rule or standard text is reproduced.

Scale
Exact rational arithmetic; amounts display 2 decimals and crossing bills remain exact fractions
Basis
Typed quantities and one declared proportional basis
Model version
1.0.0

The whole record prints. Your browser can save it as a PDF instead of printing it.

This divides the bill you enter; it does not choose a costing policy, compute duties or determine customs value.

Related

Cost allocation record

Declared allocation basis: Weight · Date:

All monetary figures use the same currency; the record marks numeric values changed from the opening scenario.

Line 1 has a landed unit cost of 65.26 and line 2 has a cost of 48.83 under weight for this 6,000.00 bill, reversing their starting price order.

Inputs as entered

Shared bill: 6,000.00 · same currency

LineQuantity, unitsUnit priceGross kg per unitCubic metres per unit
120044.009.00000.0120
220046.001.20000.0300
31,0003.000.50000.0015

* Changed from opening

Cost record

LineValueWeightVolumeAllocated bill
156.5765.2651.274,251.97
259.1448.8364.18566.93
33.864.183.911,181.10

Landed cost per unit, same currency · Allocated bill: Weight

Goods value
21,000.00
Shipment total under every basis
27,000.00
Bill minus rounded allocations
0.00
Common value multiplier
1.285714

Allocations are exact fractions before display; rounding each to cents can leave this residual, which is not assigned to a line.

Trace for line 1

  1. Quantity, units: 200
  2. Weight: 9.0000
  3. Line driver: 1800.0000
  4. Shipment driver total: 2540.0000
  5. Line share: 0.708661
  6. Allocated bill: 4,251.97
  7. Landed unit cost: 65.26

Where two unit costs meet

Line 1 and line 2: 25400/39 · First whole cent above: 651.29

Only the bill varies; all line values stay fixed, and comparisons use exact fractions before rounding to cents.

This divides the bill you enter; it does not choose a costing policy, compute duties or determine customs value.

Model version: 1.0.0 · badralghamdi.com/tools/allocation-basis