Summary of Findings

Price per tonne of paste is the figure on the quotation and the wrong basis for a decision. It captures one of five cost elements and omits the four that vary most between suppliers: how much paste the furnace consumes, how much of the consignment survives handling, what breakage costs in lost production, and what a quality excursion costs in downgraded product.

The figure that supports a decision is cost per tonne of alloy produced. Converting to it requires no financial modelling — it requires the consumption rate the furnace actually runs at, the handling loss actually incurred, and the downtime actually attributable. All three are measurable at the plant, and none of them transfers from a supplier’s literature: reported average consumption values should not be accepted as absolute where furnace load fluctuates (Wilkinson et al., Infacon IX). This article sets out the structure of the calculation. It contains no worked figures, because the inputs are plant-specific by construction.

Key Findings

• Four of five elements are invisible on the quotation. Consumption rate, handling loss, downtime and quality risk are all plant-side, and all can differ more between two supplies than the unit price does.
• The conversion factor is the consumption rate, expressed as tonnes of paste per tonne of alloy. Every other element is either added to the numerator or handled as an allocation.
• Landed price, not ex-works price. Freight, duty, insurance and inland transport belong in the numerator; a comparison between an ex-works and a delivered quotation is not a comparison.
• Handling loss reduces the tonnage that reaches the furnace, so it acts on the denominator of the delivered-paste figure and is the element most often omitted entirely.
• Supplier-quoted consumption figures are not inputs. They belong to another furnace under another load pattern, and the source most often cited for such comparisons carries its authors’ own warning against treating averages as absolute.

Contents

1. Why is price per tonne of paste the wrong basis?
2. What are the five elements?
3. How does the calculation assemble?
4. Which inputs must come from the plant?
5. What are the common errors?
6. How is quality risk handled without overstating it?
7. Frequently asked questions
8. Related reading

1. Why Is Price per Tonne of Paste the Wrong Basis?

Because it prices the material rather than its use. Two supplies at the same price per tonne can deliver different quantities of usable paste to the furnace, consume at different rates once there, and impose different amounts of unplanned downtime. A ranking on unit price is therefore a ranking on one term of a sum whose other terms have not been evaluated.

The error is not that unit price is unimportant. It is that unit price is the only element visible at the moment of decision, and the elements that are invisible are the ones that vary with the furnace rather than with the market. A purchasing process that compares what is visible will select consistently, and consistently on the wrong basis.

The correction is a unit change: from cost per tonne of paste to cost per tonne of alloy produced. That is the figure the plant is measured on, and it is the only basis on which two supplies can be compared against each other and against the alternative of changing nothing.

2. What Are the Five Elements?

Element	Where it acts	Where the number comes from
Landed price	Numerator, per tonne of paste delivered	Quotation plus freight, duty, insurance and inland transport
Handling and charging loss	Reduces the tonnage that reaches the furnace	Inventory-reconciled material balance, checked against measured waste
Consumption rate	Converts paste to alloy	Plant records over a defined period, in tonnes of paste per tonne of alloy
Downtime attributable to breakage	Allocated over production in the period	Event log, with the production lost per event
Quality risk	Allocated, or handled as a constraint	The plant’s own product downgrade or rework cost, applied to the frequency the plant has actually experienced

Table 1. Only the first element appears on a quotation. The other four are measured at the plant and are what differentiate two supplies in practice.

The first four are arithmetic once the inputs exist. The fifth is treated separately in Section 6, because it is the one most easily overstated and the one where an unsupported number does the most damage to a supplier discussion.

3. How Does the Calculation Assemble?

Written symbolically, with all quantities taken over the same defined period:

Landed cost of paste actually charged, per tonne charged: C_charged = C_landed / (1 − L_handling) where C_landed is the delivered cost per tonne received and L_handling is the unrecovered handling and charging loss divided by paste charged plus that loss, on the same inventory-reconciled mass basis. Paste cost per tonne of alloy: C_paste/alloy = C_charged × R where R is tonnes of paste actually charged per tonne of alloy over a representative period with stable electrode-column inventory. If column inventory changes materially, reconcile that change before comparing periods. Do not use a receipts-based rate that already includes handling loss in this equation. Total electrode-related cost per tonne of alloy: C_total = C_paste/alloy + (D + Q) / T where D is the cost of production lost to breakage-attributable downtime in the period, Q is the quality-related cost in the period, and T is the tonnes of alloy produced in the period.

Three properties of this structure are worth stating explicitly.

Handling loss acts as a divisor, not a subtraction. Material lost before the furnace was paid for but not used, so its cost is carried by the tonnage that was used. A separate loss-cost allocation is equivalent if calculated consistently; use one method, not both.

The consumption rate is a major lever, because it multiplies the whole of the material cost. With the other inputs fixed, both R and landed price act proportionally on the material-cost term, not on the separate downtime and quality allocations.

Downtime and quality are allocations, not rates. They are period costs divided by period production, which means the period has to be long enough to contain a representative number of events. A period containing no breakage event does not establish that D is zero.

4. Which Inputs Must Come From the Plant?

All of them except the quotation, and this is the part that makes the calculation credible rather than decorative.

• L_handling — use opening usable stock + receipts + transfers in − closing usable stock − returns/transfers out − paste charged, all on the same net-mass basis. Reconcile the residual against measured discarded fines, spills and weighing uncertainty; uncharged usable inventory is not a handling loss. Divide verified loss by paste charged plus verified loss. A closed consignment balance is suitable only after its remaining stock and returns are reconciled.
• R — the consumption rate over a defined period, with average load, product grade, campaign length and the number of breakage events recorded alongside it. The method for establishing it, and the reason a figure without those four is not comparable to any other figure, are set out in the consumption breakdown article.
• D — production lost to breakage-attributable downtime, from the event log. Attribution matters here: the breakage diagnostic guide sets out how an event is assigned between paste specification and operating practice, and only the portion attributable to the material belongs in a supplier comparison.
• Q — the plant’s own downgrade or rework cost, applied to the frequency the plant has experienced. Section 6 covers how to keep this honest.

Supplier-quoted consumption figures are not substitutes for R. They belong to other furnaces under other load patterns. The published comparison most often cited in this context reports two paste types at 3.61 and 4.11 kg/MWh on the same furnaces, and its authors state directly that average consumption values cannot be accepted as absolute given furnace load fluctuation (Wilkinson et al., Infacon IX). If an average cannot be taken as absolute for the furnace that produced it, it cannot be taken as an input for a different furnace.

5. What Are the Common Errors?

Comparing ex-works with delivered. The most frequent and the easiest to fix. Convert both to landed cost at the plant gate before anything else.

Omitting handling loss. Because it occurs before the furnace and is not measured routinely, it is often assumed to be zero. It is a divisor in the calculation, so assuming it away biases every comparison in the same direction.

Using a supplier’s consumption figure. Covered above. Where no plant figure exists, the honest position is that the comparison cannot yet be made on consumption, and the calculation should be run on the elements that are known while the consumption baseline is established.

Allocating all downtime to the paste. A breakage event has to be attributed before its cost enters a supplier comparison. Events attributable to operating cadence or to a load change belong in the plant’s own improvement case, not in a supplier’s column.

Running the comparison over too short a period. D and Q are allocations over production, and a period that contains no event produces a comparison that will not survive the first event after the decision.

Treating the result as a precise number. The output is a comparison, not a valuation. It is reliable for ranking two supplies measured the same way, and unreliable as an absolute figure to be quoted elsewhere.

6. How Is Quality Risk Handled Without Overstating It?

Quality risk is the element where an unsupported number does the most damage, in both directions. Overstated, it becomes an argument that cannot be defended in a supplier discussion and undermines the elements that can. Omitted, it removes the one cost that is large and discrete rather than small and continuous.

Three rules keep it defensible:

1. Use the plant’s own cost, not an estimated one. The cost of a downgraded heat or a rework is known to the plant’s own accounting. It does not need to be estimated.
2. Use the frequency the plant has experienced, not an assumed one. Where the plant has had no such event, the honest entry is that the frequency is not established, not a nominal figure. An unestablished frequency can be handled as a constraint — a minimum specification requirement — rather than as a cost.
3. Separate the risk that the specification addresses from the risk that operation addresses. Contamination of a heat by paste extruded during soft breakage is one path; ash elements reporting to the product is another and entirely different one. The first is largely an operating and specification interaction; the second is an ash specification question, treated in the ash article.

Where a quality risk is being used to justify a higher specification, the constraint form is usually more persuasive and always more defensible: the specification is required because the product specification requires it, not because a probability has been assiganed to a failure.

7. Frequently Asked Questions

Q1. We do not have a consumption baseline yet. Can the comparison still be made? Partly. Landed price and handling loss can be compared immediately, and both are measurable within one consignment. Consumption cannot, and the honest position is to say so rather than to substitute a supplier’s figure. Establish the baseline using the procedure in the consumption article — it requires an inventory-reconciled material balance, output and operating context over a representative period — and treat the interim comparison as provisional.

Q2. A supplier offers a lower price but a higher stated consumption. How is that traded off? Not on the stated figures. A supplier’s consumption figure belongs to another furnace, and the trade-off can only be evaluated on your own R measured for both supplies, which means a controlled trial. Where the price difference is large enough to justify the trial cost, run the trial; where it is not, the comparison stands on landed price and handling loss alone.

Q3. Should freight be included when suppliers ship from different ports? Yes, along with duty, insurance and inland transport to the plant gate. Different origins produce different freight, lead time and packing requirements, and comparing ex-works prices across origins ranks on a term that does not include the difference.

Q4. How long should the measurement period be? Long enough to contain the normal range of load and product and a representative number of breakage events. A period with no events cannot establish the downtime allocation, and a period shorter than one typical campaign will attribute normal variation to the supply.

Q5. Our finance team wants a single number. What should be reported? Report the cost per tonne of alloy with the period, the average load, the product grade and the number of breakage events stated alongside it — the same four conditions that make a consumption figure comparable. A single number without them will be compared with a future number produced under different conditions, and the comparison will mislead.

8. Related Reading

• Where the Paste Goes: Building a Consumption Breakdown for Your Own Furnace (companion article) — how R is established and why it is not transferable
• How to Compare Electrode Paste Supplier Offers Without Relying on One Test Value — the parameter side of the same decision
• Söderberg Electrode Hard Breakage vs. Soft Breakage — how downtime is attributed before it enters a supplier comparison
• Paste Block Shape and Size: How Geometry Affects Feeding and Sintering — the handling loss term
• Ash Content in Electrode Paste — the quality-risk path that a specification addresses
• What a Complete Technical Enquiry for Electrode Paste Should Contain — getting quotations that are comparable in the first place
• How to Plan a Controlled Electrode Paste Trial When Changing Suppliers — the trial referenced in Q2

Author and Review

This article was written by Sterling Yang, Senior Vice President at Jiyang Carbon. The consumption and quality-risk elements in Sections 4 and 6 were reviewed by Mr. Yang, Technical Director.

All expressions in this article are given symbolically, and no worked figures appear, because every input except the quotation is plant-specific and must be measured rather than assumed. The published consumption comparison cited in Section 4 is reproduced with its authors’ own caution against treating average consumption values as absolute. Jiyang Carbon exports to more than twenty countries, packs export consignments in one-tonne bulk bags, and issues a Certificate of Analysis traceable to the batch with every consignment.

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