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Commerce · II.06 · MMXXVI · daylight

La Bourse  /  Volume II  /  Nº II.06  /  Workbook — the executive

WORKBOOK — THE CORPORATE EXECUTIVE

Chapter II.06 · Thermodynamics and Economic Flow

Applied to a P&L, a board paper, and a business unit. In the language of the firm, without apology.

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THE PREMISE, STATED COMMERCIALLY

Your energy line is measured in the wrong unit, and the error is not small.

You buy megawatt-hours and you report megawatt-hours. What your processes consume is not megawatt-hours — it is the work capacity of those megawatt-hours, and your existing reporting cannot distinguish a stream that can drive a compressor from a stream that can only warm a room. The two appear as identical lines at identical prices.

The commercial consequence is specific and it is recurring: you are almost certainly buying high-grade energy for low-grade tasks somewhere in the estate, and your reporting cannot show you where. A condensing boiler at 90 percent first-law efficiency delivers room heat at 6.20 percent second-law efficiency. A heat pump doing the identical job runs at 24.99 percent — 4.03 times better. Your energy report rates the boiler at ninety and says nothing about the other number, because the other number requires one field it does not carry: the delivered temperature.

Adding that field is a week of analyst time and no capital.

There is a second commercial fact worth having in front of a board. Across the American century, aggregate exergy-to-useful-work efficiency rose from 2.5 percent to 13.0 percent — 1.682 percent a year, compounding, for ninety-eight years. Combined with primary energy growth of 2.337 percent, useful work grew at 4.019 percent a year against real output at 3.2 percent. Whatever share of that you credit, the productivity of the estate you run has been improving on a dimension nobody in your management pack has ever reported.

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PART ONE — DISCOVERY

Days 1–30: find the mismatches inside your own numbers

Step 1.1 — Pull the meter data you already have.

Most industrial and commercial metering already logs a flow temperature and most reporting discards it. Get it back. You need, per stream: energy, delivered temperature, and hours.

Step 1.2 — Declare the dead state, in writing.

Pick your site's annual mean — 283.15 K is a defensible temperate default — and put it on the first page of the standard. This is not a technicality. Every exergy figure moves with it, and an unremarked change makes two quarters incomparable without anyone lying. Treat a change to it exactly as you would treat a change in accounting policy: disclosed, dated, restated.

Step 1.3 — Rank the estate by mismatch.

For each thermal duty, two columns: the Carnot factor of the source and the Carnot factor the task required. Sort by the gap.

  flame, 1800 °C                     0.8634
  process stack, 300 °C              0.5060
  district heat, 90 °C               0.2203
  low-grade water, 60 °C             0.1501
  room heat, 21 °C in winter         0.0714

Any row where a source at 0.5060 or above is serving a task at 0.1501 or below is a standing loss. You will find several. They are not failures of management; they are invisible in the reporting that management has.

Step 1.4 — Cost the counterfactual, not the line.

The value of fixing a mismatch is not the energy spend on that stream. It is the spend minus what the correctly matched alternative would cost, over the asset's remaining life, including the parasitic load of the alternative. Executives skip the parasitic load and auditors put it back. Put it in first.

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PART TWO — THE ARITHMETIC

Days 31–45: the two numbers that go to the board

Step 2.1 — The estate's second-law efficiency.

One number: exergy delivered to tasks, divided by exergy purchased. It will be lower than anyone expects. For context rather than comfort, Reistad's national accounting of the United States in the 1970s produced roughly twenty-one percent, against a first-law figure about twice as large.

Treat that number as a headroom statement, not an indictment. Copper production runs at a second-law efficiency of 0.63 percent — 0.2067 MJ/kg of minimum against roughly 33.0 MJ/kg spent — and nobody thinks the copper industry is badly run. A low second-law figure is where the next decade of capital productivity lives.

Step 2.2 — The one inequality.

Same shape as the shared-savings test in Chapter I.01:

     net annual saving from the intervention
   -------------------------------------------  >  WACC
     facility + verification + admin

The chapter's worked cascade returns 22.70 percent against a WACC of 8.00 — a margin of 14.70 points. That is not an environmental proposal. It is the cheapest capital available to the firm, and it should be presented in exactly those words.

Step 2.3 — Apply the threshold before you build the report.

An exergy account earns its keep only where the exergy bill can move a decision:

  energy at 30.0 % of cost  →  a 20 % exergy saving moves total cost  6.00 %
  energy at 10.0 % of cost  →                                         2.00 %
  energy at  2.0 % of cost  →                                         0.40 %
  energy at  0.5 % of cost  →                                         0.10 %

Below roughly two percent of cost, this is bookkeeping. Run it for the industrial core of the business and not for the head office, and say so in the paper. Naming the boundary yourself is what stops the first sceptic naming it for you, and it is the difference between a proposal and an advocacy document.

Step 2.4 — The dispersal review, for the product side.

Take the three highest-value materials in your bill of materials and ask where their atoms are at end of life: lump, alloy, coating, solution, plume. The arithmetic is unforgiving. Recovering a metal that has dispersed requires mass throughput rising as 1/x while the thermodynamic minimum rises only as ln(1/x) — a seventy-million-fold dilution raises the minimum by 4.41 times and the mass handled by 20,000,000. Aluminium from clean scrap costs 0.70 kWh/kg against 14.00 from ore: a 95.0 percent saving, earned at design time by not dispersing.

This is a product-design decision with a recovery cost attached, taken years before anyone sees the cost. Put it on the design review checklist. It costs one line.

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PART THREE — DESIGN

Days 46–60: the instrument

The instrument is a waste-heat offtake agreement on an exergy-indexed tariff, financed as a self-liquidating facility against the savings stream.

The worked case.

  stack heat at 300 °C                       12.0  MW-th
  recovered and delivered at 90 °C            9.0  MW-th
  exergy in the stack, 12.0 × 0.5060         6.072 MW
  exergy delivered,     9.0 × 0.2203         1.983 MW
  cascade exergy efficiency                   32.7 %
  first-law recovery rate                     75.0 %

Note both numbers and know which one you are buying against. 75.0 percent is the vendor's figure and it is honest; it answers the first-law question. 32.7 percent is what you captured of the work capacity.

The economics.

  heat sold, 9.00 MW × 4,500 h            40,500  MWh-th/yr
  avoided-boiler value, 35.00 / 0.92       38.04  EUR/MWh-th
  revenue                               1,540,761 EUR/yr
  parasitic pumping, 1,575 MWh × 95.00    149,625 EUR/yr
  operations and maintenance              120,000 EUR/yr
  ----------------------------------------------------------
  net                                   1,271,136 EUR/yr
  capital cost                          5,600,000 EUR
  simple payback                             4.41 years
  return on facility                        22.70 %  vs WACC 8.00 %

The clause that makes it signable. Every heat offtake eventually argues about grade: the buyer contracted for ninety degrees and the stream drifts to sixty. Index the price to the temperature:

        price(T)  =  base × f(T) / f(90 °C)
        at 60 °C:  38.04 × 0.6813  =  25.92 EUR/MWh-th

Unindexed, at a flat 38.04, the sixty-degree buyer pays 253.48 EUR per megawatt-hour of exergy against 172.69 at ninety — an overcharge of 46.8 percent. Indexed, the dispute becomes a thermometer reading that both parties can compute and neither can argue with.

Balance-sheet treatment. Capitalise the recovery plant and depreciate over the offtake term rather than the host process's remaining life; raise the useful-life question with your auditors early, because it is a conversation they have every year. Where the counterparty owns the network and you own the recovery, expect the capacity right to be a right-of-use asset under IFRS 16 and the offtake to be assessed as lease-like. Get that determination before the term sheet, because it moves EBITDA and a surprise at signing kills deals that the arithmetic supported.

Term, floor, security, break. Term just past payback — a 4.41 year payback takes a seven-year term. Take-or-pay floor at roughly sixty percent of nameplate. Security is the savings stream and nothing else: if the heat does not flow there is nothing to pay, and the document should say so in one sentence. Break clause priced at remaining undepreciated capital, because a cascade is an interdependence and interdependence resists change.

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PART FOUR — DESTINY AND DELIGHT

Days 61–90: make it hold

It goes in the standing pack or it does not survive. Two lines, monthly: exergy delivered and exergy destroyed. Anything reviewed monthly persists; anything reviewed by exception evaporates. This is worth more than any presentation you will give about it.

It belongs to finance, not to sustainability. The same number produced by the controller is a number and produced by a sustainability function is a claim. This is not a comment on anybody's rigour; it is a comment on how the organisation reads a page.

The counterparty is your best guarantor. Once a district network or a neighbouring plant depends on your tail, an external party notices within a week if the stream degrades. That is a more durable control than any internal metric.

The failure modes, named so you can see them coming.

Exergy fetishism. Optimising the scalar rather than the service. It is possible to build a thermodynamically magnificent plant that makes a product nobody wants. Exergy is a constraint and an efficiency measure; it is never the objective function.

Dead-state drift. If the account ever touches compensation, the reference environment becomes negotiable. Fix it, audit it annually.

Rebound. Cheaper service raises demand for it — direct rebound in heating runs in the low tens of percent in the empirical literature. Bounded, real, and to be allowed for in the claimed saving. A saving projected without a rebound allowance will be disputed the first time somebody reads the meter.

The horizon. A 4.41 year payback is longer than many tenures. Size the first one so the verified result lands inside a budget cycle, then use the result to buy the larger programme.

And the delight, which is commercially useful. Every cascade has a walk — a path where the flow is visible, a plume on one side and something warm and alive on the other. Take customers on it. It explains the firm's competence faster than a deck does, and it is true.

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WHERE YOUR OWN NUMBERS ALREADY SUPPORT THIS

Four places in the accounts where the case is already made and nobody has assembled it.

One — the maintenance line on your boiler plant. Any thermal asset being maintained past its depreciation schedule is being kept alive by somebody who believes replacement is worse. Ask them why. That conversation usually produces the mismatch ranking faster than the meter data does.

Two — the parasitic load you already pay. Pumping, fans and compressed air are frequently the largest recoverable exergy losses on a site and they sit inside overhead rather than inside the energy line. The worked cascade's own parasitic load is 1,575 MWh a year costing 149,625 EUR — visible only because somebody put it in the model deliberately.

Three — the counterfactual on the last boiler you bought. If the estate recently replaced boilers, compute what the same capital would have bought as heat pumps at the same service level. The comparison is uncomfortable and it is the single most persuasive page you will produce, because the alternative is not hypothetical — it was available, priced, and declined.

Four — the material recovery your product team already does. Any component you already take back is a cascade you already operate. It has a cost per kilogram and a recovery rate. Put it beside the 95.0 percent saving that clean aluminium scrap achieves against smelting, and the design-review line writes itself.

The sensitivity that a board will ask for. Run the worked cascade at three gas prices and say so before being asked. Revenue is directly proportional to the avoided-boiler value of 38.04 EUR/MWh-thermal; at two thirds of that price the return falls proportionately and the payback lengthens. State the gas price at which the project stops clearing the WACC of 8.00 percent, and put it in the paper. A proposal that names its own break-even assumption is a proposal that survives its second meeting.

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THE NINETY DAYS ON ONE PAGE

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BOARD PAPER TEMPLATE

One page. In this order.

1. The finding. We buy energy in megawatt-hours and consume work capacity. On the estate's largest thermal duty we are spending a source of grade 0.5060 on a task requiring 0.1501.
2. The number that decides it. Net annual saving over facility cost, against WACC. In the worked case, 22.70 percent against 8.00.
3. The instrument. Offtake agreement, exergy-indexed tariff, self-liquidating facility, security limited to the savings stream.
4. The treatment. Capitalisation and depreciation basis; IFRS 16 determination; the auditor's position, obtained in advance.
5. The honest negative. The threshold — this discriminates in the industrial core and not in the service functions; the rebound allowance; the tenure mismatch against a 4.41 year payback.
6. The ask. One signature, one facility, one stream.

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APPRECIATIVE QUESTIONS FOR YOUR LEADERSHIP TEAM

1. Where in this business is grade already matched to task well — and who made that decision, and were they ever thanked for it?
2. Which of our engineers has been saying something like this for years without the vocabulary to make it a capital paper?
3. If exergy destroyed appeared in the monthly pack, what would change in the first two quarters?
4. Who outside this company would pay for what currently leaves our stacks, and have we ever asked them?
5. What would we design differently if the recovery cost of every material were visible at the moment of specification?
6. What is the largest number in this business that nobody has computed, and what would it cost to compute it this quarter?