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WORKBOOK — THE CORPORATE EXECUTIVE

Chapter V.02 · Work as Metabolism

For the person with a P&L, a headcount line, an overtime line and an insurance renewal. This workbook does not ask you to believe anything about the four-day week. It asks you to find out what your own working-time arithmetic already says, because in most firms nobody has ever computed it.

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THE PREMISE, STATED COMMERCIALLY

Your firm buys hours and sells output. It knows the price of the hours to the penny, because payroll is exact. It knows the output, because revenue is exact. It almost certainly does not know the relationship between them, because nobody has ever put the two series on the same page.

That is not negligence. It is that the relationship lives in an identity nobody writes down:

        Y/N   =   (Y/H)   x   (H/N)

  output per worker  =  output per hour  x  hours per worker

Three consequences follow immediately, and all three are commercial.

One. Every claim you have ever heard that "productivity rose" is a claim about one of those terms, and almost always the middle one. Output per hour rises mechanically whenever hours are cut anywhere the elasticity is below one. A firm that cut hours by a fifth and reported output per hour up 25.0 percent has reported total output exactly flat, and has been congratulated for it.

Two. You are paid on output per worker, not output per hour, because your fixed costs attach to people. Any proposal that improves the middle term while degrading the left-hand one is a proposal to lose money elegantly.

Three. The commercially interesting question is not "should we work less." It is: where on the curve are we, and what is the marginal hour actually producing? In a firm with structural overtime, the answer is frequently that the marginal hour is producing less than it costs — which is an arbitrage on your own payroll, and is the instrument this chapter builds.

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PART ONE — DISCOVERY

Days 1–30: find what your own numbers already say

Exercise 1.1 — Build the output-per-worker series (2 days of analyst time)

Twelve months, at your natural reporting frequency, from administrative data only. Not survey, not manager estimate, not self-report. Whatever you already count and cannot fudge: units despatched, claims closed, tonnes moved, cases resolved, invoices raised, revenue booked to the unit.

You need three things from it: the mean, the standard deviation, and the denominator — what it does not cover. Write the denominator down. A productivity series with unstated coverage is worse than no series.

Exercise 1.2 — Build the hours series beside it (2 days)

Actual hours worked, not contracted hours. Overtime separated out. Unpaid overtime estimated and clearly labelled as an estimate — if you do not label it, someone will quote your estimate back to you as a measurement within a year.

Exercise 1.3 — Publish the identity page (half a day, then monthly)

One page. Three lines: output per hour, hours per worker, output per worker. Same query, published together or not at all.

Then make the standing rule: every proposal touching working time must name which of the three lines it claims to move. This single page costs a monthly report and will end arguments that have been running for years, because most of them are two people each holding one term of an identity.

Exercise 1.4 — Find where you already do this well (1 day)

Somewhere in your organisation, a working-time arrangement is already working and nobody has costed it. Look in five places:

1. The shift pattern one site adopted locally and never rolled back.
2. The team whose overtime is anomalously low with no output penalty.
3. The department with unusually low turnover — and what its hours look like.
4. The handover overlap somebody protected against a cost-saving.
5. The rule a supervisor enforces that is not written anywhere.

Cost the best one properly, including the counterfactual. You are looking for evidence generated by your own firm, because that is the only evidence your board cannot wave away as somebody else's industry.

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PART TWO — THE ARITHMETIC

Days 31–45: cost the marginal hour

Exercise 2.1 — The overtime arbitrage (1 day)

Run the chapter's worked plant against your own numbers. The structure:

  overtime hours    = heads x OT hours/week x weeks
  overtime cost     = overtime hours x wage x 1.50
  straight-time     = overtime hours x wage
  the premium       = the difference
  heads to absorb   = overtime hours / productive hours per head
  loaded cost       = overtime hours x wage x on-cost multiplier
  wage line saving  = overtime cost - loaded cost

The chapter's plant: 200 workers, $28.00 an hour, 5.0 overtime hours each a week over 48 weeks.

  overtime hours    200 x 5 x 48             =     48,000 h/yr
  overtime cost     48,000 x 28 x 1.5        =  2,016,000 $/yr
  straight-time equivalent                   =  1,344,000 $/yr
  the premium you are paying                 =    672,000 $/yr
  heads to absorb   48,000 / 1,850 = 25.9    ->        26
  loaded cost       48,000 x 28 x 1.32       =  1,774,080 $/yr
  wage line saving                           =    241,920 $/yr

Exercise 2.2 — Add the two savings nobody attributes to hours (half a day)

  injury saving     12 x 42,000 x 0.20       =    100,800 $/yr
  turnover saving   36 x 9,500 x 0.15        =     51,300 $/yr
  ---------------------------------------------------------
  VERIFIED ANNUAL SAVING                     =    394,020 $/yr

Both rates are deliberately conservative, and say so in the paper before anyone else does. The injury reduction is set at 0.20 against a published overtime injury hazard ratio of 1.61. The turnover reduction is set at 0.15 when the UK four-day-week pilot reported 57 percent — because a self-reported figure from a self-selected pilot is not an input to a facility. It is a hypothesis about one.

Exercise 2.3 — Compute the number that decides it (1 hour)

This is the only figure that belongs on the front page.

  plant contribution      200 x 48,000       =  9,600,000 $/yr
  break-even fall in output per worker
                          394,020 / 9,600,000  =      4.10 %

The entire instrument is one bet: that output per worker falls by less than 4.10 percent when the overtime comes out. At a 2.00 percent fall it nets $202,020; at 3.00 percent, $106,020; at 5.00 percent it loses $85,980. Everything else in the board paper is bookkeeping.

Exercise 2.4 — State the honest negative, in the paper, first (1 hour)

Do not let the risk committee find this. Put it in yourself.

The best-identified productivity-of-hours curve we have — Pencavel's estimate on the 1915–1918 munitions records — says that below about 49 hours a week, output is proportional to hours. A move from 45 hours to 40 is entirely inside that region, and the naive reading says output per worker falls by the full proportion, which would put the facility badly under water.

The reasons to think otherwise are specific and should be named as such: the overtime hours are the fatigued hours rather than average ones; the injury and replacement savings are real and are not in the curve; and the curve was estimated on repetitive manual work a century ago. Those are reasons to measure, not reasons to assume. Which is why the facility carries a failure condition, and why you will write it before you draw on it.

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PART THREE — DESIGN

Days 46–60: the instrument and the roster

Exercise 3.1 — Structure the working-time facility (2 days)

The chapter's plant sizes at (247,000 + 60,000 + 104,000) × 1.15 = $472,650, with $25,000 of verification and $15,000 a year of admin. The decision inequality:

       394,020
  --------------------------  =  76.9 %    vs WACC 9 %
   472,650 + 25,000 + 15,000

Say the obvious thing before the treasurer does: the ratio is large because the facility is one-off and the saving recurs. The recurring cost of the twenty-six new heads is already netted inside the $241,920.

Exercise 3.2 — The balance-sheet and provisions conversation (half a day, with your auditors)

Three things to raise early, in this order.

1. The rostering and fatigue-risk system is a capitalised intangible over its useful life. Straightforward; raise it anyway so it is not a surprise.
2. Recruitment and fit-out are period costs in most regimes. Do not argue about it — the facility is what spreads them, not the accounting treatment.
3. The provision. This is the one worth the meeting. Where the firm carries a self-insured retention on employer liability, a documented fatigue-risk control is directly relevant to the actuarial estimate sitting behind that provision. That is a conversation about the estimation of a liability, which your auditors have every year, and it is where the largest single number in this workbook may turn out to live.

Exercise 3.3 — Put a fatigue model on the roster (1 week)

Adopt the shift-length and successive-night curves as an internal prescriptive limit:

The exception is signed by someone accountable for the injury statistics, not by someone accountable for the output statistics. This is the aviation move brought indoors, and it works because it takes the limit out of the negotiation. No supervisor has to be the one who declines the extra hours, so no supervisor is competing against the one who does not.

Exercise 3.4 — Size the pilot against your own noise (half a day)

The effect must exceed roughly three times the period-to-period standard deviation of your output series. Compute that from Exercise 1.1 before choosing anything. In most firms it means the pilot runs a year rather than a quarter.

And know what the field's own evidence implies about size. To detect a 5 percent difference in output per worker with a within-site standard deviation of 0.15, at 80 percent power, needs 2 × (1.960 + 0.842)² × 0.15² / 0.05² = 141.3 sites per arm — 142 per arm, 284 in total. The largest published pilot ran 61 organisations with no control arm, which is why it did not settle anything and why your own pilot will not either. Your pilot is not an experiment. It is a commercial decision under uncertainty, and it should be presented that way.

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PART FOUR — DESTINY AND DELIGHT

Days 61–90: make it hold

Exercise 4.1 — Get the three lines into the standing pack (1 day)

Anything reviewed monthly persists; anything reviewed by exception does not. Both productivity lines and hours per worker, computed by the same query, published together. Removing one then requires an explanation, and that is a conversation nobody volunteers for.

Exercise 4.2 — Put it in the insurance renewal (1 day)

Where your employer liability or workers' compensation premium is experience-rated, a documented fatigue-managed roster shows up within two renewal cycles. Brief your broker before the renewal rather than after. This is the only force in the chapter that reviews itself annually without anyone advocating for it, and it is therefore the one most likely to still be working in five years.

The failure mode, named: where the premium is not experience-rated, or where the hours are worked by contractors whose injuries land on somebody else's return, this force is absent and the economics reverse. Check which world you are in before you build the case on it.

Exercise 4.3 — Measure intensity, or do not claim the result (ongoing)

The failure mode that has killed more shorter-hours schemes than any other: hours fall, output holds, and the same work has simply been compressed with the breaks removed. Output per hour genuinely rose. Recovery genuinely fell. The health and injury consequences arrive two to five years later, outside your evaluation window, on somebody else's budget.

So measure pace, break-taking, and hours worked outside the counted ones. A working-time change that does not measure intensity alongside output is capable of producing exactly the reported result while doing the opposite of what it claims.

Exercise 4.4 — Do not over-claim, ever (ongoing)

You will be tempted to present this as a productivity story, because productivity stories travel. Do not. The evidence will not carry it, and the first well-informed person in the room will say so and take the rest of the paper with it.

Present it as what it is: an arbitrage on a premium-rate wage line, with two conservative secondary savings, a stated failure condition, and a measurement plan. That paper survives contact with a CFO. The productivity paper does not.

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THE FAILURE MODES, NAMED

So you can see them coming

The pilot sized to impress. The effect lands inside the noise band, the result is arguable whatever happens, and both sides claim it. Size against three sigma or do not run it.

The baseline built afterwards. There is then no clean comparison, and anyone who dislikes the result wins the argument by default, because the burden of proof has landed on you.

The self-reported outcome. Van Dongen's subjects were two nights of total sleep deprivation deep and rated themselves as barely affected. If your primary outcome is how people say they feel, you have chosen the one instrument the evidence says is blind to the thing you are managing.

The sponsor who moves in month five. Put the failure condition and the measurement plan in the facility document, not in a relationship.

Silent intensification. The result looks like success and is not. This is the only failure mode on this list that improves your numbers for two years first.

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THE NINETY DAYS ON ONE PAGE

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BOARD PAPER TEMPLATE

Proposal. Convert $2,016,000 of annual premium-rate overtime at the plant into straight-time capacity, financed by a $472,650 facility repaid from verified savings.

Verified annual saving. $394,020 — wage line $241,920, injury $100,800, replacement $51,300. Injury and replacement rates set conservatively against published hazard ratios and stated as assumptions.

Return. 76.9 percent against a 9 percent WACC. The ratio is large because the facility is one-off and the saving recurs.

The single risk. Output per worker. Break-even is a 4.10 percent fall. At 3.00 percent the proposal still nets $106,020; at 5.00 percent it loses $85,980.

Failure condition. Verified output per worker down more than 4.10 percent across two measured quarters: no further drawdown, schedule reverts. Agreed in advance by the sponsor and by finance.

What this paper does not claim. It does not claim that shorter hours raise productivity. The published evidence for that is weaker than its reporting, and the proposal does not require it.

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APPRECIATIVE QUESTIONS FOR YOUR LEADERSHIP TEAM

1. Where in this business has a working-time arrangement already earned its keep, and what made it stick when others did not?
2. Which of our output measures would we be willing to stake a facility on — and what makes that one trustworthy where others are not?
3. When has this leadership team changed its mind because of a number rather than an argument? What was it about that number?
4. If both productivity lines were on the front page of the monthly pack, which recurring debate in this room would simply end?
5. What would we be able to promise our people if recovery had a budget line and was defended the way maintenance is defended?
6. Who here would sign a failure condition in advance — and what would it take for that to be an ordinary thing to do?