Haute Lumière
Commerce · V.05 · MMXXVI · daylight
For the person who owns a P&L and has been told, in a meeting, that the problem with training is that people leave. This workbook gives you the arithmetic that answers that sentence, the instrument that follows from it, and the board paper that carries both. Nothing here requires a change in your firm's values. It requires a schedule your accounts do not currently produce.
Your firm holds an unscheduled asset class of material size. It is expensed on acquisition, tracked nowhere, depreciated at a rate nobody has measured, and described as "lost" when it resigns. If you treated plant this way your auditors would have something to say about it.
Three facts, all measured, all in the chapter's Works Cited:
Your decision is therefore not should we train. It is where does our payback land, and does it land inside the tenure we can count on.
Exercise 1.1 — The training cost reconstruction (one week, one analyst)
Your general ledger does not have a training cost line that means anything. Build one for a single role — the one you hire most.
per trainee, per year
------------------------------------------------------------
A trainee compensation, fully loaded ________
B supervisor time x supervisor cost per hour ________
C formal instruction, courses, certification ________
D materials, licences, equipment, rework ________
E recruitment and administration ________
GROSS COST = A + B + C + D + E ________
Line B is the one everyone omits and it is frequently the largest after A. Count it at the supervisor's fully loaded rate, not their salary.
Exercise 1.2 — The productive contribution, honestly (one week)
The Swiss surveys decompose an apprentice's productive value into three measurable factors, and you can use the same three:
productive value = time actually in the business
x share of that time on productive work
x productivity relative to a qualified person
x what a qualified person costs
Swiss three-year anchors, published: year one 0.79 × 0.77 × 0.40; year three 0.81 × 0.84 × 0.80. Relative productive values of 0.26, 0.41 and 0.54.
Get your three factors from the supervisors, not from HR, and get them role by role. Supervisors know the third number to within about ten points and have never been asked for it.
Exercise 1.3 — The tenure number, measured (two days)
Pull your last three cohorts in this role. What proportion were still employed twelve months after completing the programme? Twenty-four?
Use your own data, not an industry figure. German retention is 53 per cent and Swiss is about 35 per cent; the gap between two adjacent countries is eighteen points, so a sector average tells you nothing about your building. Call the measured result T.
Exercise 2.1 — The payback curve (half a day)
Lay the two series side by side, year by year, and cumulate.
year output cost net cumulative
--------------------------------------------------
1 20,138 28,070 -7,932 -7,932
2 31,756 28,070 +3,686 -4,245
3 41,825 28,070 +13,755 +9,510
That is the Swiss three-year apprenticeship, using the survey's own aggregate output distributed across its own published productive-value shares. The cumulative line crosses zero at month 27.7 of thirty-six. Under a rising cost profile it crosses at month 26.2. Either way, before the contract ends.
Do the same for your role. P is where your cumulative line crosses.
Exercise 2.2 — The decision (one hour)
Train on your own book when P < T
Pool, or shorten P, when P > T
That is the whole decision and it fits on one line of a board paper.
Exercise 2.3 — The sensitivity that decides the design (two hours)
Re-run P with the depreciation rate of the skill you are actually building.
delta half-life E(5 yrs) on a 4,000/yr rent at 53% retention
---------------------------------------------------------------------
1.35 %/yr 51.3 yr 10,250 EUR 0.95x cover
3.04 %/yr 22.8 yr 9,833 EUR 0.91x cover
10.41 %/yr 6.7 yr 8,264 EUR 0.77x cover
Against a €10,788 three-year investment, the slow-depreciating skill leaves you five per cent short at five years and the fast one leaves you twenty-three per cent short. Over an unbounded horizon the same rents are worth €157,037 and €20,364 — a ratio of 7.7.
The commercial conclusion, stated for a board: rapid obsolescence is an argument against long paybacks, not against training. If your δ is near ten per cent, stop modelling any recovery beyond about seven years and redesign the programme so the contribution arrives earlier.
Four instruments, and your P-versus-T result chooses among them.
One — shorten P. Free, fastest, and almost always available.
The Swiss payback lands at month 27.7 because trainees are in the business four days a week, mostly on productive work, reaching 80 per cent of a qualified person's productivity by year three. Every one of those is a design parameter.
Three levers, in order of effect:
Two — a levy, if you are setting policy rather than paying it.
The UK Apprenticeship Levy: 0.5 per cent of pay bill above £3 million, a £15,000 allowance, a ten per cent top-up, twenty-four-month expiry. A pay bill of eight million pounds pays £25,000 and holds £27,500.
Cost it before you praise it. At 229 employees and the upper measured effect of 0.5 percentage points of training intensity, that £25,000 buys 1.14 additional starts — £21,875 per marginal start, and £109,375 at the low end. National starts fell 24.1 per cent in the year it landed, while the matched evaluation found training rose at levy-payers relative to comparable non-payers. Both are true. A levy is a price signal, and the marginal unit is expensive because most of the money funds training that was already happening.
Three — the bond, and its ceiling.
Do not build your retention case on a repayment clause. German doctrine ties the lock-in to the length of training, two years being the practical ceiling, tapered monthly; English courts after Cavendish Square v Makdessi ask whether the sum is proportionate to a legitimate interest; US regulators treat aggressive versions as employer-driven debt. And §12(1) of the German Berufsbildungsgesetz voids any clause binding an apprentice after training, which removes the instrument in exactly the case where the money is largest.
A bond big enough to matter is unenforceable; a bond the law will keep is too small to matter. Put the drafting time into shortening P instead.
Four — pool, when P > T and cannot be brought inside it.
Denmark has run the reference design since 1977: every employer pays a flat per-head contribution — DKK 2,821 per full-time employee at the 2026 rate, so DKK 564,200 a year for a 200-person firm, about €75,600 — whether it trains or not, and only trainers draw reimbursement. The private equivalent is a group training organisation: a consortium that employs apprentices and rotates them across member firms.
The structure, in the form a treasurer will recognise.
Exercise 4.1 — Put P in the reporting pack (one week)
Anything reviewed monthly persists; anything reviewed by exception evaporates. Two lines, on the standing pack:
payback month, current cohort (P) ____ months
retained tenure, last three cohorts (T) ____ months
Nothing else. Two numbers on the pack will outlive every presentation you give.
Exercise 4.2 — The failure modes, named in advance (half a day)
Exercise 4.3 — Tell the trainees their payback month (one hour)
This costs nothing and changes the first year. It is the same courtesy as telling someone what their equipment cost, and it converts we are investing in you, said with slight embarrassment, into a schedule two adults can both read.
Recommendation. [Train on our own book / Form a training consortium with named members], on the basis that P = ____ months and T = ____ months.
The arithmetic. Gross cost per trainee-year ____; productive contribution by year ____ / ____ / ____; cumulative crossing at month ____. Depreciation rate of the skill family ____ per cent a year, half-life ____ years, giving ____ times cover over five years.
The comparable. Swiss training firms run a net benefit of CHF 3,170 per apprentice-year with a payback at month 27.7 of thirty-six, at 35 per cent retention. German firms run €3,596 of net cost a year at 53 per cent retention, with break-even retention of 53.9 per cent. Our position sits [here].
What we are not asking for. No capitalisation of people. No repayment bond. No change to compensation policy.
The decision number. P versus T. Everything else in this paper is how those two numbers were obtained.
Review. After the first cohort completes, against the signed cost and contribution assumptions, by internal audit.
| Day | Action | Artifact |
|---|---|---|
| 1–15 | Reconstruct gross cost per trainee-year for one role, line B included | The cost build |
| 16–25 | Get the three productivity factors from supervisors, role by role | The contribution build |
| 26–30 | Pull three cohorts and measure twelve- and twenty-four-month retention | T, measured |
| 31–40 | Build the cumulative curve; find the crossing | P, computed |
| 41–45 | Run the sensitivity at your skill family's δ | The decay table |
| 46–55 | If P < T, write the memo and stop. If P > T, name three consortium members | Decision memo |
| 56–70 | Heads of terms; price the subscription off the aggregate shortfall | Subscription schedule |
| 71–80 | Put P and T on the standing reporting pack | Two lines on the pack |
| 81–90 | Tell the current cohort their payback month | The conversation |
The two artifacts in bold are the ones that survive you. Everything else is how they were produced.
It is worth being explicit, because training proposals usually arrive with freight attached and this one does not.
It does not ask you to capitalise people. You capitalise a contract; the distinction survives audit precisely because it is the honest one.
It does not ask you to change compensation policy. The wage compression that makes firm-financed training viable already exists in your firm, whether or not anybody has named it, and nothing here proposes widening or narrowing it.
It does not ask you to accept a longer payback than you would accept anywhere else in the business. It asks the opposite: apply the same payback discipline you apply to plant, and then notice that under the discipline a large amount of training passes.