Queue item five, and the fifth article this session. This one has almost no regulation in it. The first half is arithmetic that anyone can reproduce, and the second half is a federal funding instrument whose repayment terms interact with that arithmetic in a way we have not seen written down.
Key Takeaway
A learning curve reduces unit cost as cumulative volume grows, so at a constant build rate the annual reduction shrinks every year. A contractual price step-down does not shrink. The result is not the collapse we expected. It is a hump: margin rises to a peak and then erodes for the rest of the agreement, and where the peak sits depends entirely on two numbers estimated before the first part is made.
The Verdict, Stated First
Five claims, in descending order of confidence.
One. Learning decelerates and price step-downs do not. At a constant annual build rate, an 85 percent learning curve delivers a 15 percent unit cost reduction between year one and year two, 9.07 percent between two and three, and 2.44 percent between nine and ten. A three percent annual step-down delivers three percent every year. This is arithmetic and it is not arguable.
Two. The result is a hump, not a collapse. Margin rises to a peak and then erodes. On a 90 percent curve with a three percent step-down from a twelve percent starting margin, the peak is 22.17 percent in year five, and margin does not turn negative until year 21. We expected a much faster failure and we were wrong.
Three. The sensitivity to the step-down is extreme. On that same 90 percent curve, moving the step-down from two to three to five percent moves the peak from year eight to year five to year three, and the year at which margin turns negative from 34 to 21 to 11.
Four. Across the plausible parameter box, year-twenty margin spans 98.7 percentage points, from negative 47.9 percent to positive 50.8 percent. Two numbers, both estimated before the first part is built, determine the entire economics of the agreement.
Five. A conditionally repayable federal contribution can require repaying more than was received. Innovation, Science and Economic Development Canada's own program guide says recipients will make repayments that may or may not exceed the nominal value of the contribution. Least confident of the five, not because the words are unclear but because we did not obtain an actual contribution agreement to see how the condition is written in practice.
Our Grades For These Claims
We grade our own sourcing before anyone else has to.
Claims one through four are arithmetic and depend on no source at all. They depend on the Wright learning curve formulation, which is standard and which we state in full, and on parameters we chose. Every figure in the first half of this article was computed in a separate script and can be reproduced from the formula we give. If it is wrong, it is wrong in a way anyone can check, which is the best kind of wrong.
The funding material is from ISED's own program guide, which is as good as a description of a programme gets. We used it for the three repayment structures and for the statement about exceeding nominal value.
What we did not verify is how any of this is actually written into agreements. We have the programme's description of its repayment forms. We have no contribution agreement, no royalty rate, and no repayment schedule. The two percent royalty we model is entirely ours and is illustrative.
The starting margin of twelve percent is ours. So is the choice to treat the build rate as constant, which no real programme does.
The learning rates we use, 80 to 90 percent, are conventional in the sense that they are the range the technique is usually taught and applied over. We did not obtain measured learning rates for any Canadian aerospace supplier and we would be surprised if such figures were public.
A Note On Method
What we obtained: ISED's programme guide covering the Strategic Innovation Fund and its successor and legacy programmes, for the repayment structures and the list of predecessor programmes; ISED's page on funding amounts and conditions, for the description of hybrid repayment and the reference to audited gross business revenues as a conditional metric; an internal audit report on the Strategic Innovation Fund, for the distinction between unconditional and conditionally repayable schedules; a federal page on the Aerospace Regional Recovery Initiative; and consultancy summaries for programme parameters.
What we did NOT obtain:
- Any contribution agreement. Everything about repayment mechanics comes from the programme's description of itself.
- Any real royalty rate, repayment schedule, or benefit condition.
- Any measured learning rate from a real supplier.
- Any actual long-term agreement. The step-down structure we model is the conventional one described in cost engineering literature, not one we have seen.
- The accounting guidance on government assistance under either IFRS or ASPE. We raise the classification question and deliberately do not answer it.
One naming caution. ISED material we read refers both to the Strategic Innovation Fund and to a Strategic Response Fund, with overlapping descriptions and shared legacy programmes. We could not establish with confidence whether this is a rename, a successor programme or two coexisting instruments, and we have written around it rather than guessing. Anyone relying on programme names should check the current position directly.
The Two Numbers That Decide Everything
An aerospace long-term agreement is, stripped of everything else, a commitment to supply a part at a price that falls on a schedule, for a long time.
The supplier agrees to it because of the learning curve. Unit cost falls as cumulative production grows, so a price that falls should still leave a margin, and a long agreement provides the volume that makes the learning happen. This logic is sound and it is why the industry works the way it does.
Two numbers determine whether it works out.
The learning rate. How much unit cost falls each time cumulative output doubles. Conventionally expressed as a percentage: an 85 percent curve means cost falls to 85 percent of its previous level on each doubling.
The step-down. How much the contract price falls each year.
Neither is knowable at signature. The learning rate for a part that has never been made in volume is an estimate, informed by the supplier's experience on other parts. The step-down is the outcome of a negotiation, and the customer's interest is in making it larger.
What follows is an attempt to show, with arithmetic anyone can reproduce, exactly how much those two estimates matter. The answer surprised us, and the direction of the surprise was not the one we expected.
What A Learning Curve Actually Says
The standard formulation is Wright's. Unit cost at cumulative quantity Q is the cost of the first unit multiplied by Q raised to a power b, where b is the logarithm of the learning rate divided by the logarithm of two [6].
That gives the exponents we use throughout:
- 90 percent curve: b = negative 0.1520
- 85 percent curve: b = negative 0.2345
- 80 percent curve: b = negative 0.3219
- 75 percent curve: b = negative 0.4150
Read the direction of that. A lower percentage means faster learning, because cost falls to a smaller fraction on each doubling. An 80 percent curve is aggressive. A 90 percent curve is modest and is what we would expect on a mature, low-volume, high-content aerospace part where much of the cost is material and certified process rather than touch labour.
The formulation is about cumulative quantity, and that single word is where the whole problem comes from. Cost does not fall with time, or with effort, or with management attention. It falls with doublings of everything ever made.
Learning Decelerates
Now hold the build rate constant, which is the simplest case and the one an LTA schedule implicitly assumes.
If the supplier makes the same number of units every year, cumulative volume at the end of year n is n times the annual rate. Doubling cumulative volume takes one year between years one and two, one year between two and four, two years between four and eight, four years between eight and sixteen.
The doublings get further apart. So the cost reductions do too.
On an 85 percent curve at constant rate, ours:
- Year 1 to 2: 15.00 percent reduction
- Year 2 to 3: 9.07 percent
- Year 3 to 4: 6.52 percent
- Year 4 to 5: 5.10 percent
- Year 5 to 6: 4.18 percent
- Year 7 to 8: 3.08 percent
- Year 9 to 10: 2.44 percent
By year ten the curve is delivering under two and a half percent a year and still slowing. It never stops delivering, and it never delivers much again.
A contractual step-down has none of this behaviour. Three percent a year is three percent in year two and three percent in year twenty. It is a straight line in log space against a curve that is flattening.
So the two lines must cross. The only questions are when, and what happens on the way.
What We Expected, And What The Arithmetic Said
We expected the crossing to come fast and the article to be about a supplier priced into loss within a handful of years. We built the model to show it.
It does not happen, and at conventional parameters it does not come close.
On an 85 percent curve with a three percent annual step-down and a twelve percent starting margin, here is what actually happens, ours:
- Year 1: margin 12.00 percent
- Year 2: 22.89 percent
- Year 3: 27.71 percent
- Year 5: 31.84 percent
- Year 8: 33.11 percent
- Year 10: 32.54 percent
Margin does not fall. It nearly triples, peaks in year eight, and is still above thirty percent in year ten. On that parameter set it does not turn negative inside thirty years.
The reason is straightforward once seen. In the early years the learning curve is delivering 15 percent, then 9 percent, then 6.5 percent, against a step-down of only 3 percent. The supplier is winning by a wide margin for years, and the accumulated gain is large enough that the later deceleration takes a very long time to erode it.
We publish the wrong hypothesis because the alternative is presenting the corrected model as though we had always intended it. And because the error is instructive: the intuition that a fixed step-down beats a decelerating curve is correct about the direction and badly wrong about the timing, and a supplier who believes the pessimistic version will decline agreements that are in fact highly profitable for a decade.
The Margin Is A Hump
What the arithmetic actually produces is a hump, and the hump is the right mental model.
Early on, the curve outruns the step-down and margin expands, often dramatically. The expansion decelerates as the curve does. At some point the annual learning gain falls below the annual step-down, and from that year onward margin erodes, slowly at first and then faster as the curve continues to flatten while the step-down does not.
On the more conservative 90 percent curve with the same three percent step-down, ours:
- Year 1: 12.00 percent
- Year 3: 20.86 percent
- Year 5: 22.17 percent, the peak
- Year 10: 18.43 percent
- Year 15: 10.69 percent
- Year 20: 0.45 percent
- Year 21: negative
That shape has a management consequence that we think is the practical heart of this article. The peak arrives early and it is not a level, it is a moment. Year five, on these numbers. A business that observes a 22 percent margin in year five and builds its overhead structure, its investment plan and its expectations around it has calibrated to a number that occurs exactly once and declines thereafter for fifteen years.
Nothing goes wrong in the meantime. There is no event, no failure, no bad quarter to investigate. The margin simply erodes by roughly one point a year while everyone does their job correctly.
How Much One Point Moves It
Now the finding that we think should change how the negotiation is conducted.
Hold the 90 percent curve and the twelve percent starting margin fixed. Move only the step-down. Ours:
- Two percent step-down: peak 26.10 percent in year 8, negative from year 34, year-twenty margin positive 18.07 percent
- Three percent: peak 22.17 percent in year 5, negative from year 21, year-twenty margin positive 0.45 percent
- Five percent: peak 17.49 percent in year 3, negative from year 11, year-twenty margin negative 47.90 percent
One percentage point on the step-down moves the peak from year eight to year five. Two more points move it to year three, and move the loss-making year from 34 to 11.
Now vary both parameters across the plausible box, 80 to 90 percent curves against two to five percent step-downs. Year-twenty margin ranges from negative 47.90 percent to positive 50.76 percent, a spread of 98.7 percentage points.
That is the number we would put in front of anyone about to sign one of these. The entire outcome of a twenty year commitment sits inside a range nearly a hundred margin points wide, and which point in that range you land on is determined by an estimated learning rate and a negotiated step-down.
Ours, and offered as the practical conclusion. Given that sensitivity, the step-down is not a commercial detail to be conceded late in a negotiation to close a gap on something else. It is, on this arithmetic, the single most consequential term in the agreement, and it is frequently traded against terms worth a fraction as much.
What A Rate Cut Does
Everything above assumes a constant build rate. Aerospace does not have constant build rates. Programmes ramp, plateau, and get cut.
A rate cut does something to this model that is easy to state and easy to miss. It does not raise unit cost. It stops the learning, because cumulative volume grows more slowly, and the price step-down carries on regardless.
Ours, on an 85 percent curve with a three percent step-down where the build rate halves from year eight:
- Year 7, last full-rate year: margin 33.06 percent
- Year 8, rate halves: 32.09 percent
- Year 10: 29.92 percent
- Year 12: 27.43 percent
- Year 15: 23.17 percent
Look at what the cost line does across that period. At full rate the unit cost index went from 0.5576 in year seven toward continued reductions. At half rate it moves 0.5487, 0.5404, 0.5328, 0.5257, which is roughly one percent a year against a three percent step-down.
So the rate cut converts a business that was gaining two points a year on the step-down into one losing two points a year. The margin does not fall off a cliff. It changes direction.
This is worth naming because a rate cut is usually assessed as a volume problem, and it is also a unit cost problem with a long tail. A supplier modelling a rate reduction by simply multiplying volume by a factor and holding unit cost flat will understate the damage, because holding unit cost flat is precisely what the learning curve was supposed to prevent.
The Ramp Changes The Shape, Not The Story
The constant build rate we used above is a simplification and we said so. It is worth correcting it properly rather than only declaring it, because the correction changes the numbers substantially and the conclusion not at all.
Real programmes ramp. Assume the same 85 percent curve and three percent step-down, but a build rate rising 20, 40, 60, 80 and then holding at 100 units a year. Ours:
- Year 1, 20 units, cumulative 20: margin 12.00 percent
- Year 3, 60 units, cumulative 120: 38.55 percent
- Year 5, 100 units, cumulative 300: 47.32 percent
- Year 8, cumulative 600: 50.94 percent
- Year 10, cumulative 800: 51.26 percent, the peak
- Year 15, cumulative 1,300: 49.35 percent
Against the constant-rate version, which peaked at 33.11 percent in year eight, the ramp peaks at 51.26 percent in year ten. Higher and later.
The reason is that a ramp front-loads the doublings. Cumulative volume goes from 20 to 60 to 120 to 200 in the first four years, which is more than three doublings while the price has stepped down only three times. The learning curve is doing its most powerful work in exactly the years when the step-down has barely started.
So our earlier figures understate how good the early and middle years are. A ramping programme on conventional parameters is not merely profitable, it is extremely profitable for a decade, and the peak sits later than the constant-rate model suggests.
The shape is unchanged. It is still a hump, it still turns, and everything after the peak still erodes on a schedule nobody has to do anything wrong to cause. What the ramp does is make the peak higher, which makes the calibration problem worse rather than better. A business that sets its cost structure against a 51 percent margin in year ten is calibrating to a number further above its own long-run average than one calibrating to 33 percent.
Non-Recurring Cost And Who Owns The Tools
One cost element sits outside everything above and deserves its own treatment, because it is large, it is early, and it is not subject to a learning curve at all.
Non-recurring engineering and tooling are incurred before the first shipset. Design, qualification, first article inspection, test, and the tools and fixtures themselves. None of it falls with cumulative volume, because it happens once.
How it is recovered varies and the variation matters. It may be paid directly by the customer, in which case the tools are usually the customer's. It may be amortised into the unit price, in which case the supplier is financing it and recovering it over the volume the programme actually delivers. Or it may sit somewhere in between, with a partial contribution and an amortisation of the balance.
The middle case is where the interaction with everything else in this article bites. If non-recurring cost is amortised into a unit price that then steps down, the recovery per unit falls even though the amount to recover does not. And if the build rate is cut, the volume over which it was to be recovered disappears while the cost remains spent.
Ours, and stated as a structural point rather than a modelled one. We have not put numbers on this because doing so would require assumptions about the non-recurring amount and the amortisation basis that we have no way to ground. What we can say is that amortised non-recurring cost behaves in exactly the opposite way to the learning curve: it is heaviest per unit when cumulative volume is lowest, which is when the learning curve is also at its least helpful. The two effects work against each other in the early years and only one of them improves with time.
Tooling ownership is worth a separate question. A supplier that has financed tooling it does not own has an asset on someone else's premises or an expense with no asset at all, and either way it has spent money whose recovery depends entirely on a build rate the customer controls.
The Money That Comes With A Repayment
Now the federal layer, which in Canadian aerospace is not incidental.
Development on this kind of programme is frequently supported by a federal contribution. The current instrument is the Strategic Innovation Fund, and the legacy list is long: the Strategic Aerospace and Defence Initiative, with agreements signed between 2007 and 2017, provided repayable contributions to aerospace, space, defence and security research; the Technology Demonstration Program provided non-repayable contributions between 2013 and 2017; Technology Partnerships Canada ran from 1998 to 2006; and there are programme-specific legacy files as well [5].
The critical point, stated in the programme's own guide, is that contribution amounts are repayable by default [1]. Non-repayable treatment is the exception, considered where benefits have been proven and the activity aligns with investment priorities.
Three repayment structures are described:
Unconditional. The recipient repays no more than the nominal value, that is interest free, on a fixed schedule over a predetermined period after a grace period. Amounts are known or predictable upfront.
Conditional. Repayments depend on verifiable conditions over a predetermined period.
A combination. Part unconditional on a fixed schedule, part conditional on a verifiable metric, with audited gross business revenues given as an example [2].
An unconditional contribution is an interest-free loan and behaves like one. The conditional form is where it gets interesting.
May Or May Not Exceed
The programme guide describes conditional repayment in terms worth reading slowly. Recipients will make repayments that may or may not exceed the nominal value of the contribution paid to them, with total repayments depending on certain verifiable conditions and made over a predetermined period [1].
Set that beside the unconditional form, which the same guide describes as repaying no more than the nominal value, interest free [1].
The contrast is deliberate and it is the whole point. An unconditional contribution has a ceiling equal to what was received. A conditional one does not have that ceiling. It may repay less, if the conditions are not met. It may repay more.
So a conditionally repayable contribution is not a grant, and it is not an interest-free loan either. In economic substance it looks much closer to a royalty interest in the recipient's future revenue, with the government taking programme risk on the downside and participation on the upside.
We want to be careful about how far we push that characterisation. We did not obtain a contribution agreement, and how the condition is actually drafted, whether there is a stated cap, over what period, and against what metric, are all things a real agreement would answer and a programme guide does not. What we can say is that the programme's own description expressly contemplates repayment exceeding the amount received, and that this is a materially different instrument from the one most people picture when they hear the word contribution.
Twenty Years Or More
One more feature, and it is the one that connects this half of the article to the first.
Contribution agreements under this programme can span twenty years or more, including long-term monitoring of project benefits [4]. The programme's audit material notes that most legacy programmes sit in a repayment and benefits phase [3], which is to say the money went out years ago and the obligations run on.
Twenty years is the same horizon as the long-term agreement. That is not a coincidence, because both are sized to the life of an aircraft programme.
So the supplier has two twenty-year instruments running against the same revenue stream. One sets the price it receives, declining on a schedule. The other sets an obligation measured, at least in part, against what that declining price produces.
And the two were negotiated separately, with different counterparties, on different assumptions, by different people.
Royalty On Gross, Margin On A Hump
Here is the interaction, and this section is entirely ours.
A conditional repayment measured against gross revenue takes a constant percentage of price. Margin, as the first half of this article established, is a hump: it rises, peaks, and erodes.
In percentage-point terms the royalty is flat. Two percent of revenue is two points of price, in year one and in year twenty alike. But two points of price is a completely different thing depending on where you are on the hump.
Ours, on the 90 percent curve with a three percent step-down and an illustrative two percent gross revenue royalty. The royalty as a share of the margin it comes out of:
- Year 1, margin 12.00 percent: the royalty takes 16.7 percent of it
- Year 5, margin 22.17 percent at the peak: 9.0 percent
- Year 10, margin 18.43 percent: 10.9 percent
- Year 15, margin 10.69 percent: 18.7 percent
- Year 18, margin 4.82 percent: 41.5 percent
- Year 20, margin 0.45 percent: 448.5 percent
The royalty is cheapest exactly when the business can most afford it and most expensive exactly when it cannot. It is, in effect, an obligation whose burden is inversely related to the ability to bear it, and neither instrument knows about the other.
We should be fair to the design. A conditional repayment tied to revenue is more forgiving than a fixed schedule, because if the programme fails and revenue does not materialise, the repayment does not either. That is genuine risk sharing and it is the point of the structure. The problem we are describing is not failure. It is the ordinary case where the programme succeeds, runs its full twenty years, and margin erodes on schedule while a revenue-based obligation continues at full rate.
What The Royalty Does To The Crossover
The effect on the loss-making year is smaller than the share figures suggest, and we report that because it cuts against the drama of the previous section.
On the 90 percent curve at a three percent step-down, margin turns negative in year 21 with no royalty. Ours, adding one:
- One percent gross royalty: negative from year 20
- Two percent: negative from year 20
- Three percent: negative from year 19
So a three percent royalty pulls the crossover forward by two years, not by five or ten.
The reason is that margin is falling steeply by then. In the final years it is dropping several points a year, so subtracting two or three points moves the crossing by a year or two rather than transforming the picture.
That is the honest result and it moderates our own framing. The royalty does not cause the problem. The step-down against a decelerating curve causes the problem, and the royalty makes the last few years slightly worse and the arithmetic of the final period considerably uglier as a proportion.
What the royalty does do is remove the margin of safety. A supplier planning to run the agreement to year twenty on a thin but positive margin has no cushion at all once a revenue-based obligation is sitting on top of it, and the difference between year 19 and year 21 is two years of a twenty year programme.
Liability Or Grant
This raises a classification question we can frame and will not answer.
A contribution that is repayable by default, conditionally, against a metric such as audited gross business revenues, over twenty years or more, is not obviously a liability and not obviously income.
The arguments in each direction are easy to see. It looks like a liability because there is a real obligation to pay, the programme describes contributions as repayable by default, and the amount may exceed what was received. It looks like income because the obligation is contingent on an outcome that may not occur, and until the revenue exists there is nothing to pay.
And if it is a liability, measuring it requires forecasting twenty years of revenue on a declining price schedule, which is the same forecast that determines whether the long-term agreement is any good.
That last point is the one worth carrying away. The volume and revenue forecast is used in two places. It determines whether the learning curve delivers enough cumulative volume to keep ahead of the step-down. And it determines the measurement of the repayment obligation. An optimistic forecast makes the agreement look better and the obligation look larger. A pessimistic one does the reverse. The two errors partially offset in the reported numbers while both remain wrong, which is the most difficult kind of error to detect, because the aggregate looks reasonable.
We did not obtain the accounting guidance on government assistance under either IFRS or ASPE and we are not going to reason from a programme guide to a classification conclusion. That is the move that produces confident wrong answers, and we made a version of it earlier in this session on the distillery article and published the correction. The question belongs to the auditor. What we can contribute is the observation that the same forecast feeds both instruments and that nobody appears to reconcile them.
The Terms That Actually Change The Outcome
If two numbers determine a ninety-eight point range, it is worth asking which contract terms attach to them.
The step-down itself. On our arithmetic, one point is worth roughly three years of peak position and thirteen years of loss-free operation. It should be the last thing conceded, not a rounding item.
Whether the step-down has a floor. A schedule that steps down to a stated minimum and then holds converts the hump into a hump with a plateau, and removes the tail entirely. This is the single most valuable term available and it costs the customer nothing in the early years.
Whether the step-down is tied to volume rather than to time. The learning curve is a function of cumulative units. A step-down expressed per doubling of cumulative volume, rather than per calendar year, tracks the mechanism instead of fighting it. A rate cut then slows the price reduction as it slows the learning, which is the correct behaviour and almost never how these are written.
Whether there is a rate-change provision. Our arithmetic showed a halving of build rate turning a two-point annual gain into a two-point annual loss. If the customer controls the rate and the supplier bears the consequence, that is an allocation worth pricing.
Ours, and stated as reasoning rather than as observed practice. We have not seen a real long-term agreement and we do not know how common any of these terms are. What we can say is that the arithmetic identifies exactly which terms matter, and that a supplier who has done this arithmetic negotiates differently from one who has not.
If You Supply On A Long-Term Agreement
Five things, in the order we would look at them.
Compute your own hump before signing. The formula is in this article. Put in your learning rate, your step-down and your starting margin, and find the peak year and the loss year. It takes an afternoon and it is the highest-value analysis available.
Do not calibrate overhead to peak margin. The peak is a moment, not a level. On our conservative parameters it arrives in year five and everything after it is downhill for fifteen years.
Argue about the step-down, not the price. The opening price sets year one. The step-down sets years two through twenty and, on our numbers, spans nearly a hundred margin points.
Model a rate cut properly. Multiplying volume by a factor and holding unit cost flat understates the damage, because a rate cut is a learning problem as well as a volume problem.
Read the contribution agreement against the long-term agreement. If a repayment obligation is measured on gross revenue over twenty years, and the price schedule declines over the same twenty years, someone should have both documents on the same desk. In our experience of how these are negotiated, nobody has.
If You Advise One
Four checks we would run on any aerospace supplier engagement.
Whether the learning curve assumption behind the pricing is documented anywhere. It is the largest single assumption in the business and it is frequently implicit in a spreadsheet nobody has opened since the bid.
Where the client sits on the hump. A supplier three years past its peak has a structurally declining margin that will not respond to cost programmes, because the cost programme is the learning curve and it is already running.
How any government contribution is classified, and on what forecast. If it is measured as a liability, the forecast driving that measurement should be the same one driving the pricing analysis, and it usually is not.
Whether a rate reduction has been modelled with the unit cost effect. This is the specific error we would expect to find, because it requires the modeller to understand that cumulative volume rather than annual volume drives cost.
And one thing to resist. Do not tell a client that a fixed step-down against a decelerating learning curve means the agreement is bad. We assumed that and the arithmetic disagreed. On conventional parameters these agreements are highly profitable for a decade, and the problem is the shape of the tail, not the deal.
What To Do
If you take one thing from this article, take the hump. Learning decelerates and step-downs do not, so margin rises to a peak and then erodes for the rest of the agreement. Nothing goes wrong along the way. It is the arithmetic working as designed.
If you take two, take the sensitivity. One point on the step-down moved the peak from year eight to year five in our model, and across the plausible parameter box the year-twenty margin ranges over 98.7 percentage points. That is not a detail to trade away late in a negotiation.
If you are advising an aerospace supplier this quarter, the highest-value single question is what learning rate was assumed when the current long-term agreement was priced, and whether anyone has compared it to what actually happened.
The Limits Of This Analysis
Long and specific, because a limits section that is short is decoration.
Every parameter is ours. The twelve percent starting margin, the two to five percent step-downs and the 80 to 90 percent learning rates are chosen, not measured. The formula is standard. The inputs are assumptions and every conclusion moves with them.
Our two build-rate scenarios are still simplifications. We modelled one rate cut and one ramp, and the ramp raised the peak from 33.11 percent to 51.26 percent and moved it from year eight to year ten. Real programmes have ramps, plateaus, cuts and recoveries in sequence, and each reshapes the hump. The headline figures in the verdict come from the constant-rate model and therefore understate the early and middle years.
Wright's curve is one formulation among several. Crawford's unit curve and the cumulative-average form give different answers from the same learning rate, and we used one without testing the others. A reader comparing our figures to a cost engineering text may find they do not tie, and the reason will be the formulation rather than an error.
The learning curve applies to touch labour far better than to material. On a part where material and certified process dominate cost, the effective learning rate on total cost will be much closer to 100 percent than our range suggests, which makes the hump lower and the erosion earlier.
We did not obtain a single real long-term agreement. The step-down structure we model is the conventional one, not one we have seen.
We did not obtain a contribution agreement. Every statement about repayment comes from the programme's description of itself, and the two percent royalty is entirely illustrative.
We could not resolve the programme naming. ISED material refers to both a Strategic Innovation Fund and a Strategic Response Fund with overlapping descriptions and shared legacy programmes. We wrote around the ambiguity rather than guessing which supersedes which.
We reached no accounting conclusion, deliberately. Whether a conditionally repayable contribution is a liability or income, and how it would be measured, are questions we raised and did not answer, because we did not obtain the guidance.
Inflation is entirely absent. Every figure is in constant terms. A twenty year agreement in nominal dollars with a nominal step-down behaves differently again, and escalation clauses, where they exist, change the picture materially.
Nothing here is advice on a particular agreement.
Frequently Asked Questions
Why does margin rise before it falls on a long-term agreement?
When does the peak arrive?
How much does one point on the step-down matter?
What does a build rate cut do?
Can a repayable federal contribution cost more than it provided?
How does a revenue-based repayment interact with an eroding margin?
Is a fixed step-down simply a bad deal?
References
- Innovation, Science and Economic Development Canada, programme guide covering the Strategic Innovation Fund and related instruments. Source of the statement that contribution amounts are repayable by default and determined case by case after due diligence; of the three repayment forms, being unconditional where the recipient repays no more than the nominal value interest free on a fixed schedule after a grace period, conditional where recipients make repayments that may or may not exceed the nominal value depending on verifiable conditions, and a combination of both; and of the list of legacy programmes including the Strategic Aerospace and Defence Initiative with agreements signed 2007 to 2017, the Technology Demonstration Program 2013 to 2017 and Technology Partnerships Canada 1998 to 2006. Note: the programme describing itself, which is authoritative as to design and tells you nothing about how a particular agreement is drafted. We did NOT obtain any contribution agreement.
- Innovation, Science and Economic Development Canada, page on funding amounts and conditions, for the description of the hybrid structure in which one portion of a contribution is unconditionally repayable on a predetermined schedule and another portion is conditionally repayable against verifiable metrics, with audited gross business revenues given as the example. Note: the source for our treatment of repayment as revenue-based, and the reason we model a gross revenue royalty rather than a profit share.
- Innovation, Science and Economic Development Canada, internal audit report on the Strategic Innovation Fund. Source of the distinction between unconditional schedules where set payments are made regardless of the recipient's earnings and conditionally repayable schedules where payments are calculated on the recipient's performance or earnings for each period, and of the observation that most legacy programmes sit in a repayment and benefits phase. Note: an internal audit, which makes it unusually candid about mechanics and also dated. Our copy reports figures as at 2019.
- Consultancy summaries of the Strategic Innovation Fund, used for programme parameters including the minimum contribution of $10 million for projects with budgets of at least $20 million, contributions of up to 50 percent of project costs, and the statement that contribution agreements can span 20 years or more including long-term monitoring of project benefits. Note: secondary sources. The twenty year figure is load-bearing for our interaction argument and we would rather have had it from the programme directly.
- Government of Canada, Aerospace Regional Recovery Initiative pages, for the statement that contributions to small and medium sized enterprises under that initiative are generally repayable or conditionally repayable while contributions to not-for-profits are generally non-repayable, and for the initiative's $250 million budget over three years delivered through the regional development agencies. Note: used only to show that repayable-by-default is the pattern across federal aerospace support rather than a feature of one programme.
- Wright's learning curve formulation, being unit cost at cumulative quantity Q equal to first unit cost multiplied by Q raised to the power b, where b is the natural logarithm of the learning rate divided by the natural logarithm of two. Note: a standard technique, not a source we retrieved. We state it in full so that every figure in the first half of this article can be reproduced independently, and we flag in the limits that Crawford's unit curve and the cumulative-average form give different answers from the same learning rate.