A method note. No company appears in it. Every claim here is ours, because nothing here is filed: this is a construction, offered so that a reader can run it on whatever filer they are reading.
The arrangement
A company sells equipment. It also puts money into a company that buys equipment. The money it puts in stands where a lender requires equity, and the facility that opens buys equipment, some of it from the company that supplied the money.
So the arrangement has two returns and they are of different kinds. The sale returns cash. The stock is what remains afterward.
The question that decides whether the arrangement pays for itself is narrow: how much of the resulting spending has to come back as the supplier’s own sale for the cash to be recovered.
Why the question usually stops
Because the share of a customer’s spending that goes to any one vendor is disclosed by almost nobody. It is the term that ends most attempts at this, and estimating it puts the whole result on an assumption.
The move is to stop estimating it and solve for it instead. The question shifts from what the share is to what the share would have to be.
The derivation
A contribution of E stands beside a program of E divided by one minus the advance rate a, because the lender advances a and the equity fills the rest.
Some share s of that program is spent with the supplier, at margin m, so the profit the supplier earns on it is E over one minus a, times s, times m.
Setting that equal to E is the condition for the cash to come back, and solving for s gives the line:
The share of the program that has to be spent with the supplier, for a placement to return its own cash, is one less the advance rate, divided by the margin.
required share = (1 - a) / m
What the identity does
The unknown is gone. The share was the one term nobody discloses, and asking what it has to be removes it. The two remaining inputs are ordinarily disclosed: the advance rate appears in the customer’s credit agreement, and the margin appears in the supplier’s income statement.
There is no time in it. The profit arrives as the equipment ships, against cash that left once, so no discount rate, no horizon and no cost of capital enters the calculation. It is a question about size.
It decides whether the arrangement pays for itself commercially. Above the requirement the sale has repaid the cash and the shares are a residual, so the arrangement clears whatever they do. Below it the sale has repaid part, and the shares carry the balance. The threshold is computed. Which side of it any arrangement sits on turns on the share captured, which remains undisclosed, so the identity frames the question rather than closing it.
And the margin cancels between any two facilities. The ratio of two required shares is one less the second advance rate, over one less the first. So the change across a series of facilities is a function of the advance rates alone, and it holds whatever a reader believes about the margin. A disputed level leaves the direction and the magnitude of the change intact.
A break in the series locates a facility built differently. The identity converts an advance rate into cents in the dollar that have to return, and that conversion is what makes two equal moves in the rate unequal. A ten point fall from 80 percent to 70 percent raises the requirement by half. A ten point fall from 90 percent to 80 percent doubles it. So a requirement that steps out of line in a series marks a lender underwriting a different object: a different collateral package, a different counterparty, a different claim on recourse. The identity places the facility, and the documents behind that facility supply what changed.
A worked example, on invented numbers
A supplier places 100. The lender advances 75 percent against equipment cost, so the placement stands beside a program of 400. The supplier’s margin is 60 percent.
The required share is 0.25 divided by 0.60, or 41.7 percent. The check returns the placement: 400 times 41.7 percent times 60 percent is 100.
Now the lender advances 60 percent instead. The required share becomes 0.40 divided by 0.60, or 66.7 percent. The ratio is 1.60, and it equals 0.40 over 0.25, with the margin absent from it.
Which margin, and why the first answer is a floor
The conversion rate is a choice, and the widest choice produces the smallest requirement.
Gross margin is the widest. It stands above operating cost, so converting at an operating margin raises the requirement. Profit is taxed as it is earned, so converting after tax raises it again. In the example, a 60 percent margin after a 20 percent tax rate converts at 48 percent, and the first requirement rises from 41.7 percent to 52.1 percent.
The requirement is a cash test, so the conversion should be the one that produces cash. Whatever number the gross margin gives is the floor of the answer rather than the answer.
Where it sits among the other treatments
An input a filer does not disclose has three ordinary treatments.
It cancels, where it stands unchanged on both sides of a comparison.
It bounds, where the sign is known and the size is not, so the answer becomes an inequality in a stated direction.
It decomposes, where the parts separate and each is disclosed somewhere.
An item whose sign is unknown reaches none of the three, and it is carried at zero, with the note recording that carrying it at zero reflects an undisclosed sign rather than a valuation.
The required share is a fourth treatment. Where an input is undisclosed, solve for it. What it would have to be is a question whose answer is made of disclosed numbers, even though the input is not.
Read backwards
The same line splits a position that is already carried. It says how much of the money that left has already been returned by the profit the arrangement opened, and what remains of the carrying value stands on the mark alone.
The money that left is carried as an asset. The profit it opened is recorded separately. So the accounts show both, and the identity says how much of the first the second has already covered.
Limits, stated
The identity prices a marginal dollar and holds whatever else stands in the customer’s capital structure. Applying it to a whole program, as though a single placement were the only equity behind it, is the most favorable reading available and should be labeled as such wherever it is used.
A margin taken from a company-wide income statement is company-wide across a product mix that is not the program’s mix, which is an assumption of applicability rather than a disclosed fact.
Where a supplier sells through a channel, the margin realized is the margin on the sale into the channel, and the price the end customer pays sits above it, which lowers the effective conversion and raises the requirement.
And the advance rate cannot be read apart from what the lender was underwriting. A rate that falls because collateral terms tightened and a rate that falls because the counterparty’s credit weakened are different facts wearing the same number.
What it takes to run
Two documents. A credit agreement that states what the lender advances against the relevant assets, and an income statement that states a margin. Both are ordinarily filed. It runs on those two documents alone, and any reader preferring different inputs can substitute them and run the same two lines.
Where it has been run
The construction was first published in application on August 22, 2026, in NVIDIA, What Comes Back, which computes it across four filed credit agreements and states the requirement at each.
Analysis: Cape Fear Advisors. The construction, the treatments and the limits stated here are ours. A search of published research, academic literature and market commentary found no prior version of this construction; others may exist.
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