Most valuations of private businesses are a multiple and a story. Someone finds a figure that looks like earnings, multiplies it by what businesses of roughly that kind are said to sell for, and then argues the result up or down with adjectives: the customer base is "sticky", the owner is "key", the market is "hot". Each adjective moves the number, and none of them can be checked. Two careful people can start from the same records and finish twice as far apart as either would admit, and neither can say where they parted company.
The Adaptive Valuation Kernel starts from the opposite premise. A valuation is an argument, and every step in it should be a stated input that someone else can examine and recompute. The kernel is one equation that values the equity of any business, of any size, in any industry. The industry chooses which model sits inside the equation, and the evidence decides how much each approach to value counts. The result is stated at one level of value, for one defined interest, under a standard of value fixed before any number is computed.
The top line of that equation is published here, with the reasoning behind each term. The modules beneath it, which turn a company's records into each term, are not. The top line is still a formula in the ordinary sense: every symbol is defined, every input can be measured or argued from evidence, the constraints bind, and the same inputs always give the same number.
Four things fixed before any number
Much of the disagreement about what a business is worth turns out to be disagreement about the question. Two people can each be right about a different question and still argue as though one of them is wrong. The kernel requires four things to be fixed before anything is computed, and every number that follows is conditional on them.
The standard of value
Value to whom, under what assumptions about the buyer and seller? Fair market value is the price at which a hypothetical willing buyer and willing seller, neither compelled and both reasonably informed, would transact. Investment value is the value to one particular buyer, with that buyer's synergies, financing and plans. Fair value is a legal standard, defined by a statute or by case law, and it can differ from both; in some disputes it forbids discounts that fair market value would apply.
The kernel takes the standard from the purpose of the valuation and the law that governs it, whatever setting the number is later argued in. An estate valuation is fair market value even when it ends up in a tax court. A buyer's synergies belong in investment value and nowhere else, so a fair market valuation that includes them has answered a question nobody asked.
The level of value
The same business has different values at different levels. A buyer of the whole company gets control: the power to set pay, sell assets, borrow, merge or close. A share of a listed company is a marketable minority, with no control but the ability to sell at a moment's notice. A stake in a private company may have neither control nor a ready buyer. The gaps between these levels are large, and every value has to say which level it is at before it means anything.
The subject interest
What exactly is being valued? It might be the whole equity, a 25 percent block of common shares, a class of preferred units with a liquidation preference, or an interest under a buy-sell agreement that fixes its price at death. The kernel requires the fraction of the equity and the rights attached to it to be stated. A class with senior rights is valued from those rights, and common equity takes what is left.
The premise
Is the business valued as a going concern, or as a set of assets to be sold? The kernel values the going concern and compares it, scenario by scenario, with what the assets would realize. Where liquidation would be worth more, the premise switches. Where it would not, liquidation still sets a floor.
Only when these four are fixed does the kernel compute anything. Fixing them is what makes two valuations comparable, and it settles in advance a whole class of argument that would otherwise surface at the end.
The top line
Every symbol is a quantity that is measured, or computed from a company's records and a set of stated assumptions:
- is the value today of the interest being valued, in dollars.
- is that interest's fraction of the equity, from 0 to 1, with its class rights stated.
- converts a value held at the level of control to the level the interest actually holds, such as a minority stake that cannot be sold freely. It runs from 0 to 1.
- indexes the scenarios: the base case and the specific things that could go differently, each with a probability .
- indexes the three approaches to value: income, market and asset. is the value an approach gives in scenario , and is the weight it carries.
- is what the equity would realize in scenario if the business were wound up in an orderly way, net of the cost of doing so.
Reading it from the inside out
The equation reads most easily from the innermost term outward, because that is the order in which a valuation is built.
Inside the brackets, each approach produces a value of the business in one scenario, and the weights blend them. The blend is compared with liquidation value in that same scenario, and the larger of the two is kept. The comparison happens in every scenario separately; the section on the floor explains why.
The scenario values are then weighted by their probabilities and summed. The result is a value at the level of control: what the whole equity is worth to someone who could run the business, or stop it, as they saw fit.
Finally, carries that control value to the level the interest actually holds, and takes the interest's share. Control comes first because the decisions that create value, including the decision to liquidate, belong to whoever has control. A minority interest's value is derived from the control value, never the reverse.
The constraints bind
The scenario probabilities sum to one, so the scenarios together state everything assumed about the future. The weights sum to one and none is negative, so the blend is an average of the evidence and cannot add value of its own. The market approach never carries more weight than the income approach, for reasons set out under the principles below.
Because the constraints bind, a valuation can fail them, and that is what makes it checkable. A weight of 0.7 on the market approach breaks one of them, a set of scenarios whose probabilities sum to 1.2 breaks another, and the method reports either.
The same inputs give the same number
Two analysts who agree on the record and the assumptions reach the same value. Where they disagree, the equation shows where: a probability, a weight, a cash flow in one scenario, a liquidation estimate, a conversion between levels. The argument narrows to one input, which can be settled with evidence or at least stated plainly.
The three approaches and what each measures
Valuation practice has three classical approaches, and the kernel uses all three. Each answers a different question, and each, used alone, goes wrong in a characteristic way.
The income approach
The income approach asks what cash the business will produce for its owners, and what that stream is worth today given its timing and its risk. It is the only approach that looks directly at the business being valued: its own customers, margins and capital needs. It is also the approach most exposed to optimism, because every input is a forecast, and forecasts drift upward when the person making them wants a large number.
At its simplest, a steady cash flow that grows at rate , discounted at a required return , is worth
The kernel's income model is considerably more demanding than this textbook expression, but the expression shows why the approach is sensitive. A small change in or moves the value a great deal, and an error in the cash flow carries straight through. Most of the kernel's income modules exist to control those three inputs: what counts as the cash flow, what growth is allowed to be worth, and what return the risk requires.
The market approach
The market approach asks what buyers have paid for comparable businesses, and applies that evidence to the subject. Its strength is that it rests on real transactions. Its weakness is that no other business is this business. A multiple averages over companies with different growth, risk and returns on capital, and often over a different definition of the earnings it multiplies. Applied without adjustment, it imports all of those differences unseen.
The kernel requires the earnings measure to be defined exactly as the comparable data define it, and the price to be bridged to equity on the same basis the comparables were priced. Applying a multiple of one earnings measure to a different one is among the most common errors in small-business valuation, and among the hardest to spot once made.
The asset approach
The asset approach asks what it would cost to reproduce the business's assets, or what they would fetch if sold. It looks at what is on hand, where the other two look at what the business earns. For most operating businesses it does not measure value, because they are worth what they earn, whatever their equipment cost. It does carry two kinds of information no other approach supplies.
The first is a floor. Whatever the business earns, an owner with control can stop and sell the assets, so liquidation value bounds the value from below. The second is a test. If a business earns less than it would cost to reproduce its assets, something is destroying value, and the gap has a name: economic obsolescence. If it earns much more, something is protecting it from competitors, and that protection has to be identified, because the excess will not last without it.
For operating businesses, the kernel therefore reports the asset approach as a layer and uses it for the floor and the test. It carries weight only for businesses whose assets themselves earn the return, such as a property or investment holding company.
How the method thinks
Each principle below answers a common way of valuing businesses that produces a predictable error, and states the rule the kernel uses to remove it.
The industry chooses the model; the evidence chooses the weights
A bakery, a bank and a property company are valued by one equation, with a different model inside the income term. Stated tests choose the model.
For most businesses, debt is financing. The business produces operating cash, and lenders and owners divide it, so the natural method values the operations first and then subtracts the claims of everyone senior to the owners. For a bank that logic fails, because borrowing is the bank's business. Deposits and borrowings are the raw material from which it earns a spread, and they cannot be separated from its operations. So for a financial firm the model works on equity directly, from the book value of equity and the return earned on it above what owners require.
A business that holds assets for their own return, such as a portfolio of properties, is different again. Its value is largely the value of what it holds, less what it owes, and the asset approach carries real weight.
The weights on the approaches come from the evidence each approach can bring for the business in question. A business with a deep set of comparable sales (recent, of similar size, in the same line of business, defined on the same earnings basis) earns the market approach more weight than one with three loosely similar listings from years ago. A business with a long, clean, documented record earns its own income forecast more weight than one with two years of tax returns and a handshake.
The market informs the value and cannot overrule it
Prices paid for other businesses are evidence, and the method weights them as evidence. The market approach is still an estimate of this business's value made by looking at other businesses, and the income approach is the only one about the subject itself.
So the market weight is capped at the income weight. A valuation can lean on the market, sometimes heavily, but the market never decides it alone. When a business's own cash flows and its comparables disagree sharply, the disagreement is information: either the forecast is wrong, or the business differs from its comparables, and the analyst has to find out which. If the market could dominate, that question would go unanswered.
Earnings are restated before they are valued
Reported earnings in a private business are built, reasonably, to minimize tax and to reflect the owner's choices, and they measure value poorly as a result. The owner may pay themselves far more or far less than a hired manager would cost. The business may rent its premises from the owner at a price no landlord would accept. Personal expenses may run through the books. One year may carry a lawsuit, a flood or a windfall that will not recur.
Before anything is valued, the kernel restates earnings to what the business would earn under a hypothetical owner running it properly: market pay for the work the owner does, market rent, no personal expenses, no one-off items. These restatements, often called add-backs, are where small-business valuations most often go wrong unnoticed, because each one raises the number and each one sounds reasonable. The kernel's rule is that an adjustment without a source document is zero. It also charges the real cost of keeping the assets in working order against earnings, so that the business is not valued as if its equipment would last forever.
A risk is counted once
A risk can enter a valuation in two places. It can be written into a scenario, as an event with a probability and cash flows of its own: losing the largest customer, the owner leaving with no successor, a sharp rise in the cost of a major input. Or it can be priced into the discount rate, as a higher required return to compensate for uncertainty.
The kernel's rule is that every risk enters in one place or the other, never both. Scenarios set the expected cash flow, and the discount rate prices the uncertainty around it. When an analyst models the loss of the largest customer as a scenario and also adds a "customer concentration premium" to the discount rate, the same risk has been subtracted twice. The value comes out lower by an amount that reads as prudence and is an error. The worked illustration at the end puts a number on it.
The same reasoning governs the market figure. The prices of comparable businesses already reflect the ordinary risks of businesses like them, which could also lose a customer or suffer a cost shock. So the market figure stays the same in every scenario the comparables share. Only in a state they do not share, such as the outright failure of an early-stage company, does the scenario's own value replace it.
Liquidation is a floor inside each scenario
An owner with control can always stop and sell the assets. That option is worth most in the states where the business is doing worst. In a good year it is irrelevant; in a disastrous one it may be the most valuable thing the owner has.
Applying the floor once, to the averaged result, throws that value away. A healthy base case pulls the average far above liquidation value, so the floor never binds, and the bad scenario in which liquidation would have been the better choice is counted at its going-concern value instead. Applying the floor inside each scenario keeps the option in the states where it pays. That is why the sits inside the sum in the top line.
The floor applies only when the interest being valued carries control, because only a controlling owner can force a liquidation. A minority shareholder benefits from liquidation only if the controller chooses it, and the kernel requires the probability of that choice to be stated.
Growth adds value only when it earns more than it costs
A business that reinvests a dollar and earns exactly its cost of capital on it has grown and created nothing, because the dollar it reinvested is worth exactly what it will return. Growth creates value only when the new capital earns more than investors require, and that is possible only when something stops competitors from doing the same.
Before it values any growth, the kernel asks for evidence of a barrier: a cost advantage, customers who cannot easily switch, scale a newcomer cannot match, a licence or a network. Without that evidence, growth is valued at its cost and adds nothing. With it, growth adds value for as long as the barrier is expected to hold.
An advantage fades unless something holds it up
A business earning more than its cost of capital attracts competitors, and competition erodes the extra return. The kernel assumes the erosion happens over a stated period unless there is evidence of a barrier that stops it. A business valued as though its current excess return will last forever has been valued as a monopoly, whether or not anyone said so.
The reverse is not assumed. A business earning less than its cost of capital is not expected to recover on its own, because low returns persist as stubbornly as high ones erode. An improvement is valued only when it comes with a named plan and the evidence for it: who will do what, by when, at what cost, and why it should work here when it has not worked yet. Without that, the forecast assumes no recovery.
Forecasts answer to base rates
Every forecast is a claim about what this business will do, and base rates say how often businesses like it do so. A forecast of growth, margin or return above what businesses of that size usually achieve needs named evidence specific to the business. Without it, the forecast is cut back to the base rate.
This is the strongest available defence against the planning fallacy: the near-universal tendency to forecast from the inside, from the plan and its logic, instead of from the outside, from what usually happens to plans like it. An owner's forecast is often sincere and usually high. The base rate leaves the owner's sincerity alone and asks for the evidence that this business is the exception.
Value is built once, at control, and converted once
Values arrive at different levels. A transaction multiple for whole companies is a control price. A multiple from listed companies is a marketable minority price. An income forecast built on cash flows normalized to how the business should be run sits at a level of its own. The kernel brings every approach to the level of control, combines them there, applies the floor there, and then makes one conversion, along one path, to the level of the interest being valued.
This removes two of the most common errors in valuing minority interests. The first is discounting a value that already sits at the lower level, so that a minority value is discounted for lack of control a second time. The second is stacking discounts by habit: a minority discount from one study, a marketability discount from another, perhaps a "key person" discount on top, each from a different source and each embedding assumptions the others also embed. On one path, each step is defined and computed from the facts of the case, and no step can overlap another. A discount that comes out negative is treated as a sign of inconsistent inputs, never reported as a premium.
Every price implies a forecast
Any price a business meets, whether an asking price, an offer or the price in a buy-sell agreement, implies a set of expectations: the growth, margins and returns that would have to come true for that price to be fair. After the value has been built, the kernel reverses prices into those expectations, one input at a time. An offer that looks generous may turn out to require only modest growth. An asking price that looks plausible may require the business to outperform nearly every business of its size for a decade. The negotiation can then turn on which of those futures is believable, which the parties can argue from evidence.
The method checks itself
The kernel carries its own checks: identities that must come out exactly when growth is switched off, constraints on the weights, a requirement that every adjustment to reported earnings has a source document, and others. A valuation either meets each of them or fails it.
A reference implementation computes the method, with 110 tests built from worked cases whose correct answers are known, plus tests for rules no worked case exercised. Every revision of the method records the error it fixes, and every error found and fixed in an earlier version is kept as a test, so reintroducing it makes at least one test fail. The method is written down as a specification, and where the written specification and the code disagree, the tests decide.
How the method adapts to five businesses
"Adaptive" in the name is the claim that one structure fits very different businesses. Five of them show what changes and what stays fixed.
A large public company
The interest is one share, at the level of a marketable minority, so no conversion is needed beyond the one the market already makes. The income approach governs, with a required return taken from the market and a competitive-advantage period that has to be evidenced. Listed companies in the same industry supply the market approach. The liquidation floor never binds in practice, because the business is worth far more running than broken up, and the asset approach is a layer only.
An owner-run bakery
Here almost everything that matters happens before the equation. The owner's pay is restated to what a hired baker-manager would cost. The real cost of keeping the ovens running replaces the accounting depreciation. There is no evidence of a barrier to entry, so growth is valued at its cost and today's excess return, if any, fades over a few years. The required return reflects that the likely buyer is an individual who cannot diversify the risk away. Sales of similar small businesses supply the market approach, on the earnings definition the sales data use, with any buyer-specific premiums removed and the weight capped. Liquidation value is a real floor, scenario by scenario, and the scenarios include the owner's own departure. The interest is usually the whole business, at control, with the cost and time of selling it taken into account.
A mid-size private bank
The income model works on equity, from book value and the return the bank earns on it above what owners require, and that excess return is assumed to end at some point unless peers show otherwise. Listed banks supply the market approach, priced against book value. A minority stake is converted along the one path, with its marketability discount computed from the facts of that holding rather than taken from a table.
A real estate holding company
The asset approach carries weight, because the properties themselves earn the return. Their market value, plus anything else the company owns, less its debt, other claims and any tax due on gains built into the holdings, is the core of the value. Interests in such companies are usually minority stakes in a family entity, and the conversion to the holder's level does most of the work.
An early-stage biotech
The scenarios dominate. There is a state in which the drug is approved and a state in which it fails, each with a probability that has to be stated and defended. In the success scenarios, the income approach values the business that would exist. In failure, the company is worth what its assets would realize; the market approach does not share that state, so the scenario's own value replaces it. No revenue multiple may sit in the terminal value of a company that has no revenue.
What stayed fixed
Across all five, the top line is the same. The standard, level, interest and premise are fixed first. Risk is counted once. The floor sits inside the scenarios. The market is capped at the income approach. Growth is worth nothing without a barrier. Forecasts answer to base rates. Value is built at control and converted once. What changed is which model sits inside the income term, which approach carries weight, and which scenarios matter, and a stated test chose each of those.
A worked illustration
The figures are illustrative, chosen to show the arithmetic rather than taken from any company.
The base calculation
A 25 percent stake in a private company is being valued. Two approaches carry weight, income at 0.6 and market at 0.4, which satisfies the cap. There are three scenarios, with values in millions of dollars. In the base case, with probability 0.7, the income approach gives 4.0, the market approach 3.6 and liquidation 1.2. If the largest customer is lost, with probability 0.2, income gives 2.2 and market still gives 3.6, because the comparables already carry this risk; liquidation is 1.2. Failure, with probability 0.1, is a state the comparables do not share, so both approaches take the scenario's own value of 0.5; liquidation is again 1.2.
Each scenario takes the blend of its approaches or its liquidation value, whichever is higher:
Weighted by probability, the value at the level of control is
The stake is a minority that cannot be sold freely. Suppose the conversion along the one path from control to that level gives . Then
The stake is worth about $588,000. About 64 percent of the value at control sits above the liquidation floor of 1.2. That is the share of the conclusion that depends on the business continuing to perform; the rest is covered by what its assets would fetch.
If the floor were applied after averaging
Applied once to the averaged result, the floor never binds, because the average is far above 1.2. The failure scenario is then counted at its going-concern value of 0.50 instead of 1.20:
The difference is small here, 0.07, because failure is unlikely, and it grows with the risk. If the same company had a 30 percent chance of failure and a 50 percent chance of the base case, the floor applied inside each scenario gives 2.832, and applied after averaging gives 2.622. The owner's option to stop and sell is then worth 0.21, about 7 percent of the value, and the conventional order of operations leaves it out.
If a risk were counted twice
Suppose the income approach's base-case value of 4.0 came from a steady cash flow of 0.40 a year with a gap of 10 percentage points between the required return and growth, and the customer-loss value of 2.2 from 0.22 a year on the same terms. The customer-loss scenario already carries the concentration risk. Now suppose the analyst also adds a two-point "concentration premium" to the required return, widening the gap to 12 points. The income values fall to 3.33 in the base case and 1.83 in the customer-loss case, and the value at control becomes
That is 9.6 percent below 3.36, with no new information about the business. The stake falls from about $588,000 to about $531,000, and to anyone reading the report the lower number would look like the more prudent one.
If discounts were stacked
Consider an income value of 4.0 that already sits at the level of a marketable minority, because it was built on cash flows normalized to how the business should be run. Treating it as a control value, an analyst applies a 20 percent minority discount and then a 30 percent marketability discount:
The minority discount should not have been applied, because the value was never at the level of control. The correct figure, with the marketability discount alone, is
The stacked figure is 20 percent too low. Nothing about the business justified the gap. It comes from bookkeeping between levels, and building every value at control and converting it once along one path removes it.
What the method does not claim
The kernel moves judgment into the open; it does not remove it. A probability for a scenario is still an estimate. A competitive-advantage period is still an argument from evidence. A base rate still has to be chosen for the right kind of business. Each of those judgments is stated once, as an input someone else can examine, instead of being spread through a multiple and a paragraph of adjectives.
It does not make a poor record good. A business with no reliable accounts will produce a valuation with wide uncertainty however carefully it is computed, and the method reports that width. Exact arithmetic on uncertain inputs is still uncertain, so the kernel reports the margin of safety as a number against each lower bound. A reader can see how much of the conclusion rests on forecasts and how much on what is already there.
It does not replace the standard of value that a court or tax authority will rely on. Where a valuation will be used in such a setting, the kernel's figures are set beside the methods that setting expects, and the differences are explained input by input.
Its parts are not new. Adjusted present value, earnings power and reproduction value, residual income, the integrated theory of levels of value, the fade of competitive advantage and the use of base rates are all established ideas, each with a literature behind it. The kernel holds them in one structure, with one order of operations, so that each idea is used where it belongs and nowhere else, and so that the whole can be computed, checked and tested like any other formula in finance.