Fair Value

Valuation techniques (in order)

1. Market approach

As the name suggests, under the market approach, fair value equals current market price.

IFRS 13 | ASC 820 defines fair value (emphasis added): the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date.

IFRS 13.57 | 820-10-30-2 states (edited, emphasis added): the fair value of the asset or liability is the price that would be received to sell the asset or paid to transfer the liability (an exit price).

Summarized: fair value equals the closing price on the last trading day before the end of a reporting period.

The market with the most readily observable transactions is a regulated market such as a stock or commodities exchange.

On such a market, there can be no doubt that the transactions are occurring in an orderly manner between market participants. As such, these of markets provide conclusive evidence as to the fair value of the item being measured.

Since other markets (for example foreign exchange and most publicly accessible OTC markets) may also provide comparable evidence, the guidance does not specify that the market must be regulated, merely that it must be active.

Note: as this issue has more to do with input levels than valuation approaches, it is discussed in more detail below.

When applicable, the market approach is the simplest and most objective way to determine fair value.

At the risk of stating the obvious, the market approach may only be used if an observable, reference market exists.

If an observable, reference market does not exist, an observable, reference market may often be simulated. However, this would no longer qualify as a market approach but rather as a cost approach.

Note: if a market neither exists nor can be simulated, the final option is the income approach, which does not require any observable (market-derived) inputs.

Reflecting its relative simplicity, the guidance for the market approach (IFRS 13.B5 to B7 | ASC 820-10-55-3A to 3C) is succinct, primarily pointing out that the approach is not limited to identical items are traded on active markets but includes comparable items on an observable market (IFRS 13.B6 | ASC 820-10-55-3B).

In addition, it allows measurement by reference to an index of market traded items rather than just the items themselves (IFRS 13.B7 | ASC 820-10-55-3C).

There can be no question that prices on regulated markets (stock or commodity exchanges) represent orderly transactions between market participants (above).

As fair value represents an exit price if the market approach is used, care must be taken to use the bid price for assets, offer price for liabilities.

In contrast to IFRS | US GAAP, some statutory, national accounting standards mandate the use of midpoint price.

While mid-market pricing would not be consistent with the logic behind IFRS 13 | ASC 820, it is (as a practical expedient) allowed by IFRS 13.71 | 820-10-35-36D.

OTC markets may often offer the same level of pricing objectivity as regulated markets. However, they also comprise dealer markets, principal-to-principal trades, dark pools, and others. Thus, while such markets often provide data comparable to quoted prices in active markets, they may not always be sufficient for IFRS 13 | ASC 820 measurement purposes. Nevertheless, because the data is not based on unobservable inputs, it is objective.

Thus the data derived from these markets is supported by empirical evidence (documented and verifiable market transactions) so is unequivocally objective.

Its simplicity commonly makes fair value determined using this approach readily determinable.

The "readily determinable" concept appears throughout the guidance (most prominently in IFRS 16 | ASC 842) but is not explicitly defined.

However, as market data is readily available and does not require complicated price discovery (for example soliciting third-party offers) and particularly not estimating and discounting expected, future cash flows, fair value determined using the market approach is practically always readily determinable.

In addition to using data from active markets, the market approach could also involve data from markets such as auctions. As auction data can be time consuming and difficult to acquire, using a cost approach based on manufacturer or dealer sales prices is often the more viable alternative.

However, if the cost approach would involve soliciting third party offers, it would not generally qualify as readily determinable.

If an item is traded on an exchange, its fair value can be determined with practically no effort.

If an item is traded on an observable market with readily available pricing data including (for example prices at auction for automobiles, construction equipment, machinery, etc.), determining fair value would require some effort, but not sufficient effort to disqualify fair value from being readily determinable item.

Reliable and objective market data can also be derived from observable market transaction involving, for example, structures such as office buildings, retail malls or warehouses.

However, if the item is an extreme ultraviolet lithography machine or building with unusual features (such as Apple's HQ), it may be possible to identify a market, but not a market with sufficient activity to support a fair value assessment.

Note: items lacking a readily determinable market price may still have a readily determinable fair value. For example, it can be determined by examining manufacture or dealer price lists or soliciting third party offers. However, this would be a market approach, but rather a cost approach (below).

2. Cost approach

As the name suggests, under the cost approach fair value equals current cost.

Mathematically, the market approach and cost approach yield identical results, but only if a reference market exists. In the absence of a reference market, the situation escalates quickly.

At the risk of stating the obvious, the amount a buyer agrees to pay equals the amount a seller agrees to receive. Thus, the only difference between fair value (exit price) and cost (entry price) is perspective.

But, if the transaction has occurred (historical cost) or transactions are occurring (market approach, above), perspective is irrelevant. Price is price. The amount(s) paid/being paid equal the amounts received/being received).

However, if a transaction has not occurred/transactions are not occurring, perspective is important.

For example, if a manufacturer lists a price it is willing to accept for its products (cost), this may be the price it is willing to accept for its products. However, it may also be a starting point for the discussion about the actual price it willing to accept for its products.

The inherent uncertainty associated with determining potential is also the reason the cost approach is, as a rule, less reliable than the market approach.

But, every rule has exceptions. If a potential buyer is willing to give a potential seller a firm offer, price will, again, be price.

However, in order for a potential seller to give a potential buyer a firm offer, the potential buyer has to be, among other things, knowledgeable. This implies the potential seller will need to provide the potential buyer with, for example, blueprints to the unpatented machine to see it it may, perhaps, be able to provide a duplicate, and at what price. It may also need detail the unique, special and secret technology comprising the machine so the potential seller can make an informed offer.

It is worth it? Does providing potential sellers enough information to apply a cost approach justify the risk and, as offers are not usually given for free, expense? Just to satisfy the requirements of accounting guidance?

Would it not be more rational to simply bite the bullet, estimate future cash flow, estimate the probability of the timing and amount of those cash flows, determine an appropriate discount and apply the income approach (below)?

That, dear readers, is a question every accountant has to answer for themselves.

At the risk of stating the obvious, if an identical item is actively traded on an observable market, there is no need to speculate about what potential buyers would pay or potential sellers would receive. The transactions are occurring. The buyers are buying. The sellers are selling. The consideration is being exchanged. Its amount is known. No assumptions. No speculation. No estimates. Market price is market price.

Applying the market approach is as simple as recording the item's closing, quoted price on the last trading day before the end of the period.

In the absence of a reference market, one has to speculate about what a potential, hypothetical buyer would pay. In the absence of a reference market, one has to speculate about what a potential, hypothetical seller would demand. For most accountants, speculating about the possible future actions of potential, hypothetical buyers or sellers makes them feel as if the egg salad they had for lunch was well past its best by date.

This begs the question, in the absence of a reference market, both the market and cost approach require evaluating the hypothetical so why two methods? Would not having just one be simpler?

Yes, mathematically, it would.

However, accounting is not just about mathematics. Accounting must also be practically workable.

As explained in IFRS 13.B9 | ASC 820-10-55-3E, the cost to the seller reflects the cost to the buyer, because the buyer would not pay more when they are a buyer than if they were a seller. Though perhaps, this paraphrase does not do the original justice.

IFRS 13.B9 | ASC 820-10-55-3E states: From the perspective of a market participant seller, the price that would be received for the asset is based on the cost to a market participant buyer to acquire or construct a substitute asset of comparable utility, adjusted for obsolescence. That is because a market participant buyer would not pay more for an asset than the amount for which it could replace the service capacity of that asset. Obsolescence encompasses physical deterioration, functional (technological) obsolescence, and economic (external) obsolescence and is broader than depreciation for financial reporting purposes (an allocation of historical cost) or tax purposes (using specified service lives). In many cases, the current replacement cost method is used to measure the fair value of tangible assets that are used in combination with other assets or with other assets and liabilities.

What the standard setters are, in their own particular way trying to say, finding and getting inside the need of a hypothetical seller way easier than a hypothetical buyer.

The only effort is usually required, visiting a manufacturer's or dealer's web site and opening the price page. This is usually more feasible than scouring the world for potential buyers and asking them what would, perhaps, be willing to pay.

Actually, good practice is to examine at least three price lists from three sellers of different but comparable items and record the average.

Also, as the listed prices are often for new items, one must compensate for obsolescence encompasses physical deterioration, functional (technological) obsolescence, and economic (external) obsolescence which is broader than depreciation for financial reporting purposes (an allocation of historical cost) if the item being measured is not new.

But this is just a detail.

Also, adjustments would not be necessary if the market for comparable items were sufficiently deep that one could consult information sources such as AUTO1 Group Price Index or Kelley Blue Book.

Similarly, as many industrial items are sold at action and as auction prices reflect obsolescence encompassing physical deterioration, functional (technological) obsolescence, and economic (external) obsolescence they can usually be taken without any, or at least any significant, adjustments.

Usually but not always. Occasionally finding a buyer is easier. For example, if a bank would like to sell a portfolio of loans (assuming it does not want to securitize it), it would seek out offers to buy not offers to sell.

While the market approach does not generally rely on third party offers, it does not preclude using the method to determine fair value.

The relative simplicity of the cost approach also explains why it is permitted by the guidance even though it is logically inconsistent with the guidance.

By definition, fair value is an exit price: the amount that would be received from the sale of an item in an orderly transaction between market participants. Cost, however, is an entry price: the amount required to buy an item in an orderly transaction between market participants. Where is the logic in using an entry price to determine fair value when fair value is an exit price?

The IASB acknowledged this logical inconsistency. IFRS BC 141 states (edited, emphasis added): respondents generally agreed with the descriptions of the three valuation techniques. Some respondents questioned whether a cost approach is consistent with an exit price definition of fair value because they think that the cost to replace an asset is more consistent with an entry price than an exit price. The IASB noted that an entity’s cost to replace an asset would equal the amount that a market participant buyer of that asset (that would use it similarly) would pay to acquire it (ie the entry price and the exit price would be equal in the same market). Thus, the IASB concluded that [price being price] the cost approach is consistent with an exit price definition of fair value.

Interestingly, the FASB likely concluded practitioners would likely not object to illogical guidance provided it was practically applicable, did not discuss the issue.

However, while often relatively straightforward, the cost approach is no panacea.

The cost approach is straightforward when the item being valued is similar to other items.

It is ideal for off the shelf machines and equipment (unless sold at auctions with readily determinable prices) as these items have readily determinable manufacturer or dealer prices.

The only potentially difficulty, is if the prices are for new items, the items being measured must be adjusted to reflect their age, obsolescence, wear and tear or perhaps even location. Somewhat labor intensive, but manageable.

The logic breaks down if the item is unique.

For example, how would one determine the cost of a bespoke machine, a production line with custom features, unpatented technology acquired in a business combination based on price lists?

Ok, it would be possible to virtually disassemble the production like and evaluate its components, but not if those components were custom made.

In this situation, as no observable cost can be observed must be created.

To do so, the entity would need to identify a potential, independent market participant able to transact. Next, it would provide that potential market participant with enough information to make them knowledgeable. Finally, it could ensure market participants willingness by offering to compensate that market participant for the time and effort required to draft an offer in which they firmly agree to produce and deliver a comparable item at a specified cost, even though they suspect that no delivery will actually occur.

Also known as a third-party offer to sell, the cost approach is the only possible way to objectively measure the fair value of items without observable markets.

Obviously, if it is possible to obtain an offer to sell from a market participant, it should also be possible to obtain an offer to buy from a market participant.

However, practical issues generally make this approach unsuitable.

For example, while it may be relatively simple to find a manufacturer capable of producing, for instance, a custom-designed production machine, finding a buyer willing to acquire such a machine may be impossible or prohibitively expensive.

Further, buyers are often influenced by strategic or subjective considerations unrelated to fair value, such as negotiation tactics, which can affect an offer to buy considerably more than an offer to sell.

Thus, as a general rule, if there are no market-observable transactions that can be used to confirm a market price, an offer to buy (even several offers to buy) is generally considered unreliable and would most likely be rejected by an independent auditor.

The only disadvantage of offers to sell, since they represent the price at which the offeror is willing to sell, they do not reflect just the item’s intrinsic value but the seller’s profit margin. Eagle-eyed auditors notice this and will likely require adjustments to be made.

It is also, commonly, the last resort, although exceptions do exist.

No method elicits more dread than the cost approach.

Obviously, compensating those making the offer for their effort is required, but this cost is negligible.

The real cost is ensuring the third-party is informed and knowledgeable, and thus a valid market participant.

Informed means sharing all the technical specifications (including, for example, the unpatented technology, secret formulas and similar proprietary and sensitive know-how comprising a production line) and hoping that, after the offer has been received, the information remains confidential.

This obviously means not soliciting offers from parties domiciled in China or other jurisdictions where qualms about utilizing unpatented technology, secret formulas and similar proprietary or sensitive know-how are non-existent (at least with respect to foreigners).

Faced with these challenges, the thought of estimating future cash flows and their timing and amounts, assigning probabilities to those timings and amounts, and calculating present value using a discount rate that captures any risks not addressed in step three, becomes positively inviting by comparison.

Occasionally entities prefer the cost approach because it yields superior results.

For example, during an impairment test, fair value may be determined to reflect an asset's highest and best use (income approach). This should reflect the item's intrinsic value.

However, an offer to sell from a third-party (cost approach) would likely reflect not just the item's intrinsic value, the seller's profit margin, which would increase the assets value and decrease the impairment.

Note: eagle-eyed auditors should notice this and require adjustments to be made, but not all auditors are eagle-eyed, especially in an IFRS context.

During an impairment test in IFRS, the entity compares fair value (less cost to sell) with value-in-use.

Fair value may, however be calculated using the income approach. With this approach (IFRS 13.89), the entity develops unobservable inputs using the best information available in the circumstances, which might include the its own data. True, it must also adjust the data if reasonably available information indicates other market participants would use different data or there is something particular to the entity that is not available to other market participants (e.g. an entity‑specific synergy). However, it need not undertake exhaustive efforts to obtain information about market participant assumptions.

In determining value-in-use (IAS 36.33.a), the entity bases cash flow projections on reasonable and supportable assumptions that represent management’s best estimate of the range of economic conditions that will exist over the remaining useful life of the asset while giving greater weight shall to external evidence.

Assuming developing unobservable inputs using the best information available, including the entity’s own data, does produce a different result than basing cash flow projections on management’s best estimate with greater weight on external evidence, the entity may choose the higher of the two.

Note: this is an IFRS only issue because US GAAP does not recognize value in use. In US GAAP an impairment always reflects the difference between the book value of an asset (or group) and its fair value.

The market approach (above) uses observable, contemporaneous, market transactions to determine fair value. As observable, contemporaneous, market transactions yield the best the best possible representation of fair value, why would anyone ever desire to use anything but?

Why is it best?

Because it requires any estimate. Market price is a given.

If one observes a price being paid/received on a market, the price is being paid/received on a market. It is unequivocal.

The accounting for market price is similarly unequivocal: one observes the market price, one recorded the market price, job done.

Also, because market price is unequivocal, it cannot be questioned, not by management, not by auditors, not by regulators, not even, if things really go south, a judge or, in some jurisdictions, a jury.

Thus, from an accountant's perspective, nothing beats market price (except, perhaps, winning the lottery).

At the risk of stating the obvious, the market approach requires a market.

Unfortunately, a market does not always exist. For example, it would not be hard to find a market for a stock, bond, barrel of oil or bushel of wheat.

Try finding a similar market for made to order production machine or production line with unique, bespoke features. Good luck with that.

Seriously, the market approach can be used for many physical assets even if there is no active, reference market.

For example, automobiles can be priced using the AUTO1 Group Price Index or Kelley Blue Book. Industrial items such as CNC machines, or graders, or loaders are commonly bought and sold at auction.

While it would generally be permissible to value such items using the cost approach, since the cost approach is invariably based on the cost of comparable NEW items, using it requires making adjustments to reflect obsolescence encompassing physical deterioration, functional (technological) obsolescence, and economic (external) obsolescence.

In contrast, information sources such as the AUTO1 Group Price Index, Kelley Blue Book or records of prices at auction already reflect age, wear and obsolescence. As such they can be used as, without any need for adjustment.

Fortunately, industrial equipment, manufacturing robots, CNC machines, etc. all have manufacturers and/or dealers. Manufacturers and dealers often publish price lists. Looking up prices in price lists is almost as easy as checking the price of a stock on the stock market. True, as the prices will need to be adjusted to reflect wear and tear, obsolescence, and so on, but these adjustments are far simpler than estimating future cash flows, adjusting them for timing and amount risk, and determining an appropriate discount rate.

Thus, using the entry price as a proxy for an exit price is a simple solution to a seemingly intractable problem.

The only difficulty, it is also logically inconsistent with the idea of fair value.

IFRS 13 | ASC 820 define fair value: the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date. This definition is also echoed in the guidance (for example IFRS 13.24 | ASC 820-10-35-9A).

Fair value is thus an exit price.

Cost is the price that would need to be expended to acquire a particular item.

Cost is thus an entry price.

By allowing entry price to serve as proxy for exit price while, at the same insisting fair value is an exit price, the standard setters not only overlooked the logical inconsistency of the guidance, they embraced it.

Emphatically. With both arms. Then gave it a great big, sloppy wet 💋

Fortunately, logical consistency does not always good standard setting make.

Good standard setting means achieving the desired outcome without overburdening practitioners with unnecessarily cumbersome guidance. Sometimes the standard setters, as with the cost approach, get it right.

That accounting standards require a strong, theoretical foundation cannot be disputed (as the previously ad hoc approach to accounting that precipitated the creation of today's standard setters demonstrated).

Unfortunately, systematic and disciplined intellectual inquiry aimed at posing complex questions, critically exploring ideas, evidence, and arguments to advance understanding within a scholarly community characterized by an open-ended investigation aimed not merely at establishing fixed answers but at generating new knowledge through rigorous analysis, evaluation of competing interpretations, and reasoned argumentation grounded in empirical or theoretical evidence; a process that relies both on critical thinking acumen and methodological rigor to engage with problems, test hypotheses, and contribute thoughtfully to discourse can lead to cumbersome guidance.

As the academic community has historically held greater sway over the IASB than FASB, the former at least acknowledges the inconsistency, rather than simply riding past.

IFRS BC 141 states (emphasis added): Respondents generally agreed with the descriptions of the three valuation techniques. Some respondents questioned whether a cost approach is consistent with an exit price definition of fair value because they think that the cost to replace an asset is more consistent with an entry price than an exit price. The IASB noted that an entity’s cost to replace an asset would equal the amount that a market participant buyer of that asset (that would use it similarly) would pay to acquire it (ie the entry price and the exit price would be equal in the same market). Thus, the IASB concluded that the cost approach is consistent with an exit price definition of fair value.

The FASB does not mention the issue in the basis for conclusion to FAS 157 or any updates to ASC 820.

Other times, not so much.

Sometimes, practicability, as with the cost approach, defeats the desire for methodologically robust and epistemologically sound solutions to seemingly intractable problems. Other times, not so much.

For example income tax. As the name implies, income tax derived from income. Since accounting income and taxable income are not equal, deferred tax must be recognized. The simplest and most direct way to calculate deferred tax is to compare accounting income with taxable income. But, IFRS | US GAAP are based on the asset/liability model, not an income/expense model, presenting an intractable problem.

In this particular situation, the solution was to determine deferred tax on the basis of the tax base of assets and liabilities.

Wait, what?

Yes, you heard that correctly, said the professor to the budding accountant: the tax base of assets and liabilities.

But isn't that like putting the round peg into the square hole? Opined the student.

Well, stammered the professor, perhaps it may seem so to the uninitiated, but, you see, deferred income tax is an asset or a liability, thus must be determined on the basis of the asset/liability model, about which the profession has reached the consensus that it provides the superior foundation for contemporary accounting thought than the less desirable income/expense model which, coincidentally serves as the basis for determining taxable income. Thus, not basing the preferred approach on the preferred model, while arguably less operationally complex and yielding the same mathematical result, would not be epistemologically sound, methodologically robust, conceptually acceptable or logically consistent, and would be, coincidentally, contradictory to the explicit requirements laid out in IAS 12 | ASC 740.

Aha. No wonder my roommate switched majors to applied mathematics, replied the student.

Note: the guidance is not actually as hard (as illustrated in the deferred tax section of this page) as this scene makes it. However, as an instructor, I have found that teaching deferred tax to students does require time and effort (and gnashing of teeth).

Thus, using an entry price to determine an exit price, even though the two are not the same, is perfectly acceptable as far as IFRS 13 | ASC 820 are concerned.

The cost approach is thus, generally, the second simplest, and second most objective way to determine fair value.

Finding a reference market for highly specialized, even if technically comparable, items can be challenging. For example, while a market for used extreme ultraviolet lithography machines does exist, it is limited in both scope and transaction volume. In such situations, provided sufficient internally generated data can be located, the income approach will yield a considerably more "readily determinable" fair value measurement than attempting to force a square peg into a round hole.

Depending on how it is applied, fair value determined using the cost approach may also be readily determinable.

If the cost approach consists of evaluating published price lists and similarly readily available data, fair value determined this way is practically as determinable fair value using quoted market prices.

However, it is also possible to base the cost approach on third party offers. The cost and difficulties associated with such offers generally makes fair value determined this way not readily determinable.

The concept of a "readily determinable" fair value appears throughout the guidance, most prominently in IFRS 16 | ASC 842, but is not explicitly defined.

However, if the cost approach involves soliciting third-party offers, fair value determined this way would not be generally considered "readily determinable."

Broadly speaking, cost may be subdivided:

1. Cost

Cost is the amount paid in a past, arm's length transaction and occurs only once. Nevertheless, as it represents the basis the cost approach, it belongs in this list.

The difference between the arm's length transaction (used to determine historical cost) and the orderly transaction between market participants (used to determine fair value) is explored in the first subsection of the introduction above.

2. Replacement cost

Replacement cost is the price that would need to be paid to reproduce the functionality of the item being measured. It is the only method acceptable for IFRS | US GAAP purposes.

While IFRS 13 | ASC 820 does not separately define replacement cost, it is included in the definition of the cost approach, which specifies it will reflect the amount that would be required currently to replace the service capacity of an asset. As reproduction cost is not offered as an alternative, it is disallowed by omission.

This issue becomes important when the historical and contemporaneous construction methods yield significantly different costs.

For example, if XYZ acquired a brick factory building in a business combination, it would base fair value on the cost of a similarly functional factory building built using a modern method (e.g. a steel reinforced concrete shell covered with composite cladding) rather than a building made of bricks.

3. Reproduction cost

Reproduction cost is the price needed to replicate the asset, not merely reproduce its functionality. As such, while a listed approach in, for example, IVS.70.1.b, it would not be acceptable for IFRS | US GAAP purposes except in specific circumstances.

While IFRS 13 | ASC 820 does not explicitly define replacement cost, it is implicitly defined by the definition of the (emphasis added): a valuation approach that reflects the amount that would be required currently to replace the service capacity of an asset (often referred to as current replacement cost).

As IFRS | US GAAP does not mention reproduction cost, it is prohibited by omission.

For example, if XYZ acquired a historical brick factory building in a business combination, it would determine reproduction cost by estimating the expenditures needed to replicate the structure using bricks as the construction material.

This would be inconsistent with IFRS | US GAAP unless the construction material determined the building utility.

Thus, if XYZ intends to convert the building into offices or residential space, the construction material, which is essential to the structure’s aesthetic appeal and thus will be a key element of its future selling price will be reflected in the building’s valuation.

4. Summation cost

While summation cost is presented as a separate method in IVS.70.1.c, it is not, in reality, a stand-alone valuation approach.

Instead, it is an additive way to determine the cost of an asset that cannot be measured as a whole (for example a production line, a cash-generating | reporting unit or business acquired in a business combination) but must be broken down into measurable components, which are separately priced and finally summed. However, while IFRS 13 | ASC 820 does not mention a "summation method," it would be consistent with the guidance in IFRS 13.63 | ASC 820-10-35-24B.



3. Income approach

As the name suggests, under the income approach, fair value equals income. Just not current income.

Unlike the previous approaches that reflect current conditions, the income approach rests on future conditions.

Why? Because the standard setters said it was OK. That's why.

IFRS 12.2 | ASC 820-10-05-1B spell out the objective of the guidance specifying, among other things, that it represented the amount at the measurement date under current market conditions.

By definition, the income approach does not examine current conditions, but expected future conditions. As such it contradicts this objective.

This is, obviously, a very good thing.

Occasionally, it is simply not possible to determine fair value by reference to a current market so, if an income approach were not allowed, fair value could not be determined which would present the practice with an insurmountable obstacle.

So, allowing an income approach is the standard setters way of having their cake (providing actionable information to financial statement users) and eating it (allowing practitioners to do their job effectively and reasonably) too.

And, in the immortal wisdom of Donkey, cake is almost as good as parfait.

Interestingly, while the result can only be one, three, four, five or more ways to determine it exist.

Depending on how the ways are counted.

IFRS 13.B11 | ASC 820-10-55-3G list three income techniques (present value, option pricing models multi-period excess earnings).

However, present value can be calculated using the discount rate adjustment technique (IFRS 13. 820-10-55-10… | ASC 820-10-55-10…) or expected present value technique. That makes four.

Then, expected present value can be calculated using two methods (IFRS 13.B25 |ASC 820-10-55-15) and (IFRS 13.B26 | ASC 820-10-55-16), that makes five.

Then, come the models. While the guidance explicitly mentions two Black-Scholes-Merton and binomial, a.k.a. matrix or lattice) bring the tally to six, it may also be possible to use a considered stochastic model which brings the total to almost 20.

E.g. Monte Carlo, finite difference, Longstaff-Schwartz, Heston, GARCH, Merton’s jump-diffusion, Dupire’s model, Regime-Switching models, Fourier Transform methods (COS, FFT), Variance Gamma, CGMY, Meixner, Normal Inverse Gaussian (NIG), Esscher transform, rough volatility models, affine term structure models (CIR, Vasicek, Hull-White), Hidden Markov Models, SABR, multifractal models, agent-based models, mean-field games. etc.)

And, then comes multi-period excess earnings.

However, regardless of model, the calculation always involves quantifying the contemporaneous value of expected future cash flows (either without or with the help of a random number generator).

Admittedly, IFRS 13 | ASC 820 does not explicitly endorse stochastic methods.

As a rule, randomness, while often used in valuation in practice, is not sufficiently rigorous for financial reporting purposes. Nevertheless, the Monte Carlo method is seriously considered as a plausible way to determine the fair value of employee stock options (ASC 718-10-55-22) suggesting that, in certain circumstances it would be acceptable for US GAAP purposes. While IFRS fails to give Monte Carlo such whole hearted endorsement, the fact the method is seriously discussed in IFRS 7.B20 lends credence to the interpretation that randomness could, in certain limited circumstances, be acceptable for IFRS valuation purposes as well.

But, a list would still have been darn helpful.

Be that as it may, if it makes the standard setters happy to divide the income approach into the Three Musketeers, who are we to argue. Their job is hard enough as is.

Most importantly, as the future can never be never certain, the income approach can never yield an absolutely accurate result and thus is always the approach of last resort.

As with every general rule, an exception always exists. For example, if the item being measured is a AAA rated bond, the probability that the issuer will miss an interest or principal payment, or even be late on one, is so negligible, it does not need to be rationally considered.

To emphasize the point, IFRS 13.3 | 820-10-05-1C states (edited, emphasis added): when a price for an identical asset or liability [level 1 inputs] is not observable, an entity measures fair value using another valuation technique that maximises the use of relevant observable [level 2] inputs and minimises the use of unobservable [level 3] inputs...

This is great advice.

It is particularly good advice if the remainder of the guidance (edited, emphasis added) is considered ... because fair value is a market-based measurement, it is measured using the assumptions that market participants would use when pricing the asset or liability, including assumptions about risk...

Specifically, as level 3 inputs generally comprise management’s best estimates, to use such estimates in an income approach the accountant must consider what a market participant, by definition an outsider, would conclude if they were given privileged information only available to insiders.

Speaking as an accountant, this sort of logic makes me both nostalgic and my head hurt.

But it's so simple! All I have to do is divine from what I know of you. Are you the sort of man who would put the poison into his own goblet or his enemy’s?

Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what is offered. But you must have known I was not a great fool, so I can clearly not choose the wine in front of you.

But wait! You must have suspected I would know that, so I can clearly not choose the wine in front of me!

You’ve beaten my giant, which means you’re exceptionally strong. So you could’ve put the poison in your own goblet, trusting your strength to survive what comes after. But you also bested my Spaniard, which means you’re skilled with a sword. So you could’ve put the poison in my goblet, knowing you’d survive the fight that followed.

Ha! You fell victim to one of the classic blunders! The most famous is “never get involved in a land war in Asia,” but only slightly less well-known is this: “Never go in against a Sicilian when death is on the line!”

Then Vizzini laughs maniacally and drops dead.

1. Present value

   Also known as discounted cash flow, present value is calculated:

   PV = Σ_t=1ⁿ P / CF _t
   (1 + r%)^t

   • PV = Present Value
   • P / CF_t = Principal / Cash flow at time t
   • r = Discount rate
   • n = Number of periods

   Although they involve vastly different assumptions, estimates and inputs, IFRS 13.B11.a | ASC 820-10-55-3G.a presents the following two methods under a common heading ¯\_(ツ)_/¯

1. Discount rate adjustment (risk-adjusted discount rate method)

   The discount rate adjustment technique (a.k.a. risk-adjusted discount rate method) is calculated:

   The risk-adjusted discount rate method has been around as long as financial analysis and forecasting have been around. Why didn’t the standard setters simply use this well-established terminology instead of calling it coming up with the discount rate adjustment technique?

   Probably just to be different.

   PV = Σ_t=1ⁿ P_t
   (1 + i%)^t

   • PV = Present Value
   • P_t = Principal at time t

   The single, most likely cash flow (IFRS 13.B18 | ASC 820-10-55-10).

   • i = Discount rate

   The discount rate is determined on the basis of observed rates of return for comparable assets or liabilities that are traded in the market (IFRS 13.B18 | ASC 820-10-55-10).

   However, the rate also needs to reflect (IFRS 13.B19 | ASC 820-10-55-11) the nature of the cash flows (e.g. whether the cash flows are contractual or non-contractual and are likely to respond similarly to changes in economic conditions), as well as other factors (e.g. credit standing, collateral, duration, restrictive covenants and liquidity).

   If such a rate is not observable, it must be determined.

   In practice, this involves starting with the risk free rate and adjusting it to reflect for the timing and amount (including zero in case of default) of the cash flow associates with the item being measured.

   While default risk is fairly straightforward to quantify and express in percentage terms, volatility is more challenging, except for the most diehard statisticians, leading most practitioners to favor a simpler approach (e.g. expected present value below), except in situations where the item being measured (e.g. a loan, note or bond) has fixed (or at least firmly defined) cash flows.

   • n = Number of periods

   This method assumes a single (most likely) cash flow (P) discounted using a rate adjusted for risk.

   Due to the inherent difficulty of expressing volatility in rate terms, this method is commonly used only for financial items with fixed, or at least defined, cash flows (e.g. loans, notes or bonds) and not non-financial items (e.g. machinery, equipment, production lines, business units).

2. Expected present value (risk-adjusted cash flow method)

   The expected present value technique (a.k.a risk-adjusted cash flow method) is calculated:

   When CON 7 introduced the expected present value method to the accounting community, they introduced it as if they had just discovered sliced bread, explaining in excruciation detail how to apply this all new and exotic method for calculating present value. Why? the likely reason is that accounting standard setters spent their college years studying accounting. In contrast, anyone who had taken finance classes immediately recognized the method for what it was, the risk-adjusted cash flow method. A staple of rigorous financial modeling going as far back anyone alive today can remember.

   Flash forward a decade or two, and the expected present value method has become the go to method for discounting any cash flow except cash flow associated with a loan, bond or note, or any financial instrument with a defined (preferably fixed) interest payment.

   Put another way, only an amateur would attempt to determine the present value of anything remotely resembling an asset or liability with a variable and uncertain timing and or timing of cash flow in any way but using a risk-adjusted cash flow method.

   PV = Σ_t=1ⁿ CF_t
   (1 + r_f%)^t

   • PV = Present Value
   • P_t = Cash flow at time t

   Cash flow adjusted for risk.

   Specifically, the estimate should reflect the probability and timing of the amount (including zero) and timing of the cash flows associated with the item being measured.

   Assuming all the uncertainties (risks including systemic risk) have been identified (included in the probability estimate), the cash flow may be discounted using a risk free rate, which has the advantage that it need not be estimated, but can be readily determined using accessible informant sources.

   • r_f = Discount rate

   As outlined in IFRS 13.B17.b | ASC 820-10-55-9.b and IFRS 13.B25 | ASC 820-10-55-15, provided all the risks have been reflected in the cash flow estimate, the risk free rate would be used to calculate present value.

   As outlined in IFRS 13.B17.c | ASC 820-10-55-9.c and IFRS 13.B26 | ASC 820-10-55-16, if all the risk is not captured in the cash flow estimate, the risk free rate may still be used but it must be adjusted to reflect uncaptured risks.

   While possible, from a practicality perspective, it would generally be simple to just capture all the risk in the cash flow estimate.

   As a risk free rate need not be estimated, this helps make applying the income approach more straightforward.

   • n = Number of periods

   This method assumes a probability weighted (risk-adjusted) cash flow in that both the probability of various possible amounts (including zero) and the timing of those amounts is incorporated into the cash flow estimate. If this estimate captures all the risks associated with the cash flows, a discount rate not be calculated.. Instead, a risk free rate, readily determinable on the market, may be used.

2. Option-pricing models

   The most commonly used option pricing model is calculated:

   Call option price (C) =	S × N(d1 - )K × e-r(T-t) × N(d2)
   Put option price (P) =	K × e-r(T-t) × N(-d2) - S × N(-d1)

   Where:

   • C = Price of the European call option
   • P = Price of the European put option
   • S = Current price of the underlying asset
   • K = Strike (exercise) price of the option
   • r = Risk-free interest rate (continuous compounding)
   • T − t = Time to maturity (in years)
   • N(·) = Standard normal cumulative distribution function

   And

   d1 =	ln(S/K) + (r + σ² / 2) × (T−t) σ × √(T−t)
   d2 =	d1 − σ × √(T−t)

   Where:

   • σ = Volatility of the underlying asset returns
   • ln = Natural logarithm
   • √ = Square root

   
   

   However, this model only yields acceptable results if used to calculate the value of market traded options. For options such as those granted to employees, different models would need to be applied. A supplemental discussion of this issue is provided the derivative section of the financial assets page.

3. Multiperiod excess earnings
   

   Since MPEE is mathematically identical to EPV (above), why two methods (put simply / less simply)?

   Mathematically, multiperiod excess earnings and expected present value are identical.

   Why is it presented as a separate technique?

   Because it started taking steroids.

   The only difference between EPV and MPEE is that, EPV is a bottom up approach (for example estimating the cash flow a production line will generate and then discounting it) while MPEE is a top down approach. It starts by estimating the extra income the entity as a whole will generate then allocates the present value of this amount to the individual items.

   In practice it is generally used only for business combinations where the assets acquired have no, or no easily determinable, market or cost values (e.g. patents, copyrights, trademarks, distribution systems, in-process R&D, unpatented technology, etc.). It may also be used to value an asset group that is not a business combinations, but this is considerably more rare.

   Importantly, as this method requires estimating how much an entity will make in the future compared to how much it would have made in a different future it is, put figuratively, what the EPV becomes when the EPV starts difficulty enhancing drugs.

   From a theoretical and quantitative standpoint, the expected present value (EPV) method and the multiperiod excess earnings (MPEE) method are operationally equivalent insofar as they both yield discounted cash flow valuations that reflect the time value of money associated with the asset or assets under examination.

   Notwithstanding this mathematical equivalence, the delineation of these methodologies into discrete valuation techniques arises from their fundamentally divergent conceptual frameworks and procedural implementations within financial reporting and business valuation paradigms.

   The EPV approach is characterized as a bottom-up, asset-specific discounted cash flow model. It entails the systematic projection of an asset’s anticipated net cash inflows over its economic life, appropriately adjusted for risk factors, followed by discounting those cash flows to present value utilizing a discount rate commensurate with the asset's systematic risk profile.

   In contrast, the MPEE methodology applies a top-down, residual income framework. It commences by estimating the aggregate synergetic or incremental earnings attributable to the entity as a whole, relative to a counterfactual enterprise performance baseline absent the acquired asset(s). Subsequently, it allocates the present value of these incremental earnings among constituent intangible assets through an excess earnings analysis predicated on contributory asset charges and economic obsolescence adjustments.

   Practically, the deployment of the MPEE method is predominantly confined to valuation contexts involving business combinations or acquisitions where specific intangible assets lack observable market data or reliable replacement cost inputs. Exemplars include intellectual property such as patents, trademarks, copyrights, proprietary distribution mechanisms, in-process research and development, and unpatented technological know-how. Its application to isolated asset groups external to business combinations remains comparatively infrequent, reflecting both methodological complexity and relevancy considerations.

   A critical operational aspect of the MPEE methodology is the rigorous estimation of differential future earnings performance—the 'with and without' scenario analyses—that isolate the economic benefits specifically attributable to the asset in question by eliminating earnings contributions from other assets and market factors. This procedure inherently requires extensive modeling assumptions, sensitivity analyses, and professional judgment, thus rendering the method more complex and resource-intensive than the EPV approach.

   PV = Σ_t=1ⁿ CF_t
   (1 + r_f%)^t

   • PV = Present Value
   • P_t = Cash flow at time t
   • r_f = Discount rate
   • n = Number of periods
   
   

   Specifically, while, for example, a production line possesses discrete and identifiable future cash flow, a parent, copyright, customer list, distribution system or in-process R&D acquired in a business combination only has value in as far as it enhances the future earnings of the acquiring entity.

   Admittedly, identifying and quantifying potential enhancements of future earnings and allocating them to, for example, a distribution system can be challenging. But, fundamentally, it is no different than estimating and discounting the future cash flows associated with a production line.

   In either situation, assuming the timing and amount of the future cash flows been adequality estimated and adjusted for probability, present value is present value.

   
   

Input levels (in order)

1. Level 1

Quoted prices, active market, identical items

IFRS 13 | ASC 820 does not define quoted prices but, presumably, they are prices that are quoted (e.g. prices listed on an online broker's trading platform).

IFRS 13 | ASC 820 does define quoted prices but, the definition could be better. For example:

A market in which transactions for the asset or liability take place with sufficient frequency and volume to provide pricing information on an ongoing basis.

Active:

• Frequent and regular transactions: Assets or securities are traded often and consistently.
• High trading volume: Many buyers and sellers participate, ensuring robust market activity.
• Tight bid-ask spreads: Small differences between buying and selling prices indicate efficient price discovery.
• High transparency: Prices reflect current, publicly available information.
• Sufficient liquidity: Participants can buy or sell quickly without significantly impacting prices.




Liquid:

• Quick execution: Trades can be completed rapidly without delay.
• Minimal price impact: Transactions do not cause significant price changes.
• High volume of buyers and sellers: Ensures smooth and continuous trading.
• Narrow bid-ask spread: Low transaction costs due to tight price differences.




IFRS 13 | ASC 820 does not define identical items, but presumably they are items that are identical (stocks, bonds, calls, puts, swaps, gold, silver, platinum, palladium, etc.).

2. Level 2
1. Quoted prices, active market, similar items

Some items are very similar.

For example, oil, iron or pork bellies are not identical but close. This also why it is possible to acquire oil futures, iron futures or pork belly futures.

Some items are similar but not that similar.

For example, automobiles, CNC machines, office building. While it is not possible to buy three years old Ford Mondeo futures, one three year old Ford Mondeo is quite similar to every other Ford Mondeo (assuming it has not been crashed).

2. Quoted prices, non-active market

Some non-active market are actually fairly active.

For example, OTC markets for swaps are not as active as organized and regulated stock or commodity markets, but they are still fairly active..

Some non-active markets are not as active, but still fairly active.

For example, automobiles, CNC machines ore used tractors are common bought and sold, often at auction which yields price estimates that are, for all practical intents and purposes, comparable to OTC quotes.

Some non-active markets, while they may be markets, are not very active at all.

For example, while it is fairly easy to estimate a price of standards office or retail space and hence standard office building or shopping malls, often these assets are unique enough that they cannot be measured using level 2 inputs but only level 3.

• Identical items

Most OTC traded securities fall into this category. For example, the market for interest rate swaps does not generally fulfill the definition of active nevertheless one swap is identical to every other swap with the same underlying, notational amount and settlement provisions.

Likewise, financial institutions often trade among themselves in private transactions where the items are identical but market not active or, in the case of dark pools, purposefully and intentionally non-active.

• Similar items
3. Market-observable inputs other than prices

The included list of market-observable inputs makes the term market-observable inputs self-explanatory.

But for the sake of completeness, if an item is an interest rate, yield curve, an implied volatility or credit spread, it is a market observable input.

In contrast, if an item is not an interest rate, yield curve, an implied volatility or credit spread, it is not a market observable input.

1. Interest rates and yield curves
2. Implied volatilities
3. Credit spreads
4. Market-corroborated inputs

Market-corroborated inputs represent data points or valuation assumptions that cannot be directly observed as explicit market prices for the specific asset or liability but can be supported or adjusted using related, observable market data. This validation can occur through correlations, benchmarking, matrix pricing, or by referencing market-derived factors such as interest rates, yield curves, credit spreads, or implied volatilities.

For example, matrix pricing of corporate bonds may be necessary when quoted prices for a specific bond are unavailable; fair value can then be estimated using prices of bonds with similar credit ratings, maturities, and coupons. The relationship between the bond being valued and these benchmark bonds is thus corroborated by observable market data. Valuation of interest rate swaps or loans often relies on interpolated yield curves and credit spread inputs derived from actively traded securities that impact expected cash flows. Pricing options may require using implied volatilities extracted from various similar options traded in liquid markets. Evaluating licensing or right-of-use agreements where direct market transactions are lacking may also require inputs derived from observable market data, such as market rates in comparable licensing or rental contracts.

3. Level 3

By definition, level 3 inputs are unobservable inputs for the asset or liability.

However, as specified by IFRS 13.87 | ASC 820-10-35-53, these unobservable inputs shall reflect the assumptions that market participants would use, even though, as specified by IFRS 13.89 | ASC 820-10-35-54A, the entity develops these inputs using the best information available in the circumstances, which might include its own data. While the entity must adjust those data if reasonably available information indicates that other market participants would use different assumptions, it need not undertake exhaustive efforts to obtain information about market participant assumptions.

Put simply, Level 3 inputs often reflect management's best guess, which the accountant painstakingly converts into the recognized amount(s).

This also implies, since the amount is not derived from objectively verifiable market data, it can always be second-guessed, especially with the clarity of 20/20 hindsight.

For example, while it is possible to calculate the fair value of unpatented technology acquired in a business combination by extracting and allocating future excess earnings from the profitability estimates management drafted when justifying the purchase price of the acquired business, how reliable are these estimates?

How likely is it, three, four, five, six years down the road, it becomes evident that, for example with HP’s acquisition of Autonomy, the estimates were pipedreams; the company overpaid; the allocation of the excess price to individual assets was wrong?

While Léo Apotheker claimed he and his team were deceived and that their estimates would have been, absent fraud, accurate, the verdict exonerating Mike Lynch strongly suggests his claim that HP’s management was simply poor at financial analysis and skimped on due diligence resonated with an independent and impartial jury. Mr. Apotheker's subsequent dismissal indicates that HP's board reached its own conclusion about management’s level of competence, particularly its ability to read between the lines.

For balance, a UK judge reached a different conclusion. However, as this was a civil trial, the proof of criminal intent did not need to be as conclusive.

Following the unfortunate passing of Mike Lynch, diverse public opinions emerged, including some that interpret the event as a form of divine justice. While acknowledging these beliefs, this platform is committed to presenting objectively verifiable information and refrains from speculating on spiritual or metaphysical matters, while respecting the views of those who hold them.

In any event, any accountant basing their estimates on unobservable inputs, particularly if they include management's best efforts, had better make very, very sure they have sufficient documentation to conclusively prove that it was the data source, and not the methodology, that caused the discrepancy. Failing that, if problems arise and a scapegoat is being sought, they may find themselves being served up as the roast chevon.

As discussed on in the Acquired in business combination section of this page, if management overpays, the excess purchase price should not be allocated to individual assets unless their fair value can be ascertained and substantiated. In this situation, goodwill in excess of the suggested 10% level should be recognized to prevent the financial statements from being misleading.

Techniques and inputs (combined)

1. Market approach, level 1 and 2
1. Level 1: Active markets, substantially identical items
2. Level 2.a: Active markets, not substantially identical items
3. Level 2.b: Not active market
1. Substantially identical items
2. Similar items
2. Cost approach, level 2
1. N/A: Cost

Not applicable.

cost = historical cost ≠ fair value.

2. Level 2.b: Replacement cost

Determining replacement cost can involve making an estimate of, for example, the cost to self-manufacture a machine or building. While the components costs (parts, material, labor, interest, etc.) fall squarely into level 2.b territory, the final estimate involves some judgment and so begins crossing over into level 3 territory.

Be that as it may, cost is practically always based on observable, level 2.b inputs. If not, it is as scrutinized by the auditor an any estimate utilizing level 3 inputs.

3. N/GA: Reproduction cost

Not generally applicable.

IFRS | US GAAP define cost as replacement cost. Reproduction cost, a measurement attribute in IVS, is not a measurement consistent with IFRS | US GAAP guidance.

4. Various: Summation cost

IFRS | US GAAP does not address summation cost, which is addressed by IVS. However, as combining valuation approaches and input levels, for example when evaluating the individual components of a production line or business acquired in a business combination, is permitted, it is implicitly an allowed approach.

3. Income approach, level 2 and 3
1. Level 2.c, Level 3: Present value techniques
   1. Discount rate adjustment technique (a.k.a. risk adjusted discount rate)
   2. Expected present value technique (a.k.a. risk adjusted cash flow)
2. Level 2.d or Level 3: Various models

   While level 2.c inputs are market observable so consistent with the market approach, level 2.d inputs are merely market corroborated hence unobservable and only consistent with the income approach.

   1. Black-Scholes-Merton
   2. Binomial, matrix, lattice
   3. Stochastic models and simulations (e.g. Monte Carlo, finite difference, Longstaff-Schwartz, Heston, GARCH, Merton’s jump-diffusion, Dupire’s model, Regime-Switching models, Fourier Transform methods (COS, FFT), Variance Gamma, CGMY, Meixner, Normal Inverse Gaussian (NIG), Esscher transform, rough volatility models, affine term structure models (CIR, Vasicek, Hull-White), Hidden Markov Models, SABR, multifractal models, agent-based models, mean-field games. etc.)

      IFRS 13 | ASC 820 does not endorse stochastic methods (methods employing randomness).

      As a rule, randomness, while often used in valuation in practice, is not generally sufficiently rigorous for financial reporting purposes. Nevertheless, the Monte Carlo method is seriously considered as a plausible way to determine the fair value of employee stock options (ASC 718-10-55-22) suggesting that, in certain circumstances, it would be acceptable for US GAAP purposes. While IFRS fails to give Monte Carlo such whole hearted endorsement, the fact the method is seriously discussed in IFRS 7.B20 lends credence to the interpretation that randomness could, in certain limited circumstances, be acceptable for IFRS valuation purposes as well.

3. Level 3: Multi-period excess earnings