Fair value estimation and revenue recognition

“The London Coal Exchange” Thomas Rowlandson et al. (1808)

Rudyard Kipling said “East is East and West is West and never the twain shall meet.” Observations from my career in finance and accounting lead me to re-use his words:

Valuation is valuation and accounting is accounting
and (unfortunately) never the twain shall meet.

At least that’s how many valuation and accounting professionals seem to think and act. It can be shown that financial accounting is comprised of only three dimensions: measurement, recognition, and disclosure; and accounting measurement is precisely valuation. Yet accounting professionals routinely abrogate their responsibilities for accounting measurement to valuation professionals as I’ve discussed before in an article on why accountants should be trained in econometrics. For example, accountants routinely delegate their accounting measurement responsibilities on things like purchase price allocations to valuation professionals, and often don’t adequately understand the methods used (e.g., they do not understand why a particular risk-adjusted discount rate used in accounting measurement / valuation is accurate and reliable … or not). So, accountants are not only delegating accounting measurement work to valuation professionals, they are also inappropriately delegating the responsibility for the work as well … because they often do not properly evaluate the valuation methods used.

At the same time, valuation professionals also often do not seem to fully understand accounting measurement requirements. To state the matter simply, financial reporting generally requires accounting measurements to be developed objectively–as will be seen below–and yet valuation professionals often develop valuation estimates (i.e., accounting measurements) using theories that are consistently rejected by real-world data and unsupported assumptions. In short, objectivity and supporting evidential matter is important in accounting measurement … something that valuation professionals often seem to neglect.

With all this as background, an important accounting measurement and recognition problem where understanding both accounting and valuation is required comes from the accounting standard IFRS 15–Revenue Recognition from Contracts with Customers. The most difficult aspect of solving the IFRS 15 accounting measurement problem relates to how to measure the unobservable fair value of each performance obligation component of a customer contract.

Because this is mainly an accounting topic and, accordingly, is expected to be boring, I will live up to expectations and present the topic in a dry technical way; leaving literary embellishments for other topics. :- ) So, with this caveat, let’s begin …


Under IFRS 15, revenue recognition for an identified customer contract consists of (1) determining the contract price, (2) identification of all individual performance obligations within the contract, (3) estimating the marginal fair value of performance obligations, (4) allocating contract price to performance obligations based estimated marginal fair values, and (5) recognizing revenues as performance obligations are fulfilled.

1. Determining contract price

Customer contracts generally require customers to pay cash payments (CF) and non-cash payments over time. Under IFRS 15 and IFRS 13, contract price is equivalent to fair value (FV), which focusing only on cash payments can be written as …

As the expression suggests, determining the contract price (the fair value oof the contract) generally requires using a risk-adjusted discount rate as shown here. I present methods for estimating risk-adjusted rates in my book on international cost of capital estimation and in other articles on this website. For any (positive) discount rate there is implicit interest revenue in the contract …

… which is recognized over the life of the contract under IAS 39. More specifically, for a customer contract meeting the definition of a financial instrument under IAS 39, interest revenue is recognized using the effective interest method, which holding all else but the passage of time constant can be written as …

[I thank Renzie Doem Agutaya for suggesting this clarification for interest revenue recognition on customer contracts.]

Because expected values of the contractual payments—including any contingent payments—are necessarily estimates, the estimated contract FV can change over the contract life, t = 0,1,…,T, and under the provisions of IAS 8 any such changes would be applied prospectively to revenue recognition under IFRS 15.

2. Identifying performance obligations in customer contracts

Under IFRS 15, the terms of the customer contract requiring the delivery of a good or service represents a performance obligation (PO) if the good or service can (i) be consumed by the customer and (ii) separately identified from other good and services required to be delivered under the contract. Such individual performance obligations are represented as a list similar to the following:

Each performance obligation is fulfilled over time, in fact, and such contractual obligations must be identified for the related revenue to be appropriately recognized under IFRS 15.

3. Estimating performance obligation fair values

Fair value allocation problem. The primary problem with respect to IFRS 15 is the allocation of the estimated contract FV to the contractual performance obligations discussed above, which can be represented as …

Because revenue recognition amount and timing generally differ across performance obligations, it is necessary to develop a consistent method of measuring FV for each performance objective.

Performance obligation valuation approach. Under IFRS 13, FV can generally be estimated using one of three approaches: the market approach, income approach, or cost approach. Because performance obligations represent goods and services flows—in contrast to monetary flows—only the market approach or the cost approach can be feasibly used to allocate FV to the performance obligations:

Market approach — Use of prices and other information generated in observable market transactions involving identical or similar assets or liabilities.
Cost approach — Use of replacement cost information with respect to the asset.

IFRS 13, however, further specifies a preferred hierarchy of valuation inputs that generally requires the use of market price data when available:

Level 1 inputs — Observable prices in active markets for identical assets or liabilities that can be accessed at the FV measurement date.
Level 2 inputs — Information other than Level 1 observable market prices that are either directly or indirectly observable.
Level 3 inputs — Unobservable valuation inputs including management’s expectations and assumptions.

In the context of IFRS 15, the market approach basically corresponds to Level 1 inputs and the cost approach basically corresponds to Level 2 inputs, suggesting that the market approach to allocating FV to performance obligations is the preferred approach to the extent that market prices of the good and services are observable in the relevant markets.

Estimating marginal FV of performance obligations.  Because contract price can be observed or estimated for every identified contract, and because performance obligations can be identified, it is possible to estimate the marginal effect of each performance obligation type on contract price using an econometric model similar to the following (with the null hypothesis of α = 0):

If there are sample data available for at least 1 + k contracts for the K different types of performance obligations, then FV estimates for each of the K performance obligations can be obtained from estimated parameter values:

4. Allocating contract price to performance obligations

In general, there will be a residual difference between the actual observed contract price and the estimated conditional expectation of the contract FV. If the observed contract price represents FV—which is the general assumption in accounting for exchange transactions between unrelated parties—then it reasonable to assume the actual unknown fair values of performance obligation components are proportional to the estimated expected fair values of performance obligation components. Note that the relative values of the estimated performance obligation expected fair values sum to 1:

Multiplying each side of the equation by the observed contract price results in an expression that allocates the observed contract price to the component performance obligations based on the relative FV estimates:

Some subtleties exist with respect to formulating, estimating, and testing econometric models based on that  shown in Section 4—particularly with respect to how performance obligations are measured—but discussion of the more complex aspects of applying the method of estimating the FV of performance obligation components is beyond the intended scope of this discussion.

5. Revenue recognition (and measurement)

IFRS 15 states that the revenue is to be recognized as control over benefits of the (product or service) sales contract are transferred to the buyer, which can be expressed as …   

IFRS 15 provides guidance on calculating or estimating the % earned; from IAS Plus:

An entity recognises revenue over time if one of the following criteria is met: … [1] the customer simultaneously receives and consumes all of the benefits provided by the entity as the entity performs; [2] the entity’s performance creates or enhances an asset that the customer controls as the asset is created; or [3] the entity’s performance does not create an asset with an alternative use to the entity and the entity has an enforceable right to payment for performance completed to date.

If an entity does not satisfy its performance obligation over time, it satisfies it at a point in time. Revenue will therefore be recognised when control is passed at a certain point in time. Factors that may indicate the point in time at which control passes include, but are not limited to: … [4] the entity has a present right to payment for the asset; [5] the customer has legal title to the asset; [6] the entity has transferred physical possession of the asset; [7] the customer has the significant risks and rewards related to ownership of the asset; and [8] the cutomer has accepted the asset.


Such guidance on calculating the % earned for a particular performance obligation at time t can be summarized very simply:

Under assumptions that performance obligation fair value is alternatively proportional to product units delivered, contract costs incurred, contract months completed, etc.; for example:

In essence, this aspect of revenue recognition does not differ substantially from—for example—the revenue recognition principle as presented in the FASB’s Statement of Financial Accounting Concepts No. 5 — Recognition and Measurement in Financial Statements of Business Enterprises.


And there it is; a general method for estimating unobservable fair values of products and services sold to customers and applying the method to comply with IFRS 15 revenue accounting requirements.

As a final note, it is common for accountants (and others) to disregard mathematical expressions like those presented above “because math is not necessary for understanding accounting.”  This is actually true, but not the issue: Understanding revenue recognition (and accounting) in this way is sufficient for a deep understanding and represents how computerized accounting systems must be designed; i.e., even if accountants don’t understand accounting in this way, programmers of computerized accounting systems generally must if the systems are to be accurate and reliable.

The Lesson: Valuation and accounting are both quantitative disciplines. Use math to solve quantitative problems clearly, efficiently, and effectively. :- )

São Paulo

Caveats.  Please note: (i) views presented above are my own and do not reflect those of others; (ii) like anyone, I’m not infallible and am responsible for any errors; (iii) I greatly appreciate being informed of any significant errors in facts, logic, or inferences and am happy to give credit to anyone doing so; (iv) the above article is subject to revision and correction; and, (v) the article cannot be construed as investment or financial advice and is intended merely for educational purposes.  MMc