IFRS 15 *Revenue from Contracts with Customers* discusses 2 methods of estimating the amount of variable consideration. Those estimates are used in calculating the transaction price for contracts with customers. Unfortunately, the discussion is not totally clear because the wording is a compromise between proponents of the 2 methods.

I discuss below:

- estimating variable consideration
- predicting the amount
- single items and portfolios
- binary outcomes (bimodal distributions)
- middle of the spectrum
- way forward
- further discussion of expected value and most likely amount

## Estimating variable consideration

IFRS 15 paragraph 53 describes 2 methods for estimating the amount of variable consideration and requires entities to use one of those methods. Entities must use the method which the entity ‘expects to better predict the amount of consideration to which it will be entitled’. The 2 methods described are:

- expected value—‘the sum of probability weighted amounts in a range of possible consideration amounts’.
- most likely amount—‘the single most likely amount’ in a range of possible consideration amounts.

### When to use each method

Paragraph 53 goes on to explain one case when each method ‘may be an appropriate estimate of the amount of variable consideration’:

- expected value: if an entity has a large number of contracts with similar characteristics.
- most likely amount: for a contract with only 2 possible outcomes. An example is if an entity either achieves a performance bonus or does not.

As paragraph BC196 of the Basis for Conclusions on IFRS 15 notes, the IASB’s 2010 exposure draft had proposed always measuring variable consideration using an expected value approach. Many respondents favoured the most likely amount approach in some or all circumstances.

### Compromise wording damages clarity

The final wording in IFRS 15 looks like a compromise between people who favoured the expected value approach and others who favoured the most likely amount approach. Exploiting the fact that expected value and most likely amount are the same (or similar) in some cases, the compromise wording papers over differences between the approaches. Unfortunately, that wording:

- does not say what it means by ‘predict the amount’, and does not explain how expected value can ever ‘predict the amount’.
- does not contain a clear discussion of whether to consider the same factors for a single item as for a portfolio of similar items;
- does not say clearly whether the discussion of probability distributions with binary outcomes (bimodal distributions) applies only to single items, or also to portfolio of similar items.
- does not say clearly how to assess which of the 2 approaches (expected value and most likely amount) ‘better predicts the amount’ in cases falling on the spectrum between the 2 scenarios described in sub-paragraphs 53(a) and (b).

I discuss each of these points below.

## Predicting the amount

IFRS 15 does not say what it means by ‘predict the amount’, although the Basis for Conclusions on IFRS 15 provides some clues:

- paragraph BC199 says: ‘users of financial statements are most interested in knowing the total amount of consideration that
**will ultimately**be realised from the contract’. - Paragraph BC200 says: ‘if the entity is certain to receive one of only two possible consideration amounts in a single contract, the expected value would
**not**be a**possible outcome**in accordance with the contract and, therefore,**might not be relevant in predicting**the amount of consideration’.

### Expected value is not a prediction

This wording seems to imply that ‘predicting the amount of consideration’ means forecasting the single amount to which the entity will ultimately entitled. IFRS 15 does not explain how expected value can ever provide a prediction in that sense.

Expected value is not a forecast of a single amount. It is an estimate of the probability-weighted average of all possible outcomes. In principle, estimating expected value involves 3 steps:

- identifying all outcomes that could occur; then
- estimating the probability of each outcome; then
- multiplying the amount of each outcome with its probability, and adding up all those probability-weighted amounts.

### When expected value equals most likely amount

In some cases, expected value is the same amount as the most likely (single) amount. For example, that is the case when the probability distribution of possible outcomes is symmetrical about a single peak. But, even when expected value happens to equal the most likely amount, expected value is not a forecast or prediction of the most likely amount. And financial statements should not describe the expected value in a way that makes it seem like a prediction of a single amount.

Example 1 illustrates a case when expected value happens to equal the most likely amount.

#### Example 1. Distribution symmetrical about a single peak

An item has 3 possible outcomes: £80 (probability of 30%); £100 (40%); or £120 (30%).

The most likely single amount is £100 (probability of 40%). The expected value is also £100 ([£80 x 30%] + [£100 x 40%] + [£120 x 30%]). But that expected value of £100 is not a prediction that the amount will ultimately be £100.

### Expected value does not always equal most likely amount

The most likely amount sometimes equals the mean. But this is not the case if a probability distribution is not symmetric, as it was in example 1.

Example 2 shows a probability distribution with an expected value (mean) close to the most likely single outcome.

#### Example 2. Expected value close to most likely amount

Number | Cash flow (£) | Probability (%) | Expected value |

0 | 0 | 33.0 | 0 |

1 | 1,000 | 36.9 | 369 |

2 | 2,000 | 20.3 | 405 |

3 | 3,000 | 7.4 | 222 |

4 | 4,000 | 2.1 | 82 |

5 | 5,000 | 0.4 | 22 |

Mean | 100.0 | 1,100 |

In Example 2, an item can cause between 0 and 5 events. Each event will lead to a cash flow of £1,000. Thus, the total cash flows will be £0, £1,000, £2,000, £3,000, £4,000 or £5,000. The example assumes the number of events approximates the statistical distribution known as the Poisson distribution, with a mean of 1.1 events.

The most likely outcome is one event, causing a cash flow of £1,000. The most likely cash flow (£1,000, with a probability of 36.9%) is close to the expected value of the cash flows (£1,100).

Example 3 is the same as Example 2, except the mean of the Poisson distribution is only 0.9 of an event. In this example, the most likely outcome is zero events, causing cash flows of nil (probability of 40.6%); in contrast, the expected cash flows are £900.

#### Example 3. Expected value far from most likely amount

Number | Cash flow (£) | Probability (%) | Expected value |

0 | 0 | 40.6 | 0 |

1 | 1,000 | 36.7 | 367 |

2 | 2,000 | 16.5 | 330 |

3 | 3,000 | 4.9 | 148 |

4 | 4,000 | 1.1 | 45 |

5 | 5,000 | 0.2 | 10 |

Mean | 100.0 | 900 |

#### Comparing examples 2 and 3

Table 1 summarises Examples 2 and 3.

Most likely amount (£) | Expected value (£) | |

Example 2 | 1,000 | 1,100 |

Example 3 | 0 | 900 |

As Table 1 shows, the expected value is almost unchanged between Examples 2 (£1,100) and 3 (£900). It is also close to the most likely amount for Example 2 (£1,000). But those 3 amounts all differ greatly from the most likely amount for Example 3 (nil).

Said differently, Examples 2 and 3 differ only slightly. Expected value reports them as similar, but most likely amount reports them as very different.

## Single items and portfolios

The examples in paragraph 53 of IFRS 15 say that:

- expected value ‘may be appropriate’ for a large number of contracts with similar characteristics; and
- most likely amount ‘may be appropriate’ for a contract with only 2 possible outcomes.

Estimating expected value involves weighting amounts by probabilities. As a result, many people think that expected value has a meaning for a portfolio of similar items, but for a single item they regard expected value as literally meaningless. And many of those people regard expected value as particularly meaningless if the expected value equals none of the possible outcomes.

Those views are one of the main reasons why many people support most likely amount for single items with only 2 possible outcomes. I do not share those views myself, but they are quite widely held.

### Most likely amount for a portfolio

IFRS 15 does not discuss how to estimate most likely amount for a portfolio. That is an important omission. Most likely amounts are not necessarily additive (unlike expected values). In other words, the most likely total amount of several items may not equal the sum of the most likely amounts of the individual items. Example 4 illustrates this point.

#### Example 4. Most likely amounts are not always additive.

In Example 4, items A and B each have 2 possible cash flow outcomes: £100 (with probability 40%) or £300 (probability 60%). The outcome of item A is independent of the outcome of item B.

Table 2 shows each outcome and the probability of that outcome.

The most likely amount of item A is £300 (probability 60%) and that is also the most likely amount of item B. The sum of those 2 most likely amounts is £600. But considering items A and B together, their most likely amount is £400 (with a probability of 48% =24% + 24%).

Outcomeof A (£) | Outcomeof B (£) | Total outcome £ | Probability | Expected value (£) |

100 | 100 | 200 | 16% | 32 |

100 | 300 | 400 | 24% | 96 |

300 | 100 | 400 | 24% | 96 |

300 | 300 | 600 | 36% | 216 |

440 |

Table 2 also shows the contribution of each outcome to the expected value of A and B together (£440). Unlike most likely amount, expected value is additive. The expected value of each of A and B individually is £220 (= [£100 x 40%] + [£300 X 60%]). The sum of those expected values is £440 (£220 X 2).

Unsurprisingly, the expected value of A and B (£440) is, in this example, close to the most likely amount of A and B together (£400). It is much further from the sum of the individual most likely amounts of A and B (£600).

As said above, expected values are additive but most likely amounts are not additive. Those facts are true both for similar items within a portfolio and for items that are totally dissimilar.

### Expected value for a portfolio

Illustrative Example 22 accompanying IFRS 15 claims that it illustrates an estimate of expected value for a portfolio of similar items. Unfortunately, because that example is too simple, it obscures the relationship between (a) expected values for (ai) single items and for (aii) portfolios, and (b) most likely amounts for (bi) single items and for (bii) portfolios.

#### Illustrative Example 22

In Illustrative Example 22, an entity has 100 contracts with customers to sell them each one product for CU100. The entity estimates that customers will return 3 of the products for a full refund, retaining the other 97 products.

The example claims that the entity uses the expected value approach, concluding that this approach will better predict the revenue (CU9,700). Although the example gets to the numerical answer IFRS 15 requires, I disagree with how the example reaches that answer.

#### My analysis of this example

Illustrative Example 22 says: ‘Using the expected value method, the entity estimates that 97 products will not be returned’.

This statement reinforces confusion about expected value because it implies (misleadingly) that expected value aims to predict a single outcome.

As I have discussed before, it is important to be careful using terminology such as ‘expected’ and ‘estimated’. Saying how likely something is: way forward – Accounting Miscellany

I presume that this statement in the example is a shorthand way of reporting the entity’s estimate that:

- for each customer, there is a 97% probability that the customer will retain the product (thus obtaining no refund); and
- each customer’s decision whether to return or retain the product is independent of decisions by all other customers.

If my presumptions are correct:

- the most likely revenue for any one contract is CU100, and the sum of the individual most likely revenues is CU10,000 (100 x CU100);
- the most likely revenue for the portfolio as a whole is CU9,700; and
- the expected value of the revenue for any one contract is CU97, and the sum of the individual expected values is CU9,700. The expected value of the revenue for the portfolio as a whole is CU9,700.

In my view, what the entity is actually determining in this case is not the expected value. Instead, it is the most likely amount of revenue for the portfolio as a whole—which also just happens to equal the expected value.

#### A better example

The following example would distinguish the concepts more clearly: number of contracts 100, price CU100 each. Probability of return 97% if the economy is booming and 92% if the economy turns down. Probability of boom 40% and of downturn 60%. This fact pattern gives the following results:

- the most likely revenue for any one contract is CU100, and the sum of the individual most likely revenues is CU10,000 (100 x CU100);
- the most likely revenue for the portfolio as a whole is CU9,200 (probability 60%); and
- the expected value of the revenue for any one contract is CU94 (= [CU97 x 40%] + [CU92 x 60%]), and the sum of the individual expected values is CU9,400. The expected value of the revenue for the portfolio as a whole is also CU9,400.

It is not clear to me whether paragraph 53 would lead to the answer of CU9,200 (most likely revenue for the portfolio as a whole) or to CU9,400 (expected value).

Part of the reason for my uncertainty is lack of clarity about the relationship between paragraph 53 and paragraph 4 of IFRS 15. Paragraph 4 permits applying IFRS 15 to a portfolio if the result would not differ materially from applying it to the individual contracts. This lack of clarity arises because (as noted above), most likely amounts are not additive.

## Binary outcomes (bimodal distributions)

The example in paragraph 53(b) is for a contract with only 2 possible outcomes (for example, an entity either achieves a performance bonus or does not). People sometimes call a set of 2 such items ‘binary outcomes’.

Many people object to using expected value in measuring a single item that has only 2 possible outcomes differing significantly from each other. One concern they have is that the ultimate outcome will never end up equalling the expected value. So, measuring the item at expected value will always result in a remeasurement gain or loss whichever of the possible outcomes ultimately occurs.

Instead, those people favour measurement at the most likely amount. This approach minimizes the **frequency **of reporting subsequent remeasurement gains and losses. On the other hand, this approach does not minimize the **magnitude** of remeasurement gains and losses when they are reported.

An item with binary outcomes is only one example of a slightly wider class of items with bi-modal probability distributions. An instance of that wider class is an item with possible outcomes of: £0 (35% ); £10 (20%); £90 (25%); or £100 (20%). The probability distribution for this has 2 separate regions of high probability: between £0 and £10 and between £90 and £100, with zero or low probability in the intervening region (£21-£89).

The expected value for this distribution (£44.50) falls within that region of low (or zero) probability.

### Bimodal distributions and portfolios

Paragraph 53(b) of IFRS 15 refers to a single contract that has only 2 possible outcomes. It says that most likely amount may be an appropriate method in that case. Some people might read that discussion as implying that concerns about bimodal (binary) probability distributions arise only for a single item and not for a portfolio of similar items.

I do not agree with that view. A portfolio of similar items might be subject to several uncertainties, including one uncertainty that both affects the whole portfolio equally and has only 2 possible outcomes. In such cases, it might sometimes be appropriate to use:

- the most likely amount approach for that one uncertainty; but
- the expected value approach for all the other uncertainties. Paragraph BC202 of the Basis for Conclusions on IFRS 15 points out that ‘an entity may use different methods for different uncertainties in a single contract’. (The Standard itself is less explicit on this point: Paragraph 54 requires the use of one method
**throughout a contract**when estimating the effect of**an**uncertainty.)

## Middle of the spectrum

Paragraph 53 of IFRS 15 describes one scenario where the expected value method ‘may be appropriate’ and another scenario where the most likely amount method ‘may be appropriate’. Presumably, those 2 scenarios illustrate both ends of the spectrum.

Which of the 2 approaches (expected value and most likely amount) ‘better predicts the amount’ in cases in between those 2 extreme scenarios? Unfortunately, IFRS 15 does not say clearly how to reach an answer to that question.

The lack of such guidance is a particularly important omission. As I have argued above, the expected value method is simply not designed to predict a single ultimate outcome. That makes it difficult for people to assess whether the expected value ‘better predicts’ the amount than most likely amount does. Arguably, expected value never ‘predicts ‘ the outcome better than most likely amount—especially if most likely amount for a portfolio is determined for the whole portfolio, not for each individual contract.

I can see at least 3 ways of reading paragraph 53:

**reading 1:**the expected value method will ‘better predict’ the ultimate amount almost always—except in the specific case mentioned in paragraph 53(b), namely a single contract with only 2 possible outcomes.**reading 2:**what will ‘better predict’ the ultimate amount is sometimes the expected value method, but sometimes the most likely amount method. There is no presumption that one of the methods will make a ‘better prediction’ more often than the other method.**reading 3:**the expected value method can be used in cases when the amount it produces happens to equal the most likely amount, or to be close to that amount. The most likely amount method must be used when the most likely amount differs greatly from expected value. That is because expected value does not attempt to make a prediction.

Reading 1 would appeal to people who prefer the expected value method. Reading 3 would appeal to people who prefer the expected value method. That reading might also be consistent with a view that the expected value method **never **produces a prediction. Reading 2 is perhaps more open-ended (and, arguably, vague).

## Way forward

I discuss in this section:

- whether the IASB should change IFRS 15’s discussion of expected value and of most likely amount; and
- whether the IASB should use IFRS 15’s discussion of expected value and of most likely amount unchanged in future projects on other topics.

### Amending IFRS 15?

It is not realistic to think that the IASB will make significant changes to the discussion of expected value and of most likely amount in IFRS 15 in the near future. Although the IASB is carrying out a post-implementation review of IFRS 15, I would be surprised if stakeholders tell the IASB that this discussion on this relatively marginal topic is causing large problems. As a result, it seems unlikely that reopening this aspect of IFRS 15 would pass any reasonable cost-benefit test.

### Future projects on other topics

The IASB has already re-used the material from IFRS 15 in other projects:

- in IFRIC 23
*Uncertainty over Income Tax Treatments*; and - in its 2021 Exposure Draft
*Regulatory Assets and Regulatory Liabilities*.

I understand why the project teams (and the IASB itself) just copied and pasted the ready-made off-the-shelf solution from IFRS 15:

- being consistent between different standards is generally a good idea.
- simply re-using the material avoids diverting time and energy away from core parts of a project towards rethinking something that is, at best, peripheral to that project.

I expect that project teams and the IASB would probably adopt the same approach if the question of expected value versus most likely amount arises as a small component of a future project.

#### Predicting the ultimate outcome

If by some chance the IASB does decide to look again at the question of expected value versus most likely amount in some other future project, I presume the IASB would probably stick with predicting the ultimate outcome as the overall objective.

Personally, I might not pick the approach of predicting the ultimate outcome if I were starting with a clean sheet of paper. But the IASB would not be starting with a clean sheet of paper. The benefits of changing the approach in IFRS 15 (or of diverging from that approach) might well not be large enough to justify the resulting disruption and other costs.

#### Better guidance on prediction

If this topic does arise in other projects, even if the IASB does not diverge from the IFRS 15 approach, the IASB might be able in those projects to produce better guidance on ‘prediction’:

- describing how to estimate most likely amount for a portfolio of similar items. That is not necessarily the sum of the most-likely amounts of each individual item (example 4 above). It is also not necessarily the same as expected value (example 4).
- confirming that binary (bimodal) distributions can arise for portfolios of similar items, and not just for a single item.

#### Differences between IFRS 15 and other Standards

In considering whether to apply the IFRS 15 approach to Standards on other topics, it is worth remembering that 2 other features of IFRS 15 interact with IFRS 15’s requirements on expected value and most likely amount:

- IFRS 15 imposes a ‘constraint’ that prohibits the recognition of revenue when it is not ‘highly probable’ that there will be no significant reversal of revenue on subsequent resolution of related uncertainty.
- IFRS 15 applies its requirements to predictions of how much revenue a company is entitled to, without any reduction for credit risk. Credit risk is addressed in other ways.

Those other 2 features might or might not apply to Standards on other topics. Whether those features are present for those other topics might affect whether the discussion in IFRS 15 would need tailoring to make it appropriate for those other topics.

## Further discussion of expected value and most likely amount

For more discussion of expected value and most likely amount, and for cross-references to some useful and important staff papers, please see https://accountingmiscellany.com/measurements-based-on-future-cash-flows/

## Conclusion

Unfortunately, IFRS 15’s discussion of expected value and most likely amount lacks clarity, probably because the wording papers over a compromise between 2 incompatible positions.

It seems unlikely that the IASB will amend this part of IFRS 15 in the foreseeable future, as the benefits of change would probably outweigh the limited benefits.

If the IASB needs to address expected value and most likely amount in projects on other topics, the IASB will (rightly) be strongly tempted to copy and paste the discussion from IFRS 15, without rethinking the overall requirement to make a prediction.

Nevertheless there might be some limited scope for the IASB to give clearer guidance in those projects on most likely amount for a portfolio of similar items. Adding such guidance might clarify the relationship between expected value and most likely amount.