Discount rates for very long maturities

A common question about discount rates is how to estimate a discount rate for assets and liabilities with very long maturities. Such a discount rate contains a term premium that cannot be based on evidence and can never be back-tested. As a result, that term premium is not really an estimate, it is just a guess. That guess is unfalsifiable and unverifiable.

Using those guesses in financial statements does not give existing and potential investors the most useful information. Although no perfect solution exists, the IASB should consider adopting a more prescriptive approach to determining these term premiums and at least require that each company uses the same approach. There may also be a need for better disclosure.

Let me illustrate with the following example.

Example

Fact pattern used in the example

It is the end of year 1. Company A has a liability requiring it to pay £100 at the end of year 31 (a 30-year liability). Company A and the public can observe a market interest rate of 5% for otherwise similar liabilities maturing at the end of year 21 (20-year liabilities). Although those 20-year liabilities mature before Company A’s 30-year liability, they are identical to it in all other respects. For longer maturities, no market interest rates are observable.

Company A believes that, for identical cash flows:

• market participants would expect a return of 8% on cash flows due after more than 25 years. Company A believes this is the long-term average return that market participants would expect over many years.
• for maturities of between 20 and 25 years, the return required by market participants would move by equal annual increments from the observed rate for 20 years (currently 5%) to reach the long-term average of 8% at 25 years.

The rest of this post treats those discount rates as made up of two components:

• the observed market interest rate for cash flows occurring at the latest date for which such a rate is observable.
• a term premium for the rest of the period until the date of the cash flow that is being discounted.
  (a negative premium is often called a discount)
  In this post, term premium refers only to a premium covering that period not to premiums covering other periods.

Applying discounting in that fact pattern

The following table shows Company A’s estimate of the discount rate at the end of years 1, 2, 7 and 11. In each case, the discount rate is made up of the observed rate for the latest date and a term premium. For simplicity, the example assumes that the observed interest rate for a 20-year liability remains constant at 5% at the end of each of years 1, 2, 7 and 11.

1. The rate observed in year 1 is for cash flows in year 21. The term premium is for years 22-31 (10 years).
2. The rate observed in year 2 is for cash flows in year 22. The term premium is for years 23-31 (9 years).
3. The rate observed in year 7 is for cash flows in year 27. The term premium is is 2.4% (= 3% x [4/5]). It covers years 28-31 (4 years).
4. The rate observed in year 11 is for cash flows in year 31. No term premium is needed.

No way to back test the term premium

Company A measured cash flows due in year 31 using a term premium that started at 3% in years 1 to 6 and then fell, reaching zero at the end of year 11. Nothing that happens between years 1 and 11 (or, indeed, subsequently) can ever tell Company A (or any external party) whether its estimate of the term premium—and, hence, of the discount rate—was correct.

Said differently, the term premium is based on a model and it will never be possible to back test either the model or the inputs. As I discuss later in the post, there can also be no evidence to support the model and the inputs used in it. The ‘estimate’ is simply an unverifiable and unfalsifiable guess.

Overview of this post

In the rest of this post, I discuss:

• whether including the term premiums discussed in this post provides information useful to investors;
• whether existing requirements on estimating unobservable fair values (‘level 3’ fair values) are sufficient for the term premiums discussed in this post;
• whether initial transaction prices could provide some evidence about those term premiums;
• whether there is a case for setting more setting more prescriptive requirements for these term premiums; and
• whether the matters discussed in this post have any implications for disclosure.

I also link to a 2011 staff paper discussing this topic for a joint meeting of the IASB and the US Financial Accounting Standards Board (FASB).

Information for investors

Including an unobservable term premium in the discount rate causes problems for existing and potential investors:

• Different companies make different ‘estimates’ of what the term premium is, even though no company can make better estimates than other companies.
• Without extensive disclosure, investors may be unable to make adjustments that enable them to compare companies that had used different term premiums. And without that disclosure, investors may be unable to replace the company’s own ‘estimate’ of the term premium with a premium that investors consider more suitable for their own needs.
• The term premium built into the measurement on day 1 reverses back out over time as the effect of discount ‘unwinds’. The term premium vanishes completely once the remaining maturity has become short enough for market rates to be observed (by year 11 in the example in this post). That term premium provides no information about the amount, timing or uncertainty of Company A’s future or past cash flows.

Comparison with fair value measurement

Determining the present value of a cash flow and determining the discount rate for that cash flow are two sides of the same coin. For example, suppose that a financial instrument provides a cash flow of £100 in 1 year. Estimating that the discount rate is 5% is the same task as estimating that the fair value is £95.24.¹

Note 1 £95.24 *1.05 = £100.00.

Therefore, setting an unobservable long term discount rate is, in some respects, like estimating the unobservable fair value of a financial instrument bearing interest at that rate.

IFRS 13 Fair Value Measurement already contains requirements on estimating unobservable fair values (‘level 3 fair values’). In my view, although those requirements are suitable for estimating unobservable fair values, those requirements are not sufficient for the task of ‘estimating’ unobservable term premiums for assets and liabilities with very long maturities. They are not sufficient because:

• for most items measured at fair values, there exists some observable data that can help construct estimates or components of estimates. However, for the term premium component of long-term interest rates, there is no such data.
• for most items measured at fair values, transactions occur at least occasionally, even if the market is very thin. Such transactions make it possible to back test the valuation techniques being used (and the inputs used in them) by comparing them (at least occasionally) with prices for real transactions.
  In contrast, for most assets or liabilities with very long maturities, such transactions do not occur, and such back tests are impossible.
• long-term discount rates compound over a very long period. Thus, even small differences in these rates can have large effects on financial statements.
  In the above example, the present value of a cash flow of £100 due in 30 years is: £23 if the discount rate is 5%; only £20 if the discount rate is 5.5%; and only £10 if the discount rate is 8%.
  This compounding effect exacerbates the above problems (lack of evidence to support ‘estimates’ of term premiums and inability to back test the ‘estimates’).  

Could initial transaction prices provide some evidence?

Even for assets and liabilities with very long maturities, the price for the initial transaction in which the company acquired or originated the asset or liability might provide some evidence about the term premium implicit in the price negotiated between company and the other party. I discuss in this section whether such transaction prices exist and could imply what the term premium was on day 1. I also discuss whether subsequent transactions occur.

Discussion about long-term discount rates arises most commonly for:

• environmental liabilities
• pension liabilities
• insurance liabilities

Environmental liabilities

Some long-term environmental liabilities are for large amounts and mature only in the far future.  Examples are some liabilities to restore the land or sea-bed after extracting oil or minerals. When those liabilities come into existence, there is no transaction price that could help a company estimate the present value of the liability or an appropriate discount rate.

Furthermore, subsequent transfers of the liability to another party are generally not possible. So, there are no secondary market transactions that would help people assess what the appropriate discount rate should be (or, equivalently, what the price for such transactions is).

Pension liabilities

For pension liabilities, there is a transaction between the employer and its employees. In theory, we could estimate a discount rate embedded in the transaction between the employer and its employees by considering the rate at which the two parties traded off immediate cash pay against deferred pay in the form of a pension.

But the total pay, and the pension component of total pay, tend to be ‘sticky’—not renegotiated each year starting with a clean sheet of paper. In addition, the cash flows from a pension are often subject to considerable uncertainty. Together, these factors make it unfeasible to make a clean estimate of a discount rate embedded in the transaction between the employer and its employees.

In a small number of markets, some secondary market transactions in pension liabilities do occur, but these transactions are not pervasive enough to supply much evidence in most markets. Even when these transactions do occur, they do not usually cover the full amount of the liability under a pension plan that continues unchanged.

Insurance liabilities

For insurance liabilities, there is an initial transaction between the insurer and the policyholders. So, it is possible to get some idea of the discount rate embedded in the transaction. Even there, though, many other factors are embedded in the price. Thus, it is difficult to isolate how much the discount rate contributes.  

Business combinations

Business combinations involve the acquisition of companies with environmental liabilities, pension liabilities or insurance liabilities. There are also some secondary market transactions in portfolios of insurance liabilities, But, once again, an acquired business contains so many other components that it is not feasible to infer a long-term discount rate from the acquisition price. The same also applies to the acquisition of a portfolio of insurance liabilities.  

Conclusion on initial transaction prices

As discussed above, initial transaction prices do not even exist in some cases (environmental liabilities). Even when initial transaction prices do exist, it seems unlikely that companies could infer the amount of the term premium implicit in those prices.  

More prescriptive requirements?

The IASB prefers to base its standards on principles, rather than setting prescriptive and arbitrary requirements. In general, I think that approach best meets the needs of investors. Nevertheless, a unique problem arises in determining what term premium to include in the discount rate for cash flows maturing later than the latest date for which term premiums are observable (‘later maturities’). There is a case for setting a more prescriptive requirement to deal with that unique problem.

Possible requirements

For example, the IASB could prescribe one of the following requirements—that all companies must, for all later maturities, use:

• the longest observable discount rate (without adding a term premium).
• a single long-term discount rate, independent of the longest observable discount rate.
• a model specified by the IASB. The IASB could perhaps go even further by specifying what inputs to use in that model.

The following chart illustrates for the above example yield curves resulting from the first two of those approaches and a yield curve resulting from the model used by Company A:

• For each approach, the rates for cash flows due in years 1 to 21 are observed in the market. For illustration, I picked rates starting at 3% for year 1 and moving upwards in roughly equal instalments to year 21, with minor fluctuations.
  (Although the chart shows this part of the yield curve in grey only, it is the same for all 3 approaches.)
• The blue line (labelled ‘model’) shows the yield curve produced by Company A’s model. It slopes upwards from year 22 to year 26 and then remains flat at the assumed long-term rate (8%).
  (The chart shows the flat part in grey.)
• The orange line (labelled ‘observable’) shows the yield curve produced by using the rate observed for year 21 (5%) for all future years as well. There is a sudden twist in the yield curve for year 22 and the yield curve then stays flat for each later year.
• The grey line (labelled ‘jump’) shows the yield curve produced by moving in year 22 immediately to the assumed long-term rate (8%) and then using that rate for each later year as well. There is a sudden twist in the yield curve for year 22. There is then a further sudden twist in the opposite direction to make it flat beyond that time.

Longest observable discount rate, adding no further term premium

The IASB could require companies to use the longest observable discount rate, adding no further term premium for later maturities. In the above example, the discount rate would be 5% for all years beyond year 21.

Advantage:

• this approach would rely solely on observable interest rates. Thus, all companies would use the same rates in principle. Nevertheless, there would be a little variation in practice because some judgment would still be needed.

Disadvantage:

• the resulting discount rates may sometimes seem implausible. In the above example, maybe all external parties might feel that a discount rate of 5% is much too low for a 30-year maturity in this fact pattern. Nevertheless, there might be no consensus on how much higher a plausible rate would be.
• the yield curve used in the measurement would suddenly become flat immediately at the latest date for which an interest rate is observable. This may sometimes seem implausible, as in the above example.

A single long-term discount rate for all later years

The IASB could require companies to use a single discount rate for all later maturities. In the above example, the discount rate might be 8% for year 22 and all later years.

Advantages:

• the task would be simpler for companies. They would not need to develop a model determining how the long-term premium converges from the longest observable rate (5% in the example) towards the estimated long-term rate (8% in the example).
• the task would be simpler for investors. They would not need to understand and assess such a model and they would not need to adjust its effects if they wish to use a different model in this analysis.
• the disclosure might be simpler than when every company develops its own model.

Disadvantages:

• companies would still need to estimate the long-term rate.
• investors would still want to assess the long-term rate used, so that they can decide whether they want to adjust its effects.
• in some cases, moving instantly to an assumed long-term rate may produce an implausible jump in the yield curve, as in the above example.

A single model for all companies?    

The IASB does not normally prescribe what models companies must use to achieve a particular measurement objective, nor does it normally specify the numerical value of the inputs companies must use. Requiring companies to pick a particular model to meet a specified objective is generally a good approach and produces information that is useful for investors.

However, the term premium component of the discount rate for later maturities is unobservable and its numerical value can never be verified or falsified by anyone, even in principle. For that reason, requiring companies to pick a model to determine discount rates for later maturities is unlikely to be successful.

Reason for that conclusion

To understand why I reached that conclusion, please consider again the above example. Company A’s model involves deciding:

• that interest rates tend to revert over the very long-term towards some long-term average rate.
• whether that long-term average rate is best determined in nominal (cash) terms, or in real terms (adjusted for inflation). For simplicity of illustration, the example uses nominal interest rates. A more plausible approach might be to look for a long-term real rate, but that would then require estimates of inflation many years in the future.
• how to determine that long-term average rate. A starting point might be to look at past returns over very long periods. Even if it is possible to overcome the conceptual and practical difficulties of determining what long-term average returns were in the past, it would still be necessary to assess whether future returns are likely to be consistent with returns in the past.
• the period over which interest rates would revert to the assumed long-term average rate, and the pattern in which that reversion would occur. (Company A assumed that the reversion would occur in a straight-line fashion over 5 years).

There is no evidence that could support any of those decisions (with perhaps the partial exception of estimating what, in fact, very long-term average returns were in the past). So, any result of those decisions is not an estimate; it is simply a guess. It is not possible for anyone to come up with useful or plausible estimates of the unobservable term premiums for maturities later than the last date for which interest rates are observable.

Also, there is no reason why any particular company could come up with estimates that are more useful or plausible than any other party could. So, requiring (or allowing) companies to make such ‘estimates’ simply leads to diversity and lack of comparability and does not make the resulting information any more useful.

Could the IASB do something?

In my view, for the reasons given above, there is a strong case for the IASB to at least take some action that will make companies do the same thing. Having said that, all of the above possibilities have some disadvantages, so it is not obvious which one would be best.

Of course, the IASB itself is no better placed than anyone else to identify models (and the numerical value of inputs to the models) that will produce more plausible and useful information for investors. But, if decisions by each company cannot produce more plausible and useful information, the IASB could at least require that each company uses the same approach.

Disclosure implications

Investors want to know whether companies facing the same circumstances have used the same discount rates. This enables investors to adjust the reported numbers when this adjustment will help them compare different companies, or if they view different discount rates as providing more useful information. In addition, investors want information that helps them estimate the amount, timing and uncertainty of the underlying cash flows.

To satisfy those needs of investors, the IASB could require companies to disclose more information about unobservable term premiums in discount rates they use. For example, it could require companies to disclose some or all of the following:

• the discount rates used.
• the techniques used in estimating the discount rate.
• the numerical value of the inputs used in those techniques.
• the timing and amount of the cash flows for which each rate is used.

Past IASB discussion

A staff paper discussed in March 2011 by the IASB together with the US Financial Accounting Standards Board (FASB) considered discount rates for cash flows that will occur after the date for which market prices are observable. That discussion was part of the project on insurance contracts, at that stage still a joint project by both Boards. The paper, Agenda paper 12E/61E Discounting for ultra long duration cash flows, is available at https://www.ifrs.org/content/dam/ifrs/meetings/2011/march/joint-iasb-fasb-2/ic-0311b12eobs.pdf

That staff recommended that insurers should present the effect of discount rate movements for ‘ultra long duration cash flows’ in other comprehensive income (OCI), not in profit or loss. The amount reported in OCI would be the effect of changes in what this post calls the term premium (described in that staff paper as ‘changes in measurement attributable to changes in the difference between the observable and unobservable part of the yield curve.’) Pending further discussion on other aspects of accounting for insurance contracts, the IASB and FASB did not vote on that recommendation.

Ultimately, the IASB did not need to decide whether to use OCI for these changes. In developing and finalising IFRS 17 Insurance Contracts, the IASB decided that insurers should remeasure the contractual service margin included in the measurement of insurance liabilities. Thus, a change in the term premium would often lead to both a change in the present value of the expected cash flows and an equal and offsetting change in the contractual service margin. When this offsetting occurs, there would be no overall effect of the measurement of the insurance liability—and so no need to decide whether to use OCI.

Conclusion

Determining unobservable term premiums for assets and liabilities with very long maturities poses a unique problem. Those term premiums cannot be based on evidence and can never be back-tested. As a result, the amount of such a term premium is not an estimate, it is just a guess. That guess is unfalsifiable and unverifiable.

Also, there is no reason why any particular company could come up with more useful or more plausible guesses than any other party could. So, including those guesses in the measurements used in financial statements simply causes diversity and reduces comparability, and does not give existing and potential investors the most useful information.

Although no perfect solution exists, investors might receive more useful information if the IASB were to adopt a more prescriptive approach to determining these term premiums. Because guesses by each company cannot produce more useful and more plausible information, the IASB could at least require that each company uses the same approach.

There may also be a need for better disclosure.