IRR How to calculate
The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of a project zero. In other words, it is the expected compound annual rate of return that will be earned on a project or investment.
When calculating IRR, expected cash flows for a project or investment are given and the NPV equals zero. Put another way, the initial cash investment for the beginning period will be equal to the present value of the future cash flows of that investment. (Cost paid = present value of future cash flows, and hence, the net present value = 0).
Once the internal rate of return is determined, it is typically compared to a company’s hurdle rate or cost of capital. If the IRR is greater than or equal to the cost of capital, the company would accept the project as a good investment. (That is, of course, assuming this is the sole basis for the decision).
In reality, there are many other quantitative and qualitative factors that are considered in an investment decision). If the IRR is lower than the hurdle rate, then it would be rejected, if IRR is the only investment consideration.
Under IFRS 16 ‘Leases’, a similar calculation is used to calculate discount rates are used to determine the present value of the lease payments used to measure a lessee’s lease liability. Discount rates are also used to determine lease classification for a lessor and to measure a lessor’s net investment in a lease.
For lessees, the lease payments are required to be discounted using:
- the interest rate implicit in the lease (IRIL), if that rate can be readily determined, or
- the lessee’s incremental borrowing rate (IBR).
For lessors, the discount rate will always be the interest rate implicit in the lease.
The interest rate implicit in the lease is defined in IFRS 16 as ‘the rate of interest that causes the present value of (a) the lease payments and (b) the unguaranteed residual value to equal the sum of (i) the fair value of the underlying asset and (ii) any initial direct costs of the lessor.’
The lessee’s incremental borrowing rate is defined in IFRS 16 as ‘the rate of interest that a lessee would have to pay to borrow over a similar term, and with a similar security, the funds necessary to obtain an asset of a similar value to the right-of-use asset in a similar economic environment’.
The incremental borrowing rate is determined on the commencement date of the lease. As a result, it will incorporate the impact of significant economic events and other changes in circumstances arising between lease inception and commencement.
A lessee will need to determine a discount rate for virtually every lease to which it applies the lessee accounting model in IFRS 16. However, a discount rate may not need to be determined for a lease if:
- a lessee applies the recognition exemption for either a shortterm or a low-value asset lease
- all lease payments are made on (or prior to) the commencement date of the lease, or
- all lease payments are variable and not dependent on an index or rate (eg, all lease payments vary based on sales or usage).
The interest rate implicit in the lease may be similar to the lessee’s incremental borrowing rate in many cases. Both rates consider the credit risk of the lessee, the term of the lease, the security and the economic environment in which the transaction occurs.
Interest rate implicit in the lease
The definition of interest rate implicit in the lease is the same for both a lessee and a lessor. Because it is based in part upon the initial direct costs of the lessor, it will often be difficult and in many cases impossible for the lessee to readily determine the interest rate implicit in the lease.
For some leases, including most property leases, a lack of detailed information about the fair value of the underlying asset, the expected residual value of the asset at the end of the lease term and any initial direct costs of the lessor will make it difficult or impossible for the lessee to readily determine the interest rate implicit in the lease.
In other cases, the lessee may be able to obtain the relevant information from the lessor during the lease negotiation process. The initial fair value of the underlying asset and residual value of the underlying asset may also be determinable from a reliable external source. The lessee may be able to reasonably determine that the lessor’s initial direct costs would not be significant to the overall arrangement. In leasing transactions between related parties, it is likely that most or all of the relevant information can be obtained by the lessee.
While it is relatively common for some traditional equipment finance leases to make explicit reference to an interest rate in the lease documentation, caution is warranted. This rate will not represent the interest rate implicit in the lease if it doesn’t include an estimate of residual value for the underlying asset or take the lessor’s initial direct costs into account.
What is readily determinable?
The interest rate implicit in the lease must be used only if that rate can be readily determined. The meaning of the term ‘readily determinable’ is open to some interpretation.
Sometimes, particularly in relation to leases of real estate, the lessee uses a valuation expert to determine the interest rate implicit in the lease. In general, rates determined by experts would not qualify as readily determinable and the lessee should be using its incremental borrowing rate instead.
Similarly, where the interest rate implicit in the lease can only be determined by including significant estimates and assumptions, a lessee would likely conclude that the interest rate implicit in the lease is not readily determinable.
The impact of variable lease payments on the interest rate implicit in the lease
Variable lease payments can impact the calculation of the interest rate implicit in the lease. Only variable payments based on an index or rate should be included in the calculation of the interest rate implicit in the lease (ie. variable payments that are included in the definition of lease payments).
True variable payments, such as those based on sales or usage, must be excluded. Unfortunately, this can result in rates that are potentially misleading if the lease agreement is structured in a way that most payments are variable. If the calculated interest rate implicit in the lease is negative or otherwise doesn’t make sense, in general the incremental borrowing rate should be used.
Lessee’s incremental borrowing rate
Where the lessee is unable to readily determine the interest rate implicit in the lease, the discount rate will be the lessee’s incremental borrowing rate. The incremental borrowing rate is an interest rate specific to the lessee that reflects:
- the credit risk of the lessee
- the term of the lease
- the nature and quality of the security
- the amount ‘borrowed’ by the lessee, and
- the economic environment (the country, the currency and the date that the lease is entered into) in which the transaction occurs.
It is important to note that the lessee needs to determine the incremental borrowing rate for the right-of-use asset, not the underlying physical asset.
In most cases, the lessee will need to determine its incremental borrowing rate separately for each lease. Exceptions are where:
- as a practical expedient, the entity applies lease accounting to a portfolio of leases that have similar characteristics. IFRS 16 allows this practical expedient if the effect is reasonably expected to be materially the same as a lease-by-lease approach, or
- on transition, using the modified retrospective approach, a lessee applies a single discount rate to a portfolio of leases with reasonably similar characteristics (such as leases with a similar remaining lease term for a similar class of underlying asset in a similar economic environment).
It would not be appropriate for a lessee to use its weighted average cost of capital (WACC), which includes equity as well as borrowings. An entity’s weighted average cost of capital is not specific to the term, security and amount of the lease.
It would also not be appropriate for a lessee to use its parent’s incremental borrowing rate instead of calculating and determining its own rate.
If a lessee has direct borrowings, the effective interest rate on those borrowings may serve as a helpful starting point for determining the incremental borrowing rate. However, it is important to appreciate this is a starting point and adjustments are likely to be necessary.
The interest rate on the direct borrowings may have been determined at a date when market conditions and the credit risk of the lessee were different than they are on the commencement date of the lease, or the borrowing may have been based on a different term or included different security.
Substantial adjustment may be required (in either direction) to the interest rate on direct borrowings to determine an appropriate incremental borrowing rate and significant judgement will be involved in making these adjustments.
The interest rate implicit in a lease often incorporates an ‘asset risk premium’ reflecting the lessor’s exposure to the residual value of the asset at the end of the lease term. As these premiums reflect the risks and circumstances of the lessor, they should be ignored when estimating the lessee’s incremental borrowing rate.
There is an additional complexity involving the way in which a loan’s principal will be repaid. For example, a lender charging 8% for a fully amortising loan (ie, blended payments of principal and interest over the loan term) may charge a different rate for a ‘bullet-style’ loan where the principal is repaid all at once at the end of the loan’s term.
While most leases are likely to involve payment streams similar to an amortising loan, lessees will need to exercise careful judgement and consider all facts and circumstances relevant to their situation.
Case – Blended rates |
An entity purchases a building. Assume that a loan-to-value (LTV) ratio of 80% applies, ie, the lender is only willing to provide funding for 80% of the appraised value of the building in a secured borrowing. If the entity chooses to finance 100% of the purchase it will need to finance the remaining 20% at a higher rate using an unsecured borrowing. Now assume that instead of purchasing the building, the entity decides to lease it for a period of 10 years and that a similar LTV ratio applies (ie, the lender is only willing to provide funding for 80% of the estimated value of the right-of-use asset). How should the lessee estimate its incremental borrowing rate? |
Analysis The lessee should use the rate at which it would finance 100% of the cost of the right-of-use asset. Ie. (80% x rate for secured borrowing) + (20% x rate for unsecured borrowing). This is sometimes known as the blended rate. |
A three-step approach to the composition of discount rates
While a discount rate is a single value, it is typically derived from a number of different data sources and can factor in various adjustments so that the overall discount rate is appropriate for its intended use. Comparison of the IBR with other rates used in IFRS, such as the capitalisation rate in IAS 23 Borrowing Costs or the discount rate in IAS 36 Impairment of Assets, shows that the IBR is not a direct match for these. Companies’ existing processes and data for determining these rates will therefore not necessarily be appropriate for determining an IFRS 16 IBR and so, there is a need to start with a fresh approach.
In general the IBR can be determined by considering three key components, as set out in the diagram below.
Step 1 – Determining the reference rate
Determining an appropriate reference rate through the use of risk free rates (eg government bond yields or interest yield curves such as ICE-LIBOR) is a relatively well understood and comprehensively documented process in the UK but companies adopting IFRS 16 have to ensure they consider the three factors outlined below.
Factors to consider |
Issues and challenges |
Possible solutions |
Currency |
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Economic environment |
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Examples where specific adjustments (Care should be taken that any adjustments for these factors are not double counted in the financing spread adjustment, in particular when considering the lessee entity) in this regard may be warranted include:
Cases of how such situations are considered are given on below. |
Case 1 – Foreign currency leases |
Consider a company with a Euro functional currency, which has a treasury policy to obtain financing in Euros. The company leases a ship; the lease payments are specified in US Dollars and the interest rate implicit in the lease is not readily determinable. The company has to determine the incremental borrowing rate, defined as ‘The rate of interest that a lessee would have to pay to borrow over a similar term, and with a similar security, the funds necessary to obtain an asset of a similar value to the right‑of‑use asset in a similar economic environment.’ Illustrative example 13 in IFRS 16 makes reference to determination of an incremental borrowing rate: ‘The interest rate implicit in the lease is not readily determinable. Lessee’s incremental borrowing rate is 5 per cent per annum, which reflects the fixed rate at which Lessee could borrow an amount similar to the value of the right-of-use asset, in the same currency, for a 10-year term, and with similar collateral.’ This clarifies that the currency in which the lease is determined forms part of the economic environment for which the borrowing rate is assessed. For the company in question it is the US dollar incremental borrowing rate that has to be determined. |
Case 2 – Currency union – practical considerations |
Consider a currency union comprising 10 countries with average economic growth of 1.5% per annum over the past 50 years. Country A has had average economic growth consistently above this average at around 2.5% per annum and Country B has had average economic growth consistently below this average at around 0.25% per annum. All other countries have been broadly in-line with the average. The currency union has publicly traded bonds, issued on behalf of all 10 countries. In determining a reference rate for leases entered into in any of these 10 countries, it would be normal to start by considering the risk free rates of the traded bonds. However the differing economic environments between Country A and Country B would, in general, warrant some level of adjustment to the risk free rate in order to reflect the situation a lessee in each of these two countries would find themselves in when negotiating with a lessor. Country Y and Country Z, neither of which are in the currency union, have average economic growth rates similar to Country A and Country B respectively as well as other similar economic factors. Benchmarking the risk free rates of Y and Z could therefore provide an indication of what quantum of adjustment could be made to the risk-free rates of the currency union in order to arrive at appropriate rates for A and B. |
Case 3 – Currency used is that of another country |
Consider Country A which uses and is responsible for Currency A, with monetary policy being set based on the economic growth factors of Country A only. Country B has given up using its own currency and now officially uses Currency A as its own national currency. Country B has no input into the economic policies or factors used by Country A in setting its monetary policy. If a company based in Country B were to enter into a lease, with payments being in Currency A, they would initially start to determine a reference rate by obtaining data for the risk-free rates for Country A. While those risk-free rates will align with the currency in which the lease payments are denominated, the rates are unlikely to be reflective of the economic environment of Country B, the location in which the lease was entered into. The company would therefore need to consider how to adjust the risk-free rate data points available in order to arrive at a reference rate which reflects both the currency and economic environment of Country B. This could include consideration of any publicly traded government bonds issued by Country B and the related data points, or perhaps looking at the credit rating ascribed to the country by lenders to determine a quasi-credit adjustment as if Country B were a corporate entity. |
Case 4 – Determining a weighted average lease term |
The estimated the weighted average lease term is estimated based on the following market standard approach:
The table below illustrates this for a) a 10 year £100m government bond (no interest assumed for simplicity) and b) a 10 year lease with £10m annual payments made at the end of the year. The resulting ratio is 55%. The resulting graph below outlines how the maturity payment ratio varies against the total duration of the lease. This graph shows that:
A typical approach used for setting discount rates to determine defined benefit pension scheme liabilities also matches bond durations against the weighted average duration of the pension liabilities, rather than the maximum term of the liabilities. A similar approach for leases would therefore appear appropriate. |
Step 2 – Determining the financing spread adjustment
The data available to companies to calculate their financing spread adjustment will depend on the type of organisation and the financing structures they have chosen to use. Below three cases of possible financing structures are provided; for each debt structure there are differences in the data points available to calculate the component of the IFRS 16 discount rate.
Types of debt financing |
Typical types of companies |
Data points available |
Multiple debt financing arrangements, including bonds, loan notes and bank facilities |
Large Public Interest Entity |
Multiple data points |
One primary debt financing arrangement, most likely to be a bank facility |
Public Interest Entity/Private Company |
Single data point |
No significant debt financing arrangements |
Private Company |
None |
There are two key points to note:
- For companies which have issued debt listed on a public exchange, it may be that they have rates available which comprise both the reference rate and the financing spread adjustment- an ‘all-in rate’.
- For some organisations data may be available for individual lessee entities, where subsidiaries are themselves debt issuers (see the first and second combinations below). For other organisations, data may only be available for the Group, being the parent company itself or dedicated financing companies operating on the parent company’s behalf (see the third and fourth combinations below).
Combinations of possible data points
Care should be taken when using an ‘all-in rate’ as typically companies have only a limited number of data points available (e.g. only certain currencies, or certain terms) and so it may also be appropriate to separately determine a reference rate and financing spread adjustment to ensure the three factors outlined above are fully assessed.
For companies with zero debt and/or net cash balances, this process may require consideration of both historical as well as future debt facilities, in order to assess whether the historical position is representative of the underlying position of the business. In ngeneral it is not considered reasonable to assume that companies in this situation will have a zero spread, as IFRS 16 requires the discount rate to reflect the rate of interest the lessee would have to pay to borrow.
For companies with few, if any, individual data points on their credit spread, it may be appropriate to seek indicative pricing from several banks or look to other data points available, such as similar sized companies in a similar industry as different sectors and industries can differ widely in terms of credit risk. The illustrative graph below sets out why this is the case.
Illustrative curve for debt duration vs credit spread |
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Case 5 – Determining a group and subsidiary credit adjustment |
A Group with international operations principally in Asia has a range of debt financing arrangements, including bank overdrafts, revolving credit facilities and bonds of both medium-term and long-term durations. The Group policy is to obtain all debt financing centrally from a parent company and head office perspective, in order to minimise the costs of finance. The data points for its debt arrangements are included in the graph below, the currency of which matches the currency of the majority of lease cash flows throughout the Group. For one subsidiary that operates in South America, the Group has allowed it to obtain a small local bank facility in order to comply with local regulatory and tax requirements. The Group has not guaranteed this facility, which is shown in red in the graph below. In determining a group credit adjustment, it may be appropriate for the company to exclude the local bank facility, on the basis that it does not provide reliable evidence to the credit adjustment for the Group as a whole. Additionally the local bank facility is likely to be insignificant in value when compared with the larger value Group banking facilities and so on a weighted value basis would have negligible impact compared to the other data points. Given the shortage of data points at medium-term durations, it may then be appropriate to estimate the credit spread using the remaining short‑term and long‑term data points to determine a Group credit spread curve, as illustrated. When determining a subsidiary credit adjustment for the South American entity, this single data point provides some valuable context for the individual lessee entity. It indicates a 200-300bps margin on top of the Group debt facilities of similar short-term duration. For longer durations, the company could start by estimating the South American entity credit spread by consistently supplementing the Group credit spread curve with an additional 200-300bps margin, however it is likely that the subsidiary credit spread adjustment would need to be increased for longer duration leases. |
For a number of entities, credit spreads obtained from key financing arrangements (as described above at the start of Step 2 – Determining the financing spread adjustment) will relate to the parent company of a group, which may or may not be the entity that is party to the lease arrangements.
- While companies may want to take into consideration the group’s debt structure and historical funding mechanisms to argue that all borrowings are group-led, IFRS 16 is very clear that the incremental borrowing rate is lessee specific.
- Given the lessee is responsible for making the lease payments, in general it is considered appropriate to consider what rate the lessee would achieve on their own, even if theoretically all funding would ultimately be achieved through a group debt structure.
- Depending on who the issuer is, and whether there are written guarantees for the lease payments in place, it may mean that in some instances it is appropriate to determine a group credit spread that is applicable to all lessees in a group.
To determine the lessee credit spread in the situation where group credit spread data points are available, in general companies should be taking into account the following factors:
Factors supporting an increased IBR for the lessee (a positive lessee credit spread) |
Factors supporting the same, or a decreased IBR, for the lessee (a negative lessee credit spread) |
Loss-making subsidiary, intermediate holding company or equivalent type of entity. |
Profitable trading subsidiary in good financial standing, with lender able to benefit as other creditors are structurally subordinated (ie debt lower down the group structure is more likely to be recovered in the event of a default). |
Reduced ability to generate dividend income for the parent company, so the company is not positively contributing to the overall Group credit rating. |
Lease is contractually guaranteed by the parent company, or another Group company which is profitable on a standalone basis. |
Levels of indebtedness
In considering the value of the lease in determining an IBR, one would expect that a lender considers the overall level of indebtedness of the entity (ie leverage) and whether the value of the lease results in a change to the leverage ratio such that it warrants a higher IBR.
Typically leverage is assessed by financers using the ratio of EBITDA to net debt (or an equivalent metric). Lenders have typically adjusted net debt under IAS 17 to include their estimate of the operating lease impact and so while the accounting under IFRS 16 will be different and therefore net debt: EBITDA ratios will likely change, in general the level of indebtedness remains a relevant factor in considering whether to finance a new lease arrangement.
In practice, different financing structures may lead to additional assumptions when accounting for the overall level of indebtedness:
- Revolving credit facility – Revolving credit facility rates are a useful data point for assessing the credit spread to be used in the IBR. Taking into account revolving credit facility rates preparers should consider the relevance of any tiered rates or utilisation fees depending upon their level of indebtedness which includes lease liabilities.
- Term loans/Bonds – When these types of debt funding are used as a means to determining the level of indebtedness, the lessee should consider if they would be able to raise additional funds at the same level as their previous funding achieved or if additional indebtedness would likely lead to a higher margin being charged (in line with the principles of the utilisation fees discussed above).
One notable exception is that property assets are typically financed on a loan to value basis (‘LTV’) and so the LTV ratio is also a relevant consideration in addition to the level of leverage for the lessee company. The LTV ratio is discussed further below.
In considering the value of the lease in determining an IBR, a lender considers the overall level of indebtedness of the entity (i.e. leverage) and whether the value of the lease results in a change to the leverage ratio such that it warrants a higher IBR.
Step 3: Determining the lease specific adjustment
The key requirement of IFRS 16 is that the discount rate is directly linked to the asset itself, rather than being a general incremental borrowing rate. In theory, the risk of default is mitigated for the lessor as they have the right to reclaim the underlying asset itself. With the right of use asset effectively being pledged as collateral against the risk of default, this is a secured lending arrangement. This is important because:
- when the lessee’s specific credit spread is derived from corporate borrowings, these are typically unsecured lending arrangements; and
- taking into account the security of the underlying asset could reduce the credit spread charged by a lender.
While all leases will reflect a secured borrowing position, in practice certain assets may be more valuable to a lessor and easier to redeploy.
For example:
- the costs of repossessing an asset of low value and/or short duration (eg a printer) would be high relative to the underlying value of the asset and the associated lease cash flows, so the benefits of having this security would likely be relatively insignificant; or
- for larger value assets and/or leases with a longer duration (eg a car or a property) the benefit of having security is more valuable as there is increased likelihood of the lessor obtaining value in the event of default.
Assuming the loan financing arrangement is at fair value, the value of the lease financing is equal to the value of the underlying asset which would be obtained by the financer. This means that the LTV ratio would therefore be 100%. In theory, a secured financing adjustment for a particular asset class would be broadly equal for each lease, irrespective of the individual nature of the leased assets.
For most companies with unsecured borrowings, they will not have data points available to determine an adjustment for the lease itself, to reflect the secured position the lessor has. As such, they may need to approach their bank or lender to get indicative rates for unsecured and secured borrowings of different durations, in order to be able to determine an appropriate adjustment.
A potential, complementary, approach is obtaining data to support the relative magnitude of the final discount rate or the lease specific adjustment for specific asset classes. The potential use of property yields is discussed next.
Property yields
In the basis for conclusions of IFRS 16, property yields is specifically identified as a potential data point for companies to consider:
‘The IASB noted that, depending on the nature of the underlying asset and the terms and conditions of the lease, a lessee may be able to refer to a rate that is readily observable as a starting point when determining its incremental borrowing rate for a lease (for example, the rate that a lessee has paid, or would pay, to borrow money to purchase the type of asset being leased, or the property yield when determining the discount rate to apply to property leases). Nonetheless, a lessee should adjust such observable rates as is needed to determine its incremental borrowing rate as defined in IFRS 16.’
Purpose |
For investors seeking to value property assets, a yield reflects the expected relationship at a point in time between income receivable and the valuation of the asset. The valuation is determined by a multiplier being applied to the rental income to be received, with the multiplier representing 1/Yield. |
Suitability |
Valuing commercial property where all likely buyers in the market view the asset as an investment. It is less suitable for markets where owner occupiers are more prevalent than investors (e.g. residential properties and small scale industrial units). That makes it generally a good approach for valuing commercial investments such as offices, retail properties and larger industrial properties. |
Determination |
Determined by assessing the yield profile from recent, comparable sales of similar assets with similar characteristics. The ‘equivalent yield’ reflected by comparable sales represents the weighted average of current and future rental income, smoothing out the effect of rent free periods and vacancy. |
Factors of influence |
‘All Risks’, which includes location, quality of property, specification, future rental and capital growth prospects, tenant covenant strength (i.e. the ability of that tenant to meet its financial commitments) and local supply/demand dynamics in both the tenant (occupier) and investor markets. |
In general terms, the lower the risk associated with the income from a property, the lower the applicable yield and the higher the multiplier driving the valuation.
In considering how a property yield would need to be adjusted to arrive at an IFRS 16 IBR, the table below sets out a summary of how it typically compares to the IBR and IRIIL definitions in IFRS 16.
It is difficult for companies to quantitatively adjust property yields for the above factors to arrive at an IBR. However, in general property yields provide some evidence of:
- the range in which an IBR for a property lease would sit, with the property yield likely to represent the upper end of the range; and
- the adjustments required between IBRs for properties of different types and in different locations (i.e. determining a lease specific adjustment).
For companies wanting to use property yields to help them determine lease specific adjustments, there are several important assumptions to be aware of:
- the currency of property lease cash flows are aligned with the currency in which the property is valued (ie its home market);
- the duration of the property yield data points available are aligned to the weighted average term of the lease, or that sufficient property yield data points exist bearing in mind that the longer the lease the lower the yield due to the longer period of rental income security; and
- the property yields are aligned to the characteristics of the property lease being assessed (i.e. in the quality, sector and location of the property).
While there are some publicly available data sources for benchmark property yields, these data points bring their own challenges, as they typically reflect agents’ views of likely pricing for hypothetical ‘best in class’ assets. Each asset is unique, and a bespoke view of yield could be applied to each asset, reflecting differences in perceived asset quality.
If it is not practical to get a property valuer’s view of the specific yield applicable to each asset, companies may need to consider taking out specialist subscriptions in order to get access to more detailed benchmark data, in order to address or minimise some of the above challenges. Yields for secondary assets are much more difficult to determine, since there are much greater degrees of variance in respect of asset characteristics.
Property yields can be used to value leasehold, as well as freehold interests, but leaseholds are rarely sold as investments, so these yields are especially difficult to determine and subject to a high degree of valuer judgement. Below one potential case illustrates how companies could use property yield data in this context.
Case 6 – Property yields providing additional data to determine lease specific adjustments to IBR |
Assume a company has a mixed portfolio of properties in 3 UK cities, consisting of offices, industrial warehouse and retail locations. Assume relevant prime ‘best in class’ benchmark property yields are as follows: Some themes that could be drawn from this data and used to adjust other data points to determine a more asset‑specific IBR include:
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