Using VBA functions and procedures

Functions

Sometimes it may be very tempting to use vba functions in your project model. However, if at all possible, it’s best to avoid doing so.

This is simply because:

  • Vba functions can slow down your spreadsheet considerably, which may become cumbersome when it gets large, and
  • Your model will probably need to go through a model audit prior to financial close, and model auditors don’t like functions – they’re more specialised than vanilla excel.

Procedures

On the other hand, I recommend building a toolbox of procedures and shipping it from project to project. Many of the procedures can be deleted prior to shipping the model off to the auditors, and are therefore not problematic as per bullet two above, but can save significant time during the model build. I make regular use of procedures to do the following:

  • Circular reference resolution
  • Copying the current cell across to the full row, linked to a keyboard shortcut
  • Sculpting debt
  • Sizing debt to fit funding requirements

Dealing with circular references

Circular references arise naturally in project models.

Examples of typical circular references include:

  • The DSRA is funded by a draw down at Commercial Operation Date (COD). The DSRA is sized as equal to the next 6 month’s debt service, which is in turn a function of the total debt amount, which is a function of, inter alia, the size of the DSRA…
  • The interest payable during construction is a function of the amount of debt outstanding, which is a function of, inter alia, the amount of interest already paid…

Sometimes circular references can be dealt with by referencing only past cells, which can solve the circular reference all together. If this is possible, it is the optimal solution to a circular reference.

If such a solution is not possible, it is almost always possible to resolve a circular reference by iterating through successive loops until the difference between successive iterations becomes negligible.

Please (please!) do NOT enable iterative calculations in the Excel Option / Formulas settings to do this. It works, but has the downside that an error can iterate through your circular reference and become impossible to resolve, effectively trashing your model.

A better, but more cumbersome, solution is to create a copy-past values macro. If you are not familiar with VBA, follow these steps to do so:

  • Copy the offending row
  • Paste-values the row immediately below
  • Create a named range for each row – e.g. DSRA_Copy and DSRA_Paste
  • Create a sum of each row on the left (adjacent to the description of the row)
  • Create a named range for each sum – e.g. DSRA_Copy_Sum and DSRA_Paste_Sum
  • Record a macro
    • Turn on macro recording
    • Copy the offending row
    • Paste-values the row immediately below
    • Turn off macro recording
  • Find the macro in the VBA editor (Alt + F11 opens the editor)
  • Modify the macro you just created as follows:

Dim i As Integer

For i = 1 To 100
   Range(“DSRA_Copy”).Select
   Selection.Copy
   Range(“DSRA_Paste”).Select
   Selection.PasteSpecial Paste:=xlPasteValues, Operation:=xlNone,SkipBlanks _:=False, Transpose:=False
   If Abs(Range(“DSRA_Copy_Sum”).Cells(1, 1)-Range(“DSRA_Copy_Paste”).Cells(1, 1)) <= 1 Then Exit For
Next

You already have the copy-paste syntax from the macro recording. The rest is as follows:

  • Dim i as integer tells VBA that i will be a variable of type integer – not a problem in VBA if you leave this line out
  • For i = 1 to 100 … Next is a loop which recurs 100 times. I prefer for-next loops to do-while loops because they can’t result in getting stuck in an infinite loop if the circular reference resolution doesn’t tend towards zero (or if I make a stupid error in the code!)
  • If Abs(…) is a condition which tells VBA to stop executing the loop if the sums of the rows are the same. I use an absolute value because I don’t know whether the past or copy row will be bigger, and I use 1 as an acceptable degree of difference. You can change that to be bigger or smaller depending on how much precision you require

 

  • I recommend creating another formula next to your circular reference resolution with a condition that the absolute value of the difference between the sums is less than an acceptable difference, with output “Circular reference resolved” or “Circular reference unresolved”, and applying some green and red conditional formatting to it.
  • Similarly, it’s good practice to aggregate all circular references checks into a master check at the top of the Working sheet, which should always be visible.
  • If you have more than one circular reference to resolve, it is fine to put more than one copy-paste into the for-next loop, and expand the conditions in the if statement using the AND boolean operator.

Debt corkscrews

An example of a simple Simple debt corkscrew.equal principal repayments can be downloaded here, and you can download a mortgage-style debt corkscrew here.

Debt is usually modelled by means of a debt corkscrew, so named because the principal outstanding at the beginning of the period is equal to the principal outstanding at the end of the previous period, and the principal outstanding at the end of the current period is a function of the principal outstanding at the beginning of the period, plus drawdowns, interest and repayments in the period. This creates a sawtooth (or corkscrew)-shaped dependency pattern.

An example of a Simple debt corkscrew.equal principal repayments can be downloaded here.

Pertinent points relating to the example:

  • Note the monthly period used throughout the model
  • As a consequence, indicators are required for repayment periods and capitalisation periods. I’ve used the modulus function here to identify which months an event occurs in. (Typically repayment and capitalisation periods are the same, although not always, as 3-month interest rates may be cheaper to hedge than 6-month interest rates, as their market is more liquid. I have used different periods to illustrate the point here.)
  • It is helpful to understand when in a period a figure relates to. For short periods (like a month) we use only the beginning and end of a period. Draw downs typically happen at the beginning of a period, while fees, interest and repayments typically accrue or occur at the end of a period.
  • The draw downs in this example are hard-coded. However, in a normal project model, they would feed off the capital requirements, which would in turn be a function of the capex, initial DSRA funding, postage and petties, upfront fees, etc.
  • I have split interest into three rows to account for capitalisation and payment periods being different to the model period. Interest accrued occurs only on principal outstanding at the beginning of the period and draw downs, not on previous interest accrued (at least until it is capitalised, at which point it enters into principal o/s).
  • You’ll note that I use OFFSET functions in calculating capitalised interest. I do this so that changing the input assumptions (B14) will flow through to the model. If the OFFSET is causing a #REF error, check the appropriate indicator using an IF statement. An example of this is in cell B23, where I calculated the equal principal repayment.
  • Day count conventions: I have used an actual / 365 day count convention, which simply means that I’ve calculated the number of days in the period and divided it by 365 [days in a year] when calculating how much interest accrues. Other conventions exist. Be sure you use the correct convention as per the financing documents.
  • You may hear a term such as nacq or nacs. These stand for ‘Notional annual, compounded quarterly’ and ‘Notional annual, compounded semi-annually’. These relate to the compounding convention for the interest rate. It simply means that the interest rate is stated as an annual figure, and that you should add the accrued interest back to the principal (i.e. compound it) quarterly or semi-annually, as applicable.
  • Repayment methods: There are three typical repayment methods in project finance, being equal principal repayments, mortgage-style, or sculpted.
    • The example uses equal principal repayments, the meaning of which is pretty obvious. As a consequence, total repayments (including interest) should be higher at the beginning and reduce over time. This is often a poor match for project cash flows, since the project’s revenues will often increase with time.
    • Mortgage-style repayments imply an equal repayment over both principal and interest in every period. This can be calculated using the PMT function. Note that it is good practice to use forward-looking parameters for mortgage-style repayments, rather than calculating a single repayment from the beginning. This allows sensitivities (e.g. a delay in repayment), as well as different interest rates at different durations. It’s actually good practice for equal principal repayments too, but I didn’t do it in the example! You can download a mortgage-style debt corkscrew here.
    • Sculpted repayments simply imply that the repayment schedule is manually sculpted according to criteria other than those laid out above. An often-encountered example is DSCR, in which, for example, the amount of principal repaid in each repayment period is an amount calculated to make the DSCR equal to a specified target value. Another reason to sculpt payments may be because of increasing revenues: A project may wish to have smaller early-duration repayments and larger payments towards the back end of the debt term.

Model periods

In the past, project models usually had a monthly period during construction, and a quarterly, semi-annual or annual period during operations. This made a lot of sense, because Excel allowed only a limited number of columns, and one didn’t want to run out of columns before the end of the project term!

However, this is not strictly necessary any more, since Excel now allows several thousand columns. Consequently, it is, in my opinion, far easier for the modeller to use the same period throughout the model. For a lenders’ model, I recommend that the period be one month per column. If you nonetheless want to use a multi-month period, you need to ensure that the number of months in the repayment period is divisible by the number of months in your model period.

Having a one-month period will mean that you may need to identify whether a non-monthly event occurs in a given period, such as a quarterly repayment. Modulus is a helpful function in this respect. E.g.

=if(mod(present month – starting month,3)=0,1,0)

could be used as a quarterly repayment indicator.

Period also has an effect on the way interest is calculated. If the interest compounding period is greater than that of the model, you will need to create additional rows to accrue uncompounded interest. More on this point in the Debt corkscrews article

 

Model layout

I have a profound dislike of models with excessive tabs (or sheets). I believe this makes it difficult to trace the flow of logic in a model. Consequently, I believe the model should have only three main tabs, with ancillary presentation sheets referencing those sheets, but not containing calculations themselves.

My preferred sheets are:

  • Assumptions sheet: This contains assumptions which are not series in time. The assumptions sheet should contain a Case selector at the top, the name of the assumptions down the left column, the active case assumptions next to this column, and then different scenario cases off to the right. Examples of different cases are:
    • The base case
    • Increased opex case
    • Increased construction price case
    • etc

The active case assumptions should reference the selected case through the use of the index function, or similar

 

  • A Time-based Assumptions sheet, which specifies assumptions which change in time, such as fx rates, interest rates, inflation, etc. These should generally be specified with the same periodicity as the model itself

 

  • A Working sheet, which contains all of the calculations relating to the model. Generally, the Working sheet contains the following sections:
    • Dates, period numbers, etc
    • Indicators (construction period, operations period, repayment period, etc)
    • Construction (funding requirements, VAT, etc)
    • Technical calculations (how much the plant produces, what its technical assumptions are)
    • Revenue calculations (dependent upon the technical performance of the plant)
    • Opex (dependent on, inter alia, the technical performance of the plant)
    • Equity and shareholder loan draw downs
    • Tax and depreciation calculations
    • Calculation of Cash flow available for debt service (CFADS) per the facility documents’ priority of payments (also called the cash flow waterfall)
    • Debt (draw downs over the construction period, repayments over the operating period. Possibly more than one facility, either ranking pari passu (repayments and draws occur proportionally) or not (one facility drawn or repaid after the other)
    • Debt service reserve account (DSRA) funding and draws and Maintenance Reserve Account (MRA or MMRA) funding and draws
    • Covenant ratio calculations (DSCR, LLCR and PLCR)
    • Distributions to shareholders
    • Financial statements

As mentioned above, other sheets may be required by lenders or project sponsors. These usually include presentation sheets for Annual Financial Statements and a Summary sheet.

Mixing model uses

Be careful not to mix up different model uses if they are incompatible.

An error which often arises is the following:

  • A model is created to determine the price or tariff of the project’s output. In order to do so, the tariff must change depending upon the input parameters to the model (e.g. capex, opex, cost of finance, etc)
  • The model is modified to turn it into the lenders’ base case model. However, the tariff still changes when certain input parameters change.
  • When lenders run sensitivity tests to determine the effect of an adverse scenario, the tariff increases, and the project appears to be insensitive to that particular downside scenario…

In short, tariffs and prices must be locked down prior to the model being turned into a lenders base case model.

Project finance modelling

A project finance model is written in order to assess the feasibility and bankability of a particular project (for our purposes, an infrastructure project of some kind).

Project finance models are also referred to as project models, base case models, lenders’ models or lenders’ base case models.

These models are also used to set prices or tariffs.

As such, a project finance model has specific characteristics which differentiate it from other business case models. In particular, it is much more concerned with cash flows than income statement of balance sheet.

If it is a lenders’ model, it will (obviously) contain one or more debt sections, cash flow waterfalls, covenant ratio calculations, and the ability to stress input assumptions in order to determine the effect of adverse circumstances upon the project.

Please note that the articles which follow are not necessarily project finance model gospel. Rather, they indicate my personal preferences relating to the way in which a project model should be laid out and written.

Infrastructure Project Lifecycle

As a project moves through the project lifecycle, it increases in value and new funders are required to invest at lower expected returns because:

  • The risk profile decreases at each stage indicated below;
  • Greater amounts of funding are required at each stage; and
  • Future cash flows are closer to the present, and are consequently discounted for less time.

Note that valuation of infrastructure investments are typically done on a discounted cash flow basis, with risk adjustment either on an explicit basis, such as probability-weighting of cash flows, or implicit in the discount rate.

Project development

A project developer will typically spend considerable time and a up to a few million dollars to develop a project. This entails identifying, arranging, negotiating and obtaining the following (non-exhaustive list):

  • Land usage;
  • Offtake contracts;
  • Regulatory approvals;
  • Environmental Impact Assessments (“EIAs”);
  • Engineering, Procurement and Construction (“EPC”) contracts;
  • Operating contracts; and
  • Equity and debt financing.

Often the developer will prepare and submit a tender proposal which may require bid bonds.

This work is done at risk. If a project fails to win the relevant tender, or cannot successfully obtain all of the project requirements, the project will fail and the developer will lose what funds have been put in. Because of the relatively high probability of failure at this stage in the process, project development is typically funded by equity and external investors could expect to obtain ‘zero-or-hero’ risk/return profiles with extremely high returns on funds used to develop projects.

If a tender has been awarded, the project undergoes a step-change in value, and equity becomes considerably more expensive / projected equity returns for new entrants into the project shareholding are lower. This recognises that the true value of any infrastructure project is in the payment stream which it can generate, which flows from the offtake or concession contracts, and not only the physical assets used to generate that payment stream.

Financing

Financing is a late stage in the development process. Due to the stable and predictable cash flows in infrastructure projects, projects are typically highly geared. Depending upon sector, debt:equity ratios of between 70:30 – 80:20 (typical of most power transactions) are not uncommon, while even 95:5 is not impossible.

The financing process typically requires considerable due diligence on the behalf of the lenders, which will usually be paid for by the project and guaranteed by the developer or project sponsors.

After signature of the finance contracts, it typically takes a few days or weeks until the conditions precedent to the finance contract becoming unconditional are fulfilled, at which stage the project reaches financial close and the project may draw down on the debt facilities. At the same time, the various project contracts, most importantly offtake, EPC and O&M, will be signed and become unconditional.

Project developers usually collect a development fee which may range between 1% – 10% at financial close depending upon the size of the project and the other project counterparties’ leniency. Lenders may require that this fee stays in the project until construction completion, and it is often ploughed back into the project as an equity carry.

Again, the project gains value when it reached financial close.

EPC

The project now enters the engineering, procurement and construction phase, which may be several months up to a few years in length. Typically little or no revenues are earned during construction. Construction ends on successful commissioning, and there is often a warranty or defects liability period (depending upon the asset type) for a period after completion.

The construction phase of the project is considered to be risky, as at this stage significant funds have been advanced by investors, but the ability of the infrastructure asset to generate revenues is as-yet unproven. In addition, any problems during construction which are left unmitigated will impact upon the whole of the revenue-generating operations period.

Operations

The project enters the operations phase, usually operated by a contractually-remote third party who will be financially liable for successful operations. Once the project has been demonstrated to perform successfully, the perceived risk profile of the project drops yet again, and the price of equity increases further. In addition, the project may refinance in order to gear up further (particularly if revenues are greater than originally expected) and / or to decrease debt margins.

Considerable consolidation has occurred during the operations phases of projects. For example, much of the renewable energy industry in Europe has been consolidated into relatively few utility-scale investors who receive a (relatively) low but stable return from the asset, which is boosted by undertaking the operations and maintenance of the infrastructure asset themselves.

Transfer

If the project is predicated upon a concession or government / parastatal offtake contract, the infrastructure asset may be transferred back to the state or offtaker at the end of the concession period. This is referred to as a ‘BOOT’ scheme, standing for ‘Build, Own, Operate, Transfer’. BOO and BOT schemes are also common.

At the end of the asset’s life, the project may incur decommissioning costs.

Political Risk

One of the key risk areas considered by the banks when lending to an infrastructure project is country risk. This has a number of different sub categories, including:

  • Political violence, such as revolution, insurrection, civil unrest, terrorism or war;
  • Governmental expropriation or confiscation of assets;
  • Governmental frustration or repudiation of contracts;
  • Wrongful calling of letters of credit or similar on-demand guarantees;
  • Inconvertibility of foreign currency or the inability to repatriate funds.

Of these risks, currency convertibility and repatriation is perhaps the most prevalent, as most infrastructure capex is paid for in hard currency, while the revenue stream of the project, or if not the project, at least the offtaker, is usually local currency. Consequently care needs to be taken to ensure that the project or offtaker is able to source the currency which the loan is denominated in. Unfortunately fx swaps are typically inadequate to the task of immunising a project against currency convertibility and repatriation risks for a number of reasons, being:

  • Often local currency rate curves, and therefore forward fx curves, do not usually go out to the durations of the debt. If they do, they may be illiquid and expensive;
  • Fx swaps can result in very significant credit exposure, which may nullify the benefit of having done the swap in the first place; and
  • It may be the state which prevents repatriation.

There are a number of different ways to mitigate this risk, some of which may be available only during the structuring stage of the transaction, and some of which can be bolted on afterwards.

 

Political Risk Insurance

It is possible to purchase Political Risk Insurance (“PRI”) to cover one or more of the heads of cover indicated in the list above. Premiums can be paid either up front or periodically (usually annually in advance) and may be payable by the project or the investor. Premiums range in size as well as value for money, as different providers will have different mandates to provide such cover.

 

Commercial PRI

Commercial PRI is available from any number of large commercial insurers and reinsurers, such as Lloyds.

Pricing for commercial PRI is volatile, depending upon current perceptions of the liklihood of the risk being insured against that actually occurring in the specific jurisdiction, as well as market appetite for such risk.

 

MIGA

The Multilateral Investment Guarantee Agency (“MIGA”) is an international financial institution which offers political risk insurance guarantees to help investors protect foreign direct investments made in developing countries against political risk. MIGA is a member of the World Bank Group and is headquartered in Washington, D.C. It was established in 1988 to serve as an investment insurance facility of the World Bank to help investors overcome political and other non-commercial risks and invest confidently in developing countries. Since its inception, MIGA has provided more than USD24 billion in cover for 700 projects in over 100 developing countries. MIGA currently has an outstanding guarantees portfolio of USD 9.2 billion (2012).

MIGA offers partial credit guarantees (“PCGs”) to cover the credit risk of a sovereign government or parastatal entity, and partial risk guarantees (“PRGs”) to private projects to cover a government’s failure to meet its contractual obligations. Heads of terms covered are:

  • Civil unrest, terrorism or war;
  • Governmental expropriation or confiscation of assets;
  • Inconvertibility of foreign currency or the inability to repatriate funds;
  • Non-honouring of sovereign financial obligations;
  • Breach of contract

The final head of cover above covers situations where the government or parastatal entity breaches its contractual obligations, rather than the Project breaching its obligations. Consequently if it is to be used, care needs to be taken during the structuring phase to ensure that the risks being guarded against are included in the contractual arrangements with the government or parastatal (and not only the project).

Interestingly, MIGA appears in the past to have priced its cover as a function of the heads of cover utilised, rather than risk of the cover actually being called. Consequently including an obligation from the sovereign to compensate the project in the event of the other political risks occurring or to not perpetrate them means that the project can purchase the breach of contract cover alone, with significantly lower premiums than if it had purchased the full PRI suite.

 

Export Credit Agencies

Export Credit Agencies (“ECAs”) are quasi-governmental institutions mandated to support and encourage the export of their domicile countries’ goods and services. This support can take the form of credits (financial support) or credit insurance and guarantees (pure cover) or both, depending on the mandate the ECA has been given by its government. ECAs can also offer credit or cover on their own account, similar to normal banking activities. Some agencies are government-sponsored, others private, and others a bit of both.

ECAs currently finance or underwrite about USD 400 billion of business activity abroad – about USD 55 billion of which goes towards project finance in developing countries – and provide USD 14 billion of insurance for new foreign direct investment, dwarfing all other official sources combined (such as the World Bank and Regional Development Banks, bilateral and multilateral aid, etc.). As a result of the claims against developing countries that have resulted from ECA transactions, ECAs hold over 25% of these developing countries’ USD 2.2 trillion debt. (Numbers courtesy of wikipedia – suffice it to say, ECAs are a significant contributor to infrastructure finance.)

ECAs provide both commercial cover, which covers against all risks, and PRI, provided that a qualifying percentage of the goods and services employed in the project (usually the construction) are sourced from the ECA’s home country (“Local Content”). In the case of loans covered by ECAs, 85% of debt is typically the maximum commercial cover provided, although PRI is usually available for the remainder. ECAs prefer investors to be aligned in terms of commercial risks.

ECAs charge a premium for cover, which may be up front or recurring. However, unlike commercial PRI, their mandate is not to maximise profits, but rather exports. Consequently using ECA cover may decrease the aggregate cost of debt, inclusive of the premium. Correspondingly, margins for ECA-covered debt are usually very low, as a (good) ECA will typically have a similar credit rating or quality to its home country. This reduction in margin is not effected through a reduction in the probability of default, but rather a reduction in loss given default of the loan.

 

Investment treaties

Infrastructure transactions often have geographically-dispersed equity holding structures in order to take advantage of tax- and investment treaties between the host country and the countries in which the holding companies are domiciled in. Mauritius is a good example of this, having a large number of tax treaties with various African countries. Similarly, Kenyan projects are often held out of the United Kingdom, which has the lowest withholding tax on dividends of all its investment treaty partners.

An added benefit for investors is that investment treaties provide foreign investors with potential relief when they have experienced business difficulties in a host country arising from the acts or omissions of an arm of the host state such as the executive, the courts, the legislature, or administrative or regulatory officials. An award under such arbitration can be enforced by attaching the non strategic assets of the host country in the investor country.

Project finance hedges

Project Finance hedges are typically vanilla interest rate- or fx swaps. Contractual protections are usually very similar to those of senior debt, in particular:

  • Ranking in the cash flow waterfalls; and
  • Sharing in security.

This has the consequence that between hedges and debt, Probability of Default (“PD”) is very similar, as is Loss Given Default (“LGD”).  However, the Exposure At Default (“EAD”) of a hedge has significantly different characteristics to that of debt. These similarities and differences to debt lead to synergies in determining the credit risk and consequent credit margin of a hedge, while still requiring some alternate means of quantifying such risk.

The remainder of this post will use a vanilla interest rate swap (“IRS”) as an example, as it is the most significant hedging instrument typical of project finance power transactions. However, similar principles may be applied to different derivative instruments.

Who pays who?

Under an interest rate hedge, the Project will pay the hedge provider a floating interest rate based upon a notional principal loan schedule. In return, it will receive a floating interest rate from the hedge provider based upon the same notional principal outstanding.

The notional principal schedule is usually a percentage of the debt principal. For example, it may be 80% of debt in every period, or a declining percentage, such as 100% of debt in construction and 75% for the next 10 years.

Calculating the fixed rate

The mid swap rate is calculated by setting the NPV of future interest rate payments of the fixed leg equal to that of the floating leg, where the floating leg assumes that the floating interest rate will unfold as per the forward interest rate curve (eg LIBOR or USD-SWAP). The discount rates are taken directly from the forward interest rate curve. A credit spread is then added to the mid rate so calculated to arrive at the fixed rate offered to the Project.

Consequently the day-1 PnL of the swap is equal to the NPV of the credit spread * notional, using the forward interest rate curve to discount back each payment. This is referred to as the (initial) mark-to-market and incidentally is also the initial credit exposure under the hedge.

Therefore: MtM =

∑t(Principal(t) * Fixed interest rate * (1 + i(t))^-t) – ∑t(Principal(t) * it* (1 + i(t))^-t)

where:

  • t is the number of years in the future at time t
  • Principal(t) is the notional principal outstanding at time t
  • i(t) is the forward interest rate at time t

Legal Framework and CSA

Most hedges are governed by an ISDA Master Agreement, developed by the International Swaps and Derivatives Association. This sets standards, simplifies the specific documentation required for a trade and, importantly, allows netting between different trades.

Any hedge which a non-recourse project enters into will not have a CSA – that is, neither the Project nor the Project’s counterparty will post cash collateral. This is simply because margining requirements may become sufficiently onerous as to sink the Project. For example, if the Project is paying fixed and receiving floating, and the prevailing (floating) interest rate drops significantly, then the mark to market of the swap will decrease significantly, with the result that it will be owing from the Project to the hedge counterparty. If the Project were required to post collateral, the cash flow requirement in this scenario might be more than the cash the Project has at hand, thereby rendering the Project insolvent.

Cash flow waterfall ranking pre enforcement

Pre enforcement, the interest rate swap payments will typically rank alongside the senior debt’s interest, and therefore prior to senior principal repayments and certainly prior to mezzanine debt or equity.

However, if the swap is broken and at the same time the senior lenders choose not to enforce against the Project, there may be a hedging termination amount owing to the hedge provider. The exact ranking position in the waterfall differs between transactions, but will typically rank alongside or post senior principal, but again usually prior to mezzanine debt and equity. Note that it may therefore rank post reserve account funding.

The cash flow waterfall ranking of the hedge payments inform the PD of the hedge. As the same project underlies both debt and hedge, and the payment ranking of both is very similar, the PD of both debt and hedge are very similar to each other.

Cash flow waterfall ranking post enforcement

If the Project is put into enforcement, there may again be a hedging termination amount owing to the hedge provider. This will usually rank pari passu with senior debt in the order of payments.

In addition, hedging termination amounts post enforcement will usually share pari passu in the senior security.

This speaks to the LGD of the hedge: It is consequently very similar to that of the senior debt.

Exposure

Unlike the credit exposure under the debt, which is determinable at inception with considerable certainty, the exposure under the hedge is volatile and impossible to predict with certainty. However, it does follows a probability distribution function.

This is because the mark-to-market of the swap changes from inception as time passes, for the following three reasons:

  1. As time passes, payments occur under the swap, and the NPV of the outstanding payments is reduced by the amount already paid (predictable);
  2. The time which the outstanding payments under the swap are discounted by decreases (predictable); and, most importantly
  3. The forward interest rate curve moves upwards or downwards and changes shape (unpredictable)

Exposure – Market risk

The mark-to-market of the swap can change from owing to the hedge provider to owing to the Project if the rate curve rises in aggregate. (The NPV of the fixed rate leg received by the hedge provider will reduce, because of the NPV effect of an increase in discount rates, while the NPV of the floating leg being paid by the hedge provider will remain roughly static, as the interest payable increases, but is offset by the NPV effect.)

Note, however, that the hedge provider would typically hedge his own position by entering into an equal-and-opposite position in the market to the extent that it is desirable to do so.

Exposure – Credit risk

As the mark-to-market moves increasingly in the hedge provider’s favour (as the interest rate curve decreases) the credit risk increases equally. This can be seen by considering the situation where the hedge provider has hedged out his position in turn. If the mark-to-market of the Project-hedge provider hedge is in the hedge provider’s favour, then the mark-to-market of the equal-and-opposite hedge is owing by the hedge provider in a very similar, but slightly lesser, amount.

If the Project then defaults, the hedge provider will still owe its own counterparties under the equal-and-opposite hedge and will experience a net loss.

Consequently, all other things being equal, the lower the interest rate drops the greater the credit risk on the hedge.

Potential Future Exposure (“PFE”)

The PFE of an interest rate swap is calculated by means of Monte Carlo simulations. In each of (say) 10 000 simulations, the forward interest rate curve is projected into the future at each revaluation point over the life of the hedge by means of a random process (such as Brownian motion).

In each simulation, the mark-to-market of the hedge is calculated at each revaluation point. For each revaluation point, the values are then ranked from largest to smallest and the value at each percentile is extracted from the list, generating a distribution function of the mark-to-market at each revaluation point in time. For example, the  500th point is extracted to determine the 95th percentile highest credit exposure, as would the 1000th for the 90th percentile, and so on.

As we project into the future, the projected interest distribution flattens and widens, as does the mark-to-market, resulting in greater variance. However, this effect is countered by the effect of the decreasing notional principal outstanding as the senior debt is repaid and / or the percentage of the senior debt hedged decreases.

This results in the credit exposure of the hedge being distributed roughly as follows (without mean-reverting interest rates):

Additional risk mitigants and considerations

Right-way-round risk: Interest rate swaps are said to enjoy right-way-round risk in that, as the credit exposure under the swap increases, the project benefits from a decrease in its floating interest rate bill, with the consequence that its PD decreases.