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Guidebook on Financing of Highway Public-Private Partnership Projects

December 2016
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4 Project Financial Model & Statements

4.1 Introduction

Financial models are one of the most important tools used to assess the financial feasibility of P3 projects. They incorporate a range of economic, financial, and project-specific input data and present this information in pro-forma financial statements and other formats. The models generate outputs such as the financial indicators discussed in chapter 3 that help public authorities and other parties make decisions about whether and how to proceed with P3 project implementation. The objective of this chapter is to provide an understanding of:

  • The purpose and utility of financial models
  • Financial model inputs and assumptions
  • Project financial statements
  • Amortization and depreciation
  • Income tax issues related to P3s.

4.2 Financial Model Inputs

In general, the types of assumptions that are included in a P3 financial model (in addition to project details and general economic assumptions) include:

  • Construction costs and other capital expenditures
  • O&M costs
  • Other project costs
  • Various forecasted risk costs
  • Traffic and revenue forecasts
  • Depreciation, amortization, and taxes
  • Project financing schedules
  • Other revenues (including project subsidies).

This section discusses how to incorporate these assumptions into a P3 financial model. The focus is on the first five assumptions listed above. This section also covers key concepts related to the development of these assumptions for P3 projects, including optimism bias and private sector efficiency. An in-depth discussion on depreciation and amortization appears in the next section. Other items, such as project financing schedules and other revenues (e.g., grants and subsidies) have been addressed in detail in previous chapters.

Some inputs and types of analyses that are discussed in other FHWA P3 Toolkit publications are not discussed in detail in this guidebook. These include the discount rate and Value for Money Analysis. Readers can reference the relevant Toolkit publications on these topics for more information.

4.2 1 Capital Expenditures

The construction cost worksheet includes the schedule of project outlays to construct the capital assets required to operate the concession. Construction cost assumptions typically are derived by engineers with knowledge of contemporary engineering and construction techniques. Project costs typically are expressed in nominal terms based on specific forecasts of inflation for the construction industry. Design, permitting, related development costs, including land and other acquisition costs, are typically rolled into the capital expenditure estimates for a P3.

Construction costs are not the only type of capital expenditure. Interest paid during construction is considered a capital expenditure. Fees paid to legal and financial advisors as part of the project may also count as capital expenditures. These items need to be added to construction costs to determine total capital expenditures. This is important since capital expenditures can be depreciated over time, thereby reducing the amount of taxes owed by the project company. Depreciation is addressed in the next section.

4.2.2 Operation & Maintenance Costs

O&M costs include labor, routine maintenance, payments to vendors (such as telecommunications service providers), and the like. Major maintenance, or structural maintenance, is considered a capital expenditure. These costs are typically developed by planners, engineers, and experienced facilities managers. Like construction costs, O&M costs typically are expressed in nominal terms based on specific inflation forecasts for the construction and property management industries. At an early stage in project financial assessment, it may be appropriate to use a ballpark figure to determine O&M costs, such as 5 percent of capital expenditure. However, as a project is more fully assessed, the specific line item expenses need to be estimated. This is especially important when comparing public and private costs using the Value for Money Analysis approach.

4.2.3 Other Project Costs

Other development costs include procurement, and any other costs incurred by the public sector or the private partner that cannot be categorized as project capital expenditures or O&M. These costs are typically estimated by planners and engineers based on typical project costs of similar scale and scope and in similar geographies. Other project costs are generally expressed in nominal terms.

4.2.4 Risk Costs

There are a number of risks that need to be accounted for by the private sector partner in a P3. These risks can be included in several different ways in a shadow bid estimate:

  • As an implicit factor in the P3 project construction cost, O&M, and other cost assumptions.
  • As an explicit expense line item associated with the cost of project delivery.

FHWA's P3-VALUE 2.0 uses the latter procedure. Risk costs are generally expressed in nominal terms and may be inflated at rates of similar costs in the financial model.

Risks associated with construction costs and other capital expenditures are rolled up into construction cost forecasts and flow through the financial model in the same manner. Therefore, capital expenditure risks will be represented in:

  • Depreciation expenses.
  • Capital expenditures recorded as cash outflows.
4.2.5 Revenue

As discussed in chapter 2, there are two main types of revenue for transportation P3s in the US: availability payments paid by the public authority and toll revenue. In practice, there are many other sources of revenue used to fund transportation infrastructure around the country, such as sales and property tax revenue, including those from special districts. Some of the grants used to fund P3 projects may be funded with the proceeds of bond issuance that is expected to be repaid by some of these other revenue sources. However, these external revenue sources are outside the scope of this guidebook. The reader may refer to other publications on this topic. 23

Availability Payments

As the name implies, availability payments pay for the availability of an asset. The term availability is well defined in project documents and is related to performance requirements that require an asset to be available for use. For example, a road that is covered in snow is not available. A lane that is closed for construction is not available. So, the full availability payment is made only when the asset is fully available.

The public authority typically makes an availability payment regardless of how much the asset is used. In this sense, if the asset is a tolled facility, the public authority accepts demand risk. However, some availability payment projects include some demand risk sharing with the private sector. One example is the case of shadow tolls that may be paid if traffic reaches certain levels or if certain types of vehicles use the road (e.g., heavy trucks that cause more damage and so increase maintenance costs). Another example is when usage is included as a performance indicator even when the revenue source is an availability payment. The main costs that need to be covered by an availability payment are the same items that appear in the cash flow waterfall, namely:

  • Operational expenses
  • Debt service
  • Taxes
  • Capital maintenance
  • Equity dividends.

When upfront public subsidies or construction milestone payments are used, project debt and equity is reduced and, in turn, the required availability payment is reduced. Public authorities that pay directly for construction will have an availability payment that is similar to a long-term service contract.

The reliability of the availability payment is a function of the creditworthiness of the public authority and the performance of the project company. There is almost no financial risk associated with availability payments from a AAA-rated public authority (although there may be legal, political, or regulatory risks). Since P3 agreements are performance-based contracts, the availability payment is related to project company performance. If the project company satisfies all of the performance requirements in the project agreement, then the full availability payment is made. The certainty with which the project company can guarantee its own performance is the same as the certainty with which it can predict its own revenues from the stream of availability payments. As a general rule, the maximum deductions by the public authority due to "non-availability" will still leave sufficient annual payments for the private company to meet its debt service obligations.

Toll Revenues

Toll revenues carry a much higher level of risk than availability payments. Toll revenues depend on the level of usage of the facility and the rates charged. Both may be very sensitive to general economic conditions and other factors.

P3 financial models depend on traffic and revenue (T&R) forecasts to estimate project revenues for a toll concession. Traffic and revenue forecasts are impacted by a number of factors, including but not limited to (1) toll rates, (2) the availability of alternative routes or modes, (3) planned competing or complementary infrastructure investments, (4) the economic and land development contexts driving demand, and (5) economic factors (e.g. general state of the economy, inflation, etc.) that might constrain the amount by which tolls can be raised. Firms specializing in travel demand and transportation network modeling are typically hired to conduct the traffic and revenue study. In a P3, the offeror will likely conduct its own traffic and revenue study.

Appendix 1 provides a detailed explanation of the processes, options, and challenges in conducting traffic and revenue studies, especially for toll roads. In summary, there are several modeling options to consider:

  • A four-step network assignment model forecasting regional travel demand and network behavior on the P3 roadway link at discrete times of day. These forecasts are developed based on observed average behavior within a series of small geographic zones (traffic analysis zones) and using these observations to estimate demand for and usage of the wider transportation network.
  • An activity-based model that forecasts an individual's or household's travel demand and behaviors over the course of a given day as derived from assumptions about typical activities. Assumptions are made for individuals and households based on demographic and economic attributes and transportation availability.
  • Other micro-simulation techniques that model dynamic behavior at a granular level.

The choice of modeling technique depends on project scale, scope, and budget, among other factors. Appendix 1 describes some of the strengths and weaknesses of each. Many P3s, especially those where the project company is remunerated with tolls, will want to employ the most granular level of analysis possible, as toll rates can have a major effect on the decision by drivers to use a P3 toll road or seek alternatives.

A good traffic and revenue forecast will employ a probabilistic approach to forecasting, similar to the approach for estimating distributions for cost-based risks. Appendix 1 provides a detailed discussion of how to conduct a quantified probability analysis for traffic and revenue studies.

Some traffic and revenue assumptions might be included implicitly in forecasts or explicitly in general model assumptions. These include, primarily, toll revenue leakage and toll revenue ramp-up. The former concerns loss of toll revenue due to evasion by motorists, technical problems affecting billing, etc. The latter refers to the observed phenomenon that traffic on new infrastructure, especially toll roads, tends to slowly ramp up over several years before stabilizing.

Generally speaking, revenues are expressed in project financial models in nominal terms, with any toll rate increases factored in.

4.2.6 Inflation

There are different measures of inflation. Consumer Price Index (CPI) measures the increase in the price level of a basket of goods and services over time. Construction inflation focuses only on the prices of construction materials and labor. General inflation is typically measured for an entire economy using weighted indices. Individual prices can fluctuate over time for many reasons based on demand and supply conditions.

When projecting future revenues and costs, inflation is an important consideration. The inflation rate chosen and how it is applied can greatly affect the projected profitability of a project (particularly when there are fixed costs such as interest payments or fixed revenues such as toll rate caps). In the financial model, inflation assumptions are used in several different ways:

  • An explicit rate applied to some or all project costs and revenues.
  • An implicit factor in any nominal revenue or expense forecast for other project inputs.
  • An implicit element of the discount rate if reported in nominal terms.

Note, however, that inflation is different from individual changes in prices. Variable costs or revenues are estimated as well as possible and built into the expected costs and revenues of a project. For example, if it is known that a new government policy set to begin 2 years after the start of a project will raise the price of steel by 5 percent, this change would be built into the cost projections for the project.

Inflation is important for long-term projects because increases in the price level erode the purchasing power of the dollar. If, for example, the contract specifies that the project company cannot raise the toll rate more than 2 percent per year and the inflation rate in the economy turns out to be 3 percent per year, the real value of the per-unit toll revenue that the project company collects each year will be falling by 1 percent. Furthermore, if the nominal costs to the project company are rising by 3 percent each year, the financial viability of the project will be in jeopardy.

The rate of inflation is also closely tied to the concept of discount rates. The Risk Assessment Guidebook offers a thorough discussion of this relationship. The treatment of inflation in a financial model depends on the level of sophistication and detail of the model. A relatively simple model might apply an explicit rate across all or most model inputs using a single inflation indicator for the entire economy.

Various sources can be used for constructing or validating inflation inputs. A good place to start is with the US Bureau of Labor Statistics, which reports the CPI. 24

Often, a financial model will incorporate inflation, to the extent possible, in nominal dollar forecasts for some project revenues and expenses. Prices for certain expenses, including many construction costs with volatile pricing such as fuel and steel, are often more precisely forecasted separately from the economy as a whole. Again, the CPI can provide guidance. Also, commercial publications are available to help practitioners develop or validate future-year assumptions. For example, developers typically use R.S. Means as a benchmark for construction cost and materials pricing and forecasts. 25 It is helpful to consult engineers and economists, either in-house or contracted, with strong geography-specific and subject-matter knowledge.

4.2.7 Optimism Bias

Optimism bias is the tendency of parties involved in the development of financial models to overestimate income or underestimate expenses of a capital project. This tendency has been studied in academic literature for years, but the cost over-runs of numerous large mega-projects across the world has helped focus attention on this issue and possible remedies.

Flyvbjerg, considered by many to be the authority on project cost forecasting at the planning stage, suggests there are two problems: optimism bias and strategic misrepresentation. The latter is difficult to address, as it relates to the political-economy and institutional incentives to secure funding. 26 The former is simply a psychological disposition towards overconfidence in forecasts which can be corrected for in financial modeling. His proposed remedy is called reference class forecasting, where the modeler identifies a relevant reference class based on similar past projects and compares the project with a probability distribution derived for the reference class to estimate a range of outcomes.

Governments are increasingly adopting reference class forecasting and similar processes for large public works projects. The UK has been particularly aggressive in adopting procedures for adjusting all project appraisals to account for optimism bias. 27

In the US, optimism bias is generally acknowledged as one of numerous risks and uncertainties in a major infrastructure project. 28 These are dealt with in several different ways. Contingency and reserve accounts are established to provide a buffer for over-optimistic forecasts. More advanced financial models derive probability distributions of the variation of key model assumptions and inputs and simulate the outcomes over numerous changes in the assumption scenarios. The result is a probability curve with a mean net present value (NPV) and a distribution mirroring historical volatility of assumptions. Depending on its complexity, the model may also produce distributions for any individual key line item in the financial model (e.g., net income in any given year).

Probabilistic approaches may be used to address optimism bias as a component of uncertainty. Techniques to build a financial model using probabilistic approaches are complex and typically require advanced knowledge of finance, probabilistic simulation, and programming.

The basic process for correcting for optimism bias as a component of uncertainty is as follows:

  • Use historical knowledge of key model input values to define a mean, maximum, minimum, and probability distribution form for each. 29, 30
  • Enter these values into the assumptions page in the financial model.
  • Link these cells to a Monte Carlo simulation software package and run the program.
  • Link simulation output to forecast cells in the financial model.

The generation of these distributions is covered in the Risk Assessment Guidebook.

Often, project decision-makers will choose to govern the concession on the assumption of a higher degree of confidence than mean input values. A typical rule of thumb is to use the values representing the 70th percentile (i.e., the cost outcome will be equal to or less than this value 70 percent of the time), which helps account for optimism bias and other uncertainties in transportation infrastructure financial model forecasts.

The most important consideration in assumptions for optimism bias is to acknowledge a process for addressing this phenomenon in a manner for which all parties to the transaction are comfortable.

Most practitioners involved in P3 decision-making are familiar with optimism bias, as the phenomenon is not limited to privately financed projects. Nonetheless, identifying optimism bias in financial model assumptions and input forecasts is challenging. Fortunately, processes have been developed to account for these biases and other uncertainties. Developing internal expertise in probabilistic risk assessment or the use of qualified consultants can help improve the detection and mitigation of optimism bias in financial models.

4.2.8 Private Sector Efficiency

Value for money refers to the public sector's goal of procuring a project in a way that offers the best value for the public agency. Under certain conditions the private sector can deliver greater lifecycle value on a transportation infrastructure project. Conclusions regarding the relative value for money of a P3 procurement versus an alternative approach are based on financial model assumptions and inputs that capture the impact of private sector innovation or lifecycle cost savings. These might include, for example:

  • Lower design and construction cost estimates (including risk costs) feeding financial model capital expenditure forecasts.
  • Lower long-term O&M cost estimates (including risk costs) feeding financial model forecasts of operating expenses.

There are many arguments for why P3s might justify some combination of higher revenues and/or lower costs for providing a certain level of service than might be expected under conventional public sector delivery. Research suggests there are three mechanisms by which private sector finance and project delivery can achieve greater efficiencies than conventional public procurement: 31

  • Economies of scope, or the bundling of tasks such as design and construction and O&M so as to encourage lifecycle cost-minimizing decisions.
  • Allocating risks to parties best able to control and most cost-effectively manage them.
  • Provision of contractually enforced incentives for performance.

Like optimism bias, it is important to understand if and how assumptions about private sector efficiency are addressed in the financial model. These will occur primarily in several places:

  • Project design, construction, and O&M cost assumptions.
  • Traffic and revenue forecasts.
  • Risk assessment and adjustments.

These assumptions might be provided upfront, or be implicit in model assumptions and model input forecasts. Procurement officials and other planners and practitioners reviewing P3 financial models can apply their knowledge of typical assumptions for similar projects developed through conventional methods and gain a rough idea about the relative aggressiveness of the bidder's assumptions regarding private sector efficiencies. Offerors should be able to justify these gains from efficiency on the basis of the three mechanisms previously described.

4.3 Project Financial Statements

The three main financial statements are the income statement, cash flow statement, and balance sheet. The following sections discuss each of these in turn. This section is not meant to be an authoritative guide for accounting and financial statements. Each industry and firm has its own specific financial indicators of interest and its own way of presenting and interpreting those indicators. This section focuses on the elements of the financial statements that are key to the financial assessment of P3s. Readers should consult professional tax advisors for guidance on their own projects and for specific questions and advice.

It is important to remember while reading this section that most project companies are Limited Liability Companies (LLCs). As such, they do not typically pay taxes. Instead, the parent companies or member firms pay taxes. However, since member firm financial conditions can vary widely, it is standard practice to analyze financial statements at the project company level, including the estimation of taxes.

4.3.1 Income Statement

The income statement illustrates profits and losses in a given period based on the economic value of proceeds from operations and from the economic costs of employing plant, labor, and capital to secure those income streams. In essence, the income statement provides a snapshot of whether the value of goods and services produced exceeds the cost of producing them in any given year. A positive net income indicates that a project is generating greater value in sales and revenue for the facility in a given year than the economic costs associated with deploying assets to secure that income. For a greenfield P3, the practitioner can expect negative net income in the early years during construction before operations fully commence. Annual profits typically are expected to increase steadily once construction is complete before reaching a stable or modestly growing income stream over time.

Depreciation and Amortization

There are two basic approaches to accounting: cash-based and accrual-based. Under cash-based accounting, flows of funds are recorded as they occur. Under accrual-based accounting, assets are depreciated or amortized over their useful life. Tangible assets (like roads, bridges, and tunnels) are depreciated, and intangible assets (like tolling rights) are amortized, in both cases over prescribed periods.

Almost all US corporations use accrual accounting. Increasingly, public authorities are also using accrual accounting to more accurately reflect their finances. 32 Accrual accounting is particularly relevant for P3 projects since the concept of lifecycle costing is one of the most important rationales for P3s.

Accrual-based accounting helps public or private entities understand their financial position, in particular with respect to long-term assets. Special purpose vehicles also file their federal tax returns on an accrual basis, which allows depreciation expense to be recognized over a shorter period than financial accounting rules. Depreciation and amortization involve no cash disbursements, but are considered expenses and can be deducted from taxable income to reduce required tax payments. This is relevant to P3s because public agencies do not pay taxes; therefore, they cannot take advantage of this particular benefit of depreciation and amortization. On P3 projects, the private entities are required to pay income taxes. So, they can take advantage of depreciation and amortization thereby reducing tax payments.

In the early years of a greenfield project, the project company typically will not have any revenues, so no taxes will typically be due from its operations. Once post-construction revenues begin, the project company may owe taxes depending on the level of revenues and how they compare to the negative items on the income statement (operating expenses, interest payments, depreciation, and amortization). Assets typically may not be depreciated until they are put into use.

The income statement includes a line item for depreciation. This amount is deducted from operating income, or earnings before interest, taxes, depreciation, and amortization (EBITDA), along with interest expenses before taxes are assessed. So, the higher the amount of depreciation and amortization, the lower the tax bill, all else being equal. Depreciation is also added from year to year and cumulative depreciation appears on the balance sheet (discussed later in this chapter).

The US Internal Revenue Service (IRS) has determined different depreciation schedules depending on the type of assets and other factors. Readers should consult professional tax advisors for guidance on these issues.

A key limitation of the benefits of P3s with respect to depreciation is the requirement of tax ownership. For transportation P3s, assets generally remain the sole property of the public authority. Physical ownership is never transferred to the private partner; so if private partners are to take advantage of depreciation, they need to establish tax ownership. In order to establish tax ownership with a private operator of a publicly-owned facility, the concession or lease term generally must be 50 years or longer. It may be difficult for the public authority to pursue a P3 with a shorter term than the accounting useful life of the assets. This constraint is considered in developing the terms in the issuance of the P3 procurement documents. Practitioners should consult IRS Publication 946 or a certified accountant or tax attorney to understand the specific application of tax laws to any given project. 33

Taxes

The income statement also determines the project company's required tax payments. As most project companies are LLCs, taxes are typically paid by the parent companies or member firms. However, it is standard practice in P3 financial modeling to estimate taxes at the project company level. Taxes are levied on income after certain deductions. Operating expenses, interest expenses, and depreciation are deducted from income before assessing taxes due. Once taxes are subtracted from earnings, the income statement displays net earnings, or profit. This figure is later used in the cash flow statement.

Typically one can assume that the US corporate tax rate will be 35 percent of net income. State corporate taxes may also typically apply based on the location of the P3 project. State taxes are typically deductible from Federal taxable income, and that calculation can be incorporated into the P3 financial model.

Other State and local taxes may apply. As mentioned above, P3 project companies typically do not own transportation assets and seldom have to pay property taxes on them. P3 legislation typically exempts P3 property from taxation. One exception is the Dulles Greenway, which is a special type of P3 project. Private investors bought the land required for the road and then sought permission from the Commonwealth of Virginia to operate a toll road on the property. Since the project company actually owns the road, it is required to pay property taxes which amount to approximately 3 percent of toll revenues.

4.3.2 Cash Flow Statement

The cash flow statement measures the financial liquidity of a project at any given period of time. This is the primary tool for tracking the actual flow of funds into and out of the project. A project must have sufficient funds in its accounts to cover capital expenses, current expenses, and payments on long-term obligations such as debt service. Lack of funds may require an infusion of additional equity or the securing of new debt, which might adversely affect the returns on investment to the project company. Whereas net income on the income statement may be negative in some years, and indeed will be expected to run negative in early years during construction, the cash flow statement can never show negative ending cash, as this signifies an insolvent project.

High net cash flows in a given year do not necessarily signify financial health. Cash flow balances may be highest at the beginning of a concession term, when project risks are highest. This is because proceeds from equity raising and debt issuance may have been credited to the project accounts already while major construction costs and other expenses have yet to be paid. Meanwhile construction, traffic, and other major risks are still high. Beyond meeting project requirements, the cash flow statement also indicates when there is sufficient cash available to establish or replace reserve funds, increase the rate of debt amortization, or to pay out dividends. Cash flow statements can be constructed in two different ways:

  • Direct Method: Cash flows in a given year are calculated from forecasted changes to various current accounts (i.e., accounts with cash and other short-term, liquid assets). In essence, this method provides a direct measurement of cash flows coming into and leaving the project in any given year.
  • Indirect Method: Cash flows are calculated from the income statement by removing non-cash charges (i.e., depreciation) from net earnings.

The cash flow statement allows equity investors to determine how much money will be available each year for dividend payments. These are taken from the available funds line item. Each project will differ in terms of how much of the available funds can be paid out as dividends. A variety of reserve accounts may have to be established or replenished before paying out dividends. A certain amount of cash also needs to be kept on hand, such as an amount equal to the next quarter's operational expenses. Loan and bond covenants may also restrict equity payments. For example, dividends typically are not paid during construction. Lenders may require that principal payments begin or reach a certain level before dividend payments are allowed to begin. Once equity dividends are forecast for the entire contract term, a PV of dividends and Equity IRR can be estimated and compared to upfront equity investment requirements to determine if the project meets private investor hurdle rates of return.

4.3.3 Balance Sheet

The balance sheet provides a snapshot of the financial position of the project company at the end of each fiscal year. The balance sheet is a measure of the stock of value the project is creating over time in terms of assets, liabilities, and equity.

The income statement and the cash flow statement are the measures of flow each year that contribute to (or extract from) the stock of value measured on the balance sheet. The three main parts of the balance sheet are:

  • Total assets, or total economic resources at the project company's disposal to operate and generate revenues.
  • Total liabilities, or all of the obligations on the part of the project company in the future to pay for the assets.
  • Owners' equity, which is the difference between total assets and total liabilities.

Essentially, any economic value retained in a project that exceeds long-term liabilities represents equity value to the project company or the owners of the equity position in the concession. This is represented by the accounting identity Assets minus Liabilities equals Equity (see Figure 16).

Figure 16. Calculation of Equity

A - L = E

Where

A = Assets

L = Liabilities

E = Equity

The balance sheet will always balance because Assets minus Liabilities plus Equity will always equal zero (see figure 17).

Figure 17. Relationship between Assets, Liabilities, and Equity

A - (L + E) = 0

Dividends paid out to owners will simultaneously reduce assets (cash on hand) and equity (retained earnings). A newly constructed highway segment will increase assets (economic value of the highway upon which to operate and collect revenues) and liabilities (debt incurred or equity raised to finance the construction).

The important take-away is to understand how assets, liabilities, and equity are accounted for in financial statements. In corporate finance the balance sheet will reflect the book value of equity in a given project at a given period of time, helping to inform whether it is advisable to pay dividends, retain earnings, pay debt, or make additional investments. In general, the dividend policy for project companies under project finance arrangements is very simple: pay out dividends whenever possible. In corporate finance, companies are constantly faced with a decision of whether to retain earnings to invest in new projects or to pay dividends. Under project financing, since the project company by design has only one project, it always pays dividends when it produces excess cash (see chapter 2 for more details).

We can use the financial statements to calculate the project IRR. One way is to calculate the project IRR on the free cash flow to the project. This is found by starting with net earnings from the income statement, adding depreciation, subtracting capital expenditures from the cash flow statement, and adding interest expense multiplied the tax effect. Then, we can use the IRR function in Excel to determine the project IRR.

 

Footnotes

23 Vadali, Sharada. 2014. "Using the Economic Value Created by Transportation to Fund Transportation". National Cooperative Highway Research Program Synthesis 459. Washington, DC: Transportation Research Board. Available for download at: http://www.trb.org/Economics/Blurbs/170750.aspx.

24 https://www.bls.gov/cpi/

25 https://www.rsmeansonline.com/

26 Flyvbjerg, B. (2008). Curbing Optimism Bias and Strategic Misrepresentation in Planning: Reference Class Forecasting in Practice. European Planning Studies. Vol. 16, No. 1, pp. 3-21.

27 https://www.gov.uk/government/publications/green-book-supplementary-guidance-optimism-bias

28 See for example GAO's Cost Estimating and Assessment Guide.

29 The most common and transparent distributions are the uniform distribution which assigns equal probability to all outcomes or the normal distribution aka the "bell curve", however, depending on the project, if large outlier events are possible ("black swans"), then distributions with fat tails, such as the Pareto distribution, could be used to account for this probability.

30 In probabilistic approaches where distributions are defined for different inputs, one should also take into account measures of co-variance between these distributions.

31 Macário, R., et al. (2009). ENACT - Design Appropriate Contractual Relationships, Deliverable 6. Impacts and feasibility of SMC Pricing and PPPs. FP6, EC DG-TREN.

32 Cangiano, Curristine & Lazare (eds.) 2013. Public Financial Management and Its Emerging Architecture. Washington, DC: International Monetary Fund.

33 https://www.irs.gov/pub/irs-prior/p946--2009.pdf

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