Definition of discount rate
In risk valuation there is a distinction between categories of risk. The discount rate may be used to value systematic uncertainties. This FHWA guidebook on risk assessment offers guidance on how to value the other risk categories as shown in Table A-2-1.
Table A-2-1. Categories of Risk
|Change in toll technology||Decisions affecting the project (scope)|
Risks before contract close
|Delay in go decision on project due to elections||Decisions affecting mainly time before the project starts|
|Inflation risk||Uncertainties due to market circumstances|
|Accident at construction site||Potential project-related events with a negative impact|
|Regular uncertainties||Uncertainty in volume of asphalt||Uncertainties in quantities or prices, related to the level of design of the project|
Depending on which theoretical framework is used, the term discount rate can refer to different rates as shown in Table A-2-2:
Table A-2-2. Discount Rates
|Excluding inflation||Including inflation|
|Risk free||Real risk-free rate||Nominal risk-free rate|
|Including standardized risk premium||Real rate including risk||Nominal rate including risk|
|Including project-specific risk premium||Real rate including project-specific estimation of systematic risk||Nominal rate including project-specific estimation of systematic risk|
The main purpose of the discount rate is to make it possible to compare cash flows over time. To determine the most appropriate discount rate several decisions need to be made:
We note that various countries have guidelines recommending different discount rates for different types of appraisal. For instance:
Discussed below are several approaches to determining the different components of the discount rate. Note that it is almost never possible to derive the "true" project-specific discount rate because it is almost always necessary to use historical or peer group data. The discount rate will always be an educated guess based on available benchmarking information.
Determination of risk-free rate
From a financial perspective, the risk-free rate is determined by accounting for the most recent market information. The asset that is traded in the markets that best approaches "risk-free" is a Federal government bond. For a standardized discount rate, governments tend to look at long-term historical averages. For instance the Netherlands used a discount rate of 4% (real risk-free rate) until 2008, and then subsequently reset it to 2.5%. We note that in financial markets only the nominal rate is observable, therefore to determine the real rate a correction has to be made for inflation. For instance, if a 15-year government bond has an interest rate of 3.5%, and the average Consumer Price Index (CPI) has been 2% over the last ten years, then the real discount rate would be approximately 1.5%.
The risk-free rate of the project should be determined in relation to the respective financing terms. Overall financing can be sliced into "tranches" with different durations based on the project cash flows. The tranches with early repayment have a shorter duration, which is reflected in the interest rate. In addition, in this case the rate should be the forward expected rate. The rate needs to account for the fact that the first drawdowns will occur after the date of the VfM assessment, therefore forward prices should be used to determine this expected rate. In similar fashion to the pricing of an interest rate swap, blended rates can be determined for all tranches together, facilitating the use of a single discount rate.
Pricing is a complicated exercise, and it is important to consider whether this approach is necessary for the sole purpose of conducting a VfM assessment. During the early stages of the project in particular this is often not the case, and a simpler alternative on the basis of today's rates for the indicative average duration can be used. However, after receipt of the bids, this simpler approach should be abandoned because it may inhibit a fair comparison.
Determination of the risk premium using a theoretical approach
If systematic risk has not been incorporated in the cash flows of a project, then it should be accounted for in the discount rate. Financial theory offers the Capital Asset Pricing Model (CAPM) to determine the relevant risk premium. The CAPM states that each asset has a correlation (beta) to the general market risk (rm). For relatively low-risk assets the beta is below one and for high-risk assets the beta is above one; therefore the beta is used to assess how the market's movements affect the magnitude of the value of an asset's movements. Typically, government projects such as highways are not traded on financial markets. To determine a beta for a specific highway project (or highway projects in general) it is possible to select assets (i.e., companies) that are traded on markets that best reflect the risk profile of the project, deriving a beta for this "peer group" that can be applied to the project.
The alternative to estimating a project-specific premium is to use a shortcut stating that the average beta for all assets is 1 (true by definition) and therefore the standardized risk premium equals the market risk premium. This approach can either lead to an overestimation of risk for low-risk projects - such as building extra capacity for a busy road - or an underestimation of risk for high-risk greenfield or technological innovation projects.
The market risk premium can be estimated or derived from available literature. In this literature, the market risk premium is estimated to be between 3% and 9%. 12 If a specific highway project has a beta of 0.5 (based on benchmark analysis of highway projects) and the average market risk premium is 6%, then the risk premium for this project would be 3%.
Determination of the risk premium using market-based information (WACC)
An alternative way to estimate the risk premium for projects is to look at information from bids on previous similar projects. We can then apply the weighted average cost of capital (WACC) formula to derive the average cost of finance, which is an estimate for the discount rate.
The Weighted Average Cost of Capital formula is:
Where Tc is the tax rate, D is the total amount of debt, V is the total amount of financing, is the interest rate on debt, rd is the total amount of equity, and is the return on equity. Bids from similar projects can provide clues as to the value of all of these variables, although typically this information is confidential.
In a P3 approach, a substantial portion of the risk profile is reflected in the WACC. The pricing follows the organizational structure of a P3 special purpose vehicle (SPV). Most of the risks are typically subcontracted and therefore shown in the cash flows in the bid. Some of the risks are explicitly or implicitly retained by the SPV (for example through caps on liabilities in subcontracts). These are not only typical systematic risk categories (for example inflation, interest rate, and toll risk) but also risk categories that are associated with the long-term and integrated characteristics of the contract (long-term performance risk and project coordination risks). This needs to be carefully taken into consideration to avoid double-counting, and for consistency when comparing the PSC and shadow bid/actual bid. For instance, if the cash flows of a project include an interest rate swap, transferring the variable interest rate risk to a swap counterpart will result in higher cash flows, because the interest rate will now include a premium for the swap transaction. The interest rate risk is now valued in the cash flows and should no longer be reflected in the discount rate.
Figure A-2-1. P3 Organizational Structure
The Figure A-2-1 shows that depending on the risk allocation, some systematic risk may be valued through the discount rate and some risk may be valued in the cash flows. For the cash flows a probability analysis based on Monte Carlo analysis may be used for risk valuation. Since risks are not valued in both the discount rate and the cash flows, the confidence level chosen for the probability analysis is not related to the risk premium in the discount rate.
Combined with the previous (theoretical) method this gives two estimates, which together yield a range of possible discount rates.
Quantitative risk analysis can be used to determine the value for the risk categories: pure risk and regular uncertainties. There are two main methods for performing such an analysis:
Deterministic analysis produces a single value for risks, which is expected to be the most likely. To do a deterministic analysis, the following steps are taken:
Probabilistic analysis produces a risk spread including a confidence level. This outcome is more difficult to interpret, and the single value the deterministic analysis produces is much more straightforward. However, the real value of the risks will in practice almost always be different from the single value. Therefore, the probabilistic analysis produces a more accurate outcome, and requires more expertise. There are software programs available to run a probabilistic analysis.
To do a probabilistic analysis, the following steps are taken:
Risks may be interrelated. Risks can be dependent inclusive (the subordinate risk will only occur if the dominant risks occurs), or exclusive (the subordinate risk will not occur if the dominant risks occurs), or unrelated. Risks can also be correlated. This correlation can either be positive, negative, or zero. The standard assumption is that risks are not dependent or correlated. For more extensive analysis, the inter-relations can be indicated for each specific risk.
The simulation may include as many as 1000 or more different runs. In each run, the program randomly chooses where each risk will be on the distribution. Therefore, each run produces a different outcome. The result of the simulation is a summary of all these runs, which is a distribution, as shown in figure A-3-1 below.
Figure A-3-1. Sample Distribution
Source: Virginia DOT's PPTA Risk Analysis Guidance, September 2011.
The distribution shows the spread of the risk value. The mean value in the graph is 107 million dollars, however, the value may vary between 60 and 160 million. It is now up to the public entity to choose an acceptable confidence level. To be safe, it may choose a 95% confidence level which means that only for 5% of the time, the actual value of risks will be higher. Another option is to assume the mean value, which means that 50% of the time the actual value will be higher.
Most risk assessment methods are bottom-up approaches, because they focus on identifying and quantitatively assessing individual risks. A top-down approach is focused on the risk profile of the project as a whole on the basis of a number of risk-related project characteristics.
A sample checklist for such a top-down approach is shown in table A-4-1 below:
|Project characteristics||Scoring risk profile (1 = low, 5 = high)|
|Capital Expense (CAPEX)|
|Construction methods complexity|
|Risk of damage to environment|
|Risk of damage by third parties|
|Permits and procedures risks|
|Operating Expense (OPEX)|
|Maintenance methods complexity|
This checklist provides an indication of the risk profile of the project and thereby also an indication of a typical contingency or allowance - in terms of a percentage of total project cost - that could be applied on the basis of past experience, and in relation to the applicable cost estimate methodology.
Table A-5-1 below illustrates different risk allocations based on conventional and P3 delivery methods. It is used as a high-level illustration and does not include every unique risk found in a project.
Table A-5-1. Example Risk Allocation Matrix
|Risk||Design - Bid - Build||Availability Payment P3||Toll Concession P3|
|Change in scope||Public||Public||Public|
|Delay in permits||Public||Shared||Shared|
|Delay in right-of-way acquisition||Public||Public||Public|
|Construction cost overruns||Contractor||Contractor||Contractor|
|Delay in relocation of cables and pipes||Public||Contractor||Contractor|
|Unknown ground conditions||Public||Contractor||Contractor|
|Major maintenance cost overruns||Public||Contractor||Contractor|
|Snow and ice removal cost overruns||Public||Contractor||Contractor|
|Traffic information systems||Public||Public||Public|
|Toll revenue risk||Public||Public||Contractor|
Allocation: The act of assigning responsibility for a given risk to the public or private entity, or both if the risk is shared between the two.
Availability Payment: Compensation paid to a private concessionaire for its responsibility to design, construct, operate, and/or maintain a tolled or non-tolled roadway for a set period of time. The public agency makes these payments based on the availability of the infrastructure (in terms of meeting performance standards), and also when certain milestones are met (see milestone payments).
Benefit Cost Analysis (BCA): A method to monetize the costs and benefits of a specific procurement method; in a P3 analysis this is also used to quantify the social benefits and costs of a project.
Bidder: A respondent to a request for Expressions of Interest or an invitation to submit a bid in response to a Project Request for Proposals (RFP). Typically, a bidder will be a consortium of parties, each responsible for a specific element, such as constructing the infrastructure, supplying the equipment, or operating the business. Government normally contracts with only one lead party (bidder) who is responsible for the provision of all contracted services on behalf of the consortium.
Brownfield: A project that requires modification, renovation, or demolishment of previously built infrastructure.
BRT (Bus Rapid Transit): A bus-based rapid transit system that incorporates design features often utilized in rail transit (stations, platforms, dedicated right-of-way, etc.). BRT's are designed to remove delays and reduce congestion along a bus route.
CAPM: Capital Asset Pricing Model (see appendix 2 for an explanation).
Consumer Price Index (CPI): A measure that examines the weighted average of prices of a basket of consumer goods and services, such as transportation, food and medical care. The CPI is calculated by taking price changes for each item in the predetermined basket of goods and averaging them; the goods are weighted according to their importance.
Contingency: An allowance included in the estimated cost of a project to cover unforeseen circumstances.
Concessionaire: Private entity that assumes ownership and/or operations of a given public asset (e.g., highway, train station, bus operation) under the terms of a contract with the public sector.
Debt Service Coverage Ratio: The amount of cash flow available to meet annual interest and principal payments on debt, divided by the amount of debt service payments.
Design-Build (DB): Under a DB, the private sector delivers the design and construction (build) of a project to the public sector. The public sector maintains ownership, operations, and maintenance responsibility for the asset.
Design-Bid-Build (DBB): Under a DBB, the private sector delivers a design and bids for construction of a project in two separate processes. Once the private sector has been awarded the construction contract, it assumes responsibility of project construction (build).
Design-Build-Finance-Operate-Maintain (DBFOM): Under a DBFO or a DBFOM, the private sector delivers the design and construction (build) of a project to the public sector. It also obtains project financing and assumes operations and maintenance of an asset upon its completion.
Discount rate: The discount rate is a percentage by which a cash flow element in the future (i.e., project costs and revenues) is reduced for each year that cash flow is expected to occur.
Environmental Impact Statement (EIS): An EIS is a full disclosure document that details the process through which a transportation project was developed. It includes consideration of a range of reasonable alternatives, analyzes the potential impacts resulting from the alternatives, and demonstrates compliance with other applicable environmental laws and executive orders. The EIS process is completed in the following ordered steps: Notice of Intent (NOI), draft EIS, final EIS, and record of decision (ROD).
Endogenous Risks: Created within a project or under the direct influence of the key project stakeholders.
Exogenous Risks: Caused by external events.
Force majeure: An event occurring from nature, i.e., not manmade (e.g., earthquakes, hurricanes).
Greenfield: A greenfield project is one that is designed from the beginning with no constraints from the existence of prior facilities that need to be modified or removed.
Ground Conditions: Conditions (often underground) that are unforeseen and can cause delays in construction. Examples include underground rivers, discovery of hazardous materials, etc.
Handback: The process of returning a privately operated and maintained asset to the public after a concession expires.
HAZMAT: Hazardous materials.
Interest Rate Swap: A transactional agreement between two counterparties to exchange one stream of future interest payments for another based on a specified principal amount. Interest rate swaps often exchange a fixed payment for a floating payment that is linked to an interest rate.
Leveraging: Leveraging is the degree to which an investor or business is utilizing borrowed money. The leverage ratio is defined as the ratio of borrowed money to equity, and can reach high levels in project finance.
Loan Life Coverage Ratio (LLCR): A financial ratio used to estimate the ability of the borrowing company to repay an outstanding loan. The LLCR is calculated by dividing the net present value (NPV) of the cash available for debt repayment over the term of the loan by the amount of senior debt owed by the company.
Monte Carlo Simulation: A problem solving technique used to approximate the probability of certain outcomes by running multiple trial runs, called simulations, using random variables. Often conducted during risk assessments and value for money assessments to determine the probability of risk outcomes.
National Environmental Policy Act (NEPA): Requires federal agencies to integrate environmental values into their decision-making processes by considering the environmental impacts of their proposed actions and reasonable alternatives to those actions, leading to an environmental impact statement (see above definition of EIS) .
NPV: Net present value.
Office of Innovative Program Delivery (OIPD): The OIPD is a part of the FHWA that provides tools and expertise regarding innovative finance approaches including P3s.
Public Private Partnership (P3): In a P3, a private entity assumes responsibility for more than one development phase, accepting risks and seeking rewards. This document is concerned primarily with forms of P3s where the private sector partner enters into a long-term contract to perform most or all the responsibilities conventionally procured separately and coordinated by the government.
Private Activity Bonds (PAB): PABs are a new type of financing that provides private developers and operators with access to the tax-exempt bond market, lowering the cost of capital significantly.
Project Life Cover Ratio (PLCR): The PLCR is the ratio of the net present value of the Cashflows Available for Debt Service (CFADS) over the remaining full life of the project to the outstanding debt balance in the period. This ratio is similar to LLCR, however in LLCR the CFADS is calculated over the scheduled life of the loan, whereas the cashflow for PLCR is calculated over the life of the project or term of the P3 concession.
PSC (Public Sector Comparator): A PSC represents the most efficient public procurement cost (including all capital and operating costs and share of overheads) after adjustments are made for competitive neutrality, retained risk, and transferable risk to achieve the required service delivery outcomes. This benchmark is used as the baseline for assessing the potential value for money of private party bids in projects.
Retained risk: The value of those risks or parts of a risk that a government proposes to bear under a P3 arrangement.
Risk Relation Map (RRM): A diagram demonstrating the cause-and-effect relationships between risks, clearly demonstrating their hierarchy and linkages.
RFP: Request for Proposals.
RFQ: Request for Qualifications.
Risk Allocation Matrix: A table used as a management tool throughout the procurement process to provide an overview of the major risk categories to be considered when developing procurement, to explain why the risks are transferred, shared, or retained under different procurement options. As each deal will have project-specific risk, the Risk Allocation Matrix is only a tool to help understand the principles regarding risk allocation. For each project, the actual risk allocation will need to consider the principles of allocation and the circumstances of the deal.
Risk Free Rate (Rf): The "risk free rate" is the theoretical rate of return of an investment with zero risk. U.S. Treasury Bonds (with a matching maturity to the loan) are generally used as a proxy for the risk-free rate.
Risk Register: A document that provides an overview of all identified risks, and describes the key characteristics of the risks.
Risk Transfer: The process of moving the responsibility for the financial consequences of a risk from the public to the private sector.
ROD: Record of Decision (see EIS).
Return on Equity (ROE): The amount of net income returned to investors as a percentage of the shareholder's equity. In a P3, the return on equity is used to compensate investors for the riskiness of the project.
Scope: A project management term for the combined objectives and requirements necessary to complete a project. Properly defining the scope of a project allows a manager to estimate the costs and time required to complete the project.
Special Purpose Vehicle (SPV): An SPV is a legal entity comprised of multiple shareholders created for a specific project to reduce risk exposure of its individual members and to protect the project from unrelated liabilities of its individual members. In a typical P3, an SPV is created to bid on a project and to obtain project financing.
Systematic Uncertainties: Uncertainties due to market circumstances; these risks are not diversifiable by a single actor (also referred to as market risk).
Value for Money (VfM): The procurement of a P3 project represents VfM when, relative to a public sector procurement option, it delivers the optimum combination of net life cycle costs and quality that will meet the project objectives.
WACC (Weighted Average Cost of Capital): In project finance the WACC is used to help determine the discount rate used. The WACC is a cost of capital weighted as a percentage of debt and equity (see appendix 2).