**December 2012**

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A public agency that chooses to undertake construction of a bridge might have to pay $1.0 billion. The public procurement alternative might involve borrowing the full amount and paying it back over a 30-year period through debt service payments. On the other hand, a P3 procurement alternative might involve annual payments to the private entity over a period of 50 years. To compare the alternatives, these payments (known as "cash flows") must be converted to present values. This is done by using discount rates that are applied to future cash flows to account for the time value of money.

One of the most significant decisions in a VfM analysis is the selection of a discount rate. The discount rate effectively represents the "exchange rate" between present and future sums of money. It 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. A discounted cash flow (DCF) analysis allows a public agency to develop a net present value (NPV) for revenues and costs (including costs of risks) that are not expected to occur until far into the future. This practice can be very useful when comparing two procurement options where costs and revenues occur in different amounts and at different times. Public agency officials considering a P3 approach may find themselves comparing the costs of a publicly procured project, in which the public agency finances large-scale construction costs over the first few years, against a P3 in which the public agency makes smaller but steady annual payments for several decades. Utilizing discounted cash flows, the public agency can create a single overall cost estimate for each scenario even though their financial profiles are very different.

The present value formula to calculate the discounted cash flow (DCF) is simply the nominal (i.e., inflation-adjusted) cash flow amount (C) divided by the discount rate (R) plus one (1) raised to the power of the number of years (N) into the future. In mathematical terms:

DCF = C__

(1+R)N

A discount rate may be "real" (i.e., not including inflation) and therefore applied to cash flows that do not account for inflation, or they can be "nominal" (i.e., including inflation) and therefore applied to cash flows that account for inflation. The real discount rate is made up of two elements:

- The basic Social Time Preference Rate (STPR), which represents the rate that society is willing to pay for receiving something now rather than in the future;
- An allowance for other factors, mainly to ensure that the public sector does not assess the future benefits of projects without taking account of the risk to which it exposes taxpayers in the process, e.g., the potential to incur additional costs if things go wrong.

The DCF calculation adjusts the value of a given cost, risk or revenue stream based on the number of years into the future that cost or risk is expected to occur. For example, a $1 million cost expected ten years in the future might have a net present value of around $615,000 using a discount rate of 5 percent. The same cost expected 25 years in the future would have a much smaller discounted present-day value of around $295,000.

Assuming a real discount rate of 6 percent and an inflation rate of 2.5 percent, the nominal discount rate is calculated by applying the following equation:

Nominal discount rate = (1+real discount rate) x (1+ inflation rate) – 1

= (1+6%) x (1+2.5%) -1

= 8.65%

Because the net present value (NPV) is a function of the discount rate, it can vary depending on the discount rate selected. A higher discount rate will give cash flows (i.e., expenditures and income, or costs and revenues) expected in the future less value after discounting. A lower rate, on the other hand, leads to greater weight given to future costs and revenues. Consider, as an example, the separate expenditures of $1 million dollars, discounted at 5 percent in one scenario and at 8 percent in the second (see Table 3-1).

Discount Rate |
Today | 1 Year | 5 Years | 10 Years | 25 Years | 50 Years | |

5% | $1,000,000 | $952,400 | $783,500 | $613,900 | $295,300 | $87,200 | |

8% | $1,000,000 | $925,900 | $680,600 | $463,200 | $146,000 | $21,300 | |

Difference relative to 8% | - | +3% | +15% | +33% | +102% | +309% |

For costs and revenues occurring in the years in close proximity to today, different discount rates produce moderate differences in discounted values. In this example, the discounted value at a 5 percent discount rate for a $1 million cash flow 5 years in the future is higher than the value at an 8 percent rate by about 15 percent. The difference is more pronounced as the distance into the future increases. At 25 years into the future, the 5 percent discount rate produces a value twice as large as the 8 percent discount rate. By 50 years out, the 5 percent discount rate produces a value that, while small, is 4 times as large as that produced by the 8 percent discount rate.

Thus the choice of the discount rate can have a heavy influence on which option appears to have a more attractive cost, and therefore, a heavy influence on the final result of the VfM analysis. Best practices recommend the utilization of multiple sensitivity tests using different discount rates to ensure that the outcome is not skewed or biased by the selected discount rate.

Because the discount rate has a large effect on the NPV of the procurement alternatives and therefore the final VfM analysis, public agencies have given much consideration to it. However, there is no international consensus on the appropriate methodology for calculating the rate to use and the risks that should be reflected in that rate. In some countries, fixed discount rates are used for all projects irrespective of their individual characteristics, while others determine project-specific discount rates. Each approach has its own challenges. Methodologies for determining the appropriate discount rate include:

*Social Time Preference Rate:*As discussed previously, this approach is used in the UK.*Weighted Average Cost of Capital (WACC)*which incorporates the financing principle that the cost of obtaining finance is separate from the cost of using finance, risk is inherent in a particular asset, and investors in the marketplace are the best estimators of risk value. The WACC will be equivalent to the project's internal rate of return (IRR). Partnerships British Columbia uses this approach.*Capital Asset Pricing Model (CAPM):*This approach applies different discount rates to the PSC and P3 delivery structure, utilizing the CAPM for P3 delivery to account for systematic risk within the project cash flows. With this approach, a risk markup is added to a risk-free discount rate to account for "risky" cash flows (i.e., distributions to equity investors), while the risk-free discount rate is used for the "non-risky" cash flows. The CAPM rate reflects systemic risks, i.e., risks that affect the market as a whole (such as the risk of recession) that are transferred to the private sector. The theory is that as the public sector transfers its systemic risk to the private sector, the private sector should be compensated through a higher rate of return. This approach is used by Infrastructure Australia.*Risk-Free Rate:*This approach uses the public sector's long-term borrowing rate if the project risks are reflected in the project cash flows. Historically, the rate on a federal Treasury bill or Treasury bond has been viewed as the risk-free rate in the U.S.