The public agency needs ways to compare bids with one another. There are various approaches for comparing bids involving different measures derived as outputs from the financial model discussed in Chapter 6. Some of these require converting future cash flows (i.e., expenditures and income, or costs and revenues) to present values. The method used to do so is discussed first.
Converting Future Cash Flows to Present Values
Comparison of bids requires converting toll revenues or future payments to be made by the public agency to present values. Future cash flows are converted to present values by using a calculation known as "discounting" based on a selected discount rate. The discount rate is effectively 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. The discount rate is based on the "time value" of money, i.e., it is the rate of return one would expect in exchange for receiving a future payback of dollars invested or lent today.
A discounted cash flow (DCF) analysis allows calculation of a present value for revenues and costs (i.e., income and expenditures) that are not expected to occur until far into the future. The present value formula to calculate the discounted cash flow (DCF) is simply the 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 DCF calculation adjusts the value of a given cash flow element (i.e., revenue or cost) based on the number of years into the future that the cash flow element 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.
Let is assume a real discount rate of 6 percent and an inflation rate of 2.5 percent. The nominal discount rate may be calculated as follows:
Nominal discount rate = (1+real discount rate) x (1+ inflation rate) - 1
= (1+6%) x (1+2.5%) -1
= 8.65%
Because the present value is a function of the discount rate, it can vary depending on the discount rate selected. A higher discount rate will give cash flows expected in the future less value after discounting. A lower rate, on the other hand, leads to higher present values or a 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 7-1).
| 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% |
Detailed description of Table 7-1
Present value of $1,000,000. This table is an example of how different discount rates can affect the value of $1,000,000 over time. Because the present value is a function of the discount rate, it can vary depending on the discount rate selected. In this table there are two discount rates shown: 5% and 8%; the table tracks the value of $1,000,000 today and after 1, 5, 10, 25, and 50 years at each rate. The table also tracks the difference in value relative to 8%. In this example, today $100,000,000 is worth $1,000,000 at both 5% and 8%. After 1 year it is worth $952,400 at a discount rate of 5%; it is worth $925,900 at 8%; the difference relative to 8% is +3%. At 5 years it is worth $783,500 at a discount rate of 5%; at 8% it is worth $680,600 with a difference of +15%. At 10 years it is worth $613,900 at 5% and $463,200 at 8% with a difference of +33%. At 25 years it is worth $295,300 at 5% and $146,000 at 8%; the difference is 102%. Finally, at 50 years, $1,000,000 is worth $87,200 at 5% and $21,300 at 8%; the difference in discount rate relative to 8% is 309%.
For cash flows 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.
Net Present Value (NPV) of Public Agency Subsidies
The net present value neutralizes the effects of inflation and the time value of money. When a public agency has to make payments (such as shadow toll or availability payments) to a concessionaire over several years, the net present value (NPV) of these payments is the real amount of the payments if they were paid in a lump sum at present. Public subsidies for either capital or operation costs may also be provided for a toll concession where it is known that the toll revenue will not be adequate to cover funding required for the project.
Public agencies may use several different discount rates to test their impact on the present values of the metric of interest to them. The discount rate that would likely be given the most weight would be the public sector's cost of capital, i.e., the borrowing rate of the specific public agency 2. Future public sector payments represent a form of repayment for capital expenditures made by the concessionaire at the beginning of the P3 contract period. Since the government often uses additional borrowing to fund incremental capital expenditures, it may make sense to base the discount rate on the public agency's long-term borrowing rate. As indicated in Chapter 4, this rate depends on the public agency's credit rating. Higher-rated agencies will have lower borrowing rates, and discount rates will therefore be lower.
Contract Term
A second approach that may be used to compare bids, especially for concessions involving availability payments or tolls, is to fix the level of the availability payment or the toll rates and then ask bidders to bid for whatever term of P3 contract they require. The preferred bid would then be the one requiring the lowest term.
Net Present Value (NPV) of Revenues
A third approach to evaluating bids is to leave the term open-ended and terminate the contract when the NPV of revenues required by bidders has been achieved. The bidder with the lowest required NPV of revenues wins the bid. As with the first approach, a discount rate would need to be selected to convert future revenues to a net present value.
Footnotes:
2. Note, however, that there is an alternative view that, since the public sector's principal source of revenue is taxes, which reduces private citizen/enterprise investment
