Time Value of Money Analysis in Calculating the Costs and Benefits of Large Projects

Screenshot 2014-03-13 19.14.02Time Value of Money

This posting is going to be a little bit different from my typical blog postings, in that I’m going to write about a more general analytic concept that is particularly important to keep in mind when trying to understand projects that are either paid for or receive revenues over a period of time — a concept that is often called the “time value of money“.

This posting is prompted by many comments that I have heard from friends, colleagues, fellow public officials, and other community members in reaction to the controversial decision by the Indiana Finance Authority to award a 35-year contract to design, build, operate, maintain, and finance section 5 of I-69, a 21-mile segment of I-69 from south of Bloomington to south of Martinsville — a so-called Public-Private Partnership, or P3.

Please note that the following discussion does not in any way address the issue of whether building the highway at all is a good investment by the state. All it does is address the issue of paying for a large project like this over time vs. paying for it with current revenues/cash on hand.

I-69 Example

Without getting too far into the weeds on the specifics, the arrangement is that the State of Indiana will pay a contractor $21.8M per year for 35 years for the design, construction, operation, maintenance, and financing of the 21-mile section of highway. The government estimate of the cost of the design and construction of the highway was around $350M. However, if take the $21.8M per year times 35 years, you get a total of $763M. The claim that has been made, therefore,  is that by using this P3 financing vehicle in which payments are made to the contractor over time, that the government is paying more than double for the highway than it would if paid through conventional means (i.e., up front, with cash).

However, this conclusion ignores the time value of money (TVOM).  The basic principle behind TVOM is that a given amount of money today is worth more than it is at some future point. When you think about it, this should be self-evident; just ask yourself: given the choice, would you prefer $100 to be given to you right now or in a year? Once you accept that premise, the next question is how much more is that given amount of money worth today than it is at a future point? The answer is: a given amount of money is worth more today than it is at some future point by the amount you could earn by investing (or otherwise using) that given amount of money until that future point.

In order to compare alternative investments (or financing schemes) that are made over various periods of time, we need to make sure we compare apples to apples. One way to do that is to convert all alternatives to present value (PV) and then compare. Let’s consider our I-69 example. In that example, the state will be paying the contractor $21.8M per year over 35 years. However, the $21.8M in year 2 is not worth as much as the $21.8M in year 1, and the $21.8M in year 35 is certainly not worth as much as it is in year 1. So how do we convert the entire 35-year payout to Present Value, as though it were all being paid out immediately? And more importantly — how do we compare the 35-year payout against a $350M cost if the design and construction were paid out of cash today.

Basically, we discount future payments by the amount of money we could earn on the money we save by not having to pay it this year! How much do we discount it by — in other words, how do we compute the present value?

Quick Mathematical Interlude

I’m going to take a moment to do a little math here; however, if you want to skip to the next section, you won’t lose much of the overall argument. The actual equation is: PV = FV / (1+i)^n, in which PV is Present Value, FV is Future Value, i is the interest rate per period that you could earn on the money, and n is the number of periods that you could earn that interest rate. For a quick example, let’s consider the following alternatives:

  • Alternative A: I give you $100 today
  • Alternative B: I give you $100 a year from today

First of all, we know that alternative A — the $100 I give you today has a present value of $100.To to compare it to alternative B (I give you $100 a year from now), though, we need to compute the present value today of the $100 I pay you a year from now. In the above equation, $100 is the future value (FV) — the amount that the $100 paid in one year will be worth at the time it is paid. i is the interest rate that we could be earning per year (or per any time period) with the $100.  This is where TVOM analysis gets a little squishy, and the results you get can differ a lot depending on your assumptions. How much money can you earn with $100 in a year? Depends a lot on how you invest it! If in a savings account, almost nothing — less than 1%. However many investments earn quite a bit more than a savings account. One number that is considered pretty fair to use is the average municipal bond rate. At the very least, the municipal bond rate can be considered a good proxy for the opportunity costs of the money over a given period of time.

The following Web site provides municipal bond rates for various maturity ranges and credit ratings:

Just for the sake of this example, I’m going to take a national rate for a 10-year bond with AAA credit rating (which Indiana has) — an interest rate of 2.20% per year (of course, this amount may change).

Going back to our equation, we have: FV = $100, i = 0.022 (the 2.2% interest rate), and n=1 (1 year). The present value of that $100 paid out in a year is: PV = 100/(1+0.022)^1 = 100/1.022 = $97.85. In other words, with the assumptions we made, $100 paid to you a year from now is only worth $97.85 today.

I-69 Example, Revisited

OK, so let’s apply the TVOM principle to analyzing the 35-year contract for Section 5 of I-69.  For the purposes of illustrating TVOM in comparing the 35-year contract with a conventional financing (i.e. paying for the project out of current tax receipts and cash balance), I am simplifying the situation dramatically in the following way: the 35-year $21.8M/year payout to the contractor does not only include the design and construction of the road, but also the operations and maintenance of the road — money that would have had to be spent anyway in all 35 of the outyears regardless of the method of financing the design and construction of the road. If we really want to compare alternatives fairly, we would subtract out the costs of maintaining and operating the road for all 35 years — figures I don’t have close to hand. So this TVOM analysis can really be considered to be a worst-case from the perspective of the P3 scenario. In other words, the real cost of the P3 versus conventional financing is much more in the favor of P3 than it is in the following numbers.

I created the following table for all 35 years of payments (all numbers are in millions). The first column, Payment, shows the actual payment made to the contractor each year for the 35 year period of performance. The following 5 columns show how much those 35 years of annual payments are worth today (the only fair way to compare the arrangement against a conventional financing arrangement where the whole thing is paid with cash/current taxes), using 5 different interest rate assumptions (1%, 2%, 3%, 4%, and 5%). For a project of this size, given the municipal bond rates for 30 year bonds for AAA credit, the most realistic assumption is probably somewhere around 4% (from the recent past history of municipal bonds, probably a little under 4%).

Time Value of Money I-69 Example
Time Value of Money I-69 Example

So with the 4% interest rate assumption, we can see that the present value of 35 years of $21.8M annual payments is not $763M (i.e. 35 times $21.8M), but the much lower $406.89M. Obviously that number changes depending on the interest rate assumption. The higher the interest rate, the lower the present value. This should make intuitive sense: the more opportunity I have to make use of the money up front, the less valuable it is for me to have the money in the future compared to the present.

So to get back to our hypothetical-not-so-hypothetical example. We want to compare paying for a $350M highway construction project out of current dollars against the 35-year $21.8M/year P3 arrangement. With our assumption of 4% interest rate, the present value (cost) of the 35-year arrangement is $406.89M, compared to $350M if paid in cash — more, to be sure — but dramatically less than simply adding up the 35 annual payments ($763M).  And again, this doesn’t even include the fact that some of the annual payments cover the costs of maintenance and operations of the highway, which would be paid out anyway, regardless of how the design and construction are financed.


 None of this discussion should be taken as an endorsement of the P3 process, or the fact that the P3 financing model basically guarantees that the winning contractor will be a large multinational corporation with deep access to finance. But I do want to make sure that as we move forward with an arrangement that by all accounts will only become more common, discussions of these kinds of arrangements are based on facts. And the fact is that a given sum of money is less valuable in the future than it is today.  Most certainly we will be paying more for the privilege of stretching out the payments for the road over 35 years. But we won’t be paying double…not even close.

Gateway a Useful Tool for Reporting on Local Government Finance

The Indiana Gateway for Government Units — generally just called “Gateway” — is a tool developed in 2010 by a collaboration between the State of Indiana and Indiana University (the Indiana Business Research Center) to make local government financial submissions easily accessible to the public. Local units have been required to use it for the past two years for submission of standard budget documents during the fall budget process.

Although some data has been available to the public since 2011, very recently some major upgrades were released that makes it much easier for local officials and members of the public to retrieve local government financial information. Because Gateway is now to the point where it can actually be useful to members of the public, I though I would bring it to the attention of the readers of MoCoGov.

The Report Builder for Gateway is available at: https://gateway.ifionline.org/report_builder/

The Report Builder provides a number of pre-made reports for all levels of local government — counties, cities and towns, townships, libraries, fire districts,   school districts, solid waste management districts, etc., and the user interface is pretty intuitive.

The following are a couple of reports that might be particularly interesting to taxpayers (along with some instructions for accessing the reports).

  • Employee Compensation (100R)
    • Provides the salaries of all public employees for all levels of local government, state government, public universities, and even public charter schools
    • Choose Employee Compensation (100R) ->  Employee Compensation. Choose your county and then the unit of government within that county. For state and public university employees, choose “State” as your county.
  • Budget Estimate and Tax Rate
    • Provides the information on the Form 4B — sometimes called the “16-line statement” — submitted by local governments for each fund with a tax rate.  Includes the adopted budget, the property tax levy, and the property tax rate for each fund adopted during the fall budget process for the next year.
    • Choose Budgets -> Budget Estimate – Financial Statement – Tax Rate.  Choose your county, year, unit, and fund.
    • For example, see the report for the 2013 Monroe County General Fund below.  You can see, for example, that the general fund budget adopted by the County Council and then certified by the Department of Local Government Finance is $20,300,041, with a property tax levy of $15,097,664, and a tax rate of 0.2389 for every $100 of assessed value.

2013 4B for Monroe County General Fund

  • Budget Summary
    • Provides a summary of budget estimates for each unit of government, for each fund and department, summarized by budget category (i.e., personal services, supplies, services and charges, and capital outlays).
    • Choose Budgets -> Budget Summary
  • Line-Item Budget Estimate
    • Provides a detailed line-by-line budget for each unit of government, for each fund and department.
    • Choose Budgets -> Line-Item Budget Estimate
  • Net Assessed Value by District
    • Provides the net (after exemptions and deductions) assessed value for each taxing district in a county
    • Choose Assessed Value -> Certification of Net Assessed Values by District
    • This report is particularly interesting because it shows not only the assessed value for real property and personal property (i.e., industrial equipment), but also shows the amount of assessed value captured by Tax Increment Finance (TIF) districts for each taxing district.
    • The following screen shot shows the report for Monroe County for 2013

Screen Shot 2013-03-17 at 7.51.05 PM

  • Debt Management
    • Multiple reports that show all debt owed by local government. This set of reports is particularly interesting, because it shows not only the standard property tax-based general obligation bonds (for example, the Showers purchase bond), but also equipment lease-purchases, such as the Vactor and street sweeper trucks purchased by the new Monroe County Stormwater Management Program, and the Innkeeper’s Tax-backed land purchases for the Convention Center
  • Redevelopment Commissions
    • Includes links to all of the annual reports for each of the Redevelopment Commissions in each county. The Redevelopment Commissions are responsible for the TIF districts in each county. The Monroe County Redevelopment Commission annual reports concern the county’s 3 TIF districts, and the Bloomington Redevelopment Commission annual reports concern the City of Bloomington’s 6 TIF districts as well as the City’s Certified Tech Park.
  • Disbursements by Fund and Department Report
    • Shows the actual expenditures (as opposed to the budgeted expenditures) for each fund and department of a local unit of government for a prior year.
    • Choose Annual Financial Report -> Disbursements by Fund and Department. Expenditures are summarized by category (i.e., Personal Expenses, Supplies, Services and Charges, and Capital Outlays).
  • Grants
    • Grants have become an increasingly essential funding mechanism for many aspects of local government. The Grants report shows all of the Federal (including Federal pass-through) grants received by each unit of government during the previous year. Note that this report does not include local grants and grants from non-government foundations.
    • Choose Annual Financial Report -> Grants, and choose the unit of government.

My examples above only scratch the surface of the data available in the new Gateway reports. I encourage everyone interested in local government to give the system a try!

Appropriations vs. Cash: A Crucial Distinction

The distinction between having cash in a particular fund and having an appropriation in a fund is a crucial distinction that is often confused. Both are needed before money can be spent from a fund. Neither is enough by itself.  Let’s consider the distinction:

Having cash in a fund is just like having money in a bank account. Cash can come into a fund from various sources — taxes, sales of government services, fees, etc. Once it is deposited into a fund, it sits there in a fund until it is spent, just like money in a bank account.

Example: A county could create a Dog License Fund and designate all fees from mandatory dog licenses to to into the Dog License Fund. As dog license fees are received by the county, they would be deposited into the Dog License Fund, and its balance would grow over time, until the money was spent.

Appropriation, on the other hand, is simply official permission to spend money out of a fund. In Indiana, each unit of government has a designated fiscal body which is required to provide that permission to spend; for cities, it is the city council, for counties the county council, for townships the township board, etc.  Appropriations are most typically performed during the annual budget process; however, from time to time fiscal bodies will find it necessary to appropriate additional funds after a budget year has begun (e.g., for unexpected expenses). These appropriations are called additional appropriations. In most cases, appropriations only last until the end of the budget year (the calendar year), after which they expire.

Example: The County Council could appropriate $1000 from the Dog License Fund to the Sheriff, to provide training to animal control officers. This appropriation would provide the Sheriff permission to spend $1000 out of the Dog License Fund, if the cash is available in the fund, to provide training to animal control officers.

It is probably clear by now that two things are required before a government official can spend money out of a fund: the cash must actually be there in the fund AND the official must have an appropriation from the fund. Neither is useful by itself. If cash is in a fund, it just sits there until it is appropriated and spent. But without the cash, an appropriation is worthless — although there is permission to spend, there may be no money in the fund to spend! Note that it is perfectly acceptable to appropriate more money than there actually is in a given fund — until the money is there, though, the appropriation is worthless; despite the appropriation (permission to spend) there is nothing there to spend!

Example: The County Council creates a new Dog License Fund, and designates all fees from dog licenses to go into the Dog License Fund. It also appropriates $1000 out of the fund to the Sheriff for training for animal control officers. At the beginning, before any dog license fees are deposited into the fund, the appropriation is essentially worthless. Although the Sheriff has permission to spend up to $1000 for training, until the fees are actually deposited into the fund, there is nothing to spend. After the fees start to build up in the fund, the Sheriff may start spending the money on training. Note that there may not be enough cash in the fund to support the entire appropriation. For example, let’s say dog license fees only generate $700. Even though the Sheriff has $1000 of appropriations in the fund, if there is only $700 available in the fund, she or he would only be able to spend $700 on training. Conversely, say the dog license fees generated $2000 in revenue that was deposited into the Dog License Fund. The Sheriff still only has $1000 in appropriations, and can therefore only spend up to $1000 on training.

A couple of other notes about appropriations and cash:

  • There are times in which the fiscal body may appropriate more than is available in a fund. This occurs particularly in funds that are supported by revenue sources that are uncertain — for example, fees, fines, building permits, planning fees, etc. The fiscal body may want to appropriate funds only once a year during the annual budget-setting process — but the official who has the appropriation can still only spend the appropriation when the cash is actually available in the fund. To reiterate — there is nothing wrong with this. This is NOT overspending or overdrafting, or anything like that; even with an appropriation an official can’t actually spend money that isn’t there to be spent.
  • An appropriation is permission to spend, it isn’t a requirement to spend. Just because a fiscal body appropriates money for a particular function does not mean that the official with the appropriation has to spend the appropriation (absent some other statutory requirement to spend the appropriation). For a particularly silly hypothetical example, let’s say that the County Council decides to appropriate $10,000 in a fund to the Sheriff for clown therapy in the jail. The Sheriff might decide that clown therapy is a waste of money and decline to spend the appropriation. An appropriation is not required to be spent.

Hopefully this helps clarify an important distinction that is often confused in media reporting and popular discussion about government finance.