Capital Improvement Programming: Definitions

Capital improvements planning is commonly used by both city managers and city planners. As a result, there are more than the usual number of technical terms, drawn from both domains.

  • Debt/Revenue Ratio: The debt-to-revenue ratio is a self-imposed limit which managers place on their willingness to use the city's credit. In Minnesota, cities are limited by statute from incurring a debt greater than 6.67% of the assessed value of property in the city. Prudence dictates that one should avoid coming too close to that limit. Managers commonly use the strategy of tying tax-incurred debt to the level of tax revenues, with the intention of borrowing no more than the city can afford to repay. What would be considered an acceptable ratio of debt to revenue depends on the current interest rate, the city's position on acceptable levels of risk, and other political considerations. A common debt/revenue ratio is somewhere between 10-14%.
  • Current Tax Debt & Tax Debt Retired: These terms together embody two considerations: First, these terms are concerned with debt which is charged against the general tax revenues of the city. There are other forms of debt which a local government can incur, such as industrial revenue bonds which are charged against anticipated revenues from the project which they are financing. Second, a city's debt position changes over time, and in fact will be affected by actions proposed in the capital improvement planning process. Generally, a city retires some portion of its tax debt each year. If the city is operating at the limits of its debt/revenue ratio, the tax debt retired represents, in effect, the maximum debt which can be incurred in that same year. It is important to note not only the current debt, but also the pattern of debt retirement, in planning how to phase in new capital projects.
  • Terms of Bond: The terms of a bond are the number of years within which the bond will be repaid. Some bonds are repaid gradually over the life of the issue, others are paid off in lumps at various points during the issue. For the purposes of this model, it is assumed that the principal is repaid gradually over the time allowed.
  • Issue Cost Factor: Bond houses charge a fee for handling the bond issue. The fee is usually expressed as a percentage of the value of the issue.
  • Discount Factor: In addition to the face value of the bond, market considerations may require that the bond be further discounted--much like charging "points" on a mortgage.
  • Debt Service Constant: The debt service constant is the annual payment necessary to retire the principal and the accumulated interest on a bond issue. It is defined as the ratio of the present value to the annual payments on that value. The derivation of the formula is fairly tortuous; the interested reader is referred to chapter 3 of Kleeman's Handbook of Real Estate Mathematics (1978). As a mathematical formula, it is expressed as:
    • where "N" is the number of years to repayment
  • Criterion Weights: Criterion weights are the importance assigned to each of the criteria which will be used to evaluate and rank the potential projects. The weights may be assigned by some individual or by consensus of a group (such as the city council) or by some form of survey. The weighting should be kept as simple as possible, while representing fairly the intended differences between criteria.
  • Debt Capacity: The annual debt capacity of a city is determined by its ability to carry debt, the availability of current funds for capital projects, the availability of intergovernmental transfer of funds (i.e., Federal and State grants) for capital projects, and self-supporting projects (whether general obligation or industrial revenue) which generate enough funds to retire whatever debt they incur.
  • Tax-Supported General Obligation Bonds: The debt capacity for tax-supported general obligation bonds is based on two considerations: the unused current debt capacity and the annual cost of any debt which is incurred. The unused current capacity is the total debt capacity (debt-to-revenue ratio times expected revenue), less the current tax debt (adjusted for that part of current debt which will be retired this year). The annual cost of future debt is the principal plus issuing cost and discount factors, multiplied by the debt service constant. Or, in a formula:
  • Self-Supported General Obligation Bonds (“Revenue Bonds”): Not all general obligation bonds pledge the good name of the city supported only by general tax revenues. Bonds may be sold for projects which, while backed by the full taxing authority of the city, are expected to generate a revenue flow adequate to repay the bond without recourse to tax revenues. Self-supported bonds are generally not counted against the debt-to-revenue ratio.
  • Transfer Funds: Transfer funds are funds transferred from the State or Federal governments to support specified capital projects. State and Federal highway funds are common transfers, as were Federal Revenue Sharing funds.
  • Current Funds: Current funds are monies drawn from the general fund to finance capital improvements, usually for smaller projects (like purchase of replacement vehicles). If the city has maintained a capital depreciation fund, those funds would also be available in this category.
  • Revenue Bonds: Revenue bonds are bonds which are sold to fund a third-party (usually private-market) development. While the bonds are supported by the good will of the city, they carry no encumbrance on the city's tax revenues and are supported solely by the revenue generated from the development project. These bonds are frequently sold to support industrial development and housing projects.

The mathematics of capital improvements planning is fairly simple. It is composed of "weighted ranking," to determine the relative priority of projects, and a simple system of "running totals," which can be used to decide where to cut off funding for each year.

The "running total" process is designed to add the cost of each additional program to the total cost of programs to be funded for each year. The user can try different combinations of programs to get the best use of available funds without going over the budget.

The "weighted ranking" process is equally simple to compute, but it raises serious conceptual issues. The process is based on the interaction of the project's score on each criterion and the weight given to each of the criteria. The ranking of each project is based on the sum of its weighted scores for each of the criteria. The project with the highest score is judged to have the highest priority. Because of the interaction between them, the weight and the score magnify each other. Small differences become larger.

This interaction effect is both the strength and the weakness of the weighted ranking process. It allows the decision maker to take account of criteria which are unequal in their importance. It also allows the decision maker to compare apples and bananas. If one is concerned with fruit, and has a preference for apples over bananas, the technique is quite effective. If one is concerned with color or shapes, the technique makes no sense. In other words, the criteria must be qualitatively similar; quantitative differences (how much or how little) are significant only between things that are already basically similar (qualitatively alike). The mathematics of capital improvement programming can not, however, make such a distinction. If you tell it that apples are worth "2" and bananas are worth "1", you could end up eating kumquats.

Most capital improvements projects are basically similar: they are concerned with allocating resources to build long-lived physical structures. If there is a problem of "noncomparability" (comparing apples and oranges), it is more likely to be at the level of the programs which the capital projects support. On what basis does one compare the need for housing street-people with the need for street improvements in a residential neighborhood? The prudent analyst will recognize that the formal criteria of a capital improvement planning model are secondary to the valuation which comes from the political process. The choice of criteria and the assignment of weights to the criteria only partially reflect this consideration.

Even when the choices are between basically similar projects, caution still must be exercised in using the model. There is still the possibility that projects which are essentially similar could be mis-ranked because of "measurement error." Any numerical value, when used as a measure, represents not a point but a range of values. The value "2," for instance, as the measure of a project's value on one of the capital improvement criteria, represents all values between "1.5" and "2.5." Consider this case: one project might have a true score of
2.5 on a criterion with a weight of 2, and a score of 1.5 on a criterion with a weight of 1. Another project might score 1.5 on the more important criterion and 2.5 on the other. The true score of the first should be 6.5 (2.5*2 and 1.5*1), and the true score for the second should be 5.5 (1.5*2 and 2.5*1); yet both are assigned the same score by the model for these two criteria. This problem will occur no matter how many digits one uses for scoring--there will always be imprecision at the level of the next decimal place. The more criteria the model includes, the greater the likelihood of measurement error.

There are several strategies for dealing with measurement error. One may assume that, when there are many independent measurements involved, the measurement errors will balance each other out, and thus one may ignore the issue. In the physical sciences, the rule of thumb is to report results to the same level of precision as the least precise variable--if one is dealing with single-digit weights and scores, then the final total should be rounded to a single-digit number. This is the most conservative solution, and might result in many projects sharing a tied rank. A compromise solution might be to round off the last digit for the final ranking. Whichever strategy is employed, one should always bear in mind that there is some imprecision built into the model.






1996 A.J.Filipovitch
Revised 11 March 2005