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:
- DEBT SERVICE CONSTANT = INTEREST RATE / 1 - (1 / [{1 + INTEREST
RATE}**N])
- 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:
- TAX-SUPPORTED DEBT CAPACITY =
[(DEBT/REVENUE RATIO*REVENUE) - TAX DEBT + DEBT RETIRED]
* (1 + ISSUE COST + DISCOUNT FACTOR)
* DEBT SERVICE CONSTANT
- Self-Supported General Obligation 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.
- 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 November 96
