Environmental Economics - Mathematics and Statistics for the Environment - page 222

Returning to the focus of this chapter and this topic, the person tasked with protecting people,
property, and the environment through well-founded and well-grounded environmental practices
often feels that nothing is more important than accomplishing this goal. When told that plans to do
just that must be justified through cost-benefit analysis and must add value to the business or enter-
prise at hand, environmental professionals sometimes balk at the notion that anyone can, could,
or should put a price on life or the environment. The fact is, in the real world, we are required do
this every day—environmental professionals must justify their existence within the organization.
Although environmental professionals feel that environmental compliance is the sine qua non of
any business success, the average business manager views environmental concerns as being costly
measures that do not add to the bottom line.
Those of us who have worked in the environmental profession for any length of time are accus-
tomed to this type of dysfunctional thinking. It must be pointed out, however, that we also learn
(sooner rather than later) that most of us work in the real world, where we have to deal with or within
the constraints of an economic bottom line. It does not take a rocket science mentality to understand
the implausibility of recommending a very costly fix for a current or potential environmental hazard
or situation when, at the same time, bringing about such a fix would bankrupt the company. The
implementation of environmental compliance and remediation practices must be tempered not only
by common sense but also by the economic bottom line.
With the understanding that cost-benefit analysis has its place in the environmental professions,
this chapter presents a few of the economic principles that environmental practitioners should be
familiar with. That is, we present mathematical techniques and provide practical advice for evaluat-
ing decisions during the design and preparation of environmental practices and procedures. These
procedures support the selection and justification of design alternatives, operating policies, and
capital expenditures. Thus, what follows is a brief introduction to economic equations and formulas
commonly used in the environmental profession. Keep in mind that, historically, many of the math
operations presented here may be encountered again during professional certification examinations.
10.1.1 K ey t erms
A is an end-of-period cash receipt or disbursement in a uniform series, continuing for n peri-
ods, where the entire series is equivalent to P or F at interest rate i .
F is a future sum of money that is an amount, n interest periods from the present, that is
equivalent to P with interest rate i .
i is the interest rate per interest period; in the equations, the interest rate is stated as a decimal
(e.g., 6% interest is 0.06).
n is the number of interest periods.
P is a present sum of money.
Sinking fund is a separate fund into which one makes a uniform series of money deposits ( A )
with the goal of accumulating some desired future sum ( F ) at a given future point in time.
10.2 CAPITAL-RECOVERY FACTOR (EQUAL-PAYMENT SERIES)
Annual amounts of money to be received or paid are the equivalent of either a single amount in the
future or a single amount in the present, when the annual amounts are compounded over a period
of years at a given interest rate ( i ). The value of the annual amounts can be calculated from a single
present amount ( P ) or a single future amount ( F ). We can use the capital-recovery factor (some-
times called the uniform series capital-recovery factor or annual payment from a present value )
to determine the annual payments ( A ) from an investment. This is accomplished using Equation
10.1. The equation is based on present value ( P ), the interest rate ( i ) at which that present value is
invested, and the period (term) over which it is invested ( n ).