Engineering Economic Analysis

Difficulties in Solving for an Interest Rate 233

Other examples can be found in incremental comparisons of alternatives with unequal

lives. In the next section we learn how to determine whether each of these examples has

multiple roots.

Adding an oil well to an existing field costs $4 million (4M). It will increase recovered oil by

$3.5M, and it shifts $4.5M worth of production from Years 5, 6, and 7 to earlier years. Thus,

the cash flows for Years 1 through 4 total$8M and Years 5 through 7 total -$4.5M. If the well is

justified, one reason is that the oil is recovered sooner. How many roots for the PW equation are

possible?.

SOLUTION.

The first step is to draw the cash flow diagram and count the number of sign changes. The following

pattern is representative, although most wells have a longer life.

~$4M

There are two sign changes, thus there may be 0, 1, or 2 positive roots for the PW=0 equation.

The additio}Jal recovery corresponds to an investment, and the shifting of (ecovery to earlier years

corresponds to a 10aJ;).(positive cash flow now and negative later). Thus, the oil wells are neither

anirlVe$hnent }JOtaloan; they are a combination of both.

A projecthas a first cost of $120,000. Net revenues begin at $30,000 in Year 1 and then increase

* ~ by $2000 pefyear. In Year 5 the facility is expanded at a cost of $60,000 so that demand can

confiJrueto expandat $2000per year.HowfilanYrootsfor the PWequationarepossible? _~

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