Consider this hypothetical situation. Brother is
chronically short of cash and approaches sister with
the following deal. Brother says "Hi sis. I need $300 for
a while. If you loan me $300, I'll pay you back $30 a month for
the next year." How should sister respond?
She might wonder about brother's reliability for
repayment, but again we neglect uncertainty in our analysis.
We return to consider decision making with risk later.
She might be concerned about mother's reaction.
Mother doesn't like sister to make money from brother, and she
is more generally concerned about the morality of charging interest
for loans. Again we put politics, morality and other issues aside.
This is not to say money is the most important issue, but sister
wants to be well aware of the economics of the situation. She
might adjust her decision later to keep family peace.
Although our example is personal, it is representative
of decisions that are made every day in corporate and government
settings. In this section we will see how the time value of money
models considered earlier can be used to provide a single objective
measure with which projects can be evaluated. Once we have the
measure, we will be able to answer whether to invest in a project
or not. We will actually develop three equivalent measures: present
worth, uniform worth and rate of return.
Any one can be applied to a project and all give the same answer.
We also investigate the payback measure that is widely
used in practice. Later, we adjust the models to accommodate
taxes and inflation. Both issues are important for the analysis
of multiyear projects.
The methods of this section are used throughout
the remainder of the course. In the section on Comparison
of Alternatives the methods are adapted to the comparison
of alternative solutions to a given problem. In the section on Risk we
show how the measures are used when uncertainty is explicitly
recognized. The methods will also be used for in the Project
This section is important to engineers. Projects
proposed by engineers require the investment of capital funds,
and the investment must be repaid with future revenues from sales
or savings in operating costs. It is common corporate practice
to require the engineer to justify the investment objectively
and quantitatively. The methods of this section are often employed.
Click the Quicktime symbol to view an
Before going on, answer for yourself the question
faced by sister. Should she accept brother's offer? Also answer
the question: is this a good deal for the brother? The answers
are on the bottom of this page.
The most common measure used to determine the acceptability
of an investment is the net present worth (NPW). Click the Quicktime symbol
to see the presentation. We use sister's decision problem to
illustrate the NPW method for making investment decisions. Should
sister make the investment in brother?
To keep our bullets simple, we state the main points
of the lecture in terms of investments. This is our emphasis
for most of the course.
worth method computes the NPW of the cash flow
using the investor's MARR. If the NPW ≥ 0,
accept the investment. Otherwise, reject the investment.
Brother has a decision similar to sister, but his
is a borrowing situation. Should brother accept the loan from
sister? Click the icon to see.
The method also helps in decisions related to loans.
a borrowing situation, the present worth method computes
the NPW of the cash flow using the borrower's MARB.
If the NPW ≥ 0, accept the loan. Otherwise, reject
The NPW method can be used in a variety of contexts.
The next very short presentation summarizes the present worth
method for making decisions.
There are extensive instructions for the Economics
add-in at the OM/IE sit . Click the icon below to go to the instructions.
Some simple problems are illustrated below.