Engineering Economic Analysis

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Problems 485

order by thep-rates of return. Finally, the cumulative first cost is computed. ProjectsD, I, B,and

G should be funded. The opportunity cost of capital is 12.4%if defined as the last project funded

and 10.6% if defined as the first project rejected.

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Summary

There are four general sources of capital available to an enterprise. The most important

one is money generated from the operation of the firm. This has two components: there is

the portion of profit that is retained in the business; in addition, a profitable firm generates

funds equal to its depreciation charges that are available for reinvestment.

The three other sources of capital are from outside the operation of the enterprise:

1. Borrowed money from banks, insurance companies, and so forth.


2. Longer-term borrowing from a lending institution or from the public in the form of
   mortgage bonds..


3. Sale of equity securities like common or preferred stock.

Retainedprofits and cash equalto depreciationcharges are the primary sourcesof investment

capital for most firms, and the only sources for many enterprises.

In selecting a value of MARR, three values are frequently considered:

1. Cost of borrowed money.


2. Cost of capital. This is a composite cost of the components of the overall capital-
   ization of the enterprise.


3. Opportunity cost. This refers to the cost of the opportunity forgone; stated more
   simply, opportunity cost is the rate of return on the best investment project that is
   rejected.

The MARR should be equal to the highest one of these three values.

When there is a risk aspect to the problem (probabilities are known or reasonably

estimated), this can be handled by techniques like expected value and simulation. Where

there is uncertainty (probabilitiesof the variousoutcomes are not known),there are analytical

techniques, but they are less satisfactory.A method commonly used to adjust for risk and

uncertaintyis to increase the MARR. This method has the effect of distortingthe time-value-

of-moneyrelationship.The effectis to discountlonger-termconsequencesmoreheavily than

short-term consequences, which mayor may not be desirable. Other possibilities might be

to adjust the discounted cash flows or the lives of the alternatives. ;~

15-1 Examine the financial pages of your newspaper (or
the Wall St. Journal) and detenmne the current
interest rate on the following securities, and explain
why the interest rates are different for these different
bonds.

(a)U.S. Treasury bond due in 5 years.

(b)General obligation bond of a municipal district,

city, or a state due in 20 years.

(c) Corporate debenture bond of a U.s. industrial

firm due in 20 years.

PROBLEMS

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