Engineering Economic Analysis

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532 RATIONING CAPITAL AMONG COMPETING PROJECTS

scheme occurs, occasionally,when the capital budget is more than enough fornprojects

but too little forn+ 1 projects..

In Example 17-6, a capital budget of $300,000 is just right to fund the top three

projects. But a capital budget of $550,000 is more than enough for the top five projects

(sum=$450,000) but not enough for the top six projects (sum=$650,000). When we

have this lumpiness problem, it may not be possible to say with certainty that the best use

of a capital budget of $550,000 is to fund the top five projects. There may be some other

set of projects that makes better use of the available $550,000. While some trial-and-error

computations may indicatethe proper set of projects, more elaborate techniques are needed

to prove optimality.

As a practical matter,a capital budget probably has some flexibility.If in Example 17-6

the tentative capital budget is $550,000, then a careful examination of Project 2 will dictate

whether to expand the capitalbudget to $650,000 (to be able to include Project 2) or to drop

back to $450,000 (and leaveProject 2 out of the capital budget).

SUMMARY

Prior to this chapter we had assumed that all worthwhile projects are approved and im-

plemented. But industrial firms, like individuals and governments,are typically faced with

more good projects than can be funded with the money available. The task is to select the

best projects and reject, or at least delay, the rest.

Alternatives are mutually exclusive when the acceptance of one "effectivelyprevents

the adoption of the other.This could be"becausethe alternativesperform the same function

(like PumpAvs PumpB)or would occupy the same physical location (like a gas station

vs a hamburger stand). If a project has a single alternative of doing something, "weknow

there is likely to be a mutually exclusive alternative of doing nothfug-or possibly doing

something else. A project proposal may be thought of as having two or more mutually

exclusive alternatives.Projects are assumed in this chapter to be independent.

Capital may be rationed among competing investment opportunities by either rate of

return or present worth methods. The results may not always be the same for these two

methods in many practical situations~ .". "

If projects are ranked by rate of return, a proper procedure is to go down the list until

the capital budget has been exhausted. The rate of return at this point is the cutoff rate of

return. This procedure gives the best group of projects, but does not necessarily have them

in the proper priority order.

MaximizingNPW is an appropriatepresent worthselectioncriterion when the available

projects do not exhaust the money supply. But if the amount of money required for the

best alternative from each project exceeds the available money, a more severe criterion is

imposed: adopt only alternatives and projects that have a positive NPW - p(PWof cost).

The value of the multiplierpis chosen by trial and error until the alternatives and projects

meeting the criterion just equal the available capital budget money.

It has been shown in earlier chapters that the usual business objective is to maximize

NPW, and this is not necessarily the same as maximizing rate of return. One suitable

procedure is to use the ratio (NPW/PW of cost) to rank the projects. This present worth

ranking method will order the projects so that, for a limited capital budget, NPW will be