Comparative Analysis (Part II)

Comparing Mutually Exclusive Alternatives having unequal useful lives:

Co-terminated Assumption

The co-terminated assumption uses a determinate and equal study period for all alternatives. This planning horizon combined with appropriate adjustments to the estimated cash flows plus the alternatives on a common and comparable basis. The planning horizon chosen could be:

• Life of shorter-lived alternative
• Life of longer-lived alternative
• Less than the shorter lived alternative
• Greater than the longer-lived alternative
• In between the shortest and longest-lived alternative

Two cases are involved in co-terminated assumption.

Case 1: Project’s life shorter than Analysis period

Here project lives are shorter than the firm’s predetermined required analysis period. Following assumptions are made in this case.

1. Cash flow transaction is taken to be same or an average of the previous periods for the extended periods.
2. Replacement or reinvestment is necessary for remaining period (i.e. study period – useful life) and economic consequences that are expected to happen in an alternative’s initial life span will also happen in all succeeding life span. [As in the repeatability assumption]
3. Decide to lease the necessary equipment or subcontract the remaining work for the duration of the analysis period. Here same lease cost and operating cost for remaining period to each project.

Then the alternatives can be chosen by present worth (PW) or future worth (FW) method taking until analysis period.

Case 2: Project’s life longer than Analysis period

The case of project lives that are too long is the easier one to address. A common instance of project lives that are longer than the analysis period occurs in the construction industry where a building project may have a relatively short finishing time but the equipment purchased has a much longer useful life. Here we analyze each project for only as long as the analysis period and are left with some unused portion of the equipment which we include as the salvage value in our analysis. Salvage value is the amount of money for which the equipment could be sold after its service to the specific project has been rendered.

IRR method for the unequal project lives:

This method can also be used to compare projects with unequal useful lives as long as we establish a common analysis period. This can be performed by using the Repeatability as well as Co-terminated Assumptions.

Capitalized worth Method (CW)/ Capitalized cost (CC)

Capitalized cost is the present value of an alternative project that will last for infinite period. It is the special case of PW criterion which is suitable when the life of an offered project is perpetual or the planning horizon is extremely long (say 40 years or more). Many public projects like bridges, waterway construction, irrigation systems, and hydroelectric dams are projected to generate benefits over a prolonged period of time or forever. This criterion for evaluating and comparing the alternatives is useful in places where the repeatability assumption is applicable. In this section, capitalized equivalent [CW(i)] method for evaluating such project is examined.

The capitalized cost represents the amount of money that must be invested today to yield a certain amount A at the end of each and every period forever, assuming interest rate ‘i’.

The formula to calculate CW is derived from the relation P = A(P/A, i%, N) where N → ∞

The equation of P using the P/A factor formula is

PW (i%) = A [(1 + i)^N – 1] / [i. (1 + i)^N]

Here as N → ∞, and CW replaces PW,

CW(i%) = A / i

Comparing Mutually Exclusive, Contingent and Independent Projects in Combination:

In particular, we will consider decision procedures that should be applied when we have to evaluate a set of multiple investments alternatives for which we have a limited capital budget. Here we distinguish a project from investments alternatives, which is a decision option. For a single project, we have two investment alternatives: either to accept or reject the project. For two independent projects, we can have four investment alternatives: (a) to accept both projects, (b) to reject both projects, (c) to accept only the first project, and (d) to accept only the second project. To perform a proper capital budgeting analysis, a firm must group all projects distinguishing projects as dependent or independent under consideration into decision alternatives.

Independent Project:

An independent project is one that may be accepted or rejected without influencing accept or reject the decision of another independent project. For example, the purchase of a machine, office furniture and truck are the three independent projects. Only projects that are economically independent of one another can be evaluated separately.

Dependent Project:

In many decision problems, several investment projects are related to one another such that the acceptance or rejection of one project influences the acceptance of others. The two such types of dependencies are as follows:

1. Contingent Project:

Two or more projects are said to be contingent if the acceptance of one requires the acceptance of another. For example, the purchase of a computer printer is dependent upon the purchase of a computer but the computer may be purchased without considering the purchase of the printer.

2. Mutually Exclusive Project:

When there are several alternatives to achieve the same objectives and we can choose only one of them then the alternatives are called the mutually exclusive project.

Formulation of Mutually Exclusive Alternatives:

1. If A, B are two independent projects then the mutually exclusive combinations are

2. If A, B, C are three mutually exclusive alternatives then we can make the following combination:

3. IF A, B, C are three projects where C is the contingent on the acceptance of B and acceptance of B is contingent of acceptance of A, then we can make the following combination:

Do nothing option (DN):

Selection of the DN alternative means that the current approach is maintained; nothing new is initiated. If there is certainty that one of the defined alternatives be selected, do nothing is not considered an option.

BIBLIOGRAPHY:

Chan S.Park, Contemporary Engineering Economics, Prentice Hall, Inc.
E. Paul De Garmo, William G.Sullivan and James A. Bonta delli, Engineering
Economy, MC Milan Publishing Company.
James L. Riggs, David D. Bedworth and Sabah U. Randhawa,Engineering
Economics, Tata MCGraw Hill Education Private Limited.