**3.2 Internal rates of return are non-additive**

An interesting phenomenon in connection with the internal rate of return method is that we cannot add the internal rater of return of two projects; moreover, we get very surprising results when two or more combined projects are considered together. Several authors have discussed this in the past. Treynor and Black (1976) and after them Puxty and Dodds (1991) have found that inclusion of a third project can affect the choice between the first two.

Let's suppose we have two projects (A and B) and combine them with a third one (C), as shown in Table 2.


Table 2. Example of non-additivity of internal rate of return (modified from Treynor and Black (1976) and Puxty and Dodds (1991)).

If we compare project A and B, A is the better choice, as its internal rate of return is higher. But if we include project C and there are enough funds to finance both projects, the attractiveness of A and B change: B becomes preferable (Puxty and Dodds, 1991).

Use of Discounted Cash Flow Methods for Evaluation of Engineering Projects 637

between the time periods. Non-conventional cash flows can therefore be defined as those that involve more than one change in sign. Such projects are due to modifications, reconstructions and overhauls, which require intensive investments that often cause

The problem of more than one change in sign can be overcome with the elimination of second and further changes in sign by discounting such part of equation to the article of the

A further possibility for overcoming the multiple internal rate of return problem, according Puxty and Dodds (1991), involves the net present value rule. It would have no difficulty in giving the correct advice: to reject the project because it has a negative net present value or

In connection with the internal rate of return, it is worth mentioning at least one further problem: a non-existent internal rate of return. Since the problem is very unlikely to appear

According to Pšunder and Ferlan's (2007) research among Slovenian project managers, only 37.5 percent of project managers with an education in mechanical engineering know about

Sometimes it becomes necessary to compare two projects in practice. In such cases the net present value and the internal rate of return may give opposite advice. To understand why the results of both methods differ, it is necessary to present the lines of two projects in a

Fig. 2. Conflicting indication from net present value and internal rate of return (modified

internal rates of return (*IRR*)

discount rate (*r*)

**3.4 Conflicting advice of the net present value and the internal rate of return** 

negative cash flow, quite common in engineering projects.

equation with the same sign in cash flow as the discounted one.

to accept it because it has a positive one at the given discount rate.

in practice, we will not give it any in depth attention.

the multiple internal rate of return problem.

diagram (Figure 2).

 net present value (*NPV*)

from Holmes, 1998).
