**5.1 Multiple internal rate of return in engineering projects**

The structure of cash flows in engineering projects often leads to non-conventional cash flows. As seen in Figure 4, the sign of cash flow often changes, owing to maintenance and overhauls.

The problem of more than one change in sign leads to multiple internal rates of return. Multiple internal rates of return do not mean uniform advice, so a decision about economic justification of the project cannot be made.

Use of Discounted Cash Flow Methods for Evaluation of Engineering Projects 643

In a 20-year project, the constant cash flow at a discount rate of 10 percent must amount to at least 10.6 percent of the investment on the annual level in order for the analysis to provide a positive indication. Meanwhile, at a 15 percent discount rate, it needs to be approximately

rate (r) 5 10 20

Table 4. Constant annual cash flows necessary (as a proportion of the initial investment outlay) for a positive indication of the present value analysis (modified after Pšunder and

When a 20-year project generates a constant annual cash flow that amounts to 10 percent of the investment on the annual level, the net present value will be higher than 0 at a discount rate of 9 percent, but lower than 0 at a discount rate of 10 percent. The advice from the method will change, owing to changes in the discount rate. This example shows how

The impact of the discount rate is comparatively diminished when projects are shorter and when the discount rate level is higher. However, even with 5-year projects and discount rates over 10 percent, the setting up of the discount rate could be decisive for the advice

The survey conducted in February and March 2011 among appraisers in Slovenia by Pšunder and Cirman (2011) shows that experts have a quite unified opinion about the risk free rate. The average nominal risk-free rate in the survey was 4.20 percent. This average corresponded to the returns on bonds issued by the Republic of Slovenia with a maturity of seven to eight years. By using the calculated average real rate of return, they established that the respondents' average expected future inflation was 2.25 percent, which means the respondents expect slightly higher inflation in Slovenia than the target inflation set by the

5 0.130 0.080 0.065 6 0.136 0.087 0.073 7 0.142 0.094 0.081 8 0.149 0.102 0.089 9 0.156 0.110 0.097 10 0.163 0.117 0.106 11 0.170 0.126 0.115 12 0.177 0.134 0.124 13 0.184 0.142 0.133 14 0.192 0.151 0.143 15 0.199 0.160 0.152

Discount Project duration (years)

1.5 times as high, as seen from Table 4.

Cirman, 2011).

important precise setting of the discount rate is.

from the net present value method.

Fig. 4. Non-conventional cash flows in engineering projects, owing to maintenace and overhauls.

According to Pšunder and Ferlan (2007) only slightly more than one-third of mechanical engineers are acquainted with multiple internal rate of return, so overcoming the multiple internal rate of return can cause problems in practice. However, the problem can be overcome by discounting the article with the change of sign to the period, represented by the article of the same sign in cash flow as the discounted one. A further possibility for overcoming the multiple internal rate of return problem is, according to Puxty and Dodds (1991), using the net present value rule. It would have no difficulty in giving the correct advice.
