**5. Applicability in practice**

640 Mechanical Engineering

1 1 1

*<sup>i</sup> r* 

The sum of the geometrical sequence can be written at limited number (*n*) of articles as:

*n n r*

*r r* 

In the above equation, *r* stands for the discount rate and *n* represents the number of periods. The PVFA represents the present value of the future annuities factor at limited number of

The impact of the discount rate on the present value of future annuities factor with regard to

Graph 1. Factor of the present value of future annuities in relation to the discount rate and

The above graph shows that the difference in the discount rate exerts a greater impact on projects with a longer duration, and that the differences are larger when using lower discount rates that result in higher factors of the present value of constant cash flow series (future annuities). In the case of an investment with a 20-year depreciation period (the duration of the investment is adapted to the depreciation period), it can be established that the present value of annuities at a 3 percent discount rate totals 14.88, which is over 50 percent greater than at a 9 percent discount rate with a present value factor of 9.13. This is twice the factor of the present value at a 13 percent discount rate. At the same time, this means that, in the interval of discount rates between 3 percent and 13 percent large errors

 1 1

1

*i*

*PVFA*

(4)

*n*

On the right side of the equation a geometrical sequence is seen:

the duration of a project is shown in Graph 1.

the duration of a project (Pšunder and Cirman 2011).

periods.

Kušar et al. (2008) state that the result of work by the project team in mechanical engineering is an estimate of the economic justification and feasibility of the project, including risk analysis. It is almost unavoidable to use discounted cash flow methods for estimating the economic justification. As found in the theoretical background of this chapter, the use of non-discounted methods would embody all the flaws of the group of methods, including avoiding the time of the money principle and risk sensitivity.

Using the discounting methods leads to much more trustworthy results, but with some limitations which are specific to engineering projects. As found by Pšunder and Ferlan (2007), the most commonly used methods among discounting ones are the net present value method and the internal rate of return method. Project managers with an education in mechanical engineering use the internal rate of return even more frequently.
