**4. Impact of the discount rate on engineering project evaluation**

Pšunder and Cirman (2011) claim that the key factor in estimating the present value of future cash flows is the discount rate. If it were 0, the net preen value equation (equation 1) would be reduced merely to the addition and subtraction of cash flows during different periods, without considering the time value of money. The discount rate determines the required rate of return that an investor demands for a certain investment in accordance with the risk associated with the investment, and it has a profound impact on the net present value. A higher discount rate results in a reduction of the net present value, whereas a lower one results in its increase, an effect that is evident in Figure 3.

Fig. 3. Influence of the discount rate on the net present value.

From Figure 3 we can see the relationship between the net present value and the internal rate of return. When increasing the discount rate, the net present value decreases. When the net present value reaches 0, the discount rate is equal to the internal rate of return.

The two curves belonging to two projects cross at a certain discount rate. Above this rate, the full line belongs to the superior project, below this rate, the dotted line represent the better investment. Puxty and Dodds (1991) explain the reason: the bulk of cash inflows from the project with the dotted line arrives in the later years, and hence at higher rates of

Holmes (1998) writes that the reason for conflicting advice is the two techniques make different assumptions regarding what will happen to cash inflows from investment projects. According to his findings, in such cases the net present value rule gives the correct advice. According to their own opinion, only 37.5 percent of Slovenian projects managers with an education in mechanical engineering, 33.3 percent of Slovenian project managers with education in other technical sciences, and 43.8 percent of project managers with other education know the problem of conflicting advice from the net present value method and

Pšunder and Cirman (2011) claim that the key factor in estimating the present value of future cash flows is the discount rate. If it were 0, the net preen value equation (equation 1) would be reduced merely to the addition and subtraction of cash flows during different periods, without considering the time value of money. The discount rate determines the required rate of return that an investor demands for a certain investment in accordance with the risk associated with the investment, and it has a profound impact on the net present value. A higher discount rate results in a reduction of the net present value, whereas a lower

From Figure 3 we can see the relationship between the net present value and the internal rate of return. When increasing the discount rate, the net present value decreases. When the

discount rate (*r*)

net present value reaches 0, the discount rate is equal to the internal rate of return.

**4. Impact of the discount rate on engineering project evaluation** 

one results in its increase, an effect that is evident in Figure 3.

Fig. 3. Influence of the discount rate on the net present value.

interest, they are discounted more heavily.

the internal rate of return method (see Table 1).

 net present value (*NPV*) Pšunder and Cirman (2011) state that the discount rate is the rate at which future cash flows are converted into their present value. The differences between the discount rates have significant impact on the result of investment or project analysis. The contemporary theory of the determination of the discount rate favours a more precise definition of the discount rate. As the discount rate does not include a capital recovery premium, it can only be used for assessing an investment where we do not expect changes in the value of the investment, or where we can expect that changes in the value of the investment will be considered when selling property or at the termination of the investment (adopted from Friedman and Ordway, 1989, and The Appraisal of Real Estate, 2008). Ling and Archer (2008) emphasize that it is also necessary to take into account the cash flow from the sale of a property and not only the periodic investment inflows of cash. In such cases, it is important to include in the last projected cash flow any potential (marketable) residual value of an investment. The latter usually appears as a positive cash flow, but in some cases it can also be a negative one; for example, if we are dealing with the removal of a completely derelict property or of a property with a very low value, then the cash outflows for the removal are greater than the inflows from the liquidated asset.

By definition, the discount rate represents the rate of return that can be obtained in the financial market for a similar investment with comparable risk. What rate of return will be required for a certain investment depends on the risk associated with the specific investment and on the rate of return on investments with a comparable risk (Mramor, 1993).

According to Pšunder and Cirman (2011), different risk premiums must be taken into account for different projects, enabling us to compare two quite different projects. Certainly, machinery and equipment investments are mostly subject to deterioration and obsolescence, which are the reasons an investment loses value in the long run. The loss of value can be included in cash flow from the residual value (the last cash flow in the equation when individual cash flows can be considered).

Pšunder and Cirman (2011) write that the discount rate has a significant influence on the result of the present value method; that is why the correct choice of a discount rate is a precondition for an appropriate analysis.

The above mentioned authors state that when analyzing a certain project, the size of the initial investment, expected cash flows and estimated duration of the project are known. The key factor that influences the result of the analysis is the discount rate. The discount rate is a decisive factor when evaluating whether projects are acceptable or not. The impact of the applied discount rate significantly increases with the duration of a project.

Presuming a limited period until the end of the project and constant annual cash flow of the project, we can derive a present value of future annuities (PVFA). In the case of these presumptions, the equation 1 takes following form:

$$NPV = -I\_0 + \sum\_{i=1}^{n} \frac{CF}{\left(1 + r\right)^i} = -I\_0 + CF \cdot \sum\_{i=1}^{n} \frac{1}{\left(1 + r\right)^i} \tag{3}$$

In equation 3, *CF* stands for the constant annual cash flow, *n* represents the number of periods and *r* is the discount rate.

Use of Discounted Cash Flow Methods for Evaluation of Engineering Projects 641

can be made in the assessment of the present value of cash flows, which can certainly result

In addition to the above graph, the present value of future annuities using discount rates of

rate (r) 1 3 5 7 10 15 20 3 0.97 2.83 4.58 6.23 8.53 11.94 14.88 4 0.96 2.78 4.45 6.00 8.11 11.12 13.59 5 0.95 2.72 4.33 5.79 7.72 10.38 12.46 6 0.94 2.67 4.21 5.58 7.36 9.71 11.47 7 0.93 2.62 4.10 5.39 7.02 9.11 10.59 8 0.93 2.58 3.99 5.21 6.71 8.56 9.82 9 0.92 2.53 3.89 5.03 6.42 8.06 9.13 10 0.91 2.49 3.79 4.87 6.14 7.61 8.51 11 0.90 2.44 3.70 4.71 5.89 7.19 7.96 12 0.89 2.40 3.60 4.56 5.65 6.81 7.47 13 0.88 2.36 3.52 4.42 5.43 6.46 7.02 14 0.88 2.32 3.43 4.29 5.22 6.14 6.62 15 0.87 2.28 3.35 4.16 5.02 5.85 6.26

Table 3. Factors of the present value of future annuities in relation to the discount rate and

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

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

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

mechanical engineering use the internal rate of return even more frequently.

the duration of an investment (Pšunder and Cirman, 2011).

avoiding the time of the money principle and risk sensitivity.

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

justification of the project cannot be made.

**5. Applicability in practice** 

in an incorrect decision based on the analysis (Pšunder and Cirman, 2011).

3 percent to 15 percent for selected investment durations is shown in Table 3.

Discount Project duration (years)

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

$$\sum\_{i=1}^{n} \frac{1}{\left(1+r\right)^{i}}$$

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

$$\frac{\left(\mathbf{1} + r\right)^{n} - \mathbf{1}}{\left(\mathbf{1} + r\right)^{n} \cdot r} = PVFA \tag{4}$$

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 periods.

The impact of the discount rate on the present value of future annuities factor with regard to the duration of a project is shown in Graph 1.

Graph 1. Factor of the present value of future annuities in relation to the discount rate and the duration of a project (Pšunder and Cirman 2011).

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 can be made in the assessment of the present value of cash flows, which can certainly result in an incorrect decision based on the analysis (Pšunder and Cirman, 2011).


In addition to the above graph, the present value of future annuities using discount rates of 3 percent to 15 percent for selected investment durations is shown in Table 3.

Table 3. Factors of the present value of future annuities in relation to the discount rate and the duration of an investment (Pšunder and Cirman, 2011).
