**2. Theoretical background**

We can divide project evaluation methods into two groups: a group of non-discounting methods and the discounting one. Among the most commonly used methods from the first group is certainly the payback period method.

Non-discounting methods contain several simplifications that can lead to flaws in results. It has to be stressed that non-discounting methods do not consider the time value of money. A cash inflow to be received in the future is weighed equally with a cash inflow to be received now. Since maturity of payments plays a significant role, this simplification can cause erroneous advice.

Non-discounting methods cannot be adopted for different risk levels, which means that only projects and investments with the same risk level can be mutually compared. Neither can

Following on from this research, the modified internal rate of return method is the least used among the methods studied in the research, although this method avoids the deficiencies that occur with the internal rate of return method (e. g., one avoids the presumption that all payments are reinvested at the same rate of return as the internal one). It is also interesting that the research showed that most experts simultaneously use a number of discounted cash flow methods, a technique which diminishes the possibility of false conclusions. 57.1 percent of experts with an education in mechanical engineering who evaluate investments by means of discounted cash flow methods most often use a combination of two methods, but only 35.7 percent of experts in other sciences use a

Research also shows that, according to their personal opinion, project managers are not sufficiently aware of the limitations of discounted cash flow methods. In establishing the level of knowledge about flaws in discounted cash flow methods, Pšunder and Ferlan's research (2007) established that less than half (43.2 percent) of experts (in all sciences) are familiar with multiple internal rate of return, and only 16 percent know the problem of results (conflicting advice) between the internal rate of return method and the net present value method. Major differences occur between experts of different profiles (Table 1).

> Other technical sciences

Other 0.0 % 0.0 % 0.0 % 12.5 %

Mathematical and natural sciences

37.5 % 40.0 % 20.0 % 56.3 %

Other

engineering

Table 1. Knowledge of flaws of discounted cash flow methods by field of education

We can divide project evaluation methods into two groups: a group of non-discounting methods and the discounting one. Among the most commonly used methods from the first

Non-discounting methods contain several simplifications that can lead to flaws in results. It has to be stressed that non-discounting methods do not consider the time value of money. A cash inflow to be received in the future is weighed equally with a cash inflow to be received now. Since maturity of payments plays a significant role, this simplification can cause

Non-discounting methods cannot be adopted for different risk levels, which means that only projects and investments with the same risk level can be mutually compared. Neither can

value and internal rate of return 37.5 % 33.3 % 0.0 % 43.8 % Multiple internal rate of return 37.5 % 6.7 % 0.0 % 18.8 %

Flaw Mechanical

combination of two methods.

Conflicting advice of net present

Deformation due to presumption that all payments are reinvested according to the rate of return identical to the internal one

(Pšunder and Ferlan, 2007).

erroneous advice.

**2. Theoretical background** 

group is certainly the payback period method.

capital gain be included in the calculation. This means that non-discounting methods are based on the assumption that every investment will have the same capital gain or loss.

Despite the evident deficiencies of non-discounting methods, they are wide spread among project managers and other decision makers. According to Pšunder and Ferlan (2007), approximately 80 percent of project managers with an education in mechanical engineering and approximately two thirds of other project managers with an education in engineering (e.g., civil engineering or electrical engineering) are still using them.

In contrast to non-discounting methods, in the discounting ones the calculation is based on the time value of money. That means the differences in maturity of payments can be considered. With discounting methods, capital gain or loss can be included in the (last) payment of the project. Since the methods deal with a discount rate, the differences in the risk premium can be considered as well.

Discounting methods always deal with cash flow analysis of a project or an investment. There are several methods – e.g. the net present value index and modified internal rate of return method – but by far the most commonly used among the discounting methods are the net present value method and the internal rate of return method (Pšunder and Ferlan, 2007).

The main advantage of discounting methods over non-discounting ones is the consideration of the time value of money. This is particularly important in engineering projects where duration of projects is usually long, and payments can be vastly deferred. Thus, by using discounting methods for project analyses, we can overcome the time inconsistency of payments.

By using the net present value method, we compare the present value of future payments with initial investment. In this way we determine the surplus from a project or an investment in present value terms. The advice of the method is positive if the net present value of project or investment is greater than or equal to 0, which means a project or an investment will generate a surplus by a given discount rate. Since the risk premium is included in the discount rate, the surplus represents extra gain for the investor, measured in present value terms. Of course, the investor does not receive the sum immediately, but that "extra gain" represents the present value of future surpluses from the cash flow of a project or an investment. Mathematically, the net present value can be calculated by using equation 1:

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

In equation 1, *CFi* stands for the cash flow in the period *i*, *n* represents the number of periods and *r* is the discount rate.

The internal rate of return method is quite similar to the net present value method, but despite these similarities, it produces different results. With the internal rate of return method, we calculate the return rate by equalizing the net present value with 0. The result is a measure of the rate of return earned on that capital used in the project during the time that the capital is used, after allowing for the recoupment of the initial capital outlay (Holmes, 1998).

According to Puxty and Dodds (1991) the internal rate of return method is no more difficult to understand. Though the mathematics are just as easy, it is trickier because in normal circumstances the solution can only be found by trial and error. The goal of the method is to

Use of Discounted Cash Flow Methods for Evaluation of Engineering Projects 635

Reinvestment assumption means that all cash flows from the proposed investment are reinvested at the same rate of return as the internal one. Brozik (n.d.) explains that reinvestment assumption means that, if you are really going to get, e.g., an 8 percent return on the proposed investment, each cash flow must earn 8 percent for the life of the project. The more common way to state this is that, in order to achieve an 8 percent return on the entire investment, all cash flows must be reinvested at 8 percent until maturity. No cash flows can be diverted for other purposes. No better investments can be taken should they come along. The cash is essentially tied up for the life of the project, and you must find

projects that will return 8 percent for the various time horizons each cash flow faces.

aware of the possibility of flaw in results due to reinvestment assumption.

It is unrealistic to expect that all the cash flows from the proposed project will be reinvested at exactly the same rate of return as the internal one, which means that the internal rate of return will return distorted results. How intense the distortion will be depends mainly on the difference between the internal rate of return of the proposed investment and the

The problem can be overcome by using modified internal rate of return. However, although the modified internal rate of return method clearly overcomes several problems of the internal rate of return method, according to Pšunder and Ferlan (2007), it is the least popular discounting method among engineers. Half of mechanical engineers use the modified rate of return method for project or investment evaluation, but only 13.3 percent of engineers other than mechanical engineers do so. Moreover, only 37.5 percent of mechanical engineers are

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

Project I0 PMT1 PMT<sup>2</sup> IRR A -100 0 125 11.8 B -100 110 0 10.0 C -100 130 0 30.0 A + B -200 130 125 18.0 B + C -200 240 0 20.0 Table 2. Example of non-additivity of internal rate of return (modified from Treynor and Black

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).

**3.1 Reinvestment assumption** 

reinvestment rate of return.

shown in Table 2.

(1976) and Puxty and Dodds (1991)).

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

find an interest rate at which inflows exactly equal outflows. The internal rate of return is calculated from the following equation:

$$0 = -I\_0 + \sum\_{i=1}^{n} \frac{CF\_i}{\left(1 + IRR\right)^i} \tag{2}$$

In equation 2, *CFi* stands for the cash flow in period *i*, *n* means the number of periods and *IRR* is the internal rate of return.

With investment projects in engineering we often encounter a residual value when the lifecycle of the project or investment is ended. Ling and Archer (2008) emphasise that it is 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 a project or an investment. Recent research by Pšunder and Cirman (2011) states that the residual value of an investment 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 a property with a very low value, then the cash outflows for the removal are greater than the inflows from the liquidated property.

Both the net present value method and the internal rate of return method derive from the same time value of money formula. However, they give a different type of indication. The net present value method gives an absolute size, while the internal rate of return method gives a relative indication. For optimal decision making, both methods should be used in practice. Both are valuable pieces of information in the decision process. In most cases, both the net present value method and the internal rate of return method will give the same advice (Brozik, n.d.).
