eviewed. At the same time, the limitations of traditional capital budgeting techniques are discussed and the usage of practical capital budgeting techniques to deal with these limitations. Traditional capital budgeting techniques include NPV, IRR and PB method. And the practical capital budgeting techniques involve real options method and simulation method.

## 2.1 Traditional capital budgeting techniques

Traditional capital budgeting techniques consist of discounted cash flow which involve NPV and IRR whereas non-discounted cash flow involve payback method.

## 2.1.1 Net Present Value (NPV).

Net present value is the difference between the amount invested and the present value of future cash flows (Alan, 2004). Charles et al (2009) reviewed that the NPV method calculates the expected monetary gain or loss from a project by discounting all expected future cash inflows and outflows back to the present point in time using the required appropriate rate of return. Colin (2006) added that NPV is the most straightforward way to determine whether a project yields a return in excess of the alternative equal risk investment in trade securities.

NPV is the present value of the net cash inflows less the project’s initial investment outlay, if the rate of return from the project is greater than the return from an equivalent risk investment in securities traded in the financial market, the NPV will be positive, vice versa, if the rate of return is lower, the NPV will be negative (Colin, 2006). A positive NPV shows that an investment should be accepted, while a negative NPV shows that the investment should be rejected (Colin, 2006).

Kashyap (2006) added that the key inputs of the calculation of NPV are the interest rate or discount rate which used to compute the present values of future cash flows. When the discount rate higher than the shareholders’ required rate of return, and the project has a positive NPV at this rate, then shareholders will expect an additional profit that has a present value equal to the NPV (Kashyap, 2006). Formula for computing NPV is:

Source: Kashyap (2006).

Ct is the cash flow at time t, r is the discount rate and Co is the cash outflow at time 0 (Kashyap, 2006). In other words, this technique compares the value of a pound today to the value in the future by taking inflation and returns in consideration (Kashyap, 2006).

## 2.1.2. Internal Rate of Return (IRR)

IRR is another of capital budgeting technique which same as NPV technique in using the time value of money but results in answer expressed in percentage form (Pauline, 2006). IRR represents a discount rate which leads to a net present value of zero where the present value of the cash inflows equals to the cash outflows (Pauline, 2006). Charles et al (2009) added that IRR method calculates the discount rate at which an investment’s present value of all expected cash inflows equals to the present value of its expected cash outflows. It also means that IRR is the discount rate that makes NPV=£0. Kashyap (2006) described the IRR graphically as below:

Source: Kashyap (2006).

Managers who make decision based on IRR should carry out the investment whenever the IRR is greater than the original cost of capital. Kashyap (2006) emphasized that when choosing investments or projects, the investment with the highest IRR should be chosen and of course that the IRR is greater than the cost of capital at the same time. There have two formulas for calculating IRR: one is with the help from computer tools;

Source: Kashyap (2006).

CFt = the cash flow at time t and the IRR can be computed by using excel with its inbuilt function (Kashyap, 2006).

The second simple formula of IRR is:

Lower of the pair of discount rate + [(NPV at lower rate/Difference between the NPVs) x difference in rates]

Source: Pauline (2006).

## 2.1.3. Payback Method.

Payback period, this technique used to forecast the length of time period taken to recover expected net cash inflows from investment. Alan (2004) added that this method used by a lot of firms and frequently especially at the times when the interest rates are high and/or the firms are experiencing cash flow problems. This method measures the length of time it takes to recover the original cash outlay from the stream of net cash proceeds from the investment (Alan, 2004).

Pauline (2006) defined the payback method as the investment appraisal calculates the length of time required for the stream of cash inflows from a project to equal the original cash outlay. And the payback period is the length of time required for a stream of net cash inflows from a project to equal the original cash outlay (Pauline, 2006). Kashyap (2006) reviewed that the payback method is generally used as a comparison of two or more projects and has a wide acceptance as a rule of thumb. Formula for calculating payback period is:

Source: Kashyap (2006).

## 2.2. Limitations of traditional capital budgeting techniques

Theoretically, the traditional capital budgeting techniques are the best choices for corporation to apply in evaluating its capital investment. In real business world, there have several drawbacks of traditional capital budgeting techniques which discourage the corporation apply the traditional capital budgeting techniques.

## 2.2.1. Limitations of NPV.

According to Myers’ observations, the NPV analysis ignored the time series interactions among contingent investments and this cost the delayed investments may accrue extra benefits (David, 1995).

The probability distribution of NPV which incorporates the valuation of flexibility is not symmetrically distributed as in the certainty–equivalent NPV case (David, 1995).

The use of simple risk-adjusted rates to assess investments in which there is flexibility will undervalue the investments (David, 1995).

David (1995) added that the asymmetry arises because the certainty-equivalent NPV rules ignore flexibility which provides protection against future events turning out differently from expected at the outset. Pankaj (2009) added that NPV technique does not consider the extent of management’s flexibility to respond to uncertainty over the life of the project.

Todd et al (2004) reviewed that by using NPV model, an increase in risk is accounted for increasing the discount rate which resulting in lower valuations. Pankaj (2009) noted that NPV underestimates the value of a project as it ignores the value of the implicit options that managements have in project.

NPV technique ignores the value of creating options and does not deal with uncertainty effectively when valuing the project (Pankaj, 2009).

## 2.2.2. Limitations of IRR.

IRR method is not effective in measuring returns in terms of absolute amounts of wealth changes because it only gives a percentage measure of returns and this may cause difficulties in ranking the projects when there are conditions of mutual exclusivity (Kashyap, 2006).

. IRR method, one of DCF techniques which fail to consider the flexibility to revise decisions after a project begins (Kent et al, n.d.).

This technique fails to provide proper valuation when the business environment is uncertain and forgo the value created by flexibility in management decisions (Kent et al, n.d.).

## 2.2.3. Limitations of Payback method.

This technique does not take into account cash flows after the project’s payback period and only consider the project returns up to the payback period (Kashyap, 2006). Yet, some projects, by their nature and long-term, the benefits may not accrue until certain time in the future which far beyond the normal payback period (Kashyap, 2006).

This method ignores the time value of money and fails to reflect all dimensions of profitability relevant to capital budgeting decisions (Kashyap, 2006).

## 2.3 Practical capital budgeting techniques

In real business world, there have several corporations using practical capital budgeting techniques to value their capital investment effectively. These practical capital budgeting techniques are used to deal with the limitations of traditional capital budgeting techniques. Practical capital budgeting techniques include real options method and simulation method (Monte Carlo Simulation).

## 2.3.1 Real options method.

Real options method is one of the investment appraisal techniques for capital budgeting which can deal with the limitations of the NPV. Pankaj (2009) reviewed that real options method is a method of evaluating and managing strategic investments decisions in an uncertain business environment. David (1995) added that using real option methods has been recognized that the application of standard NPV techniques can lead to wrong conclusions in the presence of unrecognized embedded options. David (1995) stated that “The central role of NPV techniques in financial decision making therefore makes it imperative that real option structures in investing opportunities are identified and accounted for. It turns out that real options can be found in most live environments where uncertainty or risk, waiting, investment irreversibility, growth opportunity, asymmetric information, staged investments, competitor response, economics of scale, project switching, suspension, abandonment and start-up are important. In fact, these include the full spectrum of investment decision making, including those concerning capital budgeting and the fact that the standard NPV techniques do not recognize or deal with these situations adequately.”

Mikael and Shuhua (2003) added that real options methods introduced to correct the problems of NPV method. This method calculates the value of an investment with techniques originally developed for valuation of financial options which gives possibility to take into consideration the managerial flexibility to take action during the lifetime of an investment (Mikael and Shuhua, 2003).

Todd et al (2004) reviewed that real options analysis is a controlled means of systematically identifying the interplay between intermediate outcome states and alternative managerial actions and specifically valuing managerial flexibility. The capital budgeting decisions often involve investment, capital assets and most decisions can be viewed as options on real assets (Todd et al, 2004).

## 2.3.2. Benefits of real options method.

Real option analysis recognizes the incremental value arising from flexibility which gives rise to additional value is recognition of the altered probability distribution of potential outcomes and its impact on risk exposure (David, 1995). And, David (1995) added that using real option methods can deal with risk in capital budgeting correctly.

Real options provide a useful framework for strategic decision making and deal with uncertainty and flexibility efficiently (Pankaj, 2009).

Mikael and Shuhua (2003) added that real option method is a helpful tool to give insight into the value of the possibilities that can be found by investing in a given investment.

Real option valuation widens the managerial horizon to take into consideration and consider the possibilities of an investment (Mikael and Shuhua, 2003).

Real option valuation used to find the optimal time of investment and to take the managerial flexibility to act in consideration in an intuitive and correct way (Mikael and Shuahua, 2003).

Real options analysis can value asymmetric payoffs which can provide a means of valuing managerial flexibility – the ability of managers to intervene proactively to take action during the time frame when the results of previous decisions are being played out (Todd et al, 2004).

Todd et al (2004) added that real options analysis able to reformulate the problem resulting in more insight into the project and the potential sources of value.

Carlsson et al (2006) added that the real options method for Research and Development (R&D) project valuation seeks to correct the deficiencies of traditional methods of valuation that based on NPV analysis, through the recognition of managerial flexibility and its interaction with the underlying investment opportunities. Carlsson et al noted that the uncertainty can bring significant value to projects.

## 2.3.3. Approaches of real options method.

There have several approaches undertaken by researchers, the approaches such as process approach, re-evaluation of NPV and framework approach.

Process approach. Real options method can be interpreted in a process view besides using calculation method. Todd et al (2004) r-eviewed that real options analysis may not be project valuation, or quantifiability, but the process of describing and understanding the project and the uncertainty embedded therein. Mikael and Shuhua (2003) noted that the real option method for capital budgeting emphasizes on ongoing learning about the risks and potentials of a new venture over time. Ongoing evaluation effort is influenced by changes in the business environment. Dahlberg and Porter (2000) added that it is a process in which the valuation even the computing process, is not intended to provide a sure answer, rather to provide decision makers an ongoing dialogue about the project/investment. Therefore, it is necessary to has a process view of real option approach in analyzing the decision support needs (Mikael and Shuhua, 2003). There have four main stages of continuous of process taken when adopting real options valuation:

1st stage – Identifying options (the possibilities on internal and external of a project) in light of newly available information and updating the decision tree at different project stages (Mikael and Shuhua, 2003).

2nd stage – Evaluating the options: quantitative and qualitative analysis of the value of the options (Mikael and Shuhua, 2003).

3rd stage – Selecting the important options: ranking of or voting for real options based on the valuation (Mikael and Shuhua, 2003).

4th stage – Execute the options if optimal, advancing in the decision tree (Mikael and Shuhua, 2003).

Requirements for process – In order to proceed the process requires several things such as up-to-date project status information readily available to decision makers; up-to-date market information and industry foresight (future events or trends) constantly made aware to decision makers and be integrated into various phases of real options valuation process (Mikael and Shuhua, 2003). Mikael and Shuhua (2003) noted that the process requires option analysis and evaluation to be done periodically and applying advanced option valuation methods. In order to able to carry out the process efficiently and effectively, the managers who responsible for a project need to be aware of the current situation of the project. Mikael and Shuhua (2003) noted that information about the project need to be obtained continuously by interpreting a process of following the large changes in the environment of the project such as shifts in the markets, etc.

Re-evaluation of NPV approach. Real options method applied to re-evaluate the traditional capital budgeting technique, NPV. David (1995) emphasized that when real options are an appropriate appraisal technique, important points of principle may need re-evaluating. The true value of an investment is given by: Expanded NPV = Passive NPV + Real option value (David, 1995). The fact that options mostly have positive values indicate that traditional NPV(passive) rejects too many opportunities without consider the value of flexibility (David, 1995). David (1995) stated that “it it important to realize that the addition of real option values in such a framework is inappropriate, unlike straightforward NPV additions, because of the interactivity of option values. For instance, abandonment of a project midstream rules out subsequent option values that would have arisen had the alternative been to continue with the project. Second order interactions may arise should a real option be exercised (i.e. when the project is undertaken), as the scale of operations may be increased so that the values of other real options which are dependent on capacity will be increased.” In conclusion is that ignore strategic or operating flexibility will lead to misjudgement on investment opportunities.

Important criteria – There have few important criteria needed to take note when valuing real options method. The criteria such as investments can be deferred; investment exposed to risk; and high interest rates.

Investments can be deferred – The possibility of deferring an investment facilitates evaluation of future events when they arise and avoids costly errors (David, 1995). Furthermore, deferring investments improved the investment timing from traditional NPV approach to one which recognizes the strategic benefits of waiting (David, 1995).

Investment is exposed to risk – “No risk, no gain”, as for each investment needs to face risks in order to gain a satisfactory returns. David (1995) noted that investments need risk to offer a sufficient return to shareholders beyond the risk-free rate and the real options have greater value in the face of risk. The real options method often undertaken to evaluate risks, if a project timings and outcomes can be manipulated to take advantage of the risk potential which in return will gain financial benefits from them (David, 1995).

Interest rates are relatively high – With higher interest rates or discount rates, it cause the future value of particular capital to be lower compared to current-day capital’s value. David (1995) reviewed that higher discount rates mean that the future capital necessary exercise a real option (undertaking a further contingent part of the project at some future date) is lower in present-day terms. Therefore, financing a new project may be done in stages where staged investments offer the opportunity of expanding the number of exit routes while lowering the present value of cash outflows (David, 1995).

Framework approach “Fuzzy capital budgeting”. There had some past researchers introduced an framework approach for real options valuation which so-called fuzzy capital budgeting. Mikael and Shuhua (2003) said that “fuzzy capital budgeting is to use fuzzy versions of the traditional capital budgeting methods and real option valuation. It needs to be observed that the fuzzy versions of the methods are original constructions, and not fuzzifications of the existing methods which means that the mathematics is that of possibility instead of probability.” To elaborate on what fuzzy mathematics can add to capital budgeting, the first thing to consider is about how efficient way of a manager to think about future cash flow estimates of a project, for example, the manager estimates that the project will produce a cash flow between 30 and 40, in three years from present day (Mikael and Shuhua, 2003). With fuzzy capital budgeting methods these estimates can be used, provided that they are the best available estimate of the future cash flow, without having to re-calculate them into one number which is done by other common approaches (Mikael and Shuhua, 2003). It is known that the uncertainty is included in the estimate and carried directly into the profitability calculation where there is no loss of information, and the picture given is not out of expected (Mikael and Shuhua, 2003). Formula for computing fuzzy real option values, suggested by Carlsson and Fuller (2000):

Sources: Mikael and Shuhua (2003) & Carlsson et al (2006)

E(So) denotes the possibilistic mean value of the present value of expected cash flows, E(X) stands for the possibilistic mean value of expected cost and σ is the possibilistic variance of the present value of expected cash flows, So (Mikael and Shuhua, 2003); whereas r is the annualized continuously compounded rate on a safe asset and T is the time to maturity of the option in years (Carlsson et al, 2006).

Mikael and Shuhua (2003) reviewed that “fuzzy numbers give a possibility to include qualitative information into capital budgeting process, in a straightforward way. The fuzzy sets presenting the cash flow estimates can be adjusted dynamically to reflect the future trends that are revealed by a foresight process, and are in a qualitative form.” A example of the method is shown in Collan and Majlender (2000), sides of fuzzy cash flow estimates are adjusted by market analysts to reflect the information about the future (Mikael and Shuhua, 2003).

Mikael and Shuhua (2003) added that real options and fuzzy capital budgeting open the chance to explore the value of flexibility inside and outside of a project, and give further details into uncertainty of large investment.

## 2.4. Monte Carlo Simulation for risk analysis in capital budgeting

## 2.4.1. Risk Analysis

Smith (1994) reviewed that “the Monte Carlo Simulation (MCS) which employed in risk analysis of capital budgeting. MCS was developed in the early 1960s and involves the use of both probability distributions and random numbers to estimate, with the aid of a computer, a distribution of possible net present values (NPVs), rather than a single value. MCS also involves the replacement of estimates of net cash flow for each year with probability distributions for each factor affecting net cash flow (eg, revenue or resource components).”

There consists of two methods of risk analysis. They are intuitive methods and analytical methods. Intuitive methods include subjective or qualitative judgement, risk-adjusted payback, risk-adjusted discount rate and risk-adjusted cash flows; analytical methods involve certainty equivalents, probability distribution, sensitivity, simulation and decision tree as shown as below:

Illustration 1. Risk Analysis Techniques.

(Source: Smith, 1994)

Monte Carlo simulation also involves the replacement of estimates of net cashflow for each year with probability distributions for each factor affecting net cashflow (for example, revenue or resource components); factors such as market share or operating costs whose value was uncertain would be modeled by means of a dispersed probability distribution, while a more certain factor would be modeled by a less dispersed probability distribution (Smith, 1994).

## 2.4.2. Monte Carlo Simulation

The simulation would be undertaken by drawing a random observation from each probability distribution by using a computer. Each probability distribution would be combined to provide an estimated net cashflow for each year in the life of the investment project. The successive yearly cashflows would be discounted and the discounted random selections would be combined to provide an estimate of the NPV of the investment project (Smith, 1994).

The simulation process would be repeated a lot of times to build up, not a single value of NPV, but a distribution of NPVs which would reflect the level of uncertainty surrounding the cashflows that made up the investment project (Smith, 1994). The process as a cycle is shown in Illustration 2.

Illustration 2. The Logic of a Simple Monte Carlo Simulation

(Source: Smith, 1994)

Implementation of Monte Carlo Simulation – The implementation of Monte Carlo simulation for risk analysis in capital budgeting involve computer simulation by using Microsoft Office Excel. Smith (1994) noted that “With facilities for processing statistics, programming advanced macros and generating graphs, many of the newer spreadsheet packages can carry out computer simulation. And computer simulation implemented on the widely used spreadsheet, Microsoft Office Excel.” Then, Monte Carlo simulation can be implemented by defining an investment appraisal project which specified in a NPV model or discounted cashflow (DCF) model. The model is illustrated in table 1:

Table 1. Investment Appraisal Using DCF

Year | Initial outlay | Net cashflow |
---|---|---|

0 | £115,000 | |

1 | £ 15,000 | |

2 | £ 30,000 | |

3 | £ 42,000 | |

4 | £48,000 | |

5 | £ 36,000 |

Discount rate: 10%

NPV = £ 10,123

Source: Smith (1994)

From table 1, the project shown an expenditure of £ 115,000 at the beginning of the project together with cashflows over five years in the future. Traditional NPV calculations show a NPV of £ 10,123 which means that this project is worth to invest into. Yet, the cashflow figures used are only estimates of quantities whose value are uncertain and will be determined or might be changed in the future (Smith, 1994).

Smith (1994) stated that “to deal with uncertainty, the values of net cashflow in each year have to be replaced by values drawn at random from probability distributions. The type of distribution will depend on the data that describe the cashflows. Typically, one might expect cashflows to have a normal distribution. And each particular distribution will be described by a mean and standard deviation where the level of uncertainty attached to each cashflow will be determined by its standard deviation.” And if the values of cashflows shown in Table 1 represent moderately uncertain forecasts, it would be reasonable to take these values as the mean in each case, with a standard deviation of perhaps 30 percent of the mean to represent the level of uncertainty which illustrated in Table 2.

Year | Cashflow mean | Cashflow standard deviation |
---|---|---|

1 | £15,000 | £4,500 |

2 | £30,000 | £9,000 |

3 | £42,000 | £12,600 |

4 | £48,000 | £14,400 |

5 | £36,000 | £10,800 |

Source: Smith (1994)

Smith (1994) noted that probability distribution is not used for the initial outlay on the investment because it is going to take place now rather than in the future and there is no uncertainty surrounding it.

Implementation of probability distributions with Microsoft Office Excel – implementing probability distributions on a spreadsheet requires recourse to facilities for random number generation, and major spreadsheets provide this facility via a mathematical function (Smith, 1994). Smith (1994) reviewed that in Excel the function RAND() returns a random number greater than or equal to 0 and less than 1. To create a probability distribution, the net cashflow value is replaced by a formula; for a normal distribution, the formula is:

a + b*(RAND()…+ RAND() – 6)

Sources: Smith (1994).

Where a is the mean of the distribution; b is the standard deviation and there are a total of 12 cells to the RAND() function (Smith, 1994). Taking the cell that contains the net cashflow for year 1, the formula to be entered is:

15,000 + 4,500*(RAND()…+ RAND() – 6)

Sources: Smith (1994).

Every time this cell is recalculated a value for the year’s net cashflow will be drawn randomly from a normal distribution with a mean of 15,000 and a standard deviation of 4,500 (Smith, 1994). The cells containing the net cashflows for years 2 to 5 utilize the same formula, with appropriate values for the mean and standard deviation inserted in each case (Smith, 1994).

By utilizing the formula on the net cashflows, the yearly net cashflow figures will be change where NPV also changes. Smith (1994) noted that a number of recalculations have to be undertaken to build up a distribution of NPVs. “By carrying out 20 simulations had produce NPVs that range from -£9,528 to +£30,304 and have a mean value of £14,064. The dispersion around the mean reflects the uncertainty associated with the cashflows. In terms of managerial decisions the benefit of such a simulation is that those charged with making capital budgeting decisions can quickly appreciate that there is a possibility that in the investment project, the NPV may prove to be negative. Not only this possibility highlighted but the distribution also show that 15 percent of the simulations generated a negative NPV” reviewed by Smith (1994).

## 2.5. Summary of literature review.

As discussed above, there have various methods and approaches to overcome the limitations of NPV technique in capital budgeting. One of them most recommended by analysts and applied by corporations is real options methods. Each corporation applies different approach of real option methods according to their own corporation’s goal, missions, strategy and culture etc. The approaches of real option methods had been evaluated into process view, re-evaluation of NPV and framework. Besides that, there have some researchers introduce simulation such as Monte Carlo Simulation for risk and uncertainty analysis in capital budgeting which the NPV cannot overcome the issue. When an investment or a project shows a positive NPV, the corporation should carry on the project. However, the traditional NPV technique unable to take some important criteria (eg. flexibility, risks and uncertainty etc) into consideration when valuing the present value of a project. Unlike real options methods and Monte Carlo Simulation which can deal all these drawbacks of traditional NPV technique.

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