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Risk Analysis in Capital Budgeting

By: Ridwan Hendra


Capital budgeting is a process of identifying, analyzing and selecting investment to determine a firm’s expenditures on assets whose cash flows are expected to extend beyond one year. It’s an important process because capital expenditures require large investment but limited by the availability of funds (Capital Rationing), greatly influences a firm’s ability to achieve its financial objectives, and can become as a tool of control


Capital Budgeting and Risk

Uncertainties can exist when the outcome of an event is not known for certain, and when dealing with assets whose cash flows are expected to extend beyond one year, certainly, there’s element of risk in that situation. The evaluation of risk therefore depends, on decision maker ability to identify and understand the nature of uncertainty surrounding the key variables and on the other, having the tools and methodology to process its risk implications

Various rules of thumb are often used to make these risk adjustment, one of them is using a simulation method


Method Used

To compares and contrasts the deterministic and probabilistic methods as a tools for capital budgeting. The method usually used in capital budgeting is to calculate a “best estimate” based on the available data and use it as an input in the evaluation model. Capital Budgeting Method used for this paper is Net Present Value.

NPV is an indicator of how much value an investment adds to the firm. It estimates the future values of the projected variables. Generally, we utilize information regarding a specific event of the past to predict a possible future outcome of the same or similar event. If there’s a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected.

But, by relying completely on single values as inputs (see figure 1), it is implicitly assumed that the values used in the appraisal are certain. The outcome of the project is, therefore, also presented as a certainty with no possible variance or margin of error associated with it.


Conventional investment appraisal uses one particular type of probability distribution for all the variables included in the appraisal model. It is called the deterministic probability distribution and is one that assigns all probability to a single value.

Monte Carlo Simulation is a tool that imitate of some real thing, state of affairs, or process, that representing certain key characteristics or behaviors of a system using random numbers. Monte Carlo simulation adds the dimension of dynamic analysis to capital budgeting by making it possible build up random scenarios which are consistent with the analyst's key assumptions about risk.

It can modifies the standard NPV calculation from all the alternatives by adjusting NPV input by the estimated probability, that can be objective data or expert opinion (see figure 2), then simulating it. The simulation runs stage is the part of the risk analysis process in which the computer takes over. Once all the assumptions, including correlation conditions, have been set it only remains to process the model repeatedly (each re-calculation is one run) until enough results are gathered to make up a representative sample of the near infinite number of combinations possible. 

During a simulation the values of the “risk variables” are selected randomly within the specified ranges and in accordance with the set probability distributions and correlation conditions. The software records the various scenario of NPV output.

The output is not a single-value but a probability distribution of all possible expected returns. The results give a complete risk/return profile, showing all the possible outcomes that could result from the decision.


The use of multi-value instead of deterministic probability distributions for the risk variables to feed the appraisal model with the data is what distinguishes the simulation from the deterministic (or conventional) approach. Some of multi-value probability distribution is illustrated in figure 3.

Situation Reviewed

Suppose PT. X plan to invest in new machinery with two options, buy used rapier machine from Europe manufacturer or buy new rapier machine from China manufacturer. Information and assumption from each option (table 1 – table 6), can be use as an input for capital budgeting model for deterministic and probabilistic methods. Deterministic approach only uses most probable estimation and mean estimation as it input.

Data for first option, buy used rapier machine from Europe manufacturer

Data for second option, buy new rapier machine from China manufacturer

The first option offer more durable machine but riskier in initial installation because there will be no manual book, difficultness to find spare part replacement, no supporting trained mechanics from previous owner. The second option, on the other hand, offer more certain initial installation but more easily damage because of lesser quality of their machine material and spare part.


Deterministic Method Result

Unit sales for 1st year can be calculated by 1st year capacity x 12 months x capacity adjustment for installation. On the second year we add phase 1 capacity with adjusted phase 2 capacity, then from year 3, the sales become phase 1 and 2 capacity.

The revenue calculated by multiplied unit sales with unit price. Then every period net cash flow can be calculated by subtract revenue with fixed cost and variable cost. In starting year and 1st year, initial investment and phase 2 investments are also included in cash flow computation. After that we can calculate the Net Present Value of the selected alternative. Repeat the process for the 2nd alternative.

The output of the method (figure 4) show that buying new machine from China manufacturer yielding higher NPV than buying used machine from Europe manufacturer, because of that, the decision is to select the second option.

Probabilistic Method Result

Probabilistic method is not a substitute of Deterministic method but rather a tool that enhances its results. A good appraisal model is a necessary base on which to set up a meaningful simulation. Risk analysis supports the investment decision by giving the investor a measure of the variance associated with an investment appraisal return estimate.


Probabilistic method is not a substitute of Deterministic method but rather a tool that enhances its results. A good appraisal model is a necessary base on which to set up a meaningful simulation. Risk analysis supports the investment decision by giving the investor a measure of the variance associated with an investment appraisal return estimate.

With Monte Carlo simulation, use 5,000 iterations, the 1st option has 95% probability to give positive NPV, its best scenario approximately yield IDR 17,780,000,000.00 and there is 5% probability that the option yield negative NPV with its worst scenario approximately IDR (5,000,000,000.00) loss, its standard deviation approximately 3.5 billion.

The 2nd alternative has 88.9% probability to yield positive NPV and has 11.1 % giving negative NPV, but the 2nd alternative also has higher min to max range, from approximately IDR (1,170,000,000.00) to IDR 21,540,000,000.00, and its standard deviation is 4.6 billion.


In this case, using the probabilistic method, buying machine from China can give higher expected return (IDR 5.79 billion) return and higher loss probability (11.1%) than buying from machine from Europe manufacturer. Then the decision rests on the risk appetite of the decision makers, whether he/she is a risk seeker, or a risk averter.


Risk analysis using Monte Carlo simulation is a useful tool to extend the depth of capital budgeting and enhancing the investment decision. The deterministic approach has the advantage of simplicity and easy to applied but it has inability to deal with uncertainties, excluding inaccuracies of input data.

On the other hand, the probabilistic method can reduces the weakness in the deterministic method when dealing with input uncertainties, In example presented above, buying from China manufacturer using deterministic method yield IDR 6.05 billion, but when the uncertainty factor exist the expected value of the alternative, using 5,000 iteration, become IDR 5.79 billion with standard deviation IDR 4.68 billion. Therefore probabilistic method can provides more in-depth risk analysis for making decision under uncertainties like liquidity and repayment problem, bridging communication gap between the analyst and the decision maker, reduce bias, highlight area that need further investigation, screen new ideas and help to identify new opportunity. In example above, the decision maker can further evaluate each alternative, which alternative suite his/her risk appetite, what can he/she do to mitigate the downside risk of the alternative, or what contingency effect can happen from every decision alternative.

Regarding of all the superiority, Monte Carlo simulation is not a remedy of all problem. Overlooking significant inter-relationships among the projected variables can distort the results of risk analysis and lead to misleading conclusions. The analyst should take due care to identify the major correlated variables and to adequately provide for the impact of such correlations in the simulation. Risk analysis also must amplify the predictive ability of sound models of reality. The accuracy of its predictions therefore can only be as good as the predictive capacity of the model employed.



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