Printer Friendly

Project risk measurement trough beta calculation.


During the last thirty years many scientists worked on the problem of risk level measurement through the beta coefficient. Papers on beta released by Hamada (1972) and Rubinstein (1973) resulted in a wider application of the beta and induced new discussions about its applicability. The main purpose of this study is to define the possibility of using beta in terms of risk level quantification in cases of the start-up business's project as well as the project that presents new business activity for the investor. The importance of defining beta coefficient in these cases is reflected in determination of the project's cost of capital in evaluating justification of project financing. The problem is that, in concerned cases, it may not be possible to estimate the project's risk level without the difficulties in the beta calculation and its ways of solution are the subject of this paper. Due to the above-mentioned, the authors expect to find the optimal way to calculate project's risk level, depending on the project's characteristics. For risk level quantification in concerned cases we will propose the Pure Play method, the Hamada formula and the Accounting beta technique, which can provide solution for described difficulties that occur in risk level measurement and lead to more accurate result of analysis.


With investment in the project or other property form the investor is taking the risk of achieving a certain yield that is expected as a result of investment and waiting for its return. "The project cost of capital depends on the use to which that capital is put. Therefore, it depends on the risk of the project and not on the risk of the company" (Brealy et al., 2001). Assessing the quality of the investment project or property in which invests, estimates probability of achieving certain results and the probability of deviation from the desired yield. "From the standpoint of quantification of uncertainty on investment, risk can be defined as knowledge of a situation in which, as a consequence of a decision, a number of results may occur. Probability of realizing of each result is known to the decision maker" (Orsag, 1997). Given that this work deals with the problem of determining the risk of investment in projects for the above-mentioned cases, it is a special reference to the individual project risk. "Individual risk of the project is presented by dispersion of project profitability from its expected profitability. It is a risk that the project has for itself, that is risk of the project observed in isolation" (Orsag, 2002). "The expected rates of return demanded by investors depend on two things: (1) compensation for the time value of money (the risk-free rate rf), and (2) a risk premium, which depends on the beta and the market risk premium" (Brealy et al., 2001). Project beta determines the cost of capital that influences on discount rate to be applied to project net cash flow at discounted cash flow techniques. The project beta is determined by the standard deviation of projects profitability rate and the profitability of market indices and their correlation.

[[beta].sub.P,T] = [[sigma].sub.P]/[[sigma].sub.T] [r.sub.P,T] (1)

Where ([[sigma].sub.P]) stands for standard deviation of project profitability, ([[sigma].sub.T]) for standard deviation of market profitability and ([r.sub.PT]) for project and market profitability correlation.

The project beta may have a value of 0 or in some cases even up to 4. The higher is the value of beta, proportionately is higher the risk of project's cash flow indraft. This value is important because of its correlation between risk and expected yield. "The riskier projects will result in taking the company beta upwards and this will result in the weighted-average cost of capital getting higher" (Parasuraman, 2002). If the result of beta calculation is 1, the project's risk is the same as the one that investor would take over if he would invest in diversificated portfolio of securities on the observed capital market. If the beta is greater than 1 the risk of the project for investors is in that case higher than market risk and is therefore necessary for analyst to adjust the discount rate which is beeing applied to cash flow. The opposite also applies.

Discount rate and required rate of return are possible to identify through the weighted average cost of capital. Beta coefficient on this parameter affects through the model for identifying the price of investor's capital used in the project financing. Therefore, project's level of risk increases or decreases the cost of investor's capital. However, in practice, especially in the case of less-developed economic systems, it is difficult to determine the real value of a project beta. In these cases it is possible to apply below elaborated methods of beta calculation.


In the case of lack of necessary data, it is possible to calculate beta using and combining the following methods.

3.1 Accounting beta

One of the serious limitations in beta calculation process can be a lack of historical rates of return from investments in securities of an observed company. In that case it is possible to use historical accounting data such as asset profitability which is determined by ratio of its EBIT coefficient and its total assets.

Ap = EBIT/TA (2)

Where (Ap) stands for asset profitability, EBIT for earnings before interests and taxes and (TA) for total assets.

This method can be used as an alternative for beta calculation for Inc. companies whose securities are not quoted on the capital market, business entities organized in other legal forms (such as Ltd.) and projects. Based on projections of financial statements of investment project (being considered as a separate entity, separate from the originator company) calculates the project profitability in each operating year using Eq. (2). In the next step the standard deviation of asset profitability throughout the observed time period and the beta of the project, using the Eq. (1), are being calculated.

3.2 Pure Play Method

If an observed project originator is a start-up company, the required historical data (the accounting data or data related to market movements), which are the basis for the beta calculation by previous equations in this case will not be available. Applying of the Pure Play method can be a solution of this problem. By this model it is possible to identify a comparable company, as the company of the same size, industrial sector and trade market as a concerned project and determine its beta. Sometimes finding a comparable company with securities that have quotation on the capital market will not be possible. In this case it is possible to combine Pure Play method and the method of Accounting beta. This means that beta will be calculated from the accounting data of comparative companies (with the help of arithmetic mean of obtained scores in the case of several comparative companies) and will be seen as a representative coefficient for the observed industry. This method can be used in cases of calculation the required rate of return for a division of a corporation that has risk characteristics that differ from the risk characteristics of the overall corporation (Collier, 2006).

3.3 Hamada formula

Beta needs to reflect the effect of financial leverage that the investor uses. Robert Hamada (1972) developed a model that connects beta of a company funded with creditor funds with beta of the company entirely funded by private funds. Eq. (3) shows the calculation of unlevered company beta by this model.

[beta]U = [beta]L/(1 + (1-T)*D/E) (3)

Where ([beta]L) stands for beta of a levered company, ([beta]U) for beta of an unlevered company, (T) for tax rate, (D) for debt and (E) for equity.

The beta of a company in the absence of debt (financial leverage) is first being calculated and afterwards is being adjusted to the value of the project financing structure. Accordingly, by identifying the comparable companies in the projects branch of activity, it is possible to calculate the average beta of levered companies, which reflects the average leverage in the same branch and therefore can be seen as representative for the branch of activity observed in a particular market. This method allows adjustment of the beta calculated through Pure play method to the observed project.

By combining the above-described methods it is possible to solve the following difficulties that occur in the concerned project's beta calculation:

* the problem of determining the market value at the Inc. companies that do not have a quotation on the capital market or companies organized in other legal forms is solved by estimating the market value based on data available (such as accounting data) as "second best" solution.

* in the case of the start-up companies projects it is especially complicated to determine the beta considering that neither the market nor historical (accounting) data are available. In that case, the beta calculation is formed under projected financial statements and the expected projects cash flow. In this case, it is important that the project is based on objective data and calculation of the annual yield.

* it is difficult to isolate a monoindustial company that will have absolutely the same activity and perform its activities in the market as the observed investment project.

* the projects for which the required returns are being calculated are mainly related to the longer time period in which the change of height of beta coefficient is highly probable. In the initial period projects can have a high level of beta coefficients, but after the start when their realization is beyond doubt, it is likely that their risk level will be reduced, and therefore project beta should be decreased, depending on the performance of operations and realization of the planned sizes. Therefore, application of the same value of a beta coefficient for the entire lifetime of the project results with projection which will probably vary from the actual results. Given the above mentioned difficulties in the beta calculation as essential element in the calculation of weighted average cost of capital, it has to be taken in consideration that the impact of evaluation and combination of different models of beta calculation by the analyst is significant.


This study emphasizes the possibility of using beta coefficient in terms of risk level quantification in cases of the start-up company projects as well as projects that present new business activity for the investor. The authors tried to shed light on difficulties that are related with the conventional approach in concerned cases project appraisal, and explained why the alternative should be implemented instead. The proposed alternative (combination of the Pure Play method, the Hamada formula and the Accounting beta depending on concerned project's characteristics) was defined with the help of empirical testing that showed that its using in the beta calculation process would lead to more accurate results.

With beta calculation, processed through the elaborated methods, in the project evaluation, analyst comes to more precise results and therefore improves the decision-making process, as by selecting the best alternative due to the project's risk level and expected yield, he or she increases the likelihood of achieving the best results for the investor.


Brealey, R.A., Myers S.C. & Marcus A.J. (2001.). Fundamentals of Corporate finance, Mc Graw-Hill, ISBN: 0-07-241627-0, S.A.D.

Collier, H. W. Grai T., Haslitt S. & McGowan C. B. (2006). Computing the divisional cost of capital using the pure play method, Available from: text=commpapers, Accessed: 2009-04-06

Orsag, S. (2002). Budzetiranje kapitala: Procjena investicijskih projekata, Masmedia, ISBN 953-157-413-8, Zagreb, Croatia

Orsag, S. (1997). Financiranje emisijom vrijednosnih papira, RIFIN d.o.o., ISBN 953-96114-3-1, Zagreb, Croatia

Parasuraman N.R. (2002). Ascertaining the divisional Beta for project evaluation--the Pure Play Method- a discussion, Available from:, Accessed: 2009-04-06
COPYRIGHT 2009 DAAAM International Vienna
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2009 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Bukvic, Ivana Bestvina; Kantor, Nalanda; Buljubasic, Dinko Bukvic
Publication:Annals of DAAAM & Proceedings
Article Type:Report
Geographic Code:4EUAU
Date:Jan 1, 2009
Previous Article:Ergonomical study regarding working in standing and seating postures.
Next Article:An existence of the optimal solution for an economic growth model.

Terms of use | Privacy policy | Copyright © 2022 Farlex, Inc. | Feedback | For webmasters |