Project risk measurement trough beta calculation.
Bukvic, Ivana Bestvina ; Kantor, Nalanda ; Buljubasic, Dinko Bukvic 等
1. INTRODUCTION
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.
2. PROJECT RISK AND BETA COEFFICIENT
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.
3. BETA CALCULATION METHODS
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.
4. CONCLUSION
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.
5. REFERENCES
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: http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1172&con 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:
http://www.icai.org/resource_file/11628p546-549.pdf, Accessed:
2009-04-06
