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Using Real Options for the Evaluation of Venture Projects
Transcript of Using Real Options for the Evaluation of Venture Projects
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Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
Gadjah Mada International Journal of BusinessVol. 18, No. 2 (May-August, 2016): 153-185
* Corresponding author’s e-mail: [email protected]
ISSN: 1141-1128http://journal.ugm.ac.id/gamaijb
Using Real Options for the Evaluation of Venture Projects
Alexander Baranov,1 and Elena Muzyko2*
1 Faculty of Economics, Novosibirsk National Research State University; Institute of Economics andIndustrial Engineering, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
2 Faculty of Business, Novosibirsk State Technical University, Novosibirsk, Russia
Abstract: This paper considers the peculiarities of the application of the real options method for assess-ing the economic efficiency of venture investments in innovative projects from the venture fund’s posi-tion. The results of the practical use of the author’s approach for the evaluation of venture investmentswith real options are analyzed. The paper shows the applicability of the real options concept to thevaluation of the effectiveness of venture capital investments. The use of the real options method raisesthe accuracy of the estimation and enhances the instruments of the venture fund in evaluating the eco-nomic efficiency of innovative projects.
Abstrak: Artikel ini membahas kekhasan aplikasi metode real options untuk menilai efisiensi ekonomisinvestasi ventura dalam berbagai proyek inovatif dari posisi dana ventura. Hasil penggunaan praktikpendekatan penulis terhadap evaluasi investasi ventura dengan real options dianalisa. Artikel ini menunjukkanaplikabilitas konsep real options untuk penilaian keefektifan investasi modal ventura. Penggunaan metodereal options meningkatkan akurasi estimasi dan menambahkan instrumen dana ventura dalam mengevaluasiefisiensi ekonomis proyek inovatif.
Keywords: financial options; innovative project; real options; uncertainty; venture capital in-vestment
JEL classification: G24; G32; M13
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Introduction
With current financial theories, tradi-tional approaches to the assessment of theefficiency of investment projects very oftenshow their limitations, since most of them arenot suitable for projects implemented in con-ditions with high risk and uncertainty. Tradi-tional discounted cash flow analysis (the NPV-method) is based on the assumption that aftermaking a decision on starting an investmentproject, the management should follow theinitially chosen strategy even in adverse cir-cumstances. However, after starting theproject’s implementation, the company’s man-agement can change the initial plan, for ex-ample, to expand or constrict the scope ofthe project, change the “inputs” or “outputs”of the project, abandon further implementa-tion of the project, or “freeze” it for a certainperiod of time, once new information be-comes available.
In this regard new methods of valuinginnovative projects become particularly impor-tant. Among such instruments is the real op-tions method. The most important feature ofthis method is its compliance with the rapidlychanging economic environment in which acompany operates, as well as taking into ac-count the company’s managerial flexibility inmaking decisions. The real options theory canexplain the fact, which is known from prac-tice, that investors often do not abandonprojects with a negative NPV (Net PresentValue), as the situation may change for thebetter, and the real option, which is incorpo-rated in the innovative project, can be used.As a result, the net present value of the projectwill be positive.
The real options concept has developedas a result of the transfer of risk managementinstruments, that use option contracts, fromthe financial sector to the real sector of the
economy. The real options theory is an alter-native view on investments and projects’ ef-fectiveness valuations. The basis of the theoryis the assumption that it is possible to presentan investment project schematically as a finan-cial option.
A financial option is a contract, which givesthe buyer (or the owner) the right, but not theobligation, to buy or sell an underlying asset orinstrument at a specified strike price on orbefore a specified date. A real option is an op-tion on a non-financial asset. The underlyingasset of the real option is the cash flow of theinvestment project.
As venture capital investments are char-acterized by high risks and high returns, andthey often have a phased nature, the traditionalNPV method can be supplemented by othermethods, which allow a more accurate valua-tion of the effectiveness of risky projects tobe obtained. Meanwhile the existing valuationmodels of real options have certain limitationsin their application for the purpose of assess-ing venture investments.
In the article the following results wereobtained:
1. The peculiarities of the application of thereal options method for assessing the eco-nomic efficiency of venture investments ininnovative projects from the venture fund’sposition were determined.
2. The author’s modification of the real op-tions method for the valuation of venturecapital investments from the venture fund’sposition was approbated using data on ven-ture projects in the industrial sector in Rus-sia. The practical effectiveness of this ap-proach was demonstrated.
3. The application of the real options methodto assess the efficiency of investmentprojects in Russia is very limited. Unfortu-nately, this method is not widely used by
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Russian financial managers. It is knownfrom experience that only one investmentcompany uses this method (“Laboratory ofinvestments “LABRATE”). Therefore oneof the objectives of our research was theextension of the practical use of the realoptions method for project analysis in Rus-sia. So, for this case we have taken Russianinnovative project in the industrial sectorand have estimated it’s effectiveness by theorder of the initiators.
Literature Review
In Russia there are separate works onventure capital financing and real options. Butno research has been done concerning theapplication of the real options method to theventure capital financing of innovative projectsup to now. We will analyze the work of for-eign scientists concerning this problem, un-fortunately the amount of such research workis quite limited.
According to which way is chosen ofusing the real options method in venture capi-tal investing, the papers analyzed by us can besplit into four groups. We will begin our analysiswith considering the papers of the first group.Botteron and Casanova (2003) proposed anoption pricing model that made it possible toevaluate the flexibility acquired by a venturecapitalist when he staged his investment pro-cess. The authors consider the start-up valueas a value of two options, namely, a Europeancall-option and a European binary call-option.
The formula developed by Black andScholes (1973) to value a European call-op-tion and the formula proposed by Geske(1979) to value a two-stage compound Euro-pean call-option can be applied only in the caseof the constant volatility of the underlyingasset’s value. Hsu in his work (2002) modified
these formulae to evaluate options with time-dependent volatility. In this paper the processof decision-making by a venture capitalist toinvest in the staged manner is analyzed in thelight of the principal-agent problem. A ven-ture capitalist can invest up front in the formof a one-time fixed amount or he can cut hisinvestment into several stages. Staged invest-ment is treated as a compound European call-option with time-dependent volatility. To as-sess the value of this option Hsu (2002) modi-fied the Geske’s formula. Venture financinginvolving a one-time fixed amount is treatedas a straight European call-option but withtime-dependent volatility. To assess the valueof this option the author modified the Black-Scholes formula (Hsu 2002).
Gong et al. (2006) proposed a model ofthe elementary compound options valuation.They introduced time-dependent volatility intothe model of valuing a multistage compoundreal option based on the model of valuing amultistage compound real option with con-stant volatility, as proposed by Lin (2002).Willner (1995) proposed to value a start-up asa real option. To determine the dynamics ofchanging the underlying asset value, the Pois-son process instead of the Winner process wasused in the model.
Let us make a critical analysis of the pa-pers. Botteron and Casanova’s (2003) paperstated that a venture project (a start-up is noth-ing else than a project) was an underlying as-set. In our opinion the underlying asset is notthe whole venture project but a portion ofthe shares of the investee company, since aventure capitalist owns only a portion of theshares but not the whole project (start-up).
In his paper, Hsu (2002) does not givean interpretation of the Black-Scholes formulaelements. In all the reviewed papers the analy-sis is made in terms of a venture project as a
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whole. The cash flows of the venture capital-ist and the cash flows of the project itself arenot separated. No approbation of the pro-posed models of assessing the options valuebased on real innovation projects with ven-ture financing is made in the papers consid-ered above. A common feature of the papersof the first group is a high degree of math-ematization while any economic interpretationof the parameters included in the proposedmodels of valuing real options in venture fi-nancing is not given.
Let us consider the second group of papers. Intheir paper, Huixia and Tao (2010) used a bi-nomial model of option valuation in the caseof venture financing, with the focus being onAmerican-style options. However, the pecu-liarities of venture financing are not analyzed.It is not explained why it is the binomial modelthat is chosen for the venture financing case.Any approbation of the binomial model basedon real data from innovative projects with ven-ture financing is not made. Seppa andLaamanen (2001) arrived at the conclusion thatthe binomial model was more appropriate forthe valuation of venture capital investmentsthan the traditional method of discounted cashflow.
Let us now analyze the third group of papers.In Li’s (2008) paper, the decision to stage theinvestment process is viewed as a choice be-tween holding an option on investing later (aninvestment delay) and investing now to ob-tain an option on further staged investment.The authors Tong and Li (2010) claimed thatwhen making initial investments, venture capi-talists obtain an option on expansion, an op-tion on the project abandonment and an op-tion on an investment delay. We believe thatin the venture financing of innovative projects,all these three types of real options could becombined into one type, namely the com-pound call option on staged investment, which
will reflect the specificity of venture financ-ing.
Wadhwa and Phelps (2010) in their pa-per characterized corporate venture financingas a two-stage compound option. An initialventure capital investment created a com-pound growth option. Forming a strategic al-liance with a portfolio company was viewedas exercising the second stage of this option.
Let us move to the last or fourth group ofpapers. Vanhaverbeke et al. (2008) analyzedthe advantages of external corporate venturefinancing as “open innovation practices” interms of the real options. They claimed that itwas necessary to take into account the valueof the real options but they do not explainhow to assess this value or by using what mod-els.
The authors of the papers in the fourthgroup (Vanhaverbeke et al. 2008; Kulatilaka andToschi 2011) wrote about the usefulness ofthe real options theory in the analysis of ven-ture financing, but they confined themselvesto detailed verbose reasoning without makingany analysis of models of the real options valu-ation that emerged in the venture financingof investment projects. Besides, they do notmake any calculations
Also let’s make a brief review of otherstudies, in which the authors apply Geske’sformula to compound real options valuationsin multi-stage investments. Carr (1988), build-ing on Margrabe (1978) and Geske (1979),provided the valuation of sequential exchangeoptions. Lee and Paxson (2000 a) suggested atwo-point confined exponential extrapolationmethod for the American option, by extend-ing Geske and Johnson’s (1984) compoundoption approach. The value of such an Ameri-can sequential exchange option is given in Leeand Paxson (2000 b). Lee and Paxson (2001)in their work modeled the stages of R&D ex-
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pense and the ultimate discovery using realsequential (compound) exchange Americanoption models.
Herath and Park (2002) investigated amulti-stage project setting, where each invest-ment opportunity derived revenues from dif-ferent markets but shared common techno-logical resources. They extend the binomiallattice framework to model a multi-stage in-vestment as a compound real option. Jensenand Warren (2001) in their paper examinedthe practicalities of applying the real optionstheory to valuing research in the service sec-tor, where the relationship between researchand subsequent business benefits is less easilydiscerned than in most previous applicationsof the options theory in, e.g. the pharmaceu-tical industry. The paper used a compoundoptions model, the Geske model, based on athree-phase lifecycle consisting of research,development and deployment. All these pa-pers had a high degree of mathematization,while any economic in-depth interpretation ofthe parameters included in the proposed mod-els of valuing the real options was not given.
Having made a critical survey of thestudies in which the real options method wasused in analyzing the venture financing of in-vestment projects we can make the followingconclusions. In Russia not many researchers arenow working on this problem. However, stud-ies concerned with the use of the real optionsmethod for the evaluation of the efficiencyof investment projects with venture financ-ing, carried out by foreign researchers are alsoscarce. In these papers any economic inter-pretation of the parameters included in theproposed models of the real options valua-tion that emerge in the venture financing ofinvestment projects is often not given. In allof the reviewed papers the analysis has beendone from the point of view of the invest-
ment project as a whole. In our opinion, it isnecessary to separate the cash flows of theventure fund and the cash flows of the projectitself. A venture fund has its own cash flows,which are different from those of the entireproject under analysis. An approbation of theproposed models based on real innovationprojects with venture financing is not made.To our mind the case for a venture capital in-vestment is a compound real call option withtime-dependent volatility.
Methods
Venture capital investments are charac-terized by high risk levels and high uncertainty,and they often have a phased nature. More-over, each phase of a venture investment hasits own risk level. So, the model, which couldbe used for the valuation of the real optionsin the venture financing of innovative projectsshould take into account the different levelsof risk at the different phases of the invest-ment.
Geske (1979) created a formula for theevaluation of the two-stage compound Euro-pean call-option. But Geske’s formula can beapplied only in the case of the constant vola-tility of the underlying asset’s value. Hsu inhis work (2002) modified this formula to evalu-ate options with a time-dependent volatility(the modified Geske’s formula).
In this paper we used the modified ver-sion of Geske’s formula, but we have changedthe sense bearing understanding of the entryparameters of the model. We believe that whenassessing the value of the real options in aventure capital investment, it should be takeninto account that there are differences betweenthe cash flow of the entire innovative projectand the cash flow of the venture fund. Forinstance, the venture fund’s investment may
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be less than the investment for the entireproject. Positive cash flows for the venturefund are less than the positive flows for theentire innovative project. Thus, we are con-sidering the economic efficiency of ventureinvestments in innovative projects from theventure fund’s position. Figure 1 shows a sche-matic representation of the venture investmentbuying a share purchase call option at thebeginning of the investment process.
Let’s appraise the efficiency of the in-novative project from the point of view ofthe venture fund, both by the traditionalmethod of the discounted cash flow (a stan-dard calculation) and using the real optionsmethod. We will now describe the suggestedprocedure in detail.
The first step is to determine the innova-tive project’s efficiency from the viewpoint ofthe venture fund using the traditional methodof discounted cash flows. This step includesan estimation of the cash flows of the ven-ture fund, it’s net present value and the inter-
nal rate of return (NPVv and IRRv respectively)for different variants of the venture fund’sshare in the charter capital of the investeecompany (starting from 25% with a step upof 4%, for shares of 29%, 33%, 41%, 45%,49%) and different values of the price-earn-ings ratio for the shares (P/E = 2, 3, 4, 5, 6,7).
The second step is to determine the inno-vative project’s efficiency from the viewpointof the venture fund by using the real optionsmethod (an estimation taking into account thevalue of the compound call option). This stepincludes the following: An estimation of theinternal rate of return of the venture fundIRRv
option and the net present value of the ven-
ture fund NPVvoption
taking into account thevalue of the compound call option as an ad-ditional cash flow, which appears at the verymoment of the venture fund’s “exit” from thebusiness of the investee company.
The compound call option for the ven-ture fund with a changed sense bearing un-
Figure 1. A Schematic Representation of a Venture Investment by Buying a Share Pur-chase Option at the Beginning of the Investment Process
To is the time when a ven-
ture fund buys a com-pound call option at the
price Iv
0 to purchase a
portion of the shares ofthe investee company atthe time T
1.
T1 is the time of purchasing a
portion of the shares of theinvestee company at the price
Iv
1, i.e. the exercise of an exter--
nal option, which means the pur-chase of an internal option onmaking a profit on selling theshares of the investee companyat the time T
2.
T2 is the time of selling
the shares held by theventure fund, i.e., gettingassets in the form of theprofit from selling theshares of the investeecompany at the price
Iv
2.
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derstanding of the entry parameters could beestimated with a developed version of theGeske model (see formula (10.1), Appendix10). As the size of the paper is limited thedetailed definitions of all parameters are givenin Appendix10.
Now we will describe the technique ofthe compound call option’s estimation in de-tail. The critical value of the investeecompany’s equity shares at the moment T
1 can
be found from the equation (10.2) (see Ap-pendix 10).
It should be said that as the venture fundusually has a portfolio of investment projects,stopping its investment, at moment T
1, in the
project will allow the venture fund to reallo-cate its limited resources to other projects. Inour interpretation, the value V
T1 is the evalua-
tion of the business at the moment T1:
.....................(1)
To obtain the VvT1
the value VT1
is mul-tiplied by the fund’s share. There is no analyti-cal solution of the equation (10.2). So, to findthe figure for the critical value of the investeecompany’s equity shares at moment T
1 it is
necessary to use an optimization method. Suchoptimization procedures as Newton’s methodand the conjugated gradient method are real-ized in Microsoft Excel. Since these methodsgive practically the same result, we can use ei-ther of them.
Selling the shares at moment T2 the ven-
ture fund will lose the current period’s profitin proportion to its share of the charter capi-tal in the investee company. We consider thisfigure to be its implicit costs and the exerciseprice of the internal call option:
I2v = NPAT
total Exit * S................(2)
where NPATtotal Exit
is the net profit (total) inthe year of the “exit” by the venture fund fromthe business it invested in; S is the share ofthe venture fund in the charter capital of theinvestee company.
The current value of the underlying as-set in our interpretation is the current valueof an equity share of the investee company,which is owned by the venture fund (Vv). It isthe evaluation of the income that the venturefund will get from the sale of its shares.
The risk-free interest rate r in our calcu-lations will be 7 percent. This figure is takenas an average of deposit rates for alternativeassets like long-term deposits in the largest andsafest Russian banks as on 19.09.2011 (“TheRosselkhozbank,” “The Sberbank of Russia,”“Gazprombank,” and the “VTB Group”).
1
is the variability index of the NASDAQ Bio-technology Index (NBI) over a 7 year period(from 14.10.2004 to 14.10.2011) (NASDAQBiotechnology Index. URL:http://w w w . n a s d a q . c o m / d y n a m i c /nasdaqbiotech_activity.stm. Date of access:09.09.2011). It was also decided to use the NBIindex over a 7 year period and not just for thelast year only, because this 7 year time periodincluded the World financial crisis (2007, 2008and 2009). The standard deviation of theNASDAQ Biotechnology Index equals 15.44percent. The variation coefficient of theNASDAQ Biotechnology Index will be 12.78percent. Thus,
1 = 12.78 percent.
The compound call option value is prac-tically independent on the
2 values. No sig-
nificant impact of 2 on the value of the com-
pound call option is explained mathematicallyfrom the formula (10.1, Appendix 10). In equa-tion (10.1)
2 is included in the first additive
component as a parameter, that influences thevalue of N
2:
EPNPATV TT /11
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160
2 2 22 1 1 1 1 2 2( , ; )N h l
.
Let’s convert the sum: 2 21 1 2 2l .
We put the value of l (see formula (10.4), Ap-pendix 10) and get the fraction:
In the obtained fraction the parameter
2 enters both the numerator and denomina-
tor. This explains the contradictory influenceof
2 on the value of the compound call op-
tion. Furthermore, the parameter 2 enters the
formula for calculating the compound calloption [see (10.1) with a positive sign (the firstcomponent) or a negative one (the secondcomponent)]. Thus, the increase of
2 in the
first component is compensated by its growthin the second component N
2. However, the
parameter 2 influences the venture fund’s
decision about its investment as it is a param-eter of the equation (10.2).
When calculating the compound calloption’s value (see formula (10.1)) it is neces-sary to calculate the two-dimensional standardnormal distribution functions:
N2(h,l;)
as well as the standard normal distribution
function ).(1 hN The two-dimensional normal
distribution function is defined by the prob-ability density f (x,y):
where a, b are mathematical expectations ofstochastic variables x, y;
x ,
y are the mean
square deviations of stochastic variables x, y;
x,y is the correlation coefficient of the sto-
chastic variables x and y.
The normal distribution with the math-ematical expectation 0 and the standard de-viation 1 is called the standard normal distri-bution. The two-dimensional standard normaldistribution function F (x,y) takes the form:
.........................................................(4)
where (x,y) is a two-dimensional random vari-able;
x,y is the correlation coefficient of the
random variables x and y. The calculation ofthe two-dimensional standard normal distri-bution functions including double integralscan be made using the Maple 14 programpackage. The one-dimensional standard nor-mal distribution function can be calculatedusing the Microsoft Excel statistical function.
Results and Discussion
The author’s modification of the realoptions method for determining the valuationof venture capital investments from the ven-ture fund’s position was approbated using datafrom a real venture project in the industrialsector in Russia. The data from this real com-pany were used to construct a financial model,to make calculations and to draw conclusions.The company’s management kindly providedus with the initial data for our calculations,with the condition that we will not disclosethe company’s name and the name of its prod-ucts.
This company uses innovations in itsmanufacturing process and is going to imple-ment an innovative project. The core purposeof this project is to organize the production
)1(2
1exp
12
1),(
2,
2
yxyx
yxf
12
1),(
)2()1(2
1
2
222
dxdyeyxFl yxyxh
),;,( 2221
211
212 lhN
N2(h,l;)
2 2 2 21 1 2 2 1 1 2 22 2
2 1 1 2 2 2
2 2 2 2 2 21 1 2 2 1 1 2 2 1 1 2 2
1 1ln ( ) ln ( )
2 ( ) 2V V
r rI I
2 2 2 21 1 2 2 1 1 2 2
2 1 1 2 2 2
2 2 2 2 2 21 1 2 2 1 1 2 2 1 1 2 2
1 1ln ( ) ln ( )
2 ( ) 2V V
r rI I
,)()()(
2)(
2
2
2
2
yyxx
bybyaxax
........(3)
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of its innovative products using its own pro-duction facilities. The project will increase thecompany’s profits, as the increase in its pro-duction capacity will ensure the growth ofsales associated with its introduction of newproducts onto the market, and increase themarket share of its existing products.
The total amount of financing requiredfrom external sources to implement the projectis 232,000,000 Rubles (7,282,000 USD). Sincethe subject of our analysis is the venture fundlet us consider the financing of the project bythe venture fund only. It is assumed that theventure fund will invest on a staged basis:35,000,000 Rubles (1,100,000 USD) in 2009and 197,000,000 Rubles (6,182,000 USD) in2010. The company-initiator of the project inits turn will invests the following resources:Its intangible assets (Russian, European andAmerican patents), a well-known brand name,the know-how (technology and formulationof the products), its unique equipment (thecompany-initiator was actively involved in thedevelopment of this equipment, with theknow-how being partly realized in this equip-ment). The cash flow forecast for the entireinnovative project is presented in Appendix1. The calculated indicators of the economicefficiency of the entire project by the tradi-tional discounted cash flow method (the NPV-method) are given in Appendix 2. We haveappraised the efficiency of the innovativeproject from the point of view of the venture fundby the traditional method using the NPVmethod (a standard calculation) and using thereal options method.
Let us determine the innovative project efficiencyfrom the viewpoint of the venture fund by the tradi-tional NVP method (a standard calculation). Frompractical experience it is known that a venturefund, as a rule, considers the possibility of in-vesting in a project beginning with 25% plus
one share of the investee company (purchas-ing a blocking parcel of shares). The blockingparcel of shares allows their owners to imposea veto on the Board of Directors’ decisions.The venture fund has its own cash flows, whichare separate from the general cash flows forthe entire project. The composition of theventure fund’s financial flows is shown in Table10.1, Appendix 10.
Let us take eight variant methods of cal-culating the cash flows of a venture fund. Wewill calculate the venture fund’s cash flows,and the indicators of the fund’s investmenteffectiveness IRRv and NPVv, for differentvariants of the venture fund’s share in the eq-uity capital of the investee company. The nec-essary calculations for every variant will bemade using various values of the P/E (Price-Earnings ratio for the shares): For P/E = 2, 3,4, 5, i.e., the rate of return is 50 percent, 33.3percent, 25 percent, and 20 percent per yearwhile for P/E = 6 and 7 the rate of return is16.7 percent and 14.3 percent per year respec-tively.
Now let us calculate the cash flows,NPVv and IRRv of the venture fund for thedifferent years of the venture fund’s exit fromthe business: In the years 2018, 2017, 2016,2015, 2014 and 2013. The venture fund willexit from the investee company in the yearwhen the IRRv values of the venture fund areat their maximum.
The results of the standard calculationof the venture fund’s internal rate of returnIRRv for the different years of the fund’s exitfrom the business of the investee companywith different levels of shareholding by thefund, and different P/E values are given inAppendix 3. This calculation is referred to asthe “standard” because it is made without tak-ing into account the value of the compoundcall option.
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The calculation of the cash flows for theNPVv and IRRv of the venture fund for thedifferent years of “exit” have demonstratedthat the venture fund must exit the investedbusiness in 2018 because this year sees thehighest internal rate of return for the venturefund. The venture fund will vary its share inthe equity capital of the investee companyfrom 25 percent to 49 percent because the cur-rent owners of the company want to retainthe majority shareholding.
Let us calculate the cash flows of theventure fund and the returns on investmentIRRv and NPVv for the year of “exit” 2018for different levels of shareholding by the ven-ture fund in the equity capital of the investeecompany (starting from 25% with a step of4%, for shareholdings of 29%, 33%, 41%,45%, 49%) and different values of the price-earnings ratio for the shares (P/E = 2, 3, 4, 5,6, 7) using the traditional NPV-method. Toobtain the net present value for the fund NPVv
we shall discount the cash flows at the ratesof 20 percent, 30 percent and 35 percent,which are widely used for appraising projects
in Russia by venture capitalists. The results ofthe standard calculation of the venture fund’sinternal rate of return IRRv for the venturefund’s exit from the business of the investeecompany in 2018 are shown in the left part ofthe Table 4.1, Appendix 4.
Let us analyze the obtained results. Weknow from our practical experience that ac-ceptable internal rates of return to the fundstart at 20 percent. According to our calcula-tions the IRRv acceptable to the fund is ob-served with a 25 percent shareholding, and aP/E = 7: IRRv = 20 percent. Although thisreturn, at only 14.3 percent, is rather low.
With the share of the venture fund inthe total equity of the investee company at 29percent the IRRv equals 20 percent or moreonly when the P/E = 6 (IRRv = 20%) or theP/E = 7 (IRRv = 22%). However the obtainedinternal rates of return, while acceptable, arestill rather low (“lower limit”). AcceptableIRRvs for the fund with the P/E = 5 and P/E= 6 are achieved with a shareholding at either45 percent or 49 percent: For a 45 percentshare at P/E = 5, the IRRv = 25 percent, at P/
Figure 2. The Correlation between the Internal Rates of Return for the Venture Fund(IRRv) and the Shares Held by the Fund
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E = 6, the IRRv = 27 percent; with a 49 per-cent shareholding at P/E = 5, the IRRv = 26percent, and at P/E = 6 the IRRv = 29 per-cent. With the fund’s shareholding at 41 per-cent and a P/E = 6 the IRRv = 26 percent.Thus, the higher the shareholding of the eq-uity capital of the investee company by theventure fund and the higher the P/E ratioare, the higher is the internal rate of returnfor the venture fund (see Figure 2).
To calculate the NPVv of the fund let usget the net present value of the fund’s cashflows according to the so called “venture” dis-count rates of 20 percent, 30 percent and 35percent. With the IRRv of the venture fundless than the discount rate, the NPVv of theventure fund is negative. The results of thestandard calculation of the venture fund’sNPVv are given in the left part of Table 5.1,Appendix 5.
We see that the positive NPVv of theventure fund starts with the fund’sshareholding at 29 percent. With a P/E = 6,the NPVv is 370,000 Rubles; at a P/E = 7, theNPVv is 27,652,000 Rubles. With the fund’sshareholding at 33 percent, the NPVv of thefund is positive only when the P/E = 6 (NPVv
= 27,892,000 Rubles) and at P/E = 7 (NPVv
= 58,937,000 Rubles). But the value P/E = 7,that is, a return of 14.3 percent per year israther low. Also the positive NPVv of the ven-ture fund for shareholdings of 29 percent, 33percent, 37 percent, 41 percent, 45 percent and49 percent is only when the discount rate is20 percent, which is the bottom limit for a“venture” rate.
For the discount rates of 30 percent and35 percent the NPVv is negative. The NPVv ispositive with the discount rate equal to 30percent only when the fund’s shareholding is49 percent and the P/E = 7 (NPVv =8,825,000 Rubles). Thus, on true “venture”
terms acceptable to the fund, the NPVv ofthe fund is negative, that is, the project doesnot provide sufficient returns to the venturefund and should be rejected by the investmentcommittee.
Let us evaluate the innovative project from theventure fund’s position using the real option’s method.The zero moment is the year 2009: Iv
0=
35,000,000 Rubles (according to the cash flowforecast, for the implementation of the projectin 2009 an external investment of 35,000,000Rubles is required) (see Appendix 1). This sumof 35,000,000 Rubles is needed to pay for theadministrative expenses and approvals (moni-toring of the project, the investment agree-ment and the land lease); the design (feasibil-ity study (a booklet), a working draft, engineer-ing works, and (gas) energy supplies) and build-ing construction (pre-payment, basement andground floor construction). Thus, the periodof expiration of the compound (external) calloption T
1 is 1 year. The period of expiration
of the internal call option T2 is 9 years. As we
are calculating the value of the compound calloption for the venture fund at the moment ofinvestment, that is, at the moment when adecision to invest has been taken, t is the start-ing moment: t = 0.
= T
1 -
t= 1 year;
= T
2 -
T
1= 9
-
1= 8 years;
= T
2 -
t=
+
= 9 years
Thus, 2 = T
2 – T
1 is the period of time
the venture fund stays in the business of theinvestee company;
1 is the moment before
the fund makes an investment in the company,in return for a share of its charter capital. Inthe case of the expiration of the compound(external) call option by the venture fund atthe moment T
1 it will make an investment Iv
1
in the amount of 197,000,000 Rubles. Thepresent value of I
1discv discounted will be equal
to 184,112,000 Rubles.
Baranov and Muzyko
164
Let us take one example – for the fund’sshareholding of 49 percent and a price-earn-ings ratio for the shares P/E = 6, the venturefund’s investment at the moment T
2 will be
(see Formula 2):
Iv2 = NPAT
total
in 2018 * the fund’s share =
591,235,000 Rubles * 0.49 = 289,705,000Rubles. The present value of Iv
2disc will be
157,580,000 Rubles.
Vv is the value of the underlying assetof the internal call option at the moment ofits expiration, that is, in the year 2018, at thenet present value at the moment of evalua-tion. The assets the venture fund acquires theright to buy at the moment T
1 are nothing but
the venture fund’s income it can get at themoment T
2 after selling the shares bought at
the moment T1. The value Vv is nothing but
the terminal value of the project for the ven-ture fund TERv in the year of the “exit” ofthe fund from the business of the investeecompany (in the year 2018). It is the evalua-tion of the income that the venture fund willget from the sale of its shares. For example,for the fund’s shareholding of 49 percent with
the price-earnings ratio for the shares P/E =6 the Vv will be:
Vv= 485,412,000 Rubles * 0.49 * 6 +47,570,000 Rubles= 1,474,682,000Rubles.
The net present value Vv at the moment zerowill be 802,129,000 Rubles.
Let us calculate the compound call op-tion value using formula (10.1) (Appendix 10)for various values of
2. Figure 3 shows the
graph of the compound call option value’sdependence on the
2 values. It is seen on the
diagram that the compound call option valueis practically independent of the
2 values.
Figure 4 shows the graph of the depen-dence of the threshold value of the investeecompany’s equity shares at the moment T
1,V
T1,
on the different 2 values.
The diagram shows, that with the reduc-tion in uncertainty and risk of the operationsof the investee company over the time period(T
1, T
2),
2, the threshold value of the investee
company increases. This could be explainedin the following way: According to Black and
Figure 3. The Diagram of the Compound Call Options’s Value Dependence on the 2
Values
165
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
Sholes’ formula, with the decrease in the levelof uncertainty the option value will decline.In other words, in order to reach the same levelof profit with a lower level of uncertainty andat a lower option value at the moment T
1, the
price of the investee company’s businessshould be higher. In this case the decrease inthe option value, as a result of the decrease in
2, is compensated for by the higher value of
the business at the moment T1.
This result, in our opinion, shows thecontradiction between the traditional methodsof investment effectiveness’ evaluation and thereal options approach. In the first case a posi-tive decision on investment will be more likelyin the case of the lower volatility of the un-derlying asset, and, therefore, with the loweruncertainty of the development of the project.In the second case the high level of uncer-tainty is considered as a factor contributing tothe growth of the assets’ value, generated as a
result of the investment project’s implemen-tation. Since the compound call option valueis practically independent of the ó
2 values, let
us take the maximum ó2 value (the “worst”
case) as a value of the riskiness of the investeecompany’s operations during the time period(T
1, T
2), under the assumption that the risk level
will diminish over time. Thus, 2 =10.22%.
Let us make a variant calculation of thecompound call option value for the venturefund with different levels of the fund’sshareholdings in the investee company’s char-ter capital. The results of calculating the com-pound call option values for the different lev-els of the venture fund’s shareholdings areshown in Appendices 6–9. The results of cal-culating the value of the compound call op-tion for the various shareholdings by the fundin the charter capital of the investee companyat different values of P/E are represented inFigure 5.
Figure 4. The Diagram of the Dependence of the Threshold Value of the InvesteeCompany’s Equity Shares at the Moment T
1 on the
2 Values
Baranov and Muzyko
166
Let us calculate the internal rate of re-turn of the venture fund IRRv and the netpresent value of the venture fund NPVv tak-ing into account the value of the compound call optionas an additional cash flow of the venture fund, whichappears at the moment T
2 (in 2018), that is, at
the moment of the “exit” of the venture fundfrom the business of the investee company.The calculated results of the internal rate ofreturn (IRRv) for the venture fund, taking intoaccount the compound call option value areshown in the right part of Table 4.1, Appen-dix 4. The calculated results of the net presentvalue for the venture fund (NPVv), taking intoaccount the compound call option value areshown in the right part of Table 5.1, Appen-dix 5.
Let us compare the calculations of NPVv
and by the traditional method of the dis-counted cash flow and by taking into accountthe value of the compound call option. Fig-ure 6 represents the dependence of the inter-nal rate of return of the venture fund on thefund’s shareholding in the standard calculation.
Figure 7 shows the dependence of the inter-nal rate of return of the venture fund on thefund’s shareholding in calculations taking intoaccount the value of the compound call op-tion.
Figure 8 shows the net present value ofthe venture fund with 49% of the charter capi-tal of the investee company at various P/Evalues and the discount rate at 20 percent. Fig-ure 9 demonstrates the net present value ofthe venture fund with 49% of the charter capi-tal at various P/E values and the discount rateat 35 percent. The standard calculation of theinternal rate of return of the venture fund andthe calculation with the real option are pre-sented in Figure 10.
So, we can observe that when incorporating the estimate of the real option,the internal rate of return and the net presentvalue of the venture fund improve. In the cal-culations using the real options method, theinnovative project has a positive value andshould be funded by a venture capital inves-tor.
Figure 5. The Value of the Compound Call Option for Various Shares of the Fund in theEquity Capital of the Investee Company at Different P/Es, in Thousands ofRubles
167
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
Figure 6. The Dependence of the Internal Rate of Return of the Venture Fund IRRv onthe Fund’s Share (A Standard Calculation)
Figure 7. The Dependence of the Internal Rate of Return of the Venture fund IRRv on theFund’s Share (A Calculation Taking Into Account the Value of the CompoundCall Option)
Baranov and Muzyko
168
Figure 8. NPVv of the Venture Fund with 49 Percent of the Equity Capital at Various P/E Values and the Discount Rate at 20 percent
Figure 9.NPVv of the Venture Fund with 49 percent of the Equity Capital at Various P/EValues and the Discount Rate at 35 percent
-5 0,0 00
0
5 0,0 00
10 0,0 00
15 0,0 00
20 0,0 00
25 0,0 00
30 0,0 00
35 0,0 00
40 0,0 00
45 0,0 00
P /E = 2 P /E = 3 P/ E = 4 P /E = 5 P /E = 6 P /E = 7
NPV
v, in thousands of Rubles
stand ard c alc ulat ion of N PVv (in th ousan ds of Rubles)
c alculat ion of NP Vv taking in to acco un t th e value of th e c om po und call o ption ( in tho usands o f Rub les)
-120,000
-100,000
-80,000
-60,000
-40,000
-20,000
0
20,000
40,000
60,000
P/E = 2 P/E = 3 P/E = 4 P/E = 5 P/E = 6 P/E = 7
NPV
v, in thousands of Rubles
standard calculation of NPVv (in thousands of Rubles)
calculation of NPVv taking into account the value of the compound call option (in thousands of Rubles)
NP
Vv ,
in t
ho
usa
nd
s o
f R
ub
les
NP
Vv ,
in t
ho
usa
nd
s o
f R
ub
les
169
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
Conclusion
1. The peculiarities of the application of thereal options method for assessing venturecapital investments in innovative projectswere revealed. The options approach isapplicable to the evaluation of innovativeprojects by venture capitalists, but only tak-ing into account the specific features ofventure investments.
2. The author’s modification of the real op-tions method from the point of view of itsapplication to the venture capital’s financ-ing of innovative projects and its approba-
tion using data on venture projects werepresented. The entry parameters of themodified version of Geske’s formula wereconstrued from the venture fund’s position.
3. The practical viability of the author’s ap-proach was demonstrated. The use of thereal options method raises the accuracy ofthe estimation and enhances the instru-ments of the venture fund in evaluating theeconomic efficiency of innovative projects.This will allow the practical use of the realoptions method for analyzing projects byventure funds to be expanded.
Figure 10. The Standard Calculation of IRRv and Calculation of IRRv Taking Into Ac-count the Value of the Compound Call option at P/E=6 for the Fund’sShareholding at 24 percent and 49 percent
0%
5%
10%
15%
20%
25%
30%
35%
40%
for venture fund's share 24%
for venture fund's share 49%
17%
29%
22%
36%
standard calculation of IRRv
calculation of IRRv taking into account the value of the compound call option
Baranov and Muzyko
170
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Black, F., and M. Scholes. 1973. The pricing of options and corporate liabilities. Journal of Political Economy81 (3): 637 - 659.
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APP
EN
DIX
1, T
able
1.1
. Cas
h F
low
For
ecas
t of
the
Ent
ire
Pro
ject
(in
tho
usan
ds o
f R
uble
s)
Sour
ce: T
he a
utho
r’s
calc
ulat
ion
resu
lts o
btai
ned
by th
e in
nova
tive
pro
ject
fina
ncia
l mod
el
Ind
icat
ors
20
09
2010
20
11
2012
20
13
2014
20
15
2016
20
17
2018
Cas
h f
low
fro
m o
per
atio
ns
28,6
67
10,8
35
59,4
17
103,
749
44,8
34
40,8
27
77,1
52
93,9
47
114,
628
140,
129
Net
pro
fit
37,6
62
77,2
53
110,
511
140,
309
184,
208
240,
604
327,
332
398,
607
485,
412
591,
235
Plu
s: D
epre
ciat
ion
79
9 88
0 3,
081
9,75
1 9,
754
9,75
4 9,
754
9,75
4 9,
754
9,75
4
Min
us:
Incr
ease
in w
ork
ing
cap
ital
-2
4,76
7 45
,501
54
,174
46
,312
55
,157
66
,781
80
,908
98
,091
11
9,01
1 14
4,50
6
Val
ue a
dd
ed t
ax (
VA
T)
pay
able
to
th
e b
udge
t 34
,562
21
,797
0
0 93
,970
14
2,74
9 17
9,02
5 21
6,32
2 26
1,52
7 31
6,35
4
Inve
stm
ent
Inve
stm
ent
in f
ixed
ass
ets
wit
ho
ut
VA
T
2,58
9 36
,114
23
1,77
4 67
8 0
0 0
0 0
0
Fin
anci
ng
35
,000
19
7,00
0 -7
,571
-1
0,83
0 -1
3,75
0 -1
8,05
2 -2
3,57
9 -2
5,70
4 -2
7,82
9 -2
9,95
4
Div
iden
d p
aym
ents
0
0 7,
571
10,8
30
13,7
50
18,0
52
23,5
79
32,0
79
39,0
63
47,5
70
Equ
ity
inve
stm
ent
mad
e b
y th
e ve
ntu
re f
und
35
,000
19
7,00
0 0
0 0
0 0
0 0
0
Net
cas
h f
low
61
,078
17
1,72
1 -1
79,9
27
92,2
41
31,0
84
22,7
75
53,5
73
61,8
69
75,5
64
92,5
58
Mo
net
ary
fun
ds
on
th
e p
roje
ct
op
erat
or’
s ac
cou
nt
at t
he
beg
inn
ing
of
the
per
iod
10
,202
71
,280
24
3,00
1 63
,074
15
5,31
5 18
6,39
9 20
9,17
4 26
2,74
7 32
4,61
6 40
0,18
0
Mo
net
ary
fun
ds
on
th
e p
roje
ct
op
erat
or’
s ac
cou
nt
at t
he
end
o
f th
e p
erio
d
71,2
80
243,
001
63,0
74
155,
315
186,
399
209,
174
262,
747
324,
616
400,
180
492,
738
Baranov and Muzyko
172
Indi
cato
rs
Tot
al
2009
-201
8 20
09
2010
20
11
2012
20
13
2014
20
15
2016
20
17
2018
1 2
3 4
5 6
7 8
9 10
11
12
In
vestm
ent i
n fix
ed as
sets,
with
out
VA
T 27
1,791
3,
225
36,1
14
231,
774
678
0 0
0 0
0 0
Inve
stmen
t in
work
ing
capi
tal i
ncre
ase
610,
766
0 0
0 46
,312
55
,157
66,78
1 80
,908
98
,091
11
9,011
14
4,506
To
tal i
nves
tmen
t 88
2,55
7 3,
225
36,1
14
231,
774
46,9
90
55,15
7 66
,781
80,9
08
98,0
91
119,0
11
144,5
06
Posit
ive c
ash
flow
incr
ease
(net
pro
fit
plus
dep
recia
tion
min
us V
AT
paya
ble
to th
e bu
dget
) as c
ompa
red
to 2
011
afte
r com
miss
ioni
ng th
e pl
ant
430,
892
0 0
0 36
,469
-1
3,60
0 -5
,983
44,4
69
78,4
47
120,0
47
171,0
43
Tota
l pos
itive
and
neg
ative
flow
s with
re
gard
to th
e te
rmin
al va
lue
relat
ive to
P/
E =
4 (fo
r the
end
of th
e pe
riod)
1,
913,
275
-3,2
25
-36,
114
-231
,774
-10,5
21
-68,
757
-72,
764
-36,
439
-19,
644
1,03
6 2,
391,
477
Tota
l pos
itive
and
neg
ative
flow
s W
ITH
OU
T re
gard
to th
e te
rmin
al va
lue
-451
,665
-3
,225
-3
6,11
4 -2
31,77
4 -1
0,521
-6
8,75
7 -7
2,76
4 -3
6,43
9 -1
9,64
4 1,
036
26,53
7
Boo
k va
lue
of fi
xed
asse
ts a
s of
the
end
of 2
018
(term
inal
val
ue)
207,
551
Ter
min
al v
alue
rela
tive
to P
/E
2,36
4,94
0
P/E
(the
com
pany
’s pr
ofit
per y
ear i
s to
be1/
4 of
the i
nves
tmen
t, i.e
. 25%
) 4
The
inte
rnal
rate
of r
etur
n (I
RR)
with
re
gard
to th
e te
rmin
al va
lue
29,85
%
num
ber o
f the
per
iod
0
1 2
3 4
5 6
7 8
9
NPV
(with
rega
rd to
the
term
inal
valu
e)
912,
554
-3,2
25
-33,
751
-202
,440
-8,5
88
-52,
455
-51,
880
-24,
281
-12,
233
603
1,30
0,80
5
Disc
ount
multip
lier:
1.0
0 0.9
3 0.8
7 0.
82
0.76
0.
71
0.67
0.62
0.
58
0.54
Payb
ack
perio
d w
ith re
gard
to
disc
ount
ing
20
qua
rters
(5 y
ears
)
Payb
ack
perio
d w
ithou
t reg
ard
to
disc
ount
ing
25 q
uarte
rs (6
yea
rs an
d 1
quar
ter)
APP
END
IX 2
, Tab
le 2
.1. I
ndic
ator
s of t
he E
cono
mic
Effe
ctiv
enes
s of t
he E
ntir
e Pr
ojec
t (in
thou
sand
s of
Rub
les)
173
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
Baranov and Muzyko
174
APPENDIX 3, Table 3.1. Venture Fund’s Internal Rate of Return IRRv for Different Yearsof the Fund’s Exit from the Business of the Investee Company, % (standard calculation)
P/E
Year of fund’s exit from the business
2018 2017 2016 2015 2014
Venture fund’s share 24%
P/E = 2 5 2 -2 -8 -17
P/E = 3 9 7 4 -2 -9
P/E = 4 12 10 8 3 -3
P/E = 5 15 13 12 7 1
P/E = 6 17 16 15 11 6
P/E = 7 19 18 17 14 9
Venture fund’s share 25%
P/E = 2 5 3 -1 -8 -16
P/E = 3 10 7 4 -1 -8
P/E = 4 13 11 9 4 -2
P/E = 5 15 14 12 8 2
P/E = 6 18 17 15 11 7
P/E = 7 20 19 18 15 10
Venture fund’s share 29%
P/E = 2 7 5 1 -5 -13
P/E = 3 12 10 7 2 -5
P/E = 4 15 14 12 7 1
P/E = 5 18 17 15 11 6
P/E = 6 20 19 18 15 11
P/E = 7 22 22 21 18 15
Venture fund’s share 33%
P/E = 2 9 7 4 -2 -10
P/E = 3 14 12 10 5 -2
P/E = 4 17 16 14 10 5
P/E = 5 20 19 18 14 10
P/E = 6 22 22 21 18 14
P/E = 7 24 24 24 21 18
Venture fund’s share 37%
P/E = 2 11 9 6 0 -7
P/E = 3 15 14 12 7 1
P/E = 4 19 18 16 12 8
P/E = 5 22 21 20 17 13
P/E = 6 24 24 23 21 18
P/E = 7 26 26 26 24 22
175
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
APPENDIX 3, Table 3.1. Continued
P/E
Year of fund’s exit from the business
2018 2017 2016 2015 2014
Venture fund’s share 41%
P/E = 2 13 11 8 2 -5
P/E = 3 17 16 14 9 4
P/E = 4 20 20 18 15 10
P/E = 5 23 23 22 19 16
P/E = 6 26 26 26 23 21
P/E = 7 28 28 28 27 25
Venture fund’s share 45%
P/E = 2 14 12 10 4 -2
P/E = 3 19 17 16 11 6
P/E = 4 22 21 20 17 13
P/E = 5 25 25 24 22 19
P/E = 6 27 27 28 25 23
P/E = 7 29 30 31 29 28
Venture fund’s share 49%
P/E = 2 16 14 11 6 0
P/E = 3 20 19 17 13 9
P/E = 4 23 23 22 19 15
P/E = 5 26 26 26 24 21
P/E = 6 29 29 30 28 26
P/E = 7 31 32 32 31 30
Baranov and Muzyko
176
APPENDIX 4, Table 4.1. Standard Calculation of the Venture Fund’s Internal Rate ofReturn IRRv and IRRv Calculations Taking into Account the Value of the CompoundCall Option for the Venture Fund’s “Exit” from the Business in 2018
P/E Standard
calculation Calculation taking into account the value of the compound call option
Venture fund’s share 24% P/E = 2 5% 5% P/E = 3 9% 9% P/E = 4 12% 14% P/E = 5 15% 19% P/E = 6 17% 22% P/E = 7 19% 25%
Venture fund’s share 25% P/E = 2 5% 5% P/E = 3 10% 10% P/E = 4 13% 15% P/E = 5 15% 20% P/E = 6 18% 23% P/E = 7 20% 26%
Venture fund’s share 29% P/E = 2 7% 8% P/E = 3 12% 13% P/E = 4 15% 18% P/E = 5 18% 23% P/E = 6 20% 26% P/E = 7 22% 29%
Venture fund’s share 33% P/E = 2 9% 9% P/E = 3 14% 16% P/E = 4 17% 21% P/E = 5 20% 25% P/E = 6 22% 28% P/E = 7 24% 31%
Venture fund’s share 37% P/E = 2 11% 11% P/E = 3 15% 18% P/E = 4 19% 23% P/E = 5 22% 27% P/E = 6 24% 31% P/E = 7 26% 33%
177
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
APPENDIX 4, Table 4.1. Continued
P/E Standard
calculation Calculation taking into account the value of the compound call option
Venture fund’s share 41% P/E = 2 13% 13% P/E = 3 17% 20% P/E = 4 20% 26% P/E = 5 23% 30% P/E = 6 26% 33% P/E = 7 28% 35%
Venture fund’s share 45% P/E = 2 14% 15% P/E = 3 19% 22% P/E = 4 22% 27% P/E = 5 25% 31% P/E = 6 27% 35% P/E = 7 29% 37%
Venture fund’s share 49% P/E = 2 16% 17% P/E = 3 20% 24% P/E = 4 23% 29% P/E = 5 26% 33% P/E = 6 29% 36%
Baranov and Muzyko
178
APPENDIX 5, Table 5.1. Standard Calculation of the Venture Fund’s NPVv and NPVv
Calculations Taking into Account the Value of the Compound Call Option for the Ven-ture Fund’s “Exit” from the Business in 2018, in thousands of Rubles
P/E Standard calculation
Calculation taking into account the value of compound call option
r = 20% r = 30% r = 35% r = 20% r = 30% r = 35% Venture fund’s share 24%
P/E = 2 - 124,346 - 145,779 - 149,963 - 124,345 - 145,779 - 149,962 P/E = 3 - 101,768 - 134,794 -142,141 - 99,513 - 133,696 - 141,359 P/E = 4 - 79,189 - 123,808 - 134,319 - 59,998 - 114,470 - 127,670 P/E = 5 - 56,611 - 112,822 - 126,497 - 15,015 - 92,583 - 112,086 P/E = 6 - 34,033 - 101,836 -118,675 30,141 - 70,612 - 96,442 P/E = 7 - 11,455 - 90,850 -110,853 75,297 - 48,640 - 80,798
Venture fund’s share 25% P/E = 2 - 121,228 - 144,081 - 148,672 - 121,226 - 144,080 - 148,672 P/E = 3 - 97,709 - 132,638 - 140,525 - 94,398 - 131,027 - 139,377 P/E = 4 - 74,190 - 121,194 - 132,377 - 51,740 - 110,271 - 124,599 P/E = 5 - 50,671 - 109,751 - 124,229 - 4,794 - 87,428 - 108,335 P/E = 6 - 27,152 - 98,307 - 116,081 42,244 - 64,541 - 92,039 P/E = 7 - 3,633 - 86,863 - 107,933 89,282 - 41,654 - 75,743
Venture fund’s share 29% P/E = 2 - 108,758 - 137,288 - 143,512 - 106,777 - 136,324 - 142,826 P/E = 3 - 81,476 - 124,014 -134,060 - 71,754 - 119,283 - 130,692 P/E = 4 - 54,194 - 110,739 - 124,609 - 18,466 - 93,355 - 112,231 P/E = 5 - 26,912 - 97,464 - 115,157 36,092 - 66,809 - 93,330 P/E = 6 370 - 84,190 - 105,706 90,656 - 40,260 - 74,427 P/E = 7 27,652 - 70,915 - 96,254 145,220 - 13,711 - 55,524
Venture fund’s share 33% P/E = 2 - 96,288 - 130,495 - 138,351 - 95,911 - 130,311 - 138,221 P/E = 3 - 65,243 - 115,389 - 127,596 - 46,915 - 106,472 - 121,247 P/E = 4 - 34,198 - 100,284 - 116,841 14,887 - 76,401 - 99,836 P/E = 5 - 3,153 - 85,178 - 106,086 76,978 - 46,190 - 78,325 P/E = 6 27,892 - 70,073 - 95,330 139,068 - 15,979 - 56,815 P/E = 7 58,937 - 54,967 - 84,575 201,158 14,232 - 35,304
Venture fund’s share 37% P/E = 2 - 83,818 - 123,702 - 133,191 - 82,358 - 122,991 - 132,685 P/E = 3 - 49,010 - 106,765 - 121,132 - 21,314 - 93,289 - 111,537 P/E = 4 - 14,202 - 89,829 - 109,073 48,248 - 59,443 - 87,438 P/E = 5 20,606 - 72,892 - 97,014 117,864 - 25,570 - 63,320 P/E = 6 55,415 - 55,956 - 84,955 187,480 8,303 - 39,203 P/E = 7 90,223 - 39,019 - 72,896 257,096 42,175 - 15,085
Venture fund’s share 41% P/E = 2 - 71,348 - 116,909 - 128,030 - 67,623 - 115,096 - 126,740 P/E = 3 - 32,777 - 98,141 - 114,668 4,474 - 80,016 - 101,762 P/E = 4 5,795 - 79,374 - 101,305 81,607 - 42,486 - 75,041 P/E = 5 44,366 - 60,606 - 87,943 158,749 - 4,951 - 48,315 P/E = 6 82,937 - 41,839 - 74,580 235,892 32,584 - 21,590 P/E = 7 121,508 - 23,071 - 61,217 313,034 70,118 5,135
Venture fund’s share 45% P/E = 2 - 58,878 - 110,115 - 122,870 - 51,649 - 106,598 - 120,366 P/E = 3 - 16,544 - 89,517 - 108,203 30,300 - 66,724 - 91,975 P/E = 4 25,791 - 68,919 - 93,537 114,967 - 25,528 - 62,643 P/E = 5 68,125 - 48,320 - 78,871 199,636 15,668 - 33,311 P/E = 6 110,459 - 27,722 - 64,205 284,304 56,865 - 3,978 P/E = 7 152,793 - 7,123 - 49,538 368,973 98,062 25,355
Venture fund’s share 49% P/E = 2 - 46,408 - 103,322 - 117,709 - 34,693 - 97,622 - 113,651 P/E = 3 - 310 - 80,893 - 101,739 56,133 - 53,430 - 82,185 P/E = 4 45,787 - 58,464 - 85,769 148,327 - 8,571 - 50,245 P/E = 5 91,884 - 36,034 - 69,799 240,522 36,288 - 18,306 P/E = 6 137,982 - 13,605 - 53,830 332,716 81,146 13,634 P/E = 7 184,079 8,825 - 37,860 424,911 126,005 45,574
APP
END
IX 6
, Tab
le 6
.1. C
alcu
latio
n of
the
Com
poun
d C
all O
ptio
n Va
lues
for t
he V
entu
re F
und’
s Sha
res a
t 24
perc
ent
and
25 p
erce
nt w
ith D
iffer
ent P
/E V
alue
sIn
put p
aram
eter
s: I 0v =
35,
000,
000
Rubl
es; I
1v = 1
84,1
12,0
00 R
uble
s; I 2v =
77,
182,
000
Rubl
es (f
or sh
are 2
4%);
I 2v =
80,3
98,0
00 R
uble
s (fo
r sha
re 2
5%);
r =7%
; 1 =
12.
78%
; 2 =
10.
224%
; T1 =
1 y
ear;
T 2 = 9
yea
rs;
1 = 1
year
; 2 = 8
year
s;
= 9
year
s.
P/E
va
lues
vV
, th
ousa
nd
Rubl
es
v TV1
, th
ousa
nd
Rub
les
vV
,
thou
sand
R
uble
s
h l
ρ N
2(h, l
, ρ)
12 1
h
22 2
12 1
l
);
,(
22 2
12 1
12 1
2
l
hN
Cv,
thou
sand
R
uble
s
Ven
ture
fund
’s sh
are
24%
P/E
= 2
139,4
09
37,08
1 54
,768
-3.3
7224
3067
3.
7046
6935
9
0.
4042
2604
2
0.0
0037
2793
-3
.2444
4306
7
4.
0208
2909
8
0.00
0588
403
2,7
P/E
= 3
202,7
76
55,62
2 54
,768
-0.4
4039
7503
4.
8897
9768
6
0.
4042
2604
2
0.3
2982
4615
-0
.3125
9750
3
5.
2059
5742
5
0.
3772
9323
7
6,32
9
P/E
= 4
266,1
44
74,16
3 54
,768
1.687
4240
44
5.
7499
1856
9
0.
4042
2604
2
0.9
5423
9077
1.8
1522
4044
6.
0660
7830
8
0.
9652
5525
7
53
,862
P/E
= 5
329,5
12
92,70
4 54
,768
3.358
5919
46
6.
4254
4815
0.
4042
2604
2
0.9
9960
8297
3.4
8639
1946
6.
7416
0788
9
0.
9997
5520
8
11
6,74
3
P/E
= 6
392,8
80
111,2
44
54,7
68
4.7
3489
4368
6.
9817
8543
1
0.
4042
2604
2
0.9
9999
8904
4.8
6269
4368
7.
2979
4517
0.
9999
9942
1
18
0,10
9
P/E
= 7
456,2
47
129,7
85
54,7
68
5.9
0492
6511
7.
4547
4289
2
0.
4042
2604
2
0.9
9999
9998
6.0
3272
6511
7.
7709
0263
2
0.
9999
9999
9
24
3,47
6
Ven
ture
fund
’s sh
are
25%
P/E
= 2
145,2
18
38,62
7 57
,509
-3
.115
5435
43
3.
7046
7243
3
0.
4042
2604
2
0.0
0091
8031
-2
.9877
4354
3
4.
0208
3217
3
0.
0014
0522
6
7
P/E
= 3
211,2
26
57,94
0 57
,509
-0.1
8367
6652
4.
8898
0938
2
0.
4042
2604
2
0.4
2713
3559
-0
.0558
7665
2
5.
2059
6912
1
0.
4777
2003
5
9,
293
P/E
= 4
277,2
34
77,25
3 57
,509
1.944
1266
71
5.
7499
2289
6
0.
4042
2604
2
0.
9740
5991
2.0
7192
6671
6.
0660
8263
6
0.9
8086
386
63
,008
P/E
= 5
343,2
42
96,56
6 57
,509
3.615
2833
44
6.
4254
4794
3
0.
4042
2604
2
0.
9998
4999
3.7
4308
3344
6.
7416
0768
3
0.
9999
0911
2
12
8,75
9
P/E
= 6
409,2
50
115,8
80
57,5
09
4.9
9157
8168
6.
9817
8215
2
0.
4042
2604
2
0.9
9999
9701
5.1
1937
8168
7.
2979
4189
2
0.
9999
9984
7
19
4,76
6
P/E
= 7
475,2
58
135,1
93
57,5
09
6.1
6162
1972
7.
4547
4432
8
0.
4042
2604
2
0.9
9999
9999
64
6.2
8942
1972
7.
7709
0406
7
0.99
9999
9998
4
26
0,77
4
179
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
APP
END
IX 7
, Tab
le 7
. Cal
cula
tion
of th
e C
ompo
und
Cal
l Opt
ion
Valu
es fo
r the
Ven
ture
Fun
d’s S
hare
s at 2
9 pe
rcen
t and
33 p
erce
nt w
ith D
iffer
ent P
/E V
alue
s
Inpu
t par
amet
ers:
I 0v = 3
5,00
0,00
0 Ru
bles
; I1v
= 18
4,11
2,00
0 Ru
bles
; I2v =
93,
262,
000
Rubl
es (f
or sh
are 2
9%);
I 2v = 1
06,1
26,0
00 R
uble
s (fo
r sha
re 3
3%);
r=
7%;
1= 1
2.78
%;
2 = 1
0.22
4%; T
1 = 1
yea
r; T 2 =
9 y
ears
; 1 = 1
year
; 2 =
8 ye
ars;
3 =
9 ye
ars.
P/E
valu
es
vV
, th
ousa
nd
Rubl
es
v TV1
, th
ousa
nd
Rubl
es
vV
, th
ousa
nd
Rub
les
h l
ρ N
2(h, l
, ρ)
12 1
h
22 2
12 1
l
);
,(
22 2
12 1
12 1
2
l
hN
Cv,
tho
usan
d Ru
bles
Vent
ure f
und’
s sha
re 29
%
P/E
= 2
168,4
52
44,80
7 68
,841
-2
.2002
7446
4
3.7
0464
5057
0.4
0422
6042
0.
0436
4838
4
-2
.0724
7446
4
4.0
2080
4797
0.0
6003
7743
5,
560
P/E
= 3
245,0
21
67,21
0 68
,841
0.
7315
9625
9
4.8
8978
3555
0.4
0422
6042
0.
7677
9244
6
0.8
5939
6259
5.2
0594
3294
0.8
0493
9026
27
,287
P/E
= 4
321,5
91
89,61
3 68
,841
2.8
5942
592
5.7
4990
7716
0.4
0422
6042
0.
9978
7795
4
2.
9872
2592
6.0
6606
7455
0.9
9859
2392
10
0,27
3
P/E
= 5
398,1
60
112,0
17
68,84
1
4.530
5791
5
6.4
2543
1371
0.4
0422
6042
0.
9999
9705
9
4.
6583
7915
6.7
4159
111
0.9
9999
8406
17
6,82
5
P/E
= 6
474,7
30
134,4
20
68,84
1
5.90
6888
123
6.9
8177
1299
0.4
0422
6042
0.
9999
9999
8
6.0
3468
8123
7.2
9793
1039
0.9
9999
9999
25
3,395
P/E
= 7
551,2
99
156,8
24
68,84
1
7.07
6927
954
7.4
5473
1869
0.4
0422
6042
0.
9999
9999
9999
22
7.2
0472
7954
7.7
7089
1608
0.9
9999
9999
9997
03
32
9,964
Vent
ure f
und’
s sha
re 33
%
P/E
= 2
191,6
87
50,98
7 80
,762
-1
.4277
5304
7
3.7
0464
0818
0.4
0422
6042
0.
0766
8142
3
-1
.2999
5304
7
4.0
2080
0558
0.0
9680
8516
1,0
59
P/E
= 3
278,8
18
76,48
0 80
,762
1.
5041
3588
7
4.8
8978
6677
0.4
0422
6042
0.
9337
2667
1
1.6
3193
5887
5.2
0594
6416
0.9
4865
3477
51
,438
P/E
= 4
365,9
48
101,9
74
80,76
2
3.63
1929
374
5.7
4989
6216
0.4
0422
6042
0.
9998
5934
1
3.7
5972
9374
6.0
6605
5955
0.9
9991
4951
13
7,76
2
P/E
= 5
453,0
79
127,4
67
80,76
2
5.30
3097
264
6.4
2542
5797
0.4
0422
6042
0.
9999
9994
3
5.4
3089
7264
6.7
4158
5537
0.9
9999
9972
22
4,892
P/E
= 6
540,2
09
152,9
61
80,76
2
6.67
9385
202
6.9
8175
7223
0.4
0422
6042
0.
9999
9999
9986
54
6.8
0718
5202
7.2
9791
6962
0.999
9999
9999
4877
312,
022
P/E
= 7
627,3
40
178,4
54
80,76
2
7.84
9436
507
7.4
5472
243
0.4
0422
6042
0.99
9999
9999
9996
7.9
7723
6507
7.7
7088
2169
0.9
9999
9999
9999
93
39
9,153
Baranov and Muzyko
180
APP
EN
DIX
8, T
able
8.1
. Cal
cula
tion
of th
e C
ompo
und
Cal
l Opt
ion
Valu
es fo
r the
Ven
ture
Fun
d’s
Shar
es a
t 37
perc
ent a
nd 4
1 per
cent
with
Diff
eren
t P/E
Val
ues
Inpu
t par
amet
ers:
I 0v = 3
5,00
0,00
0 Ru
bles
; I1v
= 18
4,11
2,00
0 Ru
bles
; I2v =
118
,989
,000
Rub
les (
for s
hare
37%
); I 2v =
131
,853
,000
Rub
les (
for s
hare
41%
); r
= 7%
; 1=
12.
78%
; 2 =
10.
224%
; T1 =
1 y
ear;
T 2 = 9
yea
rs;
1 = 1
year
; 2
= 8
year
s;
3 = 9
year
s.
P/E
valu
es
vV
, th
ousa
nd
Rubl
es
v TV1
, th
ousa
nd
Rub
les
vV
, th
ousa
nd
Rubl
es
h l
ρ N
2(h, l
, ρ)
12 1
h
22 2
12 1
l
);
,(
22 2
12 1
12 1
2
l
hN
Cv,
tho
usan
d R
ubles
Vent
ure f
und’
s sha
re 3
7%
P/E
= 2
214,9
22
57,16
7 93
,270
-0
.763
9752
64
3.
7046
6407
8
0.4
0422
6042
0.
2224
4044
9
-0
.636
1752
64
4.
0208
2381
7
0.2
6233
0946
4,
099
P/E
= 3
312,6
14
85,75
1 93
,270
2.1
6790
2913
4.
8898
0558
8
0.4
0422
6042
0.
9849
1668
5
2.2
9570
2913
5.
2059
6532
8
0.
9891
5351
77
,731
P/E
= 4
410,3
06
114,3
34
93,27
0
4.295
7121
47
5.
7499
2149
3
0.4
0422
6042
0.
9999
9128
9
4.4
2351
2147
6.
0660
8123
2
0.9
9999
5144
17
5,269
P/E
= 5
507,9
98
142,9
18
93,27
0
5.966
8724
58
6.4
2544
801
0.4
0422
6042
0.999
9999
9872
5047
6.0
9467
2458
6.7
4160
775
0.
9999
9999
9443
858
27
2,96
1
P/E
= 6
605,6
89
171,5
02
93,27
0
7.343
1568
28
6.
9817
7799
3
0.4
0422
6042
0.999
9999
9999
8436
7.4
7095
6828
7.
2979
3773
3
0.
9999
9999
9999
811
37
0,65
2
P/E
= 7
703,3
81
200,0
85
93,27
0
8.513
2042
07
7.
4547
4161
4
0.4
0422
6042
0.99
9999
9999
9844
8.6
4100
4207
7.
7709
0135
3
0.
9999
9999
9999
811
46
8,34
4
Vent
ure
fund
’s sh
are
41%
P/E
= 2
238,1
57
63,34
7 10
6,365
-0.1
8555
3711
3.7
0465
881
0.4
0422
6042
0.
4263
9458
8
-0
.057
7537
11
4.0
2081
855
0.
4769
7163
10
,454
P/E
= 3
346,4
10
95,02
1 10
6,365
2.746
3158
09
4.
8897
9682
1
0.4
0422
6042
0.
9969
8617
3
2.8
7411
5809
5.
2059
5656
1
0.9
9797
4123
10
4,548
P/E
= 4
454,6
63
126,6
95
106,3
65
4.8
7412
0508
5.
7499
1089
2
0.4
0422
6042
0.
9999
9944
9
5.0
0192
0508
6.
0660
7063
2
0.9
9999
9716
21
2,774
P/E
= 5
562,9
16
158,3
69
106,3
65
6.5
4527
8028
6.
4254
3628
2
0.4
0422
6042
0.99
9999
9999
045
6.6
7307
8028
6.
7415
9602
1
0.9
9999
9999
9796
4
32
1,027
P/E
= 6
671,1
70
190,0
42
106,3
65
7.9
2158
5085
6.
9817
7543
5
0.4
0422
6042
0.99
9999
9999
9855
8.0
4938
5085
7.
2979
3517
5
0.
9999
9999
9999
853
42
9,28
1
P/E
= 7
779,4
22
221,7
16
106,3
65
9.0
9161
7645
7.
4547
3306
6
0.4
0422
6042
0.99
9999
9999
9996
9.2
1941
7645
7.
7708
9280
6
0.
9999
9999
9999
996
53
7,53
3
181
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
APP
END
IX 9
. Tab
le 9
.1. C
alcu
latio
n of
the
Com
poun
d C
all O
ptio
n Va
lues
for t
he V
entu
re F
und’
s Sha
res a
t 45
perc
ent
and
49 p
erce
nt w
ith D
iffer
ent P
/E V
alue
sIn
put p
aram
eter
s: I 0v =
35,
000,
000
Rubl
es; I
1v = 1
84,1
12,0
00 R
uble
s; I 2v =
144
,717
,000
Rub
les (
for s
hare
45%
); I 2v =
157
,580
,000
Rub
les (
for s
hare
49%
); r =
7%
; 1=
12.
78%
; 2=
10.
224%
; T1=
1 ye
ar; T
2= 9
yea
rs;
1= 1
year
; 2=
8 ye
ars; 3
= 9
year
s.
P/E
va
lues
vV
, th
ousa
nd
Rub
les
v TV1
, th
ousa
nd
Rub
les
vV
, th
ousa
nd
Rub
les
h l
ρ N
2(h, l
, ρ)
12 1
h
22 2
12 1
l
22
11
22
11
22
(, ;
)
Nh
l
Cv ,
tho
usan
d Ru
bles
Vent
ure
fund
’s sh
are
45%
P/E
= 2
26
1,39
2 69
,528
12
0,049
0.
3243
1606
7 3.
7046
5447
9 0.
4042
2604
2 0.
6271
4178
7 0.
4521
1606
7 4.
0208
1421
9 0.
6744
0486
7 20
,287
P/E
= 3
38
0,20
6 10
4,29
2 12
0,049
3.
2561
7846
7 4.
8897
8961
3 0.
4042
2604
2 0.
9994
3492
9 3.
3839
7846
7 5.
2059
4935
2 0.
9996
4269
5 13
1,471
P/E
= 4
49
9,02
1 13
9,05
5 12
0,049
5.
3839
9511
8 5.
7499
0851
5 0.
4042
2604
2 0.
9999
9995
9 5.
5117
9511
8 6.
0660
6825
4 0.
9999
9998
2 25
0,28
1
P/E
= 5
61
7,83
5 17
3,81
9 12
0,049
7.
0551
4732
8 6.
4254
3175
8 0.
4042
2604
2 0.
9999
9999
9933
389
7.18
2947
328
6.74
1591
497
0.99
9999
9999
9182
5 36
9,09
5
P/E
= 6
73
6,64
9 20
8,58
3 12
0,049
8.
4314
3912
9 6.
9817
6474
5 0.
4042
2604
2 0.
9999
9999
9998
541
8.55
9239
129
7.29
7924
484
0.99
9999
9999
9985
3 48
7,90
9
P/E
= 7
85
5,46
4 24
3,34
7 12
0,049
9.
6014
8989
7 7.
4547
2973
5 0.
4042
2604
2 0.
9999
9999
9999
954
9.72
9289
897
7.77
0889
475
0.99
9999
9999
9999
6 60
6,72
4
Vent
ure
fund
’s sh
are
49%
P/E
= 2
28
4,62
6 75
,708
13
4,320
0.
7780
4773
4 3.
7046
5981
5 0.
4042
2604
2 0.
7817
0974
9 0.
9058
4773
4 4.
0208
1955
4 0.
8174
8629
6 32
,877
P/E
= 3
41
4,00
2 11
3,56
2 13
4,320
3.
7099
3167
4.
8898
0365
3 0.
4042
2604
2 0.
9998
9585
6 3.
8377
3167
5.
2059
6339
0.
9999
3781
9 15
8,41
2
P/E
= 4
54
3,37
8 15
1,41
6 13
4,320
5.
8377
4392
5.
7499
2077
7 0.
4042
2604
2 0.
9999
9999
3 5.
9655
4392
6.
0660
8051
6 0.
9999
9999
8 28
7,78
7
P/E
= 5
67
2,75
4 18
9,27
0 13
4,320
7.
5089
0608
8 6.
4254
4804
5 0.
4042
2604
2 0.
9999
9999
9934
227
7.63
6706
088
6.74
1607
784
0.99
9999
9999
9215
6 41
7,16
3
P/E
= 6
80
2,12
9 22
7,12
4 13
4,320
8.
8851
9487
8 6.
9817
7981
5 0.
4042
2604
2 0.
9999
9999
9998
541
9.01
2994
878
7.29
7939
554
0.99
9999
9999
9985
3 54
6,53
8
P/E
= 7
93
1,50
5 26
4,97
8 13
4,320
10
.055
2427
3 7.
4547
4362
5 0.
4042
2604
2 0.
9999
9999
9999
954
10.18
3042
73
7.77
0903
364
0.99
9999
9999
9999
6 67
5,91
4
Baranov and Muzyko
182
183
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
APPENDIX 10, Table 10.1. Definition of the Parameters
Parameters Definition of the parameters
0≤DIVv(t)<∞ dividends paid by the investee company to the venture fund in year t; positive cash flow of the venture fund
0≤SHKv ≤1 equity share of the venture fund in the charter capital of the investee company
0≤ div(t) ≤1 part of the investee company’s net profit in the previous year (t-1), used in year t for dividend payout
0≤PERv(t)<∞ interest paid to the venture fund by the investee company in year t on extended loan; positive cash flow of the venture fund
0≤LRv(t)<∞ repayment of the loan extended by the venture fund to the investee company in year t; positive cash flow of the venture fund
0≤Lv(t)<∞ the loan extended by the venture fund to the investee company in year t; negative cash flow of the venture fund
0≤Iv(t)<∞ equity investment transferred by the venture fund to the investee company in year t; negative cash flow of the venture fund
0≤TERv(T)<∞ terminal value determined as valuation of the returns the venture fund will get in the last year T of its investment from the sale of its shares in the investee company; positive cash flow of the venture fund
0<r<∞ discount rate acceptable for the venture fund
0≤NPAT(T)<∞ net profit of the investee company in the year T
0≤NPAT(T-1)<∞ net profit of the investee company in the year preceding the “exit” of the venture fund from the business
0<To<∞ initial moment of time, when the venture fund purchases the compound call option (the initial payment which allows starting the project’s implementation)
0<T1<∞ moment of time, when venture fund purchases the shares of the investee company (expiration of the compound (external) call option)
0<T2<∞ moment of time, when venture fund sells its shares of the investee company (expiration of the internal call option)
0<τ1<∞ moment before the fund makes an investment into the company in return for a share of its charter capital
0<τ2<∞ period of time the venture fund stays in the business of the investee company
0<τ<∞ period of expiration of the internal call option
0<P/E<∞ price-earnings ratio for the shares, in venture funds’ financial calculations often P/E=3, 4, 5, 6
0≤Vtν <∞ value of the shares of the investee company, which belongs to the venture fund, at the
moment t
0<Iov <∞ cost of purchasing at the moment T0 the compound call option – is the initial payment
which allows starting the project’s implementation
Baranov and Muzyko
184
APPENDIX 10, Table 10.1. Continued
Parameters Definition of the parameters
0≤I1v <∞ price of the purchase of the shares by the venture fund at the moment T1 – is the
purchase of an internal call option for buying an asset at the moment T2 with an exercise price I2
v (the exercise price of the compound (external) call option). 2
1
* 2 *1 1 2 2 2 1( ) ( ) .............(10.2)rv
ТI V N l I e N l
0≤Iv2 <∞ sum of implicit costs of the venture fund – the loss of its share of the net profit for the
last year of the fund’s participation in the business of the investee company (exercise price of the internal call option)
σ1 ≥0 risk level of operations of the investee company over the time period (0,T1)
σ2 ≥ 0 risk level of operations of the investee company over the time period (T1,T2)
0≤Сventure fund <∞ value of the compound call option at the current moment t, which belongs to the venture fund:
0≤Vν<∞ current value of the equity shares of the investee company, which belong to the venture fund
r≥0 risk-free interest rate
1);,(0 2 lhN two-dimensional standard normal distribution function
);(, lh upper limits of the integrals of the two-dimensional standard normal distribution function;
);(* l
value of l at the moment T1
-1≤ρ≤1 correlation coefficient of stochastic variables;
1)(0 1 hN one-dimensional standard normal distribution function
0V such a value of the investee company’s equity shares at the moment Т1 (1TV ), which
conforms to the equation (10.2) (the threshold figure of the value of the investee company’s equity at the moment Т1)
10 TV
value of the investee company’s equity shares at the moment Т1, which belong to the venture fund
20 TV
value of the investee company’s equity shares at the moment Т2, which belong to the venture fund
( , )v
IRR internal rate of return for the venture fund, in financial calculations only a positive IRRv is of interest for an investor
( , )V
NPV net present value for the venture fund
( , )V
optionNPV net present value for the venture fund taking into account the value of compound call option
2 21 1 1 1 1
1(ln ) / ....(10.3);
2
v
v
Vh r
V
2 2 2 21 1 2 2 1 1 2 2
2
1(ln ( )) / .....(10.4)
2
v
v
Vl r
I
2 2 21 1 1 1 2 2/ ( ) ......(10.6)
1* 2 22 2 2 2 2
2
1(ln ) / ......(10.5)
2T
v
Vl r
I
12 2 22 1 1 1 1 2 2 2 2 1 1( , ; ) ( , ; ) ( )....(10.1)rventure fund rC V N h l I e N h l I e N h
185
Gadjah Mada International Journal of Business – May-August, Vol. 18, No. 2, 2016
APPENDIX 10, Table 10.1. Continued
Parameters Definition of the parameters
( , )v
optionIRR internal rate of return for the venture fund taking into account the value of compound call option, in financial calculations only a positive IRRv is of interest to an investor
ExittotalNPAT0 total net profit of the investee company in the year of “exit” of the venture fund from the invested business
0≤S≤1 share of the venture fund in the charter capital of the investee company
I1discv≥0 discounted value of I1
v
I2discv≥0 discounted value of I2
v
0≤f (x,y)<+∞ probability density
-∞<(x,y)<+∞ values of random variables
a, b = 0 (for standard normal distribution)
mathematical expectations of stochastic variables x, y
σx≥0 mean square deviation of stochastic variable x
σy≥0 mean square deviation of stochastic variable y
-1≤ρx,y≤1 correlation coefficient of stochastic variables x and y