The theory of real options in the estimation of consecutive innovative projects Текст научной статьи по специальности «Экономика и бизнес»

M. A. Budylin

Siberian State Aerospace University named after academician M. F. Reshetnev, Russia, Krasnoyarsk

THE THEORY OF REAL OPTIONS IN THE ESTIMATION OF CONSECUTIVE INNOVATIVE PROJECTS

Approaches to the estimation of efficiency of the investment projects including consecutive improving innovations are considered, the choice of methodology of real options for the estimation of such projects is proved and its application is shown by the example of an abandon option for the project.

Keywords: real options, estimation, investment projects, innovations.

On novelty level two types of innovations are important factor as it is the competition that forces the

distinguished - radical (basic) and improving innovations. manufacturer to launch constantly innovative products.

Radical innovations are aimed at adoption of new generations Let us assume there is a company which plans to launch

of machines and materials, essentially new technics and innovativeproductsP= 1,..., Tthroughequaltimeintervals t,

technology, they make such considerable changes in where Tisthelife-timeofthetechnology.Eachofthesubsequent

processes, products or services that lead to transformation products Pt+1 istheimprovementofthepreviousproductPt and

of the existing markets or sectors or create the new markets afterthebeginningofmanufacturingofanewgenerationproduct

and sectors. Improving innovations are aimed at evolutionary Pt+1 manufacturing of a previous generation product Pt ceases.

improvement of the properties andparametres of processes, Initialinvestmentexpensesforlaunchingofeachproduct Pt make

products or services, they serve a purpose of distribution up /t-1,andthenetcashflow fromselling ofone productmakes

and perfection of the mastered generations of technics and up C. One of the majorfactors of uncertainty forthe company is

technology, creationof new models of machines andvariety thedemandfortheproductineachperiod (x()anditisknownthat

of materials, improvement of parametres of the produced the demand under good conditions makes up x + and x ^ under

goods, services and their manufacturing techniques [1]. badconditions.Inthefirstperiodtheprobabilityofhighdemand

Distinctive feature of the majority of innovative projects is is q1 and the probability of the low demand is (1 - q1). For the

constant improvement of an innovative product (improving subsequent periods the following is valid:

innovations), thatallows to mark outcertaingenerations of - ifthedemandfortheproduct Ptwashigh,theprobability

development of technology. In many projects the innovative of the high demand for the product Pt + 1 makes up q+, and

product of one generation is considered as a platform (base) with the probability (1 - q+) it will be low.

for the future generation of innovative products. The - ifthedemandfortheproduct Pt waslow,theprobability approach is offered to the estimation of innovative projects of the high demand for the product Pt + 1 makes up qt_ and

the outlet of which is limited (the demand is set by certain withprobability (1 - q tJ itwillbe low.

limits which is typical for a number of innovative sectors) On the basis of the information above it is possible to

and where the competition exists. The competition is the drawthefollowingdecision-treeofthecashflows(fig. 1).

Period 1 2 3

Fig. 1. Decision-tree of cash flows for consecutive innovative projects

According to the NPV method for estimation of the appropriateness of the project realization it is necessary to determine cash flows for each period considering the probabilities, i. e. expected cashflow ofthe period2:

f2 _ q1 * (q2 * (c2 * X2 — 12 ) + (1 — q2 ) * (c2 * X2 — ^2 )) +

+(i - q1) * q+ * (c2 * x2 12) %(1 - q+) * (c2 * x- -12)).(1)

After that each of the expected cash flows should be discounted to the initial time period at the discount rate k (where k is set from the outside, as expected rate of return from alternative investments). Formula of NPV looks as follows:

NPV = (-

f

(2)

,=0(1 + k )'

The project is accepted ifNPV 0 0 and is rejected ifNPV < 0.

At the same time the main disadvantage ofNPV method is that it does not consider the possibility of management of the project to make changes during its implementation, for example, to expand or reduce production capacity, to temporarily shut down the project with the subsequent renewal of activity, to abandon the project etc. Implementation of these measures influences NPV positively and reduces the risk of the project. For the projects implying constant renewal management decisions may include the measures of the choice of the best period of time to launch a

new product, switching over to different technologies etc. [2; 3; 4] Strategic net present value of the project (NPV *) consists of two summands:

- net present value of the project without options (NPV);

- value of options of the project (ROV).

The formulaforthe strategic (expanded) netpresentvalue looksasfollows:

NPV* = NPV+ROV. (3)

Let us consider the opportunity of the abandonment of the project by the example of the decision-tree in figure 1. The decision-tree should be analysed from the end. It makes sense to abandon the project, if discounted cash flows are less than investment expenses:

I,-i <

q, • x++ (1 - q,) • x-1 + k

(4)

The given check should be carried out in each node of the decision-tree, moving from right to left from the end of the tree (period T) to its beginning. In each node it is necessary to sum up the cash flows of the period and the future cash flows discounted to this period. The decision-tree of cash flows is transformed to a following decision-tree of value (fig. 2).

As a result of the carried out analysis economically inefficient branches of a tree will be cut downwhich leads to the modified tree of cashflows, for example, as following (fig. 3).

Period

Fig. 2. Decision-tree of value for consecutive innovative projects

1 2 3

+ ^ c, x

Fig. 3. Modified decision-tree of cash flows for consecutive innovative projects

According to the method of decision tree analysis (DTA) for the modified decision-tree of cash flows the expected cash flows are calculated and then are discounted to the initial moment of time at the rate k. That is:

NPVdta = (

(1+k )t

Period 0

-1000

1

-1300

(700 - 2000) 1000

0,3^--' 5500

1000

- 1700 (300 - 2000; 0 7

NPV = -1000 +

0.5 • (-1300) + 0.5 • (-1700) 1 + 0.3

+ 1808 = -192 c. u.). The modified decision-tree of cashflows taking into account the abandonment option at low demand for the product P1 will look as follows (fig. 6).

Period

0

(5)

where NPVdta 0 NPV

A shortcoming of the decision-tree analysis (DTA) is that it does not provide any instructions on modifying the discount rate oftheprojectinconnectionwiththe riskreductionthrough exclusion of the unfavorable branches. To solve this problem it is possible to use real options approach (ROA) which allows not only to take into account the flexibility of management decisions but also to correct the discount rate according to the theory of financial options [3;4].

Let us consider the following numerical example. The company plans to launch two consecutive products P1 and P2. Investment expenses for launching the product P1 make up 1,000 c. u., those for launching the product P2 make up 2,000 c.u. The cashflows of product P1 will make up 700 c.u. at favorable demand, 300 c. u. at unfavorable demand, for product P2 they will make up 5,500 c.u. and 2,000 c. u. accordingly. The probability of favorable demand for product P1 is50 %, of unfavorable demand 100 % - 50% = 50 %. The probability of demand for product P2 depends on demand for product P. If the demand for product P1 was high the probability of a high demand for product P2 makes up 80 % (the probability oflow demand is 100 % - 80 % = 20 %). If demand for product P1 was low the probability of a high demand for product P2 makes up 30 % (probability of low demand is 100 % - 30 % = 70 %). The discount rate of the projects of the givenbranch of industry (k) makes up30 %, riskfree rate (r) makes up10 %. It is possible to present a decision-tree of cash flows of the project in a following way (fig. 4).

1

2238

(700 - 3000 + 3538)

c-1000 + 902)

" " 108

(300 - 2000 + 1808)

Fig. 5. Decision-tree of cash flows for the company

Fig. 6. Modified decision-tree of cash flows for the company

The net present value according to the decision-tree analysis (DTA) is then worth:

NPVdta _-1,000 + 0 5*(-!,300) + 0 5*300 +

1 + 0.3

0.5 • (0.8 • 5.500 + 0.2 $1,000)

= -24 c. u.

(7)

Fig. 4. Decision-tree of cash flows for the company

Estimating the project with the NPV criterion it is possible to come to a conclusion that the project is inefficient:

+ 0.5 *(0.8* 5500 + 0.2 *1000) + 0.5* (0.3* 5500 + 0.7*1000) _ -98 (6) (1 + 0.3)2 _ '

To take into account the abandonment option we will build the following decision-tree of value (fig. 5).

Analyzing a decision-tree of value it is possible to make a conclusion that in case of the low demand for the product P1 investment in the product P2 is inefficient as the net present value of suchproject is negative (NPV1'= -I1 + PVj' = -2000 +

(1 + 0.3)"

The value of the option is worth:

ROVdta = -24 - (-98) = 74 c. u. (8)

At the same time despite of the fact that the risk of the project has been lowered due to the reduction of dispersion of the cash flows, the discount rate remained invariable. To modify the discount rate it is necessary to take advantage of the theory of real options and risk-neutral approach. The risk-neutral approach assumes the determination of the riskneutral probabilities for the cash flows of the project for the purpose of discounting the additional value of the project appearing as a result of management flexibility at the riskfree rate (as this value does not imply an additional risk). From figure 5 it follows that the present value of cash flows in period t =0 makes up 902 (S = 902), which is obtained by weighing the value of the project in period t =1bythe actual probabilities in case of favorable (S+=2,238) and unfavorable (S' = 108) scenarios and discounting the result at the interest rateof30%.

The risk-neutral probabilities canbe found as follows:

1 + r - d

P = -

u - d

(9)

where u = S+/S, d = S-/S.

Inthe example (fig. 7) u = 2238/902 = 2.48; d = 108/902 = = 0.119; p = (1+0.1 - 0.119)/(2.48 - 0.119) = 0.415or41.5 % (fig. 8).

t=0

Comparison of results of an estimation of consecutive innovative projects is presented in table.

The classical assessment criterion of the investment projects (NPV) indicates that the project is economically inefficient. At the same time the abandonment option is built into the proj ect of launching the product P2 in the case of the low demand for the product Pv There are two ways of the estimation of the existing opportunity to terminate the project (the real option to abandon): a method of the decision-tree analysis and the method of real options analysis. The method of DTA underestimates the option value as it does not consider change of the project risk. The cash flows of the projects are discounted at the cost of capital of the project к = 30 %. The present value of the option in this case makes up 74 c. u., and expanded NPV is - 24 c. u. The method of real options considers reduction of risk of the project by using the risk-neutral probabilities and discounting the cash flows at the risk-free rate r =10 %. Defined according to the method of real options the value of the option to abandon makes up 102c.u. This leads to the fact that the strategic net present value of the projectbecomes positive (NPV =4c.u.), therefore the project canbe recommended for implementation.

Bibliography

1. Фатхутдинов, P. А. РГнновационный менеджмент / P. А. Фатхутдинов // СПб: Питер, 2007.447 с.

2. Лимитовский, М. А. Инвестиционные проекты и реальные опционы на развивающихся рынках / М. А. Лми-товский//М.: ^)айг, 2008.464 c.

3. Copeland, T. E. Making real options real /T.E. Copeland, PT.Keenan//TheMcKinseyQuarterly 1998.№2.P 129-141.

4. Trigeorgis, L. Real Options: Managerial flexibility and strategy in resource allocation / L. Trigeorgis. Cambrige, MA: MIT Press, 1996.427 c.

Comparison of results of an estimation of the consecutive innovative projects received by various methods

Traditional method npv DTA method Real options’ method

Traditional NPV -98 -98 -98

Real option value to abandon the project ROV - 74 102

Extended (strategic) NPV - -24 4

© BudylinM.A., 2009

The abandonmentvalue of the projectwill look as shown infigure9.

Period 0

1

902

2238

°>5 ^ 108 Fig. 7. Present value of the project using the actual probabilities

108

Fig. 8. Present value of the project using risk-neutral probabilities

Fig. 9. The value of the abandonment option

Thus, NPVroa = NPV + ROVroa = -98 + 102 = 4c.u.