FEATURES of FINANCING of INNOVATION PROJECTS

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FEATURES of FINANCING of INNOVATION
PROJECTS

• Ivanov N.V. (ivanick_at_mail.ru), Kirsanov A.P.,
  Shomova E.N. National Research University -
  Higher School of Economics, Moscow, Russia

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INNOVATION PROJECTS

• We shall understand as innovation projects such
  as a result of which performance the product
  turns out, or the service, not having analogues
  in the world, or created with application of
  bursting, unknown before methods and
  technologies, and, hence, including in their
  development a significant share of research works
  (RD)2-5.
• Research stages of the project frequently consist
  in checking of applicability of some ideas,
  hypotheses, materials, methods for achievement of
  the purposes of the project 2,3. Checks are
  carried out with use of experiments, modelling,
  testing and other methods of research 4,5.

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Results of researches

• Results of researches can be the following
• applicability of the objectively true hypothesis
  is confirmed
• applicability of the objectively false hypothesis
  is denied
• applicability of the objectively false hypothesis
  is confirmed
• applicability of the objectively true hypothesis
  is denied.

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Designations

• Further, for definiteness,like in 1, we shall
  consider, that at a research stage some
  hypothesis is checked. If a hypothesis
  objectively true then we shall carry it to a
  class 1, otherwise to a class 2. We shall
  designate through P1 a priori probability of the
  validity of a hypothesis checked at a research
  stage. Then P21-P1 is probability of falseness
  of the hypothesis. We shall designate through
  p11(r), p22(r), p21(r), p12(r) a posteriori
  probabilities of reception of the results of a
  research stage described above at the volume of
  financing r, and through c11,c22,c21,c12 the
  appropriate additional charges at later stages of
  the project.

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Basic equation

• It is natural, that charges are higher at
  erroneous conclusions about the validity of the
  checked hypothesis, made on a research stage,
  that is c12gtc11, c21gtc22 .
• The mathematical expectation of the charges,
  connected to results of a research stage is
  described by expression

(1)
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Dependence on financing r

• Clearly, that with increase of a research stage
  financing r the volume of researches and
  correctness of received results grows.
  Differently, at increase r monoto-nously grow and
  come nearer to 1 probabilities p11(r) and p22(r)
  of reception of correct results at a research
  stage and simultaneously probabilities
  p12(r)1-p11(r) and p21(r)1-p22(r) of reception
  of erroneous conclusions decrease.
• At absence of financing correctness of results of
  researches is reduced up to levels ?1 and ?2
  which were achieved prior to the beginning of the
  researches, i.e. p11(0) ?1, p22(0) ?2.

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Function C(r)

• Expression (1) can be written down as follows
• From this representation it is visible, that
  function C(r) represents a difference of linear
  growing function P1c12P2c21r and monotonously
  growing function P1p11(r)(c12-c11)P2p22(r)(c22-c2
  1) limited from above. Two variants of behaviour
  of function C(r) are possible. Either C(0) is the
  minimal value of function C(r) at r 0 , or the
  minimum is reached at r0gt0 for which C(r0)lt C(0)
  is the minimal value of function.

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Optimization of financing ropt

• For a finding of optimum volume of financing ropt
  we shall equate a derivative of expression (1)
  to zero and we shall receive the equation

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Existence of a minimum of C(r)

• Previous equation is true when
• In figure 1 two possible variants of behaviour of
  function C(r) are represented existence of a
  minimum at
• (c111,
  c221, c218, c1220) and its
• absence
• (c112, c228,
  c212, c1210).

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Figure 1. Mathematical expectation of the charges
connected to results of a research stage.
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Two variants of an innovational stage

• It is necessary to note two variants of
  development of an innovational stage of the
  project. The first variant assumes progressive
  motion aside achievements of necessary results.
  Gradually, in process of achievement of the
  concrete scientific purposes, additional
  financial injections do not bring necessary
  equivalent results. It is explained by well-known
  practice, that for 20 of time 80 of work is
  made, and in the rest of 80 of time - is
  completed 20 of work. For this case typically
  following behaviour of probabilities pij (r), i,
  j1,2, having property of monotonous decrease of
  a derivative

i1, 2
i1,2, j1,2, i?j
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Figure 2. Dependence pij on financing r. Var1.
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Var 2 of an innovational stage

• By analogy to the first case work start, having
  initial probabilities pij, but process of
  reception of necessary results passes in another
  way. At the initial stages of work, having
  enclosed in the project of means for purchase of
  the necessary equipment (measuring), on
  development of an infrastructure, on escalating
  of potential of the project and so forth, the
  developer does not come nearer to the purposes of
  the project. And only on passing time and after
  passage of this "preparatory" stage "the work
  itself" begins (the diagram sharply goes upwards
  probabilities P11, P22 tends to 1 Figure 3),
  giving result. Thus the equations describing
  behaviour of probabilities, look as logistic
  curve

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Figure 3. Dependence pij on financing r. Var2.
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Conclusion

• Conditions of existence of optimum volume of
  financing ropt , minimizing the general
  expenses on performance of the project C(r), are
  found. The special cases appropriate to the most
  natural kinds of dependences of probabilities
  pij(r) from volume of financing r of research
  stages of the innovational project are
  considered.

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References

• 1. Ackoff R.L., Sasieni M.W. Fundamentals of
  operations research, N.Y., Wiley, 1968, p.455
• 2. Bergemann D. and Hege U. 2005. The Financing
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  Journal of Economics, The RAND Corporation, vol.
  36(4), pages 719-752, Winter.
• 3. Hall B. H. and J. van Reenen. 2000. How
  Effective are Fiscal Incentives for RD? A New
  Review of the Evidence, Research Policy 29
  449-469.
• 4. Kortum S. and Lerner J. 2000. Assessing the
  Contribution of Venture Capital to Innovation,
  Rand Journal of Economics 31(4) 674-92.
• 5. Scherer F. M. 1998. The Size Distribution of
  Profits from Innovation, Annales d'Economie et
  de Statistique 49/50 495-516.