Academic journal article International Journal of Business

Advancement to the Real Option Models in Valuing R&D

Academic journal article International Journal of Business

Advancement to the Real Option Models in Valuing R&D

Article excerpt

I. INTRODUCTION

Merton (1987) asserted the importance of information cost and documented that an investor shall demand higher stock return if higher information cost is expensed. Following the context of Merton, Bellalah (1999a, 2003b) incorporated the information cost factor in valuing both options and R&D. However, in Bellalah's setting only the factors influencing R&D's market value were considered. The truth is that R&D value will depreciate while time elapses; its value could also be vanished overnight because of any unexpected evolution. These facts imply some other exogenous factors which influence the R&D's payoff deserve to be comprehended. This study attempts to modify Bellalah's ROM as to incorporate factors like exponential decay (9 ) and Poisson event ([xi]) into consideration.

There are three types of information cost defined including the average cost prevailed in market ([[lambda].sub.M]), the cost affiliated with R&D options ([[lambda].sub.F]) and the cost affiliated with R&D yield's price ([[lambda].sub.P]). The disposal in Bellalah (1999a, 2003b) may have caused two issues: first, the individual effect of information costs was unknown and, secondly, the reason of why [[lambda].sub.M], [[lambda].sub.F] and [[lambda].sub.P] were set to be 4% for example was unknown. For the level of information cost, Bellalah stressed the hardness in defining it and proposed an alternative as to find proxies from derivates markets; though this idea was not taken eventually. We are going to observe the individual effect of information costs; we are also going to actualize Bellalah's proposal to see what the real level of information cost could be and. To sum up, the existing ROM in valuing R&D could either be too optimistic or too pessimistic. This inaccuracy could be caused by either inappropriate model setting or inappropriate parameter level setting; we are trying to reduce the mentioned inappropriateness through both statistical and mathematical means.

II. RE-MODELING

The factors of exponential decay [theta] and Poisson event [xi] are going to be considered. [mu] means the required rate of return which is the sum of expected capital gain [alpha] and dividend [delta]. While exponential decay and Poisson event are jointly considered, the project value can be:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)

The R&D project value can be deemed the function of product price 'P'. P follows the mean reverting process dPdt + [alpha]PdZ - [pi]P[xi]dt, [phi] represents the loss rate of the sudden death, [xi] represents the probability of sudden death. The revenue of an investment can be expressed as u = [alpha] + [delta], [alpha] is drift term, [delta] represents dividend yield, [mu] is the risk adjusted expected rate of return which equals to the risk free rate r under the premise of arbitrage free. The expected present value of cash flow will become:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which is the integral base of the value of entire investment V. If the stochastic process of exponential decay is further considered, its p.d.f. function will be incorporated as the (1) showed. Through (1), a spiky event like [theta] and [xi] can be smoothened as an additional discount factor in the denominator.

According to ROM, an R&D project value V can be seen as a combination of investment I and option value F therefore V(P)=I+F(P). We may utilize a portfolio [PHI] = F(P) - nP as to long one unit of option and to short n units output with price P and let its payoff be:

r[F - nP]dt = dF - ndP - n[delta]Pdt (2)

From (2) we can derive a corresponding Bellman equation:

(1/2)[[sigma].sup.2][P.sup.2][F.sub.PP] + (r - [delta])[PF.sub.p] - rF = 0 (3)

In (3), we set n = F'(P) to eliminate the disturbance term dz. (3) is a Partial Differential Equation (PDE) and we can solve F by either analytical, if it has a close form solution, or numerical way. …

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