Abstract: In the process of M&A,the key problem is how to decide the transaction price, which can be divided into two steps including the evaluation of transaction asset and the process of pricing the target asset. The former must be processed to disclose the volume of real option hidden in uncertain attained profit and cost spending, while the latter can be processed based on the game analyses of bilateral transaction sides of M&A.Up to now, the measurement of real options under continuous stochastic surroundings has been studied by many scholars all over the world, whilst the measurement of real options under discrete stochastic surroundings has also been studied by way of using binary tree and trigeminal tree methods on the condition of limited transformation times of target asset.
In this paper, the measurement of real options under unlimited times of asset transformation is studied by way of using binary tree method in reference to some existing related studies.Firstly, the distribution of real option of binary tree with unlimited transformation times of asset can be deduced to be normal function by way of applying the central limited theorem.Secondly, the detailed analyses of famous Rubinstein bargaining theorem is conducted to disclose an important fact that the transaction asset is assumed to be distributed as uniform distribution, thus how to price the normal distributed target asset is studied to attain the equilibrium price.Finally, the analytical expression of equilibrium transaction price can be deduced to measure the real option value of target asset which is assumed to be distributed as discrete binary tree, the corresponding numerical simulation is given to illustrate its rationality and the explaining power to reality.
In summary, a new idea of price the real option is proposed on the condition that the transformation status of asset is assumed to be binary tree, and then the problem solving approach can be referenced to other similar problems, especially to the discrete distributions including trigeminal tree.

Key words: transaction price, M&A, discrete binomial tree option model, Rubinstein bargaining theorem, numerical simulation