Abstract: Inter-temporal allocation is one of the new perspectives to study the M&A integration of diversified enterprise, execution and adaptability needs to be taken into the inter-temporal allocation. Division's relatedness is the key index to weigh the execution and adaptability. Execution is improved, but adaptability is reduced by high division's relatedness. Adaptability is improved, but execution is reduced by low division's relatedness. Execution is corresponded to inter-temporal allocation cost which is measured by internal transaction cost level. Adaptability is corresponded to inter-temporal allocation space which is measured by return volatility. The best division's relatedness is matched by the two key dimensions which are internal transaction cost and return volatility.
However, the matching mechanism is not clear yet, so it is needed theoretical analysis and empirical test. Based on the pricing idea of real options, the matching mechanism of division's relatedness is explained by binary tree numerical analysis of bellman dynamic programming equation. First, the current and future investment decisions are assumed as a series of dynamic real options in the model. The inter-temporal allocation of resources by headquarters could be seen as to execute call option of the division transferred into the resource and put option of the divison transferred out of the resource. Secondly, the return of the two divisions is assumed to be subject to Geometric Brownian Motion (GBM). Finally, the HJB equation model depicts the results of the inter-division capital allocation by the headquarters at time t based on the principle of maximizing expected return. The numerical analysis results of HJB equation show that the best division's relatedness is affected by the transaction cost and the volatility of return.
The matching rules are as follows:the decrease of transaction cost and the increase of return volatility are leaded by the decrease of best division's relatedness; the influence degree of one factor is affected by the other, that is to say, the transaction cost and the volatility of return are mutually moderators. The empirical chapter is based on the division's data of Chinese listed companies. The empirical results show that the division's relatedness of Chinese listed companies is significantly affected by the transaction costs and volatility of return, and the moderating effect is significant, which is consistent with the numerical analysis results of dynamic programming equations. The matching study of division's relatedness provides a new perspective for the implementation and performance evaluation of merger and acquisition integration of diversified enterprises.

Key words: the best division's relatedness, internal capital market, inter-temporal allocation, dynamic programming