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)wok*

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The Survival Curves of the Fixed Assets of

Listed Companies

TAKITA Kazuo

In this paper, the survival functions of the fixed assets of listed compa-nies in Japan are estimated using the Corporate Financial Data Bank of Development Bank of Japan (DBJ data). The parameters of Weibull sur-vival function of the fixed assets are estimated every year by calculating the solution of the simultaneous equations concerning the acquisition cost of stocks, book-value and a depreciation expense (eq.9-eq.11). The average service life and average age of a stock are then calculated from the esti-mated parameters of this survival function. Fundamental results of estima-tion are shown by the Annex Table 1. The main conclusions obtained from our analysis are summarized as follows.

1. According to the estimation results, 70% of the shape parameters!of the Weibull survival function are distributed between 1.0-2.0 in accordance with earlier research findings.

2. In 2010 fiscal year when service lives of stocks are only publicly re-leased by the Cabinet Office Private Enterprise Investment / Retirement Survey result at present, if the service lives of stocks in the Cabinet Office survey are compared with those of this paper, the correlation coefficient between them is set to r= 0.73, and it turns out that two service lives show strong correlation to some extent. However, if we investigate in detail, re-markable differences also exist depending on industry and asset. When the causes of these differences were examined, it turned out that the main causes seemed to be in the difference of sample companies, aggregation methods, the treatment of used assets, and survival assets / scrapped as-sets approach (Table 1).

3. In order to investigate further the reliability of the results of this

per, the average ages of the stocks calculated from estimation results were compared with gross / net ratios of stocks in DBJ data. And we found that both showed strong correlations in many industries and assets not only in the logarithm value but in first-difference of logarithm value (Table 2). Since change of gross / net ratio of a stock reflects its age transition basi-cally, it can be said that these strong correlations show that survival func-tion estimafunc-tion of this paper has high reliability to some extent.

4. When we investigated by simulations how much the results of this pa-per depended on the assumption of the initial values of depreciation rates or the extended values of investment series, we found that the simulation values in general were converged on the specific course with lapse of the time except for the depreciation rate values (Table 3, Table 4). Therefore, it can be said that our estimation results in general depend less and less on initial values, as estimation period becomes far from starting period of esti-mation. However, depreciation rate values were exceptions. Such a conver-gence tendency was not found about simulated depreciation rates. The rea-son of this seems to be that by the estimation system of this paper esti-mated depreciation rates react to the estimation errors of past years very sensitively, and repeat sharp changes alternately. Then, in order to control these biennial changes of estimated depreciation rates, certain smoothing mechanism should be implemented. But we decided to leave solving this problem as a future subject.