上市櫃公司現金減資之預測： 區別分析與二元Logistic迴歸之應用

Abstract

現金減資被認為對成熟公司具有提高股東權益、降低代理問題、使資金運用更有效率的效果，最早的案例出現在2002年，截至2009年為止，可用來當作樣本的現金減資公司僅47家。過去研究普遍集中在現金減資和其他減資的差異，或現金減資宣告效果、異常報酬、減資後績效等。本研究將現金減資獨立於任何減資之外，透過配對樣本與不配對之全部樣本兩種樣本設計，搭配顯著平均數、逐步兩種變數選擇方式，利用區別分析與二元Logistic迴歸對現金減資與非減資兩群體做分類預測。 實證結果發現，不配對之全部樣本受到樣本大小差異過大及產業因素影響，採用配對樣本較為適當。在變數選取上，逐步方式在樣本內有較佳的分類效果；顯著平均數方式在樣本外，有較佳的預測效果，且樣本內外的總正確率落差較小，以預測而言，使用顯著平均數似較恰當。其中負債比率和股價淨值比是最重要的兩個變數。在統計方法上，區別分析分類預測現金減資的正確率較高，二元Logistic迴歸分析在判斷非減資的效果較佳；而不管統計方法為何，預測現金減資的正確率平均在八、九成以上，都高於預測非減資約四、五成的正確率，最後總正確率在六、七成上下。

Capital stock downsizing with cash refunding to shareholders seems to be effective in enhancing stockholder’s equity and reducing agency problems. The first case of this type occurs in 2002 and until 2009 there have been 47 cases. Literatures have so far focused on differences between three kinds of capital reductions and their announcement effect, abnormal return or post-downsizing performance of cash capital reduction. This research concentrates soly on cash capital reduction event, and builds two empirical models for paired samples and non-paired samples. Both empirical models found significantly different sample means in several financial variables. These variables are then applied to discriminant analysis and binary logistic regression to classify and predict cash capital reduction. We find that paired samples are more suitable than non-paired samples for they are not affected by sample size and industry factors. When it comes to variable selection, stepwise method is good at in-sample classification while significant means method is useful in out-sample prediction. Debt ratio and price-to-book ratio are found to be the most significant variables in explaining downsizing decision. Besides, discriminant method has higher cash capital reduction accuracy whereas binary logistic method has higher non-cash capital reduction accuracy. No matter which multivariate method is used, the predict accuracy of cash capital reduction is above 80% which is higher than the predict accuracy of non-cash capital reduction of 40%. The overall accuracy ranges from 60% to 70% plus.