Previous papers which test the relationship between stock price and earnings per share mainly use linear models and achieve inconsistent result. In a different way, this paper employs the recently developed Hansen (1999) method to test the threshold effect. We first address a panel threshold regression model to investigate the existence of book value threshold effects in the relationship between stock price and earnings per share. According to the empirical results, we find that there exists a double threshold in the model, 14.19 and 22.54, which separates the firms based on their book value of equity. Therefore, the observations are divided into three regimes on whether the threshold variable is smaller or larger than the threshold value. When the book value of equity is higher than 22.54. the earnings per share has the strongest positive effect to stock price. When the book value of equity is between 14.19 and 22.54, the earnings per share has the second strongest positive effect. When the book value of equity is above 22.54. the earnings per share has the smallest positive effect. As a result the earnings per share has a significantly positive impact to stock price in the three regimes. This finding reinforces the fact that Taiwan's stock market indeed heavily depends on evaluation of accounting.