According to several empirical studies, the Present Value model fails to explain the behaviour of stock prices in the long-run. In this paper, the authors consider the possibility that a linear cointegrated regression model with multiple structural changes would provide a better empirical description of the Present Value model of U.S. stock prices. The methodology is based on instability tests recently proposed in Kejriwal and Perron (The limit distribution of the estimates in cointegrated regression models with multiple structural changes, 2008, and Testing for multiple structural changes in cointegrated regression models, 2010) as well as the cointegration tests developed in Arai and Kurozumi (Testing for the null hypothesis of cointegration with a structural break, 2007) and Kejriwal (Cointegration with structural breaks: an application to the Feldstein-Horioka Puzzle, 2008). The results obtained are consistent with the existence of linear cointegration between the log stock prices and the log dividends. However, the empirical results also show that the cointegrating relationship has changed over time. In particular, the Kejriwal-Perron tests for testing multiple structural breaks in cointegrated regression models suggest a model of three or two regimes.