A dynamic-panel model is applied in order to empirically investigate the relationship between business fixed investment and Tobin’s q for the firms listed in the Athens Stock Exchange (ASE). In particular, we search for non-linearities in the underlying relationship between investment and fundamentals, consistent with the presence of multiple regimes. The empirical results support a discontinuity identifying two-regimes: (a) wherein the first (for values of q below a certain threshold) investment is inelastic to q, while in the second it exhibits a positive relationship, and b) a further non-linearity expressed in a concavity of the investment- q relationship implying that for the segment where investment reacts to fundamentals positively, it does so at a decreasing rate evidence which is consistent with the presence of non-convexities in adjustment costs.