This paper develops a tractable two-country DSGE model with sticky prices a la Calvo (1983) and local-currency pricing. We analyze the capital investment decision in the presence of adjustment costs of two types, the capital adjustment cost (CAC) specification and the investment adjustment cost (IAC) specification. We compare the investment and trade patterns with adjustment costs against those of a model without adjustment costs and with (quasi-) flexible prices. We show that having adjustment costs results into more volatile consumption and net exports, and less volatile investment. We document three important facts on U.S. trade: a) the S-shaped cross-correlation function between real GDP and the real net exports share, b) the J-curve between terms of trade and net exports, and c) the weak and S-shaped cross-correlation between real GDP and terms of trade. We find that adding adjustment costs tends to reduce the model's ability to match these stylized facts. Nominal rigidities cannot account for these features either.