This paper investigates if tax planning by large multinationals distorts competition in their favour and allows them to crowd out other firms. The competitive implications of tax planning are frequently mentioned in the tax policy debate, but not yet documented empirically to our knowledge. This paper aims to fill this gap. Drawing on firm-level data from the ORBIS database, it compares price-cost mark-up rates of firms with different tax planning opportunities, using several proxy measures of these opportunities, such as links to tax havens. Tax-planning multinationals are found to have higher mark-up rates than other firms, even after controlling for other factors influencing mark-ups. However, the direction of causality is difficult to establish since a high mark-up can be a factor encouraging a firm to engage in tax planning. Based on a new indicator of industry concentration, the empirical analysis also shows that industries with a strong presence of tax-planning multinationals tend to be more concentrated than other industries, but less so when strong rules against tax planning are in place. Overall, the results support the hypothesis that large multinationals use their tax savings to crowd out other firms and ultimately obtain higher mark-ups.