High inheritance tax payments may cause firm discontinuation which entails liquidation costs. As a result policies often allow for preferential inheritance tax treatment of capital that is invested in continued private businesses. In this paper I highlight that preferential treatment also entails costly distortions on succession and capital structure decisions of firms. In order to study the quantitative and welfare consequences of a preferential tax treatment in the inheritance tax code I develop a structural general equilibrium model with occupational choice and business owners who have the option to run a private (family) business or to go public tapping external equity via selling shares of their business. The effects of preferential tax treatment in the inheritance tax code are twofold: First, it may induce unskilled heirs to continue an inherited business. Second, owners use less external equity, and thus, fail to diversify risk. More risk increases saving for precautionary reasons which increases wealth inequality. I calibrate the model to the German economy where capital invested in private businesses is eligible for large inheritance tax deductions. I find that abolishing the preferential tax treatment decreases the share of entrepreneurs by 21.5%. Fewer unskilled heirs continue an inherited business. Interestingly, fewer skilled agents which did not inherit a firm are crowded out from entering entrepreneurship. The gini coefficient measuring overall wealth inequality decreases by 4%p. The overall effects of capital structure decisions on wealth inequality are small. The model predicts overall welfare losses in life time consumption of -0.005%.