Inheritance tax planning with uncertain future payroll expenses: an analytical solution to the optimal choice between full and standard exemption

Under the German Inheritance Tax and Gift Tax Act, the transfer of business assets can be exempted from taxation up to 100%. However, this exemption depends on the evolution of the company’s payroll, which is highly uncertain. We model the uncertain nature of payroll evolution using a Geometric Brownian motion. We obtain closed-form solutions for the expected effective exemption and for the expected effective tax rate. We find that the uncertainty effect is most pronounced for moderate negative and positive growth rates. Furthermore, higher uncertainty reduces the value of the effective tax exemption. Also, we find that the (partially progressive) German inheritance tax function by trend promotes standard exemption. The results enable tax planners to make an optimal choice between standard or full exemption and allow for calculating the expected tax burden.