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Tax system nonlinearities are often ignored but with uncertainty may have important implications for the magnitude and direction of tax effects. This paper studies a particular nonlinear tax rule. The policy subsidizes asset values, but may discourage some investments and encourage earlier shutdown of some projects. The marginal effective tax rate varies with project risk. Furthermore, a corporate cash-flow tax can encourage investment due to interactions with the nonlinear policy. The paper also presents a general statement of the stochastic equilibrium valuation method which can be used to analyze other nonlinear taxes. Numerical examples demonstrate computational feasibility.