Valuation of Irreversible Entry Options under Uncertainty and Taxation

We analyze the tax effects on a potential firm with an irreversible entry option and subject to risky post-entry earnings. We formulate the problem in terms of optimal stopping and derive both the necessary conditions for optimal entry and the value of the optimal premium by relying on the classical theory of diffusions and the Greenian representation of the stochastic value functional. We show that to make the entry option invariant with respect to the tax policy when the government owns a call option on a fraction of firm's earnings, the tax allowance has to satisfy a first-order non-linear differential equation. We derive qualitive results for the neutrality of the tax policy. Using standard geometric Brownian motion to model price uncertainty, we provide examples of the requirements for tax invariance. The Johansson-Samuelson theorem is re-examined.