An Analytical Real Option Replacement Model with Depreciation

A replacement model is presented for a productive asset subject to stochastic input decay, tax allowances due to a deterministic depreciation variable, and a fixed investment cost. The risk neutral valuation function is formulated and optimal trigger levels signalling replacement for the two factors is determined analytically although not as a closed-form solution. We demonstrate that the operating cost trigger level depends on asset age and increases monotonically due to positive volatility changes and that the model solution furnishes the results for certain special cases. The analysis is conducted both for a depreciation schedule specified by the declining balance and straight line method. The comparative analysis shows that although no universal ideal depreciation schedule exists between the two, the declining balance method is preferred. Finally, the solution method is sufficiently tractable to be applied in principle to real option models where time is a critical factor.