Terminal Value Modeling in Finance: Using the Z-Transform

The study introduces a novel methodology for assessing the terminal value of investment projects and enterprises, emphasizing an analytical framework based on the capital cost domain through the application of the Z transform, under the premise of a discrete rate of return. Within this framework, and assuming a predefined cost of capital, the analysis may be expanded to include other variables affecting cash flows, particularly those characterized by stochastic or uncertain behavior. The proposed approach enables the representation of terminal value through any function f(t) for which a Z transform is defined. By transitioning from the time domain to the capital cost domain, the methodology allows for a time-invariant formulation of the valuation problem. This shift facilitates the identification of the optimal stopping moment, with the exercise time treated as an endogenous variable within the transformed analytical space. This conceptual decoupling simplifies the treatment of residual value in relation to various underlying parameters influencing cash flow generation. It also supports the modeling of uncertainty and the integration of stochastic parameters, even in scenarios where the terminal value exhibits a complex temporal structure. The article presents four exemplary models of residual value construction to illustrate the application of the method; however, its primary contribution lies in establishing a generalizable modeling framework, rather than prescribing a fixed set of solutions. Theoretical justifications and practical examples are provided to demonstrate how the Z transform can be effectively employed in the valuation of terminal value, particularly in conjunction with decision options. The advantages of this transformation-based approach are underscored, notably the increased analytical flexibility afforded by removing time as a direct variable from the valuation process.