Terminal Value Modeling in Finance: Using the Laplace-Transform

The article presents an innovative approach to the valuation of the terminal value of investment projects and enterprises. A key element of the proposed methodology is the analysis conducted in the capital cost domain using the Laplace transform, under the assumption of a continuous rate of return. Given a specific cost of capital, the analysis may be extended to other variables on which cash flows depend—particularly those subject to uncertainty. The proposed framework enables the modeling of terminal value using any function f(t) for which the Laplace transform exists. Decoupling the analysis from the time domain facilitates the determination of optimal parameter values, such as decision moments, prices of products and raw materials, which become new variables within the domain of analysis. This perspective simplifies the examination of residual value across various parameters influencing cash flows. Such an approach enhances the modeling of uncertainty and allows for the inclusion of parameters exposed to variability, even when the terminal value is described by complex time-dependent functions. The article presents four illustrative models of terminal value; however, the methodology is oriented toward model development rather than merely applying the examples provided herein. The study offers a detailed exposition of the theoretical foundations and application of the Laplace transform in the valuation of residual value, incorporating decision options. The analysis highlights the analytical advantages of conducting valuation in the capital cost domain, particularly through the time-independent formulation of the problem.