Valuation practice makes extensive use of the discounted cash flow and residual income valuation models and, to a lesser extent, options-based models. Despite their popularity, implementation of these models relies on a number of simplifying assumptions. For example, earnings/dividend forecasts are typically based on assumptions such as constant dividend growth or constant dollar value of reinvestment. These assumptions are made more for analytical convenience than for their realism.
As an alternative, the valuation literature has recently embraced the Stochastic Earnings Valuation Model (SEVM). The SEVM explicitly recognises that earnings is both the main driver and the primary source of uncertainty for firm value. Rather than make simplistic assumptions about the evolution of earnings through time, the SEVM models earnings as a stochastic process calibrated to observed earnings patterns. From the underlying earnings process, the SEVM seeks to estimate firm value as a continuous process through time.
This thesis explores the potential usefulness of the SEVM as a new tool for firm valuation. Particular attention is focused on numerical and computation difficulties that arise in the implementation of the SEVM. Two acute problems are identified. First, an appropriate functional form for the earnings process must be identified. Fitting a continuous-time process to earnings is a difficult task given how infrequently earnings are reported. Second, firm value under the SEVM is given by the solution of a second order partial differential equation. Since this PDE cannot be solved analytically, numerical solutions are required.
This thesis examines two methods of solving the firm value PDE. The discretisation error associated with implementing each method is documented and ways to significantly reduce this discretisation error are explored. This thesis also develops a parameter estimation method for the continuous time earnings process. This method has an objective function that uses Kolmogorov-Smirnov test statistics to measure the difference between the "observed" and simulated firm value, where the simulated firm value is numerically generated using the refined numerical method of lines.
The results from this study suggest that non-trivial challenges must be overcome before the SEVM is likely to challenge the track valuation approaches. Simulation analysis shows that the performance of the method is largely affected by the initial guesses employed in the optimisation routine and the number of grid points in the firm value surface. The improvement in the estimation ability is much greater for initial guesses with smaller initial guess for the drift term. However, further studies along the lines of this thesis are required before a conclusion can be drawn on the consistency of the estimates. Thus, this study provides some guidelines for future research in the area of SEVM.