# A stochastic DCF model with a recursive calculation of the value of an enterprise

Brian Jeppesen

Student thesis: Master thesis

## Abstract

The present thesis focuses on the discounted cash flow model. The discounted cash flow model is also known under the name DCF model. The DCF model is used for valuation of an enterprise. As the name implies the discounted cash flow model determines the value of the enterprise by discounting a future cash flow to a present value. However, the discounting rate used for the discounting is in itself a function of the enterprise value, i.e. the enterprise value in the DCF model is a result of a function that depend on the result of that same function. In the literature this is known as a recurrence problem (Larkin, 2011) or a circularity problem (Mohanty, 2003). For a DCF model in discrete time the recurrence problem has been solved with iteration algorithms without major difficulties. However, for a stochastic DCF model in continuous time the recurrence problem seems to be more difficult to solve. It is therefore asked how it is possible to account for the recursive nature of the enterprise value in a stochastic DCF model. The recurrence problem is solved by proposing an iterative DCF model. The iterative DCF model takes its starting point with the Monte Carlo method. The Monte Carlo method is suitable for numerically generating a cash flow as a function of time. The cash flow is then discounted backwards step by step until present time. This stepwise discounting allows for an isolation of the enterprise value such that there is no recursive or circular relationship between the enterprise value and the discounting rate. With the proposed iterative DCF model it becomes possible to see how the recursively calculated enterprise value compare to a more simple DCF model. For a low leveraged enterprise there is no difference between the iterative DCF model and a simple DCF model. Thus, for the low leveraged enterprise it would seem ok to use a simple DCF model when determining a value of an enterprise. However, for a high leveraged enterprise it surprisingly turns out that the error on the enterprise value by using a simple DCF model is quite large. Thus, for the high leveraged enterprise an iterative DCF model should be used or it should at least be borne in mind that there is a large error involved in using a simple DCF model.

Educations MSc in Finance and Accounting, (Graduate Programme) Final Thesis English 2013 91