Stochastic Method of Discounted Cash Flows
Authors: Solodov A. A. 
Published: March 2021

The method of discounted cash flows (DCF) is one of the main and popular methods of economic assessment of business, which is used all over the world. However, the actual behavior of business projects evaluated by this method often differs from that predicted, and the difference can be tens of times.

It should be noted that at present, the discounted cash flow method is a subject of extensive literature, but there are no analytical arguments for large discrepancies between the theory and practice of the method. The aim of the study is to provide a theoretical explanation of the forecasting errors inherent in the discounted cash flow method. The research method is related to the analysis of the traditional method of discounted cash flows, which shows that the key indicator that affects the final result is the net income for a certain period of time. Analyzing the economic content of the flows that appear in the formation of net income, we can conclude that for a trade-type enterprise, the cash flow of receipts associated with current operations is significantly random and, therefore, requires the use of stochastic description methods.

The paper offers a mathematical model of the mentioned cash flow. It is assumed that the event associated with a purchase (cash receipt) is modeled on the time axis by a point with a random time of occurrence. Then, obviously, the number of points n that appear on a fixed time interval will be a random number. A justification is given for the fact that the point process is a Poisson random point process or simply a Poisson point process, in which the times of occurrence of points W1 ,W2 , ..., Wi and their number N(t) at time t are random variables. We introduce the function λ(t), which characterizes the average number of cash receipts (purchases) per unit of time. From an economic point of view, it is driven by consumer preferences of buyers, and from a mathematic point of view it is a function of the intensity of appearance of points of the Poisson process. The monetary values of purchases made by customers are described by random positive ui values which arise at the Wi moments of the occurrence of shopping events, simulate a random process of cash receipts at the enterprise.

Introduction to the consideration of the random Poisson flow of business receipts and their values, which are also random positive values with an arbitrary probability distribution, is the key assumption of the work. The proposed approach allowed us to develop a stochastic model of the company’s revenues, generalize the method of discounted cash flows, obtain a number of simple ratios, and on this basis explain the growth of the method forecast error with an increase in the duration of the forecast horizon.

New results of the study are the use of stochastic methods to describe business revenues and expressions obtained on this basis for the variance and standard deviation of the company’s net cash flow, depending on the number of forecasting periods. It is shown that the growth of the standard deviation of the net cash flow, i.e. the forecasting errors, is a fundamental feature of the method in this interpretation. For the initial estimates, a simple expression is obtained and corresponding graphs are given.

In conclusion, it is noted that the presented graphs of the behavior of the standard deviation of the method estimates show that the estimate from below of the mentioned deviation slowly grows with an increase in the number of prediction periods and depends only on the number of periods. It is noted that this growth is calculated in relation to the first forecast period, which itself may contain errors, and it is determined only by consumer preferences. Of course, you can choose the forecast period not a month, but, for example, a year, but then the error of the first period will be significantly increased. Thus, this review makes it possible to explain some aspects of the growth of the error of the discounted cash flow method with the forecast time.