Out With the Old, in With the Network Effects: Dynamic Stochastic Cash Flow Forecasting and Valuation Estimation for Software Companies using Panel Vector Error Correction and Revised Discounted Cash Flow Models

Abstract

This paper sets out to revise the discounted cash flow (DCF) valuation model to reduce model biases and hypersensitivities to subjective risk premia assumptions, static/linear free cash flow forecasting, imprecise discount rate selection, and an inability to internalize revolutions within the unit economics that underpin the network-effect driven business models of contemporary software companies. Ultimately, the paper introduces a simplified DCF model that solely depends on cash flow forecasts and the risk-free discount rate, which is represented by the annual average 10-Year U.S. Treasury Yield. Eliminating the DCF model's reliance on case-by-case discount rate and risk premia selection necessitated developing a methodology that could achieve more precise cash flow forecasting and assign tighter probabilities to a company's future cash flow outcomes. To accomplish this, the paper aggregates contributions from previous economic research on the application of econometric methods to model cross-sectional, time-series corporate financial data. To improve forecasting precision, analysis begins by segmenting the selected basket of companies according to a respective company's current growth rate within its long-term logistic growth function. Segmentation produced three network classes including: the exponential growth cluster, the linear growth cluster, and the logarithmic growth cluster. Following segmentation, a multiple leave-one-out cross-validated panel vector error correction method (LOOCV pVECM) is adopted to fit and forecast the dataset's 11 selected companies over a 44-quarter observation period from 2010Q1 to 2020Q4. The model's set of endogenous variables include free cash flow, operational expenses, gross profits, revenue, net income, average revenue per user, market capitalization, and user population as a proxy for a company's network. The 11 network-enabled U.S. software companies include Amazon, Apple, eBay, Facebook, Groupon, Netflix, TripAdvisor, Twitter, Yelp, and Zillow. Endogenous variable relationships are visualized through impulse response functions, variance decomposition graphs, historical decomposition graphs, and estimation. Performance between the aggregate set of company model and network segment models is measured using a menu of goodness of fit tests. The revised DCF model then uses LOOCV pVECM ex-post cash flow forecasts and real data as cash flow inputs to produce two ex-post predictions of each company's 2010Q4 market capitalization. The two valuation estimates are then compared to each company's observed 2010Q4 market capitalization to test the model's performance. Average outlier-adjusted divergence of the simplified DCF valuation estimates from observed 2010Q4 market capitalizations using forecasted and real data inputs were 12% and 15% respectively. The LOOCV pVECM is also used to produce ex-ante cash flow and user population forecasts from 2021Q1 to 2024Q4.