Business valuation models: Consistent valuation, Inflation-related tax distortions, and Earnings growth rates

Abstract

This thesis comprises three studies that aim to modify and clarify business valuation models. The academic community commonly employs the adjusted present value (APV) method to create new versions of valuation models (e.g., Krause and Lahmann, 2016; Arnold et al., 2018) as it independently considers the net effect of debt financing on value. Conversely, practitioners mostly rely on the cost of capital (CoC) method (Ross, 2006). To achieve equivalence between these methods, the discount rate in the CoC method must incorporate the unleveraged discount rate, tax benefits, and tax costs presented in the APV method. This implies that the updated version of the APV leads to the latest iteration of the discount rate in the CoC method. The first study introduces a new version of the APV that considers stochastic debt and the trade-off between corporate income taxes (CIT) and personal income taxes (PIT), as well as the trade-off between tax benefits and the costs of financial distress. Additionally, we develop the discount rate in the CoC method to ensure CoC-APV consistency. In other words, the first study primarily focuses on the denominator of the discounted cash flow (DCF) technique. In contrast, the second and third studies address issues related to the numerator of the DCF model, namely cash flows. The second paper analyzes the inflation-related tax distortions in business valuation models (i.e., tax perspective) by clarifying the distortions in free cash flow to the firm. On the other hand, the third paper focuses on earnings growth rates (i.e., accounting perspective). Consistent valuation: Extensions from bankruptcy costs and tax integration with time-varying debt The first study in the thesis considers all the necessary conditions to achieve a con- sistent valuation between the CoC method and the APV method at the highest level of generalization. The developed equivalent formulas in this study consider stochastic debt, account for the trade-off between CIT and PIT, and the balance between tax benefits and the costs associated with financial distress. The valuation aspect ensures that the value of expected bankruptcy costs is practical for valuers to apply using the formulas. Furthermore, the equivalence captures the disparity in the tax shield perspective between stockholders and debtholders when PITs are introduced. Finally, the results demonstrate that the equivalence established in this study aligns with previous standard formulas under their strong assumptions. Macroeconomic contexts and business valuation models: Inflationrelated tax distortions The second study modifies tax distortions in business valuation models when countries experience inflation. This study is considered to analyze valuation methods from the tax perspective. The current CIT expense occupies just one line item on the statement of profit or loss and other comprehensive income. However, it is a unique line item following tax rules and not financial reporting rules. The difference between these rules is that it reflects the effective tax rate (ETR), which can differ from the statutory tax rate (STR). With inflation, this ETR-STR difference can be more significant due to the contribution of tax distortions. In this study, we expand on the standard formulas for the ETR by analyzing the effects of inflation-related tax distortions when computed under the following four cases: (i) Historical-cost-based accounting under a nominal tax basis, (ii) Fair-value-based accounting under a nominal tax basis, (iii) Historical-costbased accounting under a real tax basis, and (iv) Fair-value-based accounting under a real tax basis. Further, we suggest a modified model for business valuation considering these tax distortions and provide a general formula to independently calculate the value of inflation-related tax distortions. Published in the North American Journal of Economics and Finance, Vol. 66, 2023. Earnings growth rates in business valuation models: Impossible quaternity The third study aims to clarify earnings growth rates in business valuation models to prevent valuation errors. This study analyzes valuation methods from an accounting perspective. Initially, we demonstrate that cross-referencing in calculation between the reinvestment rate, RIR, and return on invested capital, ROIC (i.e., average invested capital), can lead to valuation errors. Subsequently, we clarify the formulas for earnings growth rates to avoid mistakes in two scenarios: reinvestment at the end of each year and reinvestment at any time during the year. The study also identifies the timing of capital reinvestment, where the erroneous growth rate resulting from cross-referencing equals the actual growth rate. Furthermore, we highlight cases where the incorrect growth rate consistently exceeds or falls below the actual growth rate. Numerical examples are provided to demonstrate the correctness of our models and the errors caused by cross-referencing. We offer a practitioner guide for two scenarios: when valuers estimate earnings growth rates directly and when clients provide future earnings and related information. Lastly and importantly, our results imply the principle of impossible quaternity for estimating earnings growth in the DCF framework. Specifically, it is impossible for a business valuation to possess an available-expected growth rate, a fixed change in ROIC, independence in the timing of reinvestment, and a fixed level of actual reinvestment.