Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.

Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Mô hình thẩm định giá doanh nghiệp: Định giá nhất quán, Biến dạng thuế do lạm phát, và Tốc độ tăng trưởng lợi nhuận.Ministry of Education and Training UNIVERSITY OF ECONOMICS HO CHI MINH CITY Business valuation models Consistent valuation, Inflation related tax distortions, and Earnings growth rates by Nguyen Kim D.

Ministry of Education and Training UNIVERSITY OF ECONOMICS HO CHI MINH CITY Business valuation models: Consistent valuation, Inflation-related tax distortions, and Earnings growth rates by Nguyen Kim Duc A thesis submitted for the degree of Doctor of Philosophy in the UEH School of Economics UEH College of Economics, Law and Government Ho Chi Minh City, Monday 10th April, 2023 Business valuation models: Consistent valuation, Inflation-related tax distortions, and Earnings growth rates by Nguyen Kim Duc B.A in Economics (Valuation), UEH, 2011; B.A in Accounting (Audit), UEH, 2014 M.Sc in Finance and Banking (Finance), UEH, 2015 Practicing Valuer Registration | Certificate No XI16.1479, 2016 Submitted to the UEH School of Economics on Monday 10th April, 2023, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Development Economics supervised by Assoc Prof Pham Khanh Nam, Ph.D Ph.D Thesis Copyright 2023 by Nguyen Kim Duc All Rights Reserved ii Declaration of Authorship I, Nguyen Kim Duc, declare that this thesis titled "Business valuation models: Consistent valuation, Inflation-related tax distortions, and Earnings growth rates" and the work presented in it are my own I confirm that: • This work was done wholly or mainly while in candidature for a research degree at the University of Economics Ho Chi Minh City • Where any part of this thesis has previously been submitted for a degree or any other qualification at the University of Economics Ho Chi Minh City or any other institution, this has been clearly stated • Where I have consulted the published work of others, this is always clearly attributed • Where I have quoted from the work of others, the source is always given With the exception of such quotations, this thesis is entirely my own work • I have acknowledged all main sources of help • Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself Nguyen Kim Duc Ho Chi Minh City, Monday 10th April, 2023 iii iv Acknowledgements This thesis would have remained a dream had it not been for the assistance of professors, partners, friends, classmates, and my family I am indebted to all people who helped me throughout my Ph.D journey and made this thesis possible Above all, I owe my deepest gratitude to my big family I started my Ph.D journey in my early 30’s and could not have come this far without their trust, support, and unconditional love I am deeply indebted to my mother, Mong Hang, and my wife, Lan Anh, for their love and sacrifice My mother has always been by my side, while my wife has supported me and sacrificed at all times In addition, my Ph.D journey is also associated with my son’s childhood I started my Ph.D thesis in December 2018, and my son, Phuc Bao, was born in February 2019 His affectionate actions and sunny smile are an endless source of positive energy for me to complete this thesis This dissertation is as much them as it is mine The thesis would not have been possible without my supervisor’s guidance, support, and discussion—Assoc Prof Pham Khanh Nam With immense gratitude, I acknowledge the guidance and support of Dr Khanh Nam for his patience, advice, and warm-hearted support throughout my Ph.D study at the UEH School of Economics He has constantly challenged me to think critically and has taught me the value of thorough research His enthusiasm, patience, knowledge, and inspiration for research have encouraged me and helped me when I was writing this thesis His expertise in economics and new ideas have improved my research skills and prepared me for future challenges Assoc Prof Khanh Nam has given me autonomy in decision-making and researching the topic while continuing to provide valuable feedback, advice, and encouragement I enjoy the long discussions with him in his office, from whom I have learned how to develop research ideas, understand research experience, and write professional academic articles I would never imagine having a better advisor for my Ph.D study I would like to thank the board of professors for my thesis in UEH—Prof Nguyen Trong Hoai, Dr Nguyen Hoang Bao, Dr Vu Viet Quang, Dr Duong Nhu Hung, Dr Le Trung Thanh, Dr Tran Thi Tuan Anh, Dr Pham Ha, and Dr Nguyen Thi Hong Nhung—for their valuable comments and suggestions I also want to thank the professors—Prof Nguyen Trong Hoai, v Prof Gabriel S Lee, Dr Tran Thi Tuan Anh, Assoc Prof Tran Tien Khai, Dr Nguyen Luu Bao Doan, Dr Truong Dang Thuy, Dr Ho Quoc Thong, MA Luong Vinh Quoc Duy, Dr Ly Thi Minh Chau, and Dr Le Van Chon—who provided the knowledge foundation and methodology on which I could my Ph.D thesis I sincerely thank two anonymous reviewers of the North American Journal of Economics and Finance and two independent external reviewers of the UEH board of professors, for many constructive comments and suggestions, which significantly enhance my paper’s exposition I also thank the conference participants at the 22nd ASEAN Valuers Association Congress in Thailand in 2019, the 38th EBES Conference hosted in Poland in 2022, and the 40th EBES Conference hosted in Turkey in 2022, for helpful comments I would like to thank my dear colleagues at UEH and UEH School of Economics for their substantial influence They provide the best environment for teaching, studying, and researching I also give my thanks to colleagues in the UEH Department of Valuation at UEH School of Economics— Dr Hay Sinh, MA Tran Bich Van, Dr Nguyen Quynh Hoa, MA Huynh Kieu Tien, and Dr Nguyen Thi Tuyet Nhung—they always supported and encouraged me in this study and helped me throughout my career I also would like to thank professors, reviewers, and professional valuers in global and local valuation firms who gave me a lot of valuable comments and bits of advice Their comments are one of the major contributing factors that allowed me to complete this version of the thesis I would also like to thank all my classmates and friends for their support and suggestions along the way, especially Thanh Tam, Hoang Minh, Tuyet Nhung, Thanh Truc, Phuong Vy, Anh Nguyet, and Thiet Ha—Ph.D students like me I really enjoy studying and discussing with all of them Special thanks also go to the administrative staff in UEH School of Economics, Ph.D program office, and UEH Finance-Accounting Department Their generous support and kind help greatly eased my daily life and the Ph.D journey Thank you all very much Nguyen Kim Duc Ho Chi Minh City, 06:00 Monday 10th April, 2023 vi Abstract This thesis contains three studies that provide a set of modifications and clarifications of business valuation models The academy usually employs the adjusted present value (APV) method to develop new valuation models (e.g., Krause and Lahmann, 2016; Arnold et al., 2018) because it independently considers the net effect on value due to debt financing In contrast, the cost of capital (CoC) method is almost always used by practitioners (Ross, 2006) Under the equivalence, the discount rate in the CoC method must capture the unleveraged discount rate, tax benefits, and tax costs in the APV method This means that the new version of the APV leads to the latest version in the discount rate of the CoC method Therefore, the first study provides a new version of the APV, allowing the stochastic debt and considering the trade-off between corporate income taxes (CIT) and personal income taxes (PIT), and between tax benefits and costs of financial distress Then, we develop the discount rate in the CoC method to meet the CoC-APV consistency In other words, the first study focuses on the denominator of the discounted cash flow (DCF) technique In contrast, the second and third studies resolve the problems in the numerator of the DCF model (i.e., cash flows) Paper Consistent valuation: Extensions from bankruptcy costs and tax integration with time-varying debt The first study in the thesis considers all the conditions required to provide a consistent valuation between the CoC method and the APV method at the highest level of the generalization The equivalent formulas developed in this study allow the stochastic debt and consider the trade-off between CIT and PIT, and between tax benefits and costs of financial distress The value of expected bankruptcy costs follows the valuation aspect to ensure that it is possible for valuers to practically apply the formulas The equivalence also captures the difference in the point of view of tax shields, between stockholders and debt holders when PITs are introduced Finally, the results show that the equivalence in this study can collapse to, and is consistent with, previous standard formulas under their strong assumptions vii Paper Macroeconomic contexts and business valuation models: Inflation-related 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) Historicalcost-based 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 Paper Earnings growth rates in business valuation models: Impossible quaternity The third study clarifies earnings growth rates in business valuation models to avoid valuation errors This study analyzes valuation methods from the accounting perspective First, we illustrate that cross-reference in calculation between the reinvestment rate, RIR (i.e., under the assumption that all reinvestment is at the end of each year), and return on invested capital, ROIC (i.e., average invested capital) leads to valuation errors We then clarify the formulas of earnings growth rates to avoid mistakes in two situations: reinvestment is at the end of each year, and reinvestment is at any time of each year The study also shows the timing of capital reinvestment, where the false growth rate due to cross-referencing will be equal to the actual growth We also highlight the case in which the incorrect growth rate is always higher than or lower than the actual growth rate Numerical examples are used to illustrate that our models are correct and provide errors due to cross-referencing We deliver a practitioner guide for two scenarios: valuers directly estimate earnings growth rates, and clients provide future earnings and related information Finally and most importantly, our results imply the principle of impossible quaternity for estimating earnings growth in the DCF framework More precisely, it is impossible for a business valuation to have an available-expected growth rate, a fixed change in ROIC, independence in the timing of reinvestment, and a fixed level of actual reinvestment viii List of Abbreviations APV Adjusted Present Value ASEAN Association of Southeast Asian Nations BC Bankruptcy Costs BTD Book-Tax Difference CAPM Capital Asset Pricing Model CapEx Capital Expenditures 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• ΦBC,e denotes the percentage of bankruptcy costs (at time t) to debt (at time t − 1) from the point of view of equity holders, i.e., ΦBC,e = ρφ [τcs (1 − τpe ) + τpe ] + ρψ(1 − τpe ); • ΦBC,d denotes the percentage of bankruptcy costs (at time t) to debt (at time t − 1) from the point of view of debt holders, i.e., ΦBC,d = ρφτpd Eq (3.18) can be rewritten as V EBC t = Dt ΦBC,d Dt ΦBC,e BC,e BC,e + Υ Φ − + ΥBC,d ΦBC,d t t κBC,e κBC,d V e EBC t e V d e (A.4) d EBC t d We have E = [V Au + V ET S − V ET S − V EBC + V EBC −D] by combining the equation V A = D + E of the CoC method and Eq (2.8) of the APV method Eq (3.16) in the main text becomes1 κ E Eu =κ V ET S − E V EBC + E e Eu κ −κ e κEu − κBC,e T S,e V ET S + E V EBC − E d κEu − κT S,d (A.5) d κEu − κBC,d D Eu + κ − κDp E Towards that end, we define d BC,d t = V EBC t = Dt ΦBC,d κBC,d + ΥBC,d Dt BC,d,D t (A.6) BC,d,Υ t Eq (3.22) in the main text becomes Eu κE − t =κ + Dt Et Dt Et T S,e T S,e Φ t BC,e BC,e Φ t κEu − κT S,e + κEu − κBC,e − Dt Et Dt Et T S,d T S,d Φ t BC,d BC,d Φ t κEu − κT S,d κEu − κBC,d + Dt Eu κ − κDp Et (A.7) In terms of the CIT–PIT trade-off, the difference between ΦT S,e and ΦT S,d reflects the tradeoff for tax benefits whereas the difference between ΦBC,e and ΦBC,d shows that for bankruptcy costs The CoC–APV equivalence is still appropriate because ΦT S,e (or ΦBC,e ) can be larger than or smaller than or equal to ΦT S,d (or ΦBC,d ) For the TS–BC trade-off aspect, the difference between ΦT S,e and ΦBC,e captures the tradeoff from the point of view of equity in a world with PIT whereas the difference between ΦT S,d e d e d E + D − V ET S + V ET S + V EBC − V EBC Eu κ E e d e d V ET S T S,e V ET S T S,d V EBC BC,e V EBC BC,d D D + κ − κ − κ + κ − κ E E E E E Because κE = 144 and ΦBC,d implies that from the viewpoint of debt holders When distinguishing between gross and net V EBC [I] (i.e., the excess rates of the promised yield), the CoC–APV equivalence differs from that in section 3.3 in two ways First, there is a new component in the equivalent formulas, ΦBC,d , reflecting the excess rates of the promised yield from the debt holders’ viewpoint The second is the difference in the formula of ΦBC,e —ρφ [τcs (1 − τpe ) + τpe ] + ρψ(1 − τpe )—in this situation rather than (ρφ + ρψ)(1 − τpe ) in section 3.3 Most importantly, two issues lead to the mismatch for the perspective from the TS–BC trade-off First, ΦT S,d (i.e., κDp τpd ) is always larger than ΦBC,d (i.e., ρφτpd ), because κDp is often larger than φ and ρ is always less than one Hence, ΦT S,d − ΦBC,d is unable to reflect the trade-off between tax benefits and indirect bankruptcy costs from the viewpoint of debt holders This leads to the second issue that ΦT S,e is always larger than ΦBC,e if ΦBC,e only considers the indirect bankruptcy costs In other words, in this situation, ΦT S,e − ΦBC,e only captures the TS–BC trade-off if and only if there is the presence of direct costs of financial distress These [I] confusions imply that V EBC, in general, and V EBC , in particular, should only follow the viewpoint of equity in the presence of PIT 145 146 Appendix B Appendices of Chapter Proof of the difference in the present value of the change of debt in the future period in a world without PIT D (ST R − ET R)— In general, the difference in ∞ ∞ t=1 DtIT D —is ∞ DtIT D = ftD t=1 (kt ReInvFt ) (B.1) t=1 Using Eq (B.1), the actual present value of the change in debt in the future period in a world without PIT, E[Υ](.) , is Υ†(.) is ∞ E[Υ](.) = i=2 t+i−1 j=t+1 + κ(.) Dj i ∞ − D ft+i−1 t+i−1 j=t+1 (kj ReInvFj ) (.) i (B.2) 1+κ i=2 Υ(.),IT D Υ(.) The second term on the right-hand side of Eq (B.2) gives Eq (4.27) of the main text Similarly, the actual present value of the change in debt in the future period in a world with PIT, E[Υ](.) , is ∞ E[Υ](.) = i=2 t+i−1 j=t+1 + κ(.) Dj i ∞ − i=2 D ft+i−1 t+i−1 j=t+1 (kj ReInvF j ) (.) i (B.3) 1+κ Υ(.),IT D Υ(.) and the second term on the right-hand side in Eq (B.3) gives Eq (4.34) of the main text 147 Panel A: Under STR Panel B: Under ETR FY1 D1 D1 FY1 D1 D1 D (Cap0 + ReInvF1 )f1D (Cap0 + ReInvF1 )f1D − D0 (Cap0 + ReInvF1 )f1D − D0 D (Cap0 + ReInvF1 − k1 ReInvF1 )f1D (Cap0 + ReInvF1 − k1 ReInvF1 )f1D − D0 (Cap0 + ReInvF1 − k1 ReInvF1 )f1D − D0 D in FY1 (ST R − ET R): k1 ReInvF1 f1D Difference in FY2 FY2 D2 ReInvFt )f2D (Cap0 + D2 t=1 D2 t=1 ReInvFt )f2D − D1 (Cap0 + D2 D t=1 kt ReInvFt )f2D − D0 ReInvFt − (Cap0 + t=1 kt ReInvFt )f2D − D1 ReInvFt − t=1 ReInvFt )f2D − D0 (Cap0 + kt ReInvFt )f2D t=1 (Cap0 + t=1 D ReInvFt − (Cap0 + t=1 t=1 Difference in (kt ReInvFt )f2D D in FY2 (ST R − ET R): t=1 FYN FYN N N DN D ReInvFt )fN (Cap0 + DN t=1 N t=1 N DN D − DN −1 ReInvFt )fN (Cap0 + DN D t=1 N D − D0 kt ReInvFt )fN ReInvFt − (Cap0 + t=1 t=1 D kt ReInvFt )fN − DN −1 ReInvFt − t=1 N D ReInvFt )fN − D0 (Cap0 + D kt ReInvFt )fN t=1 N (Cap0 + t=1 N D N ReInvFt − (Cap0 + t=1 N Difference in D in FYN (ST R − ET R): D (kt ReInvFt )fN t=1 Note: Summary of notation is shown in Appendix 148 Appendix C Appendices of Chapter Proof of the incorrect growth rates formulas From Eq (5.11) in the main text: Et (1 − τcs ) ReInvt−1 + Capt−2 + νt−1 ReInvt−1 × −1 Et−1 (1 − τcs ) Capt−1 + νt ReInvt Capt−1 + νt−1 ReInvt−1 Et (1 − τcs ) × − = Et−1 (1 − τcs ) Capt−1 + νt ReInvt gtE = (C.1) Taking Eq (C.1) minus Eq (5.2) gives: Errorst = Et (1 − τcs ) Capt−1 + νt−1 ReInvt−1 × −1 Et−1 (1 − τcs ) Capt−1 + νt ReInvt (C.2) where Errorst is the growth bias between the incorrect growth (i.e., Eq (5.11)) and the actual growth (i.e., Eq (5.2)) Under positive earnings, Errorst = when Capt−1 +νt−1 ReInvt−1 Capt−1 +νt ReInvt = This condition leads to Eq (5.15) in the main text, that shows the timing of reinvestment in year t which the incorrect growth rate intersect the actual growth Eq (C.2) also shows that the relationship between the incorrect growth rate in year t (or the growth bias in year t) and levels of νt (i.e., from 0% to 100%) is always negative Proof of the correct growth rates formulas The proof follows along the same lines as in Subsection "Proof of the incorrect growth rates formulas" above with Eq (5.11) replaced by Eqs (5.13) and (5.14) From Eq (5.13) in the main text: gtE = ReInvt−1 + Capt−2 Et (1 − τcs ) × − Et−1 (1 − τcs ) Capt−2 + ReInvt−1 Rearranging Eq (C.3) yields Eq (5.2) of the main text 149 (C.3) Similarly, from Eq (5.14) in the main text: gtE = Et (1 − τcs ) µt−1 ReInvt−1 + νt ReInvt + Capt−2 + νt−1 ReInvt−1 − × Et−1 (1 − τcs ) Capt−1 + νt ReInvt Rearranging Eq (C.4) yields Eq (5.2) of the main text 150 (C.4)