Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates.

Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates. Business valuation models Consistent valuation, Inflationrelated tax distortions, and Earning growth rates.

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 10 th 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 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 Acknowledgements This thesis would have remained a dream had it not been for the assistance of professors, part- ners, 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 guid- ance and support of Dr Khanh Nam for his patience, advice, and warm-hearted support through- out 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, knowl- edge, 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 encour- agement 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, 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 pro- gram 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 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 integra- tion 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 generaliza- tion 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 Trotman-Dickenson, D I (1996) The Theory of Taxation and the Tax System In In Economics of the Public Sector, pages 113–137 Trugman, G R (2017) Understanding Business Valuation: A Practical Guide to Valuing Small to Medium Sized Businesses Wiley, New York, 5th edition Van, B J H., Graham, J R., and Yang, J (2010) The Cost of Debt The Journal of Finance, 65(6):2089–2136 Van Horne, J (1971) A note on biases in capital budgeting introduced by inflation The Journal of Financial and Quantitative Analysis, 6(1):653–658 Vickers, D (1966) Profitability and reinvestment rates: A note on the gordon paradox The Journal of Business, 39(3):366–370 Warner, J B (1977) Bankruptcy Costs: Some Evidence The Journal of Finance, 32(2):337 Weiss, L A (1990) Bankruptcy resolution Journal of Financial Economics, 27(2):285–314 Zurita, S., Castillo, A., and Niño, J (2019) Inflation, tax integration and company valuation: The Latin American case Journal of Business Research, 105:370–380 Appendix A Appendices of Chapter VEBC with PIT on interest income Appendix A demonstrates that the indirect costs of bankruptcy should not be distinguished between gross and net excess rates of the promised yield, and should not employ two types of discount rates like the idea of V˜ET S In doing this, we begin with considering the CIT–PIT trade-off for the excess promised yield (i.e., φ) similar to the analysis of V˜ET S In this situation, the indirect costs of bankruptcy at time t can be rewritten as [I] B˜C t = Dt+i−1 φ [(1 − τpd ) − (1 − τcs )(1 − τpe )] Following the idea that T˜S includes T˜S e d ˜ and , we divide ˜ BC T S [I] , indirect costs of bankruptcy under the point of view of equity, B˜C of view of debt, [I] We define BC, and ,d e B ˜C κ κ [I] BC ˜ BC,d ,e  D φ[τcs(x1s− τpe) + τpe˛] ¸ t+i−1 ∞ + ˜ i ρ = ρ V EBC  t t s i=1 − ρt s i=1 ∞ D t (1 + iτ pd φ τ s [I],e V˜EB[I],d C B˜C t+i ¸ xs ˛ d + κBC,d(1 − t C V˜EB ) ) x ˛ ¸ [I],d 14 , and that under the point ˜ BC ∞ [D] +t (A.2) i ¸Dt+i−1 ψx(s1 − τpe˛) BC,e(1 − (1 + κ i=1 τpe ))x ˛ ¸ t into two components, as the discount rate to discount bankruptcy +t (1 + κBC,e(1 − τpe e [I] (A.1) ))x V˜EB˛¸C [D] t (A.3) We introduce some additional notations: BC,d • Υ˜t denotes the present value of the change of debt in the future period in a Σ world with BC,d PIT, , i.e., Υ˜ Σdiscounted at κ˜ = t BC,d ∞ i=2 14 t+i−1 j=t+ ˜ ODj ) (1+κ BC,d i ; ˜ BC,e denotes the percentage of bankruptcy costs (at time t) to debt (at time •Φ ˜ holders, i.e., ΦBC,e = ρφ [τcs(1 − τpe) + t − 1) from the point of view of equity τpe] + ρψ(1 − τpe); ˜ BC,d denotes the percentage of bankruptcy costs (at time t) to debt (at time •Φ Eq (3.18) can be rewritten as t − 1) from the point of view of debt holders, i.e., Φ˜ BC,d = ρφτpd + + V EBCt = Φ Φ κBC,e κBC,d Σ Υ Υt t ˜ BC,e BC,e DtΦ˜ BC,e s ˜ ˜ ˜ ˜ V˜E˛B¸Ce x − ˜BC,d ˜BC,dΣ DtΦ˜ BC,d V˜E˛B¸C d s t x e (A.4) t d d e We have E = [V˜ Au +V˜ET S − V˜ET S − V˜EBC +V˜EBC − D] by combining the equation V i i i AA = D + E of the CoC method and Eq (2.8) of the APV method Eq (3.16) in the main text becomes1 EA κ ˜ Eu = κV˜ − ET S E ˜ e e d Eu ˜ET κ κT S,e + V ˜ ˜ S Σ− Σ Eu BC,e ˜ + V EB κ˜ − κ˜ − E C V˜EBC E d E κ˜ Eu − κ˜ T S,d (A.5 ) Σ κ˜ Eu − κ˜ BC,d Σ + D E κ˜ Eu − κ˜ Dp Σ Towards that end, we define V˜EBC d BC,d k˜ = t Dt Φ˜ BC,d Υ ˜= BC,d+ ˜ sκ ˛¸ x t Eq (3.22) in the main text becomes BC,d ˜kBC,d, D (A.6) Dt t s ˜ k ˛¸ BC x ,d,Υ Σ Dt ˜T S,e ˜ T S,e Eu Dt ˜T S,d ˜ T S,d k Φ κ˜ − κ˜ET S,e + k Φ Σ Σ Σ t t Dt TBC,e D Dt Eu t ˜BC,d ˜ BC,d S,d κ˜ Eu k κ˜ Eu − κ˜ BC,d + κ˜ − + − κk˜t˜ Φ˜ BC,e κ˜ Eu − κ˜ BC,e −t Φ E E E t t t (A.7 ) Σ κ˜ EA = κ˜ Eu E − κ˜ Dp T In terms of the CIT–PIT trade-off, the difference˜ between ˜ Φ S,e and ΦT S,d reflects the trade- off 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 to ΦT S,d (or ΦBC,d) (or ΦBC,e) ˜can be larger than or smaller than or equal ˜ ˜ between ˜ For the TS–BC trade-off aspect, the difference ΦT S,e and ΦBC,e captures the trade- off from the point of view of equity in a world with˜ PIT whereas thedifference between ΦT S,d Because κ = +˜E T e V S u κE e − V˜EBC d E + D − V˜ET S e + V˜ET S d + V˜EBC d ˜ V˜ ET S T S, E V˜EeB C V˜E B C TS,d d BC,e + κBC,d − ˜ D D e E ˜κ − E ˜κ − E ˜κ E ˜ E ˜κ 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 ˜ new component in the equivalent formulas, ΦBC,d, reflecting the excess rates of a ˜ 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 ˜ First, ΦT TS–BC trade-off S,d (i.e., κDpτpd) 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 Φ BC,d S,d − is unable to reflect the trade-off between tax benefits and indirect ˜ ˜ This ˜leads to the second bankruptcy costs from the viewpoint of debt holders 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 confusions imply that V˜EBC, in general, and V˜EBC [I], in particular, should only follow the viewpoint of equity in the presence of PIT 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 In general, the difference in Σ OD (ST R − ET R)— ∞  t= ∞ ODtIT D = tf D  Σ∞ t t=1 OD IT D —is (ktReInvFt) t= (B.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 Σ t+i−1 − j=t+1 1+ OD jΣ i κ(.) s Υ˛(¸.) f t+i− D ∞ i=2 Σ t+i−1 (k j=t+1 ReInvF )j + κ(.) j ˛¸ x Υ(.) s Σi (B.2) x , IT D 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˜ ] (.) ∞ Σ t+i−1  j=t+1 = i= s 1+ ODj Σi κ˜(.) Υ˜˛(¸.) x s fDt+i− − ∞ i=2 Σt+i−1 j=t+1 +Σ )j ReInvF i κ˜(.) Υ˜ (.)˛,¸IT D ˜(k j x (B.3) Panel A: Under STR Panel B: Under ETR FY1 FY1 (Cap0 + 1ReInvF1)f (Cap0 + ReInvF1 − k1ReInvF 1)f D D1 D1 D OD1 (Cap0 + ReInvF 1)f D − D0 Σ Σ OD (Cap0 + ReInvF1)f D − D10 OD − D0 Difference in FY2 D OD in FY1 (STR − ETR): k1ReInvF 1f FY2 (Cap0 + D2 Σ OD1 (Cap0 + ReInvF1 − k11ReInvF 1)f D − D0 (Cap0 + ReInvF1 − k1ReInvF1)f D Σ ReInvFt)f D (Cap0 + D2 Σ ReInvFt − Σ 2 ktReInvFt)f t= t = Σ D − D0 Σ OD (Cap0 + Σ t = t = Σ OD2 (Cap0 + ReInvFt)f D − D1 − D1 t=1 2Σ (Cap0 + ReInvFt)f D OD 2 ReInvFt − Σ OD2 (Cap0 + t=1 ReInvFt − Σ kt2ReInvFt)f D t=1 2 Σ t = t ktReInvFt)f D − D0 Difference in Σ OD in FY2 (STR − ETR): Σ (ktReInvFt)f t=1 FYN DN (Cap0 + FYN Σ N Σ t= N ODN (Cap0 + Σ OD Σ t= N ReInvFt)f D D N DN (Cap0 + ReInvF t )f D − DN−1 N ReInvFt)f D − D0 t= (Cap0 + Σ N t= N Σ ODN (Cap0 + Σ OD (Cap0 + N Differen Σ O ce in D ReInvFt − ReInvFt Σ− Σ N ΣktReInvFt)f D − DN−1 t= t= N N t= ReInvFt − ktReInvFt)f D N t= N N Σ ktReInvFt)f D − D0 t= ReInvFt fN Σ ): N (k t in STR − FYN ETR ( Note: Summary of notation is shown in Appendix N ) Appendix C Appendices of Chapter Proof of the incorrect growth rates formulas From Eq (5.11) in the main text: t Et(1 − τcs) ReInvt−1 + Capt−2 + νt−1ReInvt−1 × −1 Capt−1 + νtReInvt t−1(1 − gE = E (C.1) τcs) Et(1 − τcs) Capt−1 + νt−1ReInvt−1 =Et−1(1 − τcs)× Capt−1 + νtReInvt − Taking Eq (C.1) minus Eq (5.2) gives: Errors Et(1 − τcs) × t= Et−1(1 − τcs) Σ Σ Capt−1 + νt−1ReInvt−1 −1 Capt−1 + νtReInvt (C.2) where Errorst is the growth bias between the incorrect growth (i.e., Eq (5.11)) and the actual D growth (i.e., Eq (5.2)) Under positive earnings, Errorst = when = Capt +νtReInvt1 Capt−1+νt−1ReInvt−1 − 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: gE = Et(1 − τcs) × ReInvt−1 + Capt−2 − (C.3) t Et−1(1 − τcs) Capt−2 + ReInvt−1 Rearranging Eq (C.3) yields Eq (5.2) of the main text Similarly, from Eq (5.14) in the main text: gtE = Et(1 cs) àt1ReInvt1 + tReInvt + Capt2 + t1ReInvt1 ì − Et−1(1 − τcs) Capt−1 + νtReInvt Rearranging Eq (C.4) yields Eq (5.2) of the main text (C.4)