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Earnings growth rates in business valuation models: The impossible quaternity

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  • Kim-Duc, Nguyen
  • Nam, Pham Khanh

Abstract

We develop formulae for earnings growth rates in business valuation models that justify the timing of reinvestment. First, we show that the cross-reference in the calculation between the reinvestment rate (RIR) and return on invested capital (ROIC; i.e., the weighted average of invested capital) introduces valuation errors. We then explain the formulae of earnings growth rates to avoid errors in two situations: reinvestment at the end of each year and at any time. The study also shows the timing of capital reinvestment, where the false growth rate occurring due to cross-referencing will match the actual growth rate. We also study the case where the false growth rate is always higher or lower than the actual growth rate. We use numerical examples to show that our models are correct and highlight arising from cross-referencing. We provide a practitioner's 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 discounted cash flow (DCF) framework. More specifically, a business valuation cannot have an available expected growth rate, a fixed change in ROIC, an independent reinvestment timing, and a fixed level of actual reinvestment.

Suggested Citation

  • Kim-Duc, Nguyen & Nam, Pham Khanh, 2024. "Earnings growth rates in business valuation models: The impossible quaternity," Global Finance Journal, Elsevier, vol. 60(C).
  • Handle: RePEc:eee:glofin:v:60:y:2024:i:c:s1044028324000024
    DOI: 10.1016/j.gfj.2024.100930
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    References listed on IDEAS

    as
    1. repec:eme:mfppss:mf-09-2017-0335 is not listed on IDEAS
    2. Robert A. Taggart & Jr., 1991. "Consistent valuation and Cost of Capital Expressions With Corporate and Personal Taxes," Financial Management, Financial Management Association, vol. 20(3), Fall.
    3. Peter Molnár & Kjell G. Nyborg, 2013. "Tax†adjusted Discount Rates: a General Formula under Constant Leverage Ratios," European Financial Management, European Financial Management Association, vol. 19(3), pages 419-428, June.
    4. Marko Volker Krause & Alexander Lahmann, 2016. "Reconsidering the appropriate discount rate for tax shield valuation," Journal of Business Economics, Springer, vol. 86(5), pages 477-512, July.
    5. Christian Koziol, 2014. "A simple correction of the WACC discount rate for default risk and bankruptcy costs," Review of Quantitative Finance and Accounting, Springer, vol. 42(4), pages 653-666, May.
    6. Nguyen Kim-Duc & Hay Sinh & Tran Bich-Van & David McMillan, 2021. "Modeling the selection of comparable firms: A novel approach for business valuation in ASEAN nations," Cogent Economics & Finance, Taylor & Francis Journals, vol. 9(1), pages 1958980-195, January.
    7. Collins, Wa & Hopwood, Ws, 1980. "A Multivariate-Analysis Of Annual Earnings Forecasts Generated From Quarterly Forecasts Of Financial Analysts And Univariate Time-Series Models," Journal of Accounting Research, Wiley Blackwell, vol. 18(2), pages 390-406.
    8. Myron J. Gordon & Eli Shapiro, 1956. "Capital Equipment Analysis: The Required Rate of Profit," Management Science, INFORMS, vol. 3(1), pages 102-110, October.
    9. Mike Dempsey, 2013. "Consistent Cash Flow Valuation with Tax†Deductible Debt: a Clarification," European Financial Management, European Financial Management Association, vol. 19(4), pages 830-836, September.
    10. Michael Dempsey, 2019. "Discounting methods and personal taxes," European Financial Management, European Financial Management Association, vol. 25(2), pages 310-324, March.
    11. Ian A. Cooper & Kjell G. Nyborg, 2018. "Consistent valuation of project finance and LBOs using the flows†to†equity method," European Financial Management, European Financial Management Association, vol. 24(1), pages 34-52, January.
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