Skip to main content
SpringerLink
Log in

The implied cost of capital: accounting for growth

Review of Quantitative Finance and Accounting volume 61, pages 1029–1056 (2023)Cite this article

Abstract

This paper involves a critique of the Implied Cost of Capital (ICC) that leads to an alternative measure which, like the ICC, is extracted from accounting data. The critique deals with how the ICC handles the accounting involved. First, the ICC fails an accounting consistency condition. Second, expected earnings growth conveys risk and return, but this is not recognized when a growth rate is inserted in the reverse engineering exercise. Empirical tests so confirm. An alternative accounting-based measure accommodates these points and validates on criteria indicating risk and return. The resulting measure is a yield to maturity for equities, much like that for a bond.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Notes

  1. The point is recognized in Fama (1997). In the words of Fisher Black, “the key issue in investments is estimating the expected return. It is neither explaining return…nor explaining average return” (Black 1993, emphasis in the original).

  2. For reviews, see Easton and Monahan (2005 and 2016), Easton (2007), Guay et al. (2011), Botosan and Plumlee (2005) and Botosan et al. (2011), and Echterling et al. (2015).

  3. See, for example, Easton and Sommers (2007), Hou et al. (2012), Larocque (2013), Mohanram and Gode (2013), Fitzgerald et al. (2013), Li and Mohanram (2014), and Wang (2020).

  4. Papers that allow varying growth rates include Easton et al. (2002), Huang et al. (2006), Nekrasov and Ogneva (2011), Ashton and Wang (2013), Ketterer et al. (2017), and Wang et al. (2019).

  5. Others, such as Callen and Segal (2004), Lyle et al. (2013), Lyle and Wang (2015), and Wang et al. (2019), impose an assumed auto-regressive process for the evolution of accounting numbers, some with the (autoregressive) model of Voulteenaho (2002). These papers are not covered here. They are critiqued separately in Penman (2016) and Penman and Yehuda (2019, appendix) with the point that an autoregressive process is not consistent with how accounting evolves under accounting principles that indicate risk and return.

  6. See Easton and Monahan (2005) and Clubb and Makrominas (2018) on validation with forward realized returns.

  7. An unlevered version of the model valuing the business enterprise is sometimes applied with the growth rate then being the growth in residual income for the business (without the effect of leverage). The same critique offered here applies.

  8. Feltham and Ohlson (1995) and Zhang (2000) show that accounting determines growth rates. Penman (1997) shows that g in a “terminal value” calculation is determined by a parameter capturing the accounting for earnings and book value. Monahan (2011), and Ketterer, Tsalavoutas, and Eierle (2017) recognize the point in the context of ICC calculations. The latter paper shows that growth in the abnormal earning growth model of Ohlson and Juettner-Nauroth (2005) better captures the effect of conservative accounting on earnings.

  9. The empirical support is in Penman and Reggiani (2013), Penman, Reggiani, Richardson and Tuna (2018), Penman and Reggiani (2018), and Penman and Zhang (2021). Penman and Yehuda (2019) show how the revenue recognition principle and conservative accounting for investment convey “discount-rate news” to the market.

  10. The simple model is presented just to convey the ideas. The full payout assumption may not be palatable, but payout (retention) other than full payout adds to earnings growth, g, but does not add price under M&M conditions. So the model isolates the growth that potentially affects price and the expected return, r, and at the same time is M&M consistent. The point here can be made with an M&M consistent model accommodating all payouts, as with the Ohlson and Juettner-Nauroth (2005) model with the added accounting assumptions in Penman, Reggiani, Richardson, and Tuna (2018).

  11. To maximize coverage of stocks, these numbers are for the trailing E/P rather than the forward E/P in the valuation model (1), but the same point can be made from observed (trailing) earnings at t, with growth forecast from that point rather than from t + 1.

  12. g(r) = gEarnings if the growth rate in book value equals the growth rate in earnings (with a constant r). That will be the case if \(\frac{{Earnings}_{t+\tau +1}}{{B}_{t+\tau }}\) is constant all τ. (Note that this is not the expected book rate of return, rather a ratio of expectations.) As a special case, note that gEarnings > 0 can occur with g(r) = 0.

  13. The methods in Mohanram and Gode to deal with samples selection and data, forecasting dates, and short-term EPS growth rates, are different from the original papers they referenced and also ours (which imitate those papers). Therefore, we reconstructed ICC estimates unadjusted for analyst errors, as in their paper. The results were similar to those in Panel A of Table 2. Note that the PEG model in Mohanram and Gode (2013) differs somewhat from the MPEG, so we performed calculations with both, with similar results.

  14. Our analysis is for 1981–2016. To ensure consistency with the ETSS findings, we first replicated their analysis for their sample period up to 1998. We maintained their criteria for dealing with data issues and reinvestment rates for the longer period. We also obtained similar results when we used analysts’ forecasts and P/B ratios three months after fiscal-year end rather than at fiscal-year end, when we used IBES prices and shares outstanding rather than those from Compustat, when we made adjustments for differences in IBES and Compustat numbers for shares outstanding, and when we used different dividend reinvestment rates.

  15. While most of the ICC here have little correlation with returns (by themselves), even slightly negative, Mohanram and Gode (2013) report positive correlation. As we kept to the methods in the original papers (see footnote 10) that may explain some of the difference. Further, the samples differ somewhat because of different sample periods and availability of forecasts on IBES. Several research assistants replicated with their procedures for the period covered by their sample, 1983–2008, but with the number of firm/years observations reduced from 36,012 in their sample to 21,073 due to availability of forecasts and corresponding firm data on Compustsat. Results were similar to those here.

  16. For such a survey, see Fernandez et al. (2021) that covers 88 countries and provides links to previous surveys from 2008 to 2020. The Duff and Phelps SBBI Yearbook (once published by Ibbotson and Associates) updates estimates of the market risk premium annually.

References

  • Ashton D, Wang P (2013) Terminal valuations, growth rates and the implied cost of capital. Rev Account Stud 18:261–290

    Article  Google Scholar 

  • Ball R (1978) Anomalies in relationships between securities’ yields and yield-surrogates. J Financ Econ 6:103–126

    Article  Google Scholar 

  • Black F (1993) Estimating expected return. Financ Anal J 49:36–38

    Article  Google Scholar 

  • Blume M (1975) Betas and their regression tendencies. J Finance 30:785–795

    Article  Google Scholar 

  • Botosan C, Plumlee M (2005) Assessing alternative proxies for the expected risk premium. Account Rev 80:21–53

    Article  Google Scholar 

  • Botosan C, Plumlee M, Wen J (2011) The relation between expected returns, realized returns, and firm risk characteristics. Contemp Account Res 28:1085–1122

    Article  Google Scholar 

  • Callen J, Segal D (2004) Do accruals drive firm-level stock returns? A variance decomposition analysis. J Account Res 42:527–560

    Article  Google Scholar 

  • Cheng C, Fang J (2021) Noise and deficiency of the implied cost of capital as an expected return proxy. Unpublished paper, Hong Kong Polytechnic University. At https://ssrn.com/abstract=3951890

  • Claus J, Thomas J (2001) Equity risk premium as low as three percent? Evidence from analysts’ earnings forecasts for domestic and international stocks. J Finance 56:1629–1666

    Article  Google Scholar 

  • Clubb C, Makrominas M (2018) Analysing the relationship between implied cost of capital metrics and realized stock returns. Unpublished paper, Kings College London and Frederick University

  • Easton P (2004) PE ratios, PEG ratios, and estimating the implied expected rate of return on equity capital. Account Rev 79:73–95

    Article  Google Scholar 

  • Easton P (2007) Estimating the cost of capital implied by market prices and accounting data. Found Trends Account 2:241–364

    Article  Google Scholar 

  • Easton P, Monahan S (2005) An evaluation of accounting-based measures of expected returns. Account Rev 80:501–538

    Article  Google Scholar 

  • Easton P, Monahan S (2016) Review of recent research on improving earnings forecasts and evaluating accounting-based estimates of the expected rate of return on equity capital. Abacus 52:35–58

    Article  Google Scholar 

  • Easton P, Sommers G (2007) Effect of analysts’ optimism on estimates of the expected rate of return implied by earnings forecasts. J Account Res 45:983–1015

    Article  Google Scholar 

  • Easton P, Taylor G, Shroff P, Sougiannis T (2002) Using forecasts of earnings to simultaneously estimate growth and the rate of return on equity investment. J Account Res 40:657–676

    Article  Google Scholar 

  • Echterling F, Eierle B, Ketterer S (2015) A review of the literature on methods of computing the implied cost of capital. Int Rev Financ Anal 42:235–252

    Article  Google Scholar 

  • Fama E, French K (1997) Industry cost of capital. J Financ Econ 43:153–193

    Article  Google Scholar 

  • Fama E, French K (2020) Comparing cross-section and time-series factor models. Rev Financ Stud 33:1891–1926

    Article  Google Scholar 

  • Feltham G, Ohlson J (1995) Valuation and clean surplus accounting for operating and financial activities. Contemp Account Res 11:689–731

    Article  Google Scholar 

  • Fernandez P, Bañuls S, Acin P (2021) Survey: market risk premium and risk-free rate used for 88 countries in 2021. At https://ssrn.com/abstract=3861152

  • Fitzgerald T, Gray S, Hall J, Jeyaraj R (2013) Unconstrained estimates of the equity risk premium. Rev Acc Stud 18:560–639

    Article  Google Scholar 

  • Gebhardt W, Lee C, Swaminathan B (2001) Toward an implied cost of capital. J Account Res 39:135–176

    Article  Google Scholar 

  • Gode D, Mohanram P (2003) Inferring the cost of capital using the Ohlson–Juettner model. Rev Account Stud 8:399–431

    Article  Google Scholar 

  • Gordon J, Gordon M (1997) The finite horizon expected return model. Financ Anal J 53:52–61

    Article  Google Scholar 

  • Grambovas C, Lara J, Ohlson J, Walker M (2017) Earnings: concepts versus reported. J Law Finance Account 2:347–384

    Article  Google Scholar 

  • Guay W, Kothari S, Shu S (2011) Properties of implied cost of capital using analysts’ forecasts. Aust J Manag 36:125–149

    Article  Google Scholar 

  • Hou K, van Dijk AM, Zhang Y (2012) The implied cost of capital: a new approach. J Account Econ 53:504–526

    Article  Google Scholar 

  • Hou K, Xue C, Zhang L (2015) A comparison of new factor models. Working paper, Charles. A. Dice Center for Research in Financial Economics, Ohio State University

  • Huang R, Natarajan R, Radhakrishnan S (2006) Estimating firm-specific long-term growth and cost of capital. Unpublished paper, University of Texas at Dallas

  • Hughes J, Liu J, Liu J (2009) On the relation between expected returns and implied cost of capital. Rev Account Stud 14:246–259

    Article  Google Scholar 

  • Ketterer S, Tsalavoutas I, Eierle B (2017) Integrating conservative accounting when estimating the cost of capital. Unpublished paper, University of Bamberg and Adam Smith Business School, University of Glasgow

  • Larocque S (2013) Analysts’ earnings forecast errors and the cost of equity capital estimates. Rev Account Stud 18:135–166

    Article  Google Scholar 

  • Li K, Mohanram P (2014) Evaluating cross-sectional forecasting models for implied cost of capital. Rev Account Stud 19:1154–1185

    Article  Google Scholar 

  • Lyle M, Wang C (2015) The cross section of expected holding period returns and their dynamics: a present value approach. J Financ Econ 116:505–525

    Article  Google Scholar 

  • Lyle M, Callen J, Elliott R (2013) Dynamic risk, accounting-based valuation and firm fundamentals. Rev Account Stud 18:899–929

    Article  Google Scholar 

  • Modigliani F, Miller M (1958) The cost of capital, corporation finance and the theory of investment. Am Econ Rev 48:261–297

    Google Scholar 

  • Mohanram P, Gode D (2013) Removing predictable analyst forecast errors to improve implied cost of capital estimates. Rev Account Stud 18:443–478

    Article  Google Scholar 

  • Monahan S (2011) Discussion of “using earnings forecasts to simultaneously estimate firm-specific cost of equity and long-term growth. Rev Account Stud 16:458–463

    Article  Google Scholar 

  • Nekrasov A, Ogneva M (2011) Using earnings forecasts to simultaneously estimate firm-specific cost of equity and long-term growth. Rev Account Stud 16:414–457

    Article  Google Scholar 

  • Ohlson J (2008) Risk, growth, and permanent earnings. Unpublished paper, Arizona State University

    Google Scholar 

  • Ohlson J, Juettner-Nauroth B (2005) Expected EPS and EPS growth as determinants of value. Rev Account Stud 10:349–365

    Article  Google Scholar 

  • Penman S (1997) A synthesis of equity valuation techniques and the terminal value calculation for the dividend discount model. Rev Account Stud 2:303–323

    Article  Google Scholar 

  • Penman S (2013) Financial statement analysis and security valuation, 5th edn. The Mc-Graw Hill Companies, New-York

    Google Scholar 

  • Penman S (2016) Accounting for risk and the expected return. Abacus 52(1):106–129

    Article  Google Scholar 

  • Penman S, Reggiani F (2013) Returns to buying earnings and book value: accounting for growth and risk. Rev Account Stud 18:1021–1049

    Article  Google Scholar 

  • Penman S, Reggiani F (2018) Fundamentals of value vs. growth investing and an explanation for the value trap. Financ Anal J 74(4):102–119

    Article  Google Scholar 

  • Penman S, Yehuda N (2019) A matter of principle: the identification of cash-flow news and discount-rate news in financial statements. Manage Sci 65(12):5584–5602

    Article  Google Scholar 

  • Penman S, Zhang X (2020) A theoretical analysis connecting conservative accounting to the cost of capital. J Account Econ 65:1–25

    Google Scholar 

  • Penman S, Zhang X (2021) Connecting book rate of return to risk and return: the information conveyed by conservative accounting. Rev Account Stud 26(1):391–423

    Article  Google Scholar 

  • Penman S, Zhu J (2014) Accounting anomalies, risk and return. Account Rev 89:1835–1866

    Article  Google Scholar 

  • Penman S, Zhu J (2022) An accounting-based asset pricing model and a fundamental factor. J Account Econ 73(2–3):101476

    Article  Google Scholar 

  • Penman S, Reggiani F, Richardson S, Tuna İ (2018) A framework for identifying accounting characteristics for asset pricing models, with an evaluation of book-to-price. Eur Financ Manag 24:488–520

    Article  Google Scholar 

  • Vasicek O (1973) A note on using cross-sectional information in Bayesian estimation of security betas. J Finance 28:1233–1239

    Article  Google Scholar 

  • Vuolteenaho T (2002) What drives firm level stock returns? J Finance 57:233–264

    Article  Google Scholar 

  • Wang P, Peng Z, Christodoulou D (2019) Firm fundamentals, future earnings expectations and expected stock returns. Unpublished paper, University of New South Wales, University of Exeter, and University of Sydney

  • Wang X (2020) The implied cost of capital: a deep learning approach. Unpublished paper, Michigan State University. https://ssrn.com/abstract=3612472

  • Zhang X (2000) Conservative accounting and equity valuation. J Account Econ 29:125–149

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Columbia Business School, Columbia University, 1104 Kravis Hall, 665 W. 130th St., New York, NY, 10027, USA

    Stephen Penman

  2. Bocconi University, Via Roberto Sarfatti, 25, 20100, Milan, MI, Italy

    Stephen Penman

  3. Fanhai International School of Finance, Fudan Fanhai School of Business, Shanghai, 200433, China

    Julie Zhu

  4. Shanghai Advanced Institute of Finance, Shanghai Jiao Tong University, Shanghai, 200030, China

    Haofei Wang

Authors
  1. Stephen Penman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julie Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haofei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stephen Penman.

Ethics declarations

Conflict of interest

The authors are unaware of any conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Penman, S., Zhu, J. & Wang, H. The implied cost of capital: accounting for growth. Rev Quant Finan Acc 61, 1029–1056 (2023). https://doi.org/10.1007/s11156-023-01175-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11156-023-01175-y

Keywords

JEL Classification

search

Navigation