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Accounting based valuation: a simultaneous equations model for forecasting earnings to proxy for ‘other information’

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Abstract

This paper develops and tests a simultaneous equations model (SEM) for extending accounting based valuation models used in empirical studies. Rather than using analysts’ forecasts, we derive forecasts of operating income from the SEM to calculate the ‘other information’ variable in the Ohlson (Contemp Account Res 11:661–687, 1995) model. The SEM forecasts are based on observable data contained in the firms’ reporting, like order backlog, and other publicly available information. The SEM produces more accurate out-of-sample forecasts of operating income compared to simple benchmark models particularly in years around economic changes and instability, like the years 2001 and 2009. Integrating the SEM forecast as ‘other information’ in market value regressions significantly increases the explanatory power compared to simpler versions without or with single information proxies for ‘other information’. Finally, we find that the SEM forecast is able to explain a major portion of the information advantage of analysts relevant for explaining market values.

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Notes

  1. Recent evidence by Bradshaw et al. (2012) questions the widely accepted superiority of analysts’ forecasts over time-series models’ forecasts. They find that under certain conditions, i.e. for small firms and long horizons, random walk EPS forecasts are more accurate than analysts’ EPS forecasts. For large and stable firms, over short horizons, however, analysts’ forecasts are superior to random walk forecasts.

  2. For the remaining equations to set up complete financial statements see the “Appendix”.

  3. However, including this relationship in the model would not alter the final reduced form of Eqs. (3.8)–(3.10).

  4. As the rate is negotiated between the banks and not determined by the Federal Reserve System (FED), we use the effective rate, i.e. the weighted average across all rates.

  5. EBIT is earnings before interests and taxes and equals operating income (OI) as it is defined in this paper.

  6. As outliers are a not a major concern for the SALES forecast, MAPE is reported. MdAPE yields similar results.

  7. ASC 810-10-45 requires that non-controlling interests are reported within equity. For calculation of the WACC it does not matter where these interests are considered as long as the weights correspond to the respective cost rates.

  8. In contrast to debt, book values of preferred stock and non-controlling interests typically do not equal their market values. Book values are used as proxies due to data constraints. Hence, V D = #9 + #34 + #38 and V PS = #130.

  9. For a detailed discussion of the Vuong (1989) test, see Dechow (1994), Appendix 2. The Vuong test cannot be applied for comparing M1 and M2 as this test is only valid for non-nested models.

  10. We use real GDP annual growth rate forecasts released at the beginning of the respective year. PPI forecasts are not available.

  11. Strictly speaking, net dividends are dividend payments (including share repurchases) less capital contributions from shareholders. These items have to be considered when forecasting the payout ratio.

  12. This identity is also known as the cash conservation equation (Penman 2010, p. 236). If it is assumed that the change of cash and cash equivalents is zero, FCF can be expressed as the sum of net transactions with equity investors (d) and net transactions with debt investors (NFE − ∆NFO).

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Acknowledgement

We gratefully acknowledge helpful comments by Anne Wyatt, Stephen Salter, Thorsten Sellhorn, Tami Dinh, Andreas Weiler, Marco Wilkens, Maria Assel and workshop participants at the University of Augsburg, participants at the Eden doctoral and young scholar seminar on visualizing, measuring and managing intangibles 2010 in Catania, the EAA Annual Congress 2013 in Paris and 2014 in Tallinn, the AAA Annual Meeting in Anaheim and the AAA IAS Midyear Meeting in San Antonio. We gratefully acknowledge financial support by the Wissenschaftliche Gesellschaft für Prüfung und Controlling, Augsburg e.V. and the Research Center for Global Business Management, University of Augsburg.

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  1. School of Accounting and Control, University of Augsburg, Universitaetsstr. 16, 86159, Augsburg, Germany

    Iris Bergmann & Wolfgang Schultze

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  1. Iris Bergmann
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Correspondence to Wolfgang Schultze.

Appendix

Appendix

The cost of debt capital or borrowing cost determines next-period’s net financial expenses (NFE), i.e. interest income less interest expense.

$$NFE_{t} = r_{D} \times \left( {1 - tax} \right) \times NFO_{t - 1}$$

where NFO = net financial obligations, NFE = net financial expenses

Earnings are defined as forecasted OI (after tax) less NFE.

$$E_{t} = OI_{t} \times \left( {1 - tax} \right) - NFE_{t}$$

The payout ratio is applied to the earnings forecast in order to determine net dividends.Footnote 11 Net financial obligations (NFO), i.e. financial assets less financial obligations or liabilities, can be calculated asFootnote 12

$$NFO_{t} = NFO_{t - 1} + NFE_{t} - FCF_{t} + d_{t}$$
$${\text{with}}\,FCF_{t} = OCF - ICF = OI_{t} \times \left( {1 - tax} \right) - NOA_{t} + NOA_{t - 1}$$

where FCF = free cash flow, OCF = operating cash flow, ICF = investing cash flow, d = net dividends.

Free cash flow (FCF) (after tax) can be determined by cash flow from operations less cash investment, but also by operating income (after tax) less the change in NOA. Thus, FCF can be directly derived from forecasts of accounting measures and one does not need to forecast cash flows.

Finally, book value of equity is the residual amount calculated as

$$B_{t} = NOA_{t} - NFO_{t} = B_{t - 1} + E_{t} - d_{t}$$

Taken these forecasts together, complete pro forma balance sheet, income statement and cash flow statement can be set up.

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Bergmann, I., Schultze, W. Accounting based valuation: a simultaneous equations model for forecasting earnings to proxy for ‘other information’. Rev Quant Finan Acc 50, 1057–1091 (2018). https://doi.org/10.1007/s11156-017-0654-9

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