Abstract
The growth rate plays an important role in determining a firm’s asset and equity values, nevertheless the basic assumptions of the growth rate estimation model are less well understood. In this paper, we demonstrate that the model makes strong assumptions regarding the financing mix of the firm. In addition, we discuss various methods to estimate firms’ growth rate, including arithmetic average method, geometric average method, compound-sum method, continuous regression method, discrete regression method, and inferred method. We demonstrate that the arithmetic average method is very sensitive to extreme observations, and the regression methods yield similar but somewhat smaller estimates of the growth rate compared to the compound-sum method. Interestingly, the ex-post forecast shows that arithmetic average method (compound-sum method) yields the best (worst) performance with respect to estimating firm’s future dividend growth rate. Firm characteristics, like size, book-to-market ratio, and systematic risk, have significant influence on the forecast errors of dividend and sales growth rate estimation.
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Notes
For a more detailed survey of the literature, see Brick et al. (2014).
Gordon and Shapiro’s (1956) model assume that dividends were paid continuously and hence \(P_{0} = {{d_{1} } \mathord{\left/ {\vphantom {{d_{1} } {(r - g)}}} \right. \kern-0pt} {(r - g)}}\).
Earnings in this model are defined using the cash-basis of accounting and not on an accrual basis.
The growth rates for Pepsico obtained by continuous and discrete regression methods are not statistically different from zero.
The growth rates for Pepsico obtained by continuous and discrete regression methods are not statistically different from zero.
When applying Gordon’s growth model, internal growth model, and sustainable model, additional information should be obtained, including the required rate of return for equity holders, ROE, ROA, and the retention rate. As defined by Eq. (2), ROE and ROA are obtained from the ratios of net income of the year to the book value of common equity and the book value of total assets at the beginning of year. Retained earnings are computed as one subtract to the ratio of cash dividends to the income before extraordinary items. We apply Gordon’s growth model with cost of equity by CAPM, in that the CAPM-based cost of equity is calculated as individual firm’s beta times market risk premium plus risk-free rate. Individual firm’s beta is estimated over the past three years monthly returns and risk-free rate and market risk premium is retrieved from Kenneth French’s website, http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.
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Brick, I.E., Chen, HY., Hsieh, CH. et al. A comparison of alternative models for estimating firm’s growth rate. Rev Quant Finan Acc 47, 369–393 (2016). https://doi.org/10.1007/s11156-015-0504-6
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DOI: https://doi.org/10.1007/s11156-015-0504-6
Keywords
- Equity valuation
- Estimation of growth rate
- Gordon’s growth model
- Determinants of growth forecast errors