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Review of Managerial Science
Erschienen in: Review of Managerial Science 4/2012

01.10.2012 | Original Paper

Residual income valuation and management remuneration under uncertainty: a note

verfasst von: Simon Elsner, Hans-Christian Krumholz, Frank Richter

Erschienen in: Review of Managerial Science | Ausgabe 4/2012

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Abstract

The so-called Residual Income Valuation theorem states that the value of a project or a firm can be determined either on the basis of cash flows between the firm and its owners or by using residual incomes, provided that cash flows and residual incomes are derived from a set of accounting data that fulfills certain regularity conditions. Residual income is defined as accounting earnings reduced by a capital charge on book equity capital. In this paper it is shown that this theorem also applies when residual incomes and in particular the discount factors are uncertain. Risk-aversion of principals and agents is taken into account on the basis of properly defined risk-adjusted discount rates. This approach is preferred as it facilitates practical application. Implications are drawn with regards to valuation but also to the design of management remuneration systems. It is shown that the capital charge rate used to determine the performance-related compensation component should be reduced below the risk-adjusted rate, if the fixed component falls below a certain threshold. Absent agency cost or other externalities, the reduction of the capital charge rate is required to avoid underinvestment.
Vorheriger Artikel Analysis and evaluation of moderator effects in regression models: state of art, alternatives and empirical example
Nächster Artikel Pricing of flexible products

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Fußnoten
1
Ibd., p. 305.
 
2
See, e.g., Shiller (1981) or LeRoy and Porter (1981).
 
3
Ibd., p. 179.
 
4
Campbell et al. (1997), p. 334.
 
5
See Feltham and Ohlson (1995), p. 694, excluding the “dirty part”, Van Cauwenbrege and De Beelde (2007), p. 14, including this element.
 
6
For a detailed discussion see Isidro et al. (2006), Van Cauwenbrege and De Beelde (2007), and Krotter (2007).
 
7
Similar Peasnell (1982), p. 364.
 
8
See Smith and Wickens (2002).
 
9
A rigorous definition of the flow of information and conditional expectations in this context can be found in Wilhelm and Schosser (2007).
 
10
Campbell et al. (1997), p. 294; Cochrane (2005), p. 24.
 
11
See also Cochrane (2005), p. 25.
 
12
Wilhelm (1983), p. 58, Campbell et al. (1997), p. 293.
 
13
For details of the derivation see Appendix 1.1.
 
14
Ohlson (1999), pp. 150, 160.
 
15
See also Ohlson (1995), p. 148.
 
16
Krotter (2007) analyzes the impact of permanent and temporary dirty surpluses in more detail.
 
17
Numerical examples can be found on the internet as an electronic supplemental material (ESM) to the online publication.
 
18
Fama used the term “expectation adjustment variable” already in 1977 to derive conditions for the application of the single-period CAPM in a multi-period setting.
 
19
Similar Wilhelm (2005), p. 642.
 
20
Laitenberger (2006) comes to a similar conclusion.
 
21
See also Campbell et al. (1997), p. 255.
 
22
Parts of the English literature refer to this as the “EBO” model, referring to the contributions by Edwards and Bell (1961) and Ohlson (1995); see, e.g., Neill and Pfeiffer (2005), p. 42.
 
23
Refer to Table 1 and the corresponding literature mentioned in the introduction.
 
24
See, e.g., Ewert and Wagenhofer (2008), p. 76.
 
25
See also Peasnell (1982) for the case of certain residual incomes and certain discount rates, p. 367.
 
26
For details see Appendix 1.1.
 
27
See for example Hermann and Richter (2003).
 
28
E.g., Koller et al. (2005), pp. 284–286.
 
29
See for an empirical application Dimson et al. (2002).
 
30
See Goldenberg and Schmidt (1996) for a support of this statement on the basis of simulations.
 
31
See, e.g., Gebhardt et al. (2001), Claus and Tomas (2001), Daske et al. (2006).
 
32
See also Hughes et al. (2009).
 
33
See also Butler and Schachter (1989), p 15.
 
34
See Jacquier et al. (2005) for compound factors with normal distributed error terms.
 
35
See Christensen et al. (2002), p. 6, also Dutta (2003), p. 83, both with further references.
 
36
The risk inherent in a cash flow is called idiosyncratic if \( Cov_{t} \left[ {\tilde{C}_{t + 1} ,\tilde{M}_{t + 1} } \right] = 0 \) and systematic otherwise. See Cochrane (2005), p. 15.
 
37
\( \tilde{s}_{t + \tau } \) denotes the compensation payment, \( \tilde{S}_{t} \) the value of the payment as of t.
 
38
See already Ross (1974).
 
39
See, e.g., Christensen et al. (2002), p. 6., Dutta (2003), p. 74, Baldenius et al. (2007), p. 841.
 
40
See, e.g., Stewart (1991), pp. 224, 282, Ehrbar (1998), p. 3 and pp. 93–115.
 
41
Velthuis (2003), p. 18, comes to a similar result in the context of the CAPM.
 
42
See the sources in fn. 40. The human resources literature includes empirical evidence on the relationship between (among multiple other factors) the compensation of executives and firm size; e.g., Kostluk (1989). This relation seems to apply to the fixed salary component as well; Core et al. (1999), p. 386.
 
43
Similar Hughes et al. (2009), p. 249.
 
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Metadaten
Titel
Residual income valuation and management remuneration under uncertainty: a note
verfasst von
Simon Elsner
Hans-Christian Krumholz
Frank Richter
Publikationsdatum
01.10.2012
Verlag
Springer-Verlag
Erschienen in
Review of Managerial Science / Ausgabe 4/2012
Print ISSN: 1863-6683
Elektronische ISSN: 1863-6691
DOI
https://doi.org/10.1007/s11846-010-0058-x

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