ADVANCES IN QUANTITATIVE ANALYSIS OF
FINANCE AND
ACCOUNTING
Volume 4
dito
Cheng-Fe
ADVANCES IN QUANTITATIVE ANALYSIS OF
FINANCE AND
ACCOUNTING
Advances in Quantitative Analysis of Finance and Accounting
Editorial Board
Cheng F. Lee
Mike J. Alderson
James S. Ang
K. R. Balachandran
Thomas C. Chiang
Thomas W. Epps
Thomas J. Frecka
Robert R. Grauer
Puneet Handa
Der-An Hsu
Prem C. Jain
Jevons C. Lee
Wayne Y. Lee
Scott C. Linn
Gerald J. Lobo
Yaw Mensah
Thomas H. Noe
Oded Palmon
Louis O. Scott
Andrew J. Senchak

Syracuse University, USA
Rutgers University, USA
ADVANCES IN QUANTITATIVE ANALYSIS OF
FINANCE AND
ACCOUNTING
Editor
Cheng-Few Lee
Rutgers University, USA
YJ?
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Scientific
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ADVANCES IN QUANTITATIVE ANALYSIS OF FINANCE AND ACCOUNTING
Advances in Quantitative Analysis of Finance and Accounting — Vol. 4
Copyright © 2006 by World Scientific Publishing Co. Pte. Ltd.
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tives; 2. Management Compensation, Debt Contract, and Earnings Manage-
ment
Strategy;
3. Estimated Operating Cash
Flow,
Reported Cash Flow from
Operating Activities, and Financial Distress; 4. Earnings Surprise and the
Relative Information Content of Short Interest; 5. Group Types and Earn-
ings Management; 6. The
Tendency
of Firm Managers
to
Avoid Small Losses;
7. Beating or Meeting Earnings-Based
Target
Performance in CEOs' Annual
Cash Bonuses.
Two of the remaining seven papers are related to option theory and appli-
cation:
1.
Real
Option
Based Equity
Valuation
Models: An Empirical Analysis;
2.
The Shift Function for the Extended
Vasicek
Model.
Three of the remaining

Real Option Based Equity
Valuation
Models:
An Empirical Analysis 1
A. William Richardson, Raafat R. Roubi,
Hemantha S. B. Herath
Chapter 2 Firm Performance and Compensation-Based Stock
Trading
by Corporate Executives 37
Zahid Iqbal
Chapter 3 Management Compensation, Debt
Contract,
and
Earnings Management Strategy 59
Chia-Ling Lee, Victor
W.
Liu
Chapter 4 Risky Debt-Maturity Choice under Information
Asymmetry 75
Sheen Liu, Chunchi Wu
Chapter 5 Estimated Operating Cash
Flow,
Reported Cash Flow
from
Operating
Activities, and Financial Distress 97
Terry J. Ward, Benjamin
P.
Foster, Jon Woodroof
Chapter 6 Earnings Surprise and the Relative Information

Wei,
Ying-Foon Chow
Chapter 11 The Shift Function for the Extended
Vasicek
Model 255
Shyan Yuan Lee, Cheng Hsi Hsieh
Chapter 12 Beating or Meeting Earnings-Based
Target
Performance
in CEOs' Annual Cash Bonuses 271
Simon S. M. Yang
Chapter 13 Corporate Diversification and the Price-Earnings
Association 299
Ben-Hsien Bao, Da-Hsien Bao
Chapter 14
Taking Positive
Interest Rates Seriously 327
Enlin Pan, Liuren Wu
Index
357
List of Contributors
Chapter 1
A.
William Richardson
DeGroote School of Business
McMaster University
1280 Main Street
Hamilton, Ontario L8S 4M4, Canada
Tel:
905-525-9140 Ext. 23993

Houston, TX 77004
Tel.:
713-313-7737
Fax: 713-313-7722
Email:
Chapter 3
Chia-Ling Lee
Department of Accounting and Information Technology
National Chung Cheng University
168 University Rd., Min-Hsiung
Chia-Yi 621
Taiwan, R.O.C.
Tel:
886-5-2720411 Ext. 34502
Fax:886-5-2721197
Email:
Victor W. Liu
Department of Business Management
National Sun Yat-sen University
70 Lien-hai Rd.
Kaohsiung 804, Taiwan, R.O.C.
Tel.:
886-7-5254661
Fax: 886-7-5254662
Email:
Chapter 4
Sheen Liu
Williamson College of Business Administration
Youngstown State University
Youngstown, OH 44504, USA

865-974-1762
Email:
Chapter 6
Jose Mercado-Mendez
Department of Economics and Finance
Central Missouri State University
Warrensburg, MO 64093, USA
Tel.:
660-543-8650
Email:
xii List of
Contributors
Roger J. Best
Department of Economics and Finance
Central Missouri State University
Warrensburg, MO 64093, USA
Tel.:
660-543-4246
Email:
Ronald W. Best
Department of Accounting and Finance
University of West Georgia
Carrollton, GA 30118, USA
Tel.:
678-839-4812
Email:
Chapter 7
Min-Jeng Shiue
Department of Accounting
National Taipei University, Taiwan

Mohamed A. Ismail
United Arab Emirates University
P.O.
Box 17555, UAE
Tel.:
9713-7133342
Fax: 9713-7622944
Email:
Chapter 9
Yi-Tsung Lee
Department of Accounting
National Chengchi University
64,
Tz-nan Rd., Sec. 2, Wenshan
Taipei 11623, Taiwan, R.O.C.
Tel:
886-2-29393091 Ext. 81027
Fax:886-2-29387113
Email:
Ging-Ginq Pan
Graduate Institute of Finance
National Pingtung University of Science and Technology
1,
Hseuh Fu Road, Neipu Hsiang
Pingtung, Taiwan, R.O.C.
Tel.:
886-8-7703202 Ext. 7818
Fax: 886-8-7703202 Ext. 7833
Email:
xiv List of

Shatin, New Territories
Hong Kong
Tel.:
852-2609-7638
Fax: 852-2603-6586
Email:
Chapter 11
Shyan Yuan Lee
Department of Finance
National Taiwan University
Room 1012, 10F, 50, Sec. 4, Keelung Rd.
106,
Taipei, Taiwan
Tel:
886-2-2362-1845
Fax: 886-2-2362-1845
Email:
Cheng Hsi Hsieh
Department of Finance
National Taipei College of Business
321,
Sec. 1, Jinan Rd.
Jungjeng Chiu, 100, Taipei, Taiwan
Tel.:
886-2-2916-2133
Fax: 886-2-2232-6378
Email:
Chapter 12
Simon S. M. Yang
School of Business, Adelphi University

847-863-4747
Email:
Liuren Wu
Zicklin School of Business
Baruch College
One Bernard Baruch Way
Box B10-225
New
York,
NY 10010, USA
Tel.:
646-312-3509
Fax: 646-312-3451
Email:
Chapter 1
Real Option Based Equity Valuation Models: An
Empirical Analysis
A. William Richardson
McMaster
University,
Canada
Raafat R. Roubi and Hemantha S. B. Herath
Brock
University,
Canada
This paper provides empirical evidence in support of real option based equity valuation models
that relate share price to accounting earnings and book
value.
Our empirical results are generally
consistent with the predictions of several models, all of which are based on real options theory.

William
Richardson, Raafat
R.
Roubi & Hemantha S. B. Herath
and Feltham and Ohlson (1995) combine the two approaches and show that,
under a certain reasonable set of assumptions, a firm's value can be modeled as
a function of both the book value of equity and the level of earnings.
Although considerable progress has been made, there remain some funda-
mental questions that have still not been completely resolved. These include
(1) the real option fraction of equity value to expand or contract the scale of
operations; (2) financial implications of measures such as dividend payout,
capital structure, and capital expenditure (Rees, 1997); and (3) to a lesser
extent, the negative price-earnings anomaly observed for loss firms in the cur-
rent paper and in Jan and Ou (1995), Burgstahler and Dichev (1997), and
Kothari and Zimmerman (1995). Collins, Pincus, and Xie (1999) provide a
reasonable explanation and suggest adding the book value of equity to the
simple earnings model.
In his seminal paper, Myers (1977) conceptualized the idea of viewing a
firm's growth opportunities as real options. He provides the theoretical frame-
work to value a firm as income generating assets-in-place plus the value of
growth opportunities arising from future discretionary investments. Although
there has been extensive research on theoretical real option models and appli-
cations since Myers' (1977) article, there have been only a few empirical
studies in the real options literature. More specifically, Paddock, Siegel, and
Smith (1988), Bailey (1991), Quigg (1993), and Moel and Tufano (2002) com-
pare the net present value (NPV) with real options models. McConnell and
Muscarella (1985) investigate market reaction to positive NPV projects, and
Belkaoui (2000) uses a general regression model with corporate reputation,
multinationality, size, profitability, leverage, and systematic risk as variables
to estimate growth opportunities. In addition, Burgstahler and Dichev (1997)

that are ignored in Zhang's (2000) basic model and discuss the value relevance
of debt in equity valuation for cross-sectional stratified sub-samples. Third,
despite apparent anomalies, our empirical results are consistent with those of
previous research and provide further evidence on the variability of coefficients
in valuation models and suggest that Collins, Pincus, and Xie's (1999) warning
on the interpretation of the coefficient of earnings be extended. This coefficient
appears to depend not just on whether earnings are positive or negative but
also on the profitability of the firm. Finally, the current research contributes
to the valuation literature by illustrating the convergence of two different the-
oretical valuation approaches that explain the value relevance of earning and
book value.
The rest of this paper
is
organized as follows: Section
2
provides the theoret-
ical background of
the
basic valuation
model,
derives predictions, and discusses
prior research. Section 3 discusses real option based equity valuation models
for analyzing the cross-sectional behavior of the properties of the valuation
function. It
also
develops predictions for the signs of the coefficients of the oper-
ational regression
models.
Section 4 provides details of
the

and Xie (1999) supplement the basic earnings capitalization model with book
value in order to address the loss firm anomaly. With their revised model, they
show that the anomalous results disappear and that the earnings coefficient of
the basic capitalization model is biased upward (downward) for profit (loss)
firms when the beginning of
the
period book value of net assets is not included
in the empirical tests (Collins, Pincus, and Xie, 1999).
Burgstahler and Dichev (1997) introduce the notion that market value
comprises two elements of
value.
These are adaptation value, which exempli-
fies the potential use of existing resources for alternative purposes, and recur-
sion value, which assumes the continued use of existing resources for current
purposes.
They model market
value
as
a
function of a
fixed
adaptation
value
plus
a call option on the recursion
value.
Collins, Pincus, and Xie (1999) specifically
address the anomalous negative coefficient of earnings in the basic earnings
capitalization model and motivate the addition of book value by appealing to
Ohlson's (1995) valuation model and the clean surplus relation. Their model

efficiency
and
derives several
specific additional models
for
relating equity value
to
accounting numbers.
In Zhang's (2000) basic model,
the
equity value depends
on
anticipated
future actions, specifically abandonment
or
discretionary additional invest-
ments.
The decision
as to
which action
to
take depends on
a
firm's efficiency and
growth potential.
In
conservative accounting settings, equity value
is
shown
to

+
GC
e
(q),
(A)
where
V
t
is
the market value of equity
at
time
t; B
t
,
the book value of equity
at
time
t; X
t
, the
accounting earnings
for the
current period ending
at
time
f, G,
the amount invested
in new
opportunities because

the
value
of
the
put
option
set,
that is,
to
discontinue operations;
and
V
Ce(q)
=
R(R
_ ^ / [
y
f+i
+9t-q*eW(v
t
+\)
-
dv
t+l
it-It
is
the
value
of
the call option set, that is,

t+
\ <
q%);
q*
is the
upper bound
of
operating efficiency that will trigger
an
expansion
of
the firm's operation (i.e., q
t+i
>
q*);
v
t+i
is a
zero mean noise term pertaining
to operational efficiency that cannot
be
predicted; f(y
t
+\)
is the
probability
density function
of
operational efficiency defined over the region
v

efficiency and/or growth potential:
(i) Low efficiency firms have a high probability of discontinuing and a low
probability of growth. For these firms, the put option Pj (.) is valuable, and
so BP
d
{q) accounts for a significant portion of the total value, whereas
the call option C
e
(.) is negligible.
(ii) Steady state
firms
have a sufficiently high efficiency that the probability of
discontinuing is low, but there is no growth potential. They are expected to
stay on the current course of operations, i.e., current earnings will continue
in perpetuity, and both P</(.) and C
e
{.) are negligible.
(iii) High efficiency firms have a high growth potential. For these firms, the
call option C
e
{.) is valuable, and so the value due to current earnings is
supplemented by G
C
e
(.),
which makes up a significant portion of the total
value, whereas P^(.) is negligible.
3. Real Option Based Equity Valuation Models
3.1.
Model 1

e
it is the error term.
Since G>0, r
f
= R-l>0 and the put and call options cannot
take negative values, we have the following predictions for the sign of the
parameters:
• The coefficient related to the call option will be zero or positive for all firms
(«i > 0).
• The coefficient related
to the
put option will be positive for all firms
(y6i
> 0).
Real Option Based Equity Valuation Models 1
• The coefficient related to the current earnings will be positive and equal for
all firms (yi > 0 = constant).
The form of Model 1 suggests that the contribution of various terms of the
valuation function will vary with the efficiency of operations, as proxied by
profitability, q, of the firm. Analysis of the dependence of the coefficients of
Model 1 on profitability based on the properties summarized in Appendix A
shows that the following relations hold:
• dai/dq = GC'
e
(q),
• dfii/dq =
P'
d
(q),
• dyi/dq = 0.

the book value, which could happen if the book value is small.
The predictions made here are consistent with predictions 1, 3, 5-7 in Zhang (2000).
8 A. William Richardson, Raafat R. Roubi & Hemantha S. B. Herath
For low efficiency firms, the following regression model (Model 2) is
derived:
V
it
= a
2
+
P
2
B
it
+
YiX-it
+ h
B
it
+ £u,
(2)
where
2
a
2 —
ft =
¥2 —
X
1
[l+r

f
+
+ C'
c
(r
f
)-C'>{r
f
)r
f
C^r
f
)r}'
(>+"»)••
0 < Q < 1 is the cost of discontinuation; u, the accounting bias between the
accounting and economic values; Au = u
t
—
u
t
^i, the bias between accounting
and economic earnings; and, e,
r
is the error term.
Since it is assumed that accounting measures are free of
bias,
Au = 0 and
u = 0. Note that
V
CM) = _ / [v,+i +q

Model 1.
3
Note that these predictions are based on the assumption that accounting numbers are unbiased.
If there is a bias, the major change is that a
2
and «3 may be < 0 or > 0. See Zhang (2000,
pp.
281-282) where u > 0 but Au may be < 0 or > 0.