Advances In Business And Management Forecasting

ADVANCES IN BUSINESS AND
MANAGEMENT FORECASTING

ADVANCES IN BUSINESS AND
MANAGEMENT FORECASTING
Series Editors: Kenneth D. Lawrence and
Ronald K. Klimberg
Recent Volumes:
Volume 1: Advances in Business and Management
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ADVANCES IN BUSINESS AND MANAGEMENT
FORECASTING VOLUME 7
ADVANCES IN BUSINESS
AND MANAGEMENT
FORECASTING
EDITED BY
KENNETH D. LAWRENCE
New Jersey Institute of Technology,
Newark, USA
RONALD K. KLIMBERG
Saint Joseph’s University,
Philadelphia, USA
United Kingdom – North America – Japan
India – Malaysia – China

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First edition 2010
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ISSN: 1477-4070 (Series)
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CONTENTS
LIST OF CONTRIBUTORS ix
EDITORIAL BOARD xiii
PART I: FINANCIAL FORECASTING
TWO-DIMENSIONAL WARRANTY POLICIES
INCORPORATING PRODUCT DEVELOPMENT
Amitava Mitra and Jayprakash G. Patankar 3
FORECASTING THE USE OF SEASONED
EQUITY OFFERINGS
Rebecca Abraham and Charles Harrington 23
THE IMPACT OF LIFE CYCLE ON THE
VALUE RELEVANCE OF FINANCIAL
PERFORMANCE MEASURES
Shaw K. Chen, Yu-Lin Chang and Chung-Jen Fu 37
FORECASTING MODEL FOR STRATEGIC
AND OPERATIONS PLANNING OF
A NONPROFIT HEALTH CARE ORGANIZATION
Kalyan S. Pasupathy 59
PART II: MARKET FORECASTING
SEASONAL REGRESSION FORECASTING
IN THE U.S. BEER IMPORT MARKET
John F. Kros and Christopher M. Keller 73
v

A COMPARISON OF COMBINATION
FORECASTS FOR CUMULATIVE DEMAND
Joanne S. Utley and J. Gaylord May 97
CHANNEL SHARE PREDICTION IN DIRECT
MARKETING RETAILING: THE ROLE OF
RELATIVE CHANNEL BENEFITS
Eddie Rhee 111
PREDICTING A NEW BRAND’S LIFE
CYCLE TRAJECTORY
Frenck Waage 121
PART III: METHODS AND PRACTICES OF
FORECASTING
FORECASTING PERFORMANCE MEASURES –
WHAT ARE THEIR PRACTICAL MEANING?
Ronald K. Klimberg, George P. Sillup,
Kevin J. Boyle and Vinay Tavva
137
FORECASTING USING FUZZY MULTIPLE
OBJECTIVE LINEAR PROGRAMMING
Kenneth D. Lawrence, Dinesh R. Pai and
Sheila M. Lawrence
149
A DETERMINISTIC APPROACH TO SMALL
DATA SET PARTITIONING FOR NEURAL
NETWORKS
Gregory E. Smith and Cliff T. Ragsdale 157
PART IV: FORECASTING APPLICATIONS
FORECASTING THE 2008 U.S. PRESIDENTIAL
ELECTION USING OPTIONS DATA
Christopher M. Keller 173
CONTENTS
vi

RECOGNITION OF GEOMETRIC AND
FREQUENCY PATTERNS FOR IMPROVING SETUP
MANAGEMENT IN ELECTRONIC ASSEMBLY
OPERATIONS
Rolando Quintana and Mark T. Leung 183
USING DIGITAL MEDIA TO MONITOR
AND FORECAST A FIRM’S PUBLIC IMAGE
Daniel E. O’Leary 207
EVALUATING SURVIVAL LIKELIHOODS IN
PALLIATIVE PATIENTS USING MULTIPLE
CRITERIA OF SURVIVAL RATES AND
QUALITY OF LIFE
Virginia M. Miori and Daniel J. Miori 221
Contents vii

LIST OF CONTRIBUTORS
Rebecca Abraham Huizenga School of Business and
Entrepreneurship, Nova Southeastern
University, Fort Lauderdale, FL,
USA
Kevin J. Boyle Department of Decision and Systems
Science, Haub School of Business,
Saint Joseph’s University, Philadelphia,
PA, USA
Yu-Lin Chang Department of Accounting and
Information Technology, Ling Tung
University, Taiwan
Shaw K. Chen College of Business Administration,
University of Rhode Island, Kingston,
RI, USA
Chung-Jen Fu Department of Accounting, National
Yunlin University of Science and
Technology, Taiwan
Charles Harrington Huizenga School of Business and
Entrepreneurship, Nova Southeastern
University, Fort Lauderdale, FL, USA
Christopher M. Keller College of Business, East Carolina
University, Greenville, NC, USA
Ronald K. Klimberg Department of Decision and Systems
PA, USA
John F. Kros College of Business, East Carolina
University, Greenville, NC, USA
ix

Kenneth D. Lawrence School of Management, New Jersey
Institute of Technology, North
Brunswick, NJ, USA
Sheila M. Lawrence Rutgers Business School, Rutgers
University, North Brunswick,
NJ, USA
Mark T. Leung College of Business, University
of Texas at San Antonio, San Antonio,
TX, USA
J. Gaylord May Wake Forest University, Winston-Salem,
NC, USA
Daniel J. Miori Palliative and Ethics Service, Millard
Fillmore Gates Circle Hospital,
Buffalo, NY, USA
Virginia M. Miori Department of Decision and Systems
PA, USA
Amitava Mitra College of Business, Auburn University,
Auburn, AL, USA
Daniel E. O’Leary Marshall School of Business, University
of Southern California, Los Angeles,
CA, USA
Dinesh R. Pai Penn State Lehigh Valley,
Center Valley, PA, USA
Kalyan S. Pasupathy Health Management and Informatics,
MU Informatics Institute, School of
Medicine, University of Missouri,
Columbia, MO, USA
Jayprakash G. Patankar Department of Management, University
of Akron, Akron, OH, USA
Rolando Quintana College of Business, University
of Texas at San Antonio, San Antonio,
TX, USA
x LIST OF CONTRIBUTORS

Cliff T. Ragsdale Department of Business Information
Technology, Virginia Polytechnic
Institute and State University,
Blacksburg, VA, USA
Eddie Rhee Department of Business Administration,
Stonehill College, Easton, MA, USA
George P. Sillup Department of Decision and Systems
PA, USA
Gregory E. Smith Williams College of Business, Xavier
University, Cincinnati, OH, USA
Joanne S. Utley School of Business and Economics,
North Carolina A&T State University,
Greensboro, NC, USA
Vinay Tavva Department of Decision and Systems
Saint Joseph’s University,
Philadelphia, PA, USA
Frenck Waage University of Massachusetts at
Boston, Boston, MA, USA
List of Contributors xi

EDITORIAL BOARD
EDITORS-IN-CHIEF
Kenneth D. Lawrence Ronald Klimberg
New Jersey Institute of Technology Saint Joseph’s University
SENIOR EDITORS
Lewis Coopersmith Virginia Miori
Rider College Saint Joseph’s University
John Guerard Daniel O’Leary
Anchorage, Alaska University of Southern California
Douglas Jones Dinesh R. Pai
Rutgers University The Pennsylvania State University
John J. Kros William Stewart
East Carolina University College of William and Mary
Stephen Kudbya Frenck Waage
New Jersey Institute of Technology University of Massachusetts
Sheila M. Lawrence David Whitlark
Rutgers University Brigham Young University
xiii

TWO-DIMENSIONAL WARRANTY
POLICIES INCORPORATING
PRODUCT DEVELOPMENT
Amitava Mitra and Jayprakash G. Patankar
ABSTRACT
Some consumer durables, such as automobiles, involve warranties
involving two attributes. These are time elapsed since the sale of the
product and the usage of the product at a given point in time. Warranty
may be invoked by the customer if both time and usage are within the
specified warranty parameters and product failure occurs. In this
chapter, we assume that usage and product age are related through a
random variable, the usage rate, which may have a certain probabilistic
distribution as influenced by consumer behavior pattern. Further, product
failure rate is influenced by the usage rate and product age. Of importance
to the organization is to contain expected warranty costs and select
appropriate values of the warranty parameters accordingly. An avenue to
impact warranty costs is through research on product development. This
has the potential to reduce the failure rate of the product. The objective
then becomes to determine warranty parameters, while constraining the
sum of the expected unit warranty costs and research and development
(R&D) costs per unit sales, under a limited R&D budget.
Advances in Business and Management Forecasting, Volume 7, 3–22
Copyright r 2010 by Emerald Group Publishing Limited
All rights of reproduction in any form reserved
ISSN: 1477-4070/doi:10.1108/S1477-4070(2010)0000007004
3

INTRODUCTION
A majority of consumer products provide some sort of assurance to the
consumer regarding the quality of the product sold. This assurance, in the
form of a warranty, is offered at the time of sale. The Magnuson–Moss
Warranty Act of 1975 (US Federal Trade Commission Improvement Act,
1975) also mandates that manufacturers must offer a warranty for all
consumer products sold for more than $15. The warranty statement assures
consumers that the product will perform its function to their satisfaction up
to a given amount of time (i.e., warranty period) from the date of purchase.
Manufacturers offer many different types of warranties to promote their
products. Thus, warranties have become a significant promotional tool for
manufacturers. Warranties also limit the manufacturers’ liability in the case
of product failure beyond warranty period.
Taxonomy of the different types of warranty policies may be found in
the work of Blischke and Murthy (1994). Considering warranty policies
that do not involve product development after sale, policies exist for a single
item or for a group of items. With our focus on single items, policies may
be subdivided into the two categories of nonrenewing and renewing. In a
renewing policy, if an item fails within the warranty time, it is replaced by
a new item with a new warranty. In effect, warranty beings anew with
each replacement. However, for a nonrenewing policy, replacement of a
failed item does not alter the original warranty. Within each of these two
categories, policies may be subcategorized as simple or combination.
Examples of a simple policy are those that incorporate replacement or repair
of the product, either free or on a pro rata basis. The proportion of the
warranty time that the product was operational is typically used as a basis
for determining the cost to the customer for a pro rata warranty. Given
limited resources, management has to budget for warranty repair costs and
thereby determine appropriate values of the warranty parameters of, say,
time and usage.
Although manufacturers use warranties as a competitive strategy to boost
their market share, profitability, and image, they are by no means cheap.
Warranties cost manufacturers a substantial amount of money. The cost
of a warranty program must be estimated precisely and its effect on the
firm’s profitability must be studied. Manufacturers plan for warranty costs
through the creation of a fund for warranty reserves. An estimate of the
expected warranty costs is thus essential for management to plan for
warranty reserves. For the warranty policy considered, we assume that the
product will be repaired if failure occurs within a specified time and the
AMITAVA MITRA AND JAYPRAKASH G. PATANKAR
4

usage is less than a specified amount. Such a two-dimensional policy is
found for products such as automobiles where the warranty coverage is
provided for a time period, say five years, and a usage limit of, say, 50,000
miles. In this chapter, we assume minimal repair, that is, the failure rate of
the product on repair remains the same as just before failure. Further, the
repair time is assumed to be negligible.
In this chapter, we consider the aspect of expenditures on research and
development (R&D) to improve a product. Improvement of a product
occurs through a variety of means, some of which could be improved design,
improved processes, improved labor and equipment, or improved raw
material, among others. While R&D expenditures may have an impact on
the short run on reducing net revenue, there is a greater benefit when the
long-term objectives of an organization are considered. A major impact of
R&D is a reduction in the failure rate of the product. With a better product,
the warranty costs associated with products that fail within a prescribed
warranty time or usage will be lower. This may lead to an increase in the net
revenue, whereby the increase in R&D expenditures per unit sales is more
than offset by the decrease in the expected warranty costs per unit sales.
LITERATURE REVIEW
Research on estimation of warranty costs has been studied extensively for
about four decades. One of the earliest papers by Menke (1969) estimated
expected warranty costs for a single sale for a linear pro rata and lump-sum
rebate plans for nonrenewable policies. Blischke and Scheuer (1975)
considered the costs associated with the free replacement and pro rata
policy under different time-to-failure distributions and later applied renewal
theory (Blischke & Scheuer, 1981) to estimate warranty costs for two types
of renewable warranty policies. Other researchers have also used renewal
theory (Blacer & Sahin, 1986; Frees & Nam, 1988; Mamer, 1982; Mamer,
1987) to estimate warranty costs for various warranty policies.
A good review of the various warranty policies is found in Blischke
and Murthy (1992). Murthy and Blischke (1992a) provide a comprehensive
framework of analyses in product warranty management and further
conduct a detailed review of mathematical models (Murthy & Blischke,
1992b) in this research area. A thorough treatment of warranty cost models
and analysis of specific types of warranty policies, along with operational
and engineering aspects of product warranties, is found in Blischke
and Murthy (1994). The vast literature in warranty analysis is quite disjoint.
Two-Dimensional Warranty Policies Incorporating Product Development 5

A gap exists between researchers from different disciplines. With the
objective of bridging this gap, Blischke and Murthy (1996) provided a
comprehensive treatise of consumer product warranties viewed from
different disciplines. In addition to providing a history of warranty, the
handbook presents topics such as warranty legislation and legal actions;
statistical, mathematical, and engineering analysis; cost models; and the role
of warranty in marketing, management, and society.
Murthy and Djamaludin (2002) provided a literature review of warranty
policies for new products. As each new generation of product usually
increases in complexity to satisfy consumer needs, customers are initially
uncertain about its performance and may rely on warranties to influence
their product choice. Additionally, servicing of warranty, whether to repair
or replace the product by a new one, influences the expected cost to
the manufacturer (Jack & Murthy, 2001). A different slant on studying the
effect of imperfect repairs on warranty costs has been studied by Chukova,
Arnold, and Wang (2004). Here, repairs are classified according to the depth
of repair or the degree to which they restore the ability of the item
to function. Huang and Zhuo (2004) used a Bayesian decision model to
determine an optimal warranty policy for repairable products that undergo
deterioration with age.
Wu, Lin, and Chou (2006) considered a model for manufacturers to
determine optimal price and warranty length to maximize profit, based on a
chosen life cycle, for a free renewal warranty policy. Huang, Liu, and
Murthy (2007) developed a model to determine the parameters of product
reliability, price, and warranty strategy that maximize integrated profit for
repairable products sold under a free replacement/repair warranty strategy.
Another angle of approach to reduce warranty costs is the concept of burn-
in of the product, where products are operated under accelerated stress
for a short time period before their release to the customer. A study of
optimal burn-in time and warranty length under various warranty policies is
found in Wu, Chou, and Huang (2007). A warranty strategy that combines
a renewing free-replacement warranty with a pro rata rebate policy is found
in Chien (2008). In a competitive market place as the twenty-first century,
products are being sold with long-term warranty policies. These are in the
forms of extended warranty, warranty for used products, service contracts,
and lifetime warranty policies. Since lifespan in these policies are not
well-defined, modeling of failures and costs are complex (Chattopadhyay &
Rahman, 2008).
The majority of past research has dealt with a single-attribute
warranty policy, where the warranty parameter is typically the time since
6

purchase of the product. Singpurwalla (1987) developed an optimal
warranty policy based on maximization of expected utilities involving both
proﬁt and costs. A bivariate probability model involving time and usage as
warranty criteria was incorporated. One of the ﬁrst studies among two-
dimensional warranty policies using a one-dimensional approach is that by
Moskowitz and Chun (1988). Product usage was assumed to be a linear
function of the age of the product. Singpurwalla and Wilson (1993, 1998)
modeled time to failure, conditional on total usage. By choosing a
distribution for total usage, they derived a two-dimensional distribution
for failure using both age and usage. Singpurwalla (1992) also considered
modeling survival in a dynamic environment with the usage rate changing
dynamically.
Moskowitz and Chun (1994) used a Poisson regression model to
determine warranty costs for two-dimensional warranty policies. They
assumed that the total number of failures is Poisson distributed whose
parameter can be expressed as a regression function of age and usage
of a product. Murthy, Iskander, and Wilson (1995) used several types of
bivariate probability distributions in modeling product failures as a random
point process on the two-dimensional plane and considered free-replace-
ment policies. Eliashberg, Singpurwalla, and Wilson (1997) considered the
problem of assessing the size of a reserve needed by the manufacturer to
meet future warranty claims in the context of a two-dimensional warranty.
They developed a class of reliability models that index failure by two scales,
such as time and usage. Usage is modeled as a covariate of time. Gertsbakh
and Kordonsky (1998) reduced usage and time to a single scale, using a
linear relationship. Ahn, Chae, and Clark (1998) used a similar concept
using a logarithmic transformation.
Chun and Tang (1999) found warranty costs for a two-attribute warranty
model by considering age and usage of the product as warranty parameters.
They provided warranty cost estimation for four different warranty policies
(rectangular, L-shaped, triangular, and iso-cost) and performed sensitivity
analysis on discount rate, usage rate, and warranty terms to determine their
effects on warranty costs. Kim and Rao (2000) considered a two-attribute
warranty model for nonrepairable products using a bivariate exponential
distribution to explain item failures. Analytical expressions for warranty
costs are derived using Downtone’s bivariate distribution. They demonstrate
the effect of correlation between usage and time on warranty costs.
A two-dimensional renewal process is used to estimate warranty costs.
Wang and Sheu (2001) considered the effect of warranty costs on
optimization of the economic manufacturing quality (EMQ). As a process

deteriorates over time, it produces defective items that incur reworking costs
(before sale) or warranty repair costs (after sale). The objective of their
paper was to determine the lot size that will minimize total cost per unit of
time that includes set-up cost, holding cost, inspection cost, reworked cost,
and warranty costs. Sensitivity analysis is performed on various costs to
determine an optimum production lot size.
Yeh and Lo (2001) explored the effect of preventive maintenance actions
on expected warranty costs. A model is developed to minimize such costs.
Providing a regular preventive maintenance within the warranty period
increases maintenance cost to the seller, but the expected warranty cost is
significantly reduced. An algorithm is developed that determines an optimal
maintenance policy. Lam and Lam (2001) developed a model to estimate
expected warranty costs for a warranty that includes a free repair period
and an extended warranty period. Consumers have an option to renew
warranty after the free repair period ends. The choice of consumers has
a significant effect on the expected warranty costs and determination of
optimal warranty policy.
Maintenance policies during warranty have been considered by various
authors (Jack & Dagpunar, 1994; Dagpunar & Jack, 1994; Nguyen &
Murthy, 1986). Some consider the repair/replacement policy following
expiration of the warranty. Dagpunar and Jack (1992) consider the situation
where, if the product fails before the warranty time, the manufacturer
performs minimal repair. In the event of product failure after the warranty
time, the consumer bears the expenses of either repairing or purchasing a
new product. Sahin and Polatoglu (1996) study two types of replacement
policies on expiration of warranty. In one policy, the consumer applies
minimal repair for a fixed period of time and replaces the unit with a
new one at the end of this period, while in the second policy the unit is
replaced at the time of the first failure following the minimal repair period.
Thomas and Rao (1999) provide a summary of warranty economic decision
models. In the context of two-dimensional warranty, Chen and Popova
(2002) study a maintenance policy which minimizes total expected servicing
cost.
An application of a two-dimensional warranty in the context of
estimating warranty costs of motorcycles is demonstrated by Pal and
Murthy (2003). Majeske (2003) used a general mixture model framework
for automobile warranty date. Rai and Singh (2003) discussed a method
to estimate hazard rate from incomplete and unclear warranty data.
A good review of analysis of warranty claim data is found in Karim and
Suzuki (2005).
8

Research Objectives
In this chapter, we consider a two-dimensional warranty policy where the
warranty parameters, for example, could be time and usage at the point of
product failure. A warranty policy in this context, such as those offered for
automobiles, could be stated as follows: product will be replaced or repaired
free of charge up to a time (W) or up to a usage (U), whichever occurs first
from the time of the initial purchase. Warranty is not renewed on product
failure. For example, automobile manufacturers may offer a 36 months or
36,000 miles warranty, whichever occurs first. For customers with high
usage rates, the 36,000 miles may occur before 36 months. On the contrary,
for those with limited usage, the warranty time period of 36 months may
occur first. Fig. 1 shows a two-dimensional warranty region.
We assume that the usage is related to time as a linear function through
the usage rate. To model a variety of consumers, usage rate is assumed to be
a random variable with a specified probability distribution. This chapter
develops a model based on minimal – repair or replacement of failed items.
In this chapter, we develop a model from the manufacturer’s perspective.
We consider the aspect of product development. Through advances in R&D
of products as well as processes, the failure rate of the product may be
impacted. This may cause a reduction in the expected warranty costs due to
Fig. 1. Two-Dimensional Warranty Region.

the lower failure rate. By incorporating the sum of the R&D expenditures
per sales dollar along with the expected warranty costs per sales dollar as the
objective function, the problem is to determine the parameters of a warranty
policy that minimizes the above objective function. The manufacturer
typically has an idea of the upper and lower bounds on the price, warranty
time, usage, and unit R&D expenditures. Optimal parameter values are
determined based on these constraints.
MODEL DEVELOPMENT
The following notation is used in the chapter:
W Warranty period offered in warranty policy
U Usage limit offered in warranty policy
R Usage rate
t Instant of time
Y(t) Usage at time t
X(t) Age at time t
l(t|r) Failure intensity function at time t given R ¼ r
N(W,U|r) Number of failures under warranty given R ¼ r
c Unit product price
cs Unit cost of repair or replacement
RD R&D expenditures per unit sales
Relationship between Warranty Attributes
We assume that the two attributes, say time and usage, are related linearly
through the usage rate, which is a random variable. Denoting Y(t) to be the
usage at time t and X(t) the corresponding age, we have
YðtÞ ¼ RXðtÞ, (1)
where R is the usage rate. It is assumed that all items that fail within the
prescribed warranty parameters are minimally repaired and the repair time
is negligible. In this context, X(t) ¼ t.
10

Distribution Function of Usage Rate
To model a variety of customers, R is assumed to be a random variable with
probability density function given by g(r). The following distribution
functions of R are considered in this chapter:
(a) R has a uniform distribution over (a1, b1):
This models a situation where the usage rate is constant across all
customers. The density function of R is given by
gðrÞ ¼
1
b1 a1
; a1 r b1
¼ 0; otherwise:
(2)
(b) R has a gamma distribution function:
This may be used for modeling a variety of usage rates among the
population of consumers. The shape of the gamma distribution
function is inﬂuenced by the selection of its parameters. When the
parameter, p, is equal to 1, it reduces to the exponential distribution.
The density function is given by
gðrÞ ¼
er
rp1
GðpÞ
; 0 ro1; p40. (3)
Failure Rate
Failures are assumed to occur according to a Poisson process where it is
assumed that failed items are minimally repaired. If the repair time is small,
it can be approximated as being zero. Since the failure rate is unaffected
by minimal repair, failures over time occur according to a nonstationary
Poission process with intensity function l(t) equal to the failure rate. As
discussed previously, expenditures on RD will create an improved product
with a reduction in the failure rate.
Conditional on the usage rate R ¼ r, let the failure intensity function at
time t be given by
lðtjrÞ ¼ y0 þ y1r þ ðy2 þ y3rÞt a5RD. (4)
(1) Stationary Poisson process:
Under this situation, the intensity function l(t|r) is a deterministic
quantity as a function of t when y2 ¼ y3 ¼ 0. This applies to many

electronic components that do not deteriorate with age and failures are
due to pure chance. The failure rate in this case is constant.
(2) Nonstationary Poisson process:
This models the more general situation where the intensity function
changes as a function of t. It is appropriate for products and
components with moving parts where the failure rate may increase
with time of usage. In this case y2 and y3 are not equal to zero.
Expected Warranty Costs
The warranty region is the rectangle shown in Fig. 1, where W is the
warranty period and U the usage limit. Let g1 ¼ U|W. Conditional on the
usage rate R ¼ r, if the usage rate rZg1, warranty ceases at time Xr, given by
Xr ¼
U
r
. (5)
Alternatively, if rog1, warranty ceases at time W. The number of failures
under warranty, conditional on R ¼ r, is given by
NðW; UjrÞ ¼
Z W
t¼0
lðtjrÞ dt; if rog1
¼
Z Xr
t¼0
lðtjrÞ dt; if r g1.
(6)
The expected number of failures is thus obtained from
E½NðW; UÞ ¼
Z g1
r¼0
Z W
t¼0
lðtjrÞ dt

gðrÞdr
þ
Z 1
r¼g1
Z Xr
t¼0
lðtjrÞ dt

gðrÞdr.
(7)
Expected warranty costs (EWC) per unit are, therefore, given by
EWC ¼ csE½NðW; UÞ, (8)
whereas the expected warranty costs per unit sales (ECU) are obtained
from
ECU ¼
cs
c

E½NðW; UÞ. (9)
12

We now develop an expression for the average failure rate (lave) that is
influenced by RD expenditures. We have
lave ¼
Z g1
r¼0
Z W
t¼0
lðtjrÞ dt

gðrÞ dr
þ
Z 1
r¼g1
Z Xr
t¼0
lðtjrÞ

gðrÞ dr.
(10)
The unit product price is impacted by the average failure rate, which is
given by
c ¼ a4 þ
b4
lave
, (11)
where a4 and b4 are appropriate constants. Accordingly, the unit cost of
repair or replacement is obtained from
cs ¼ a3 þ b3c, (12)
where a3 and b3 are appropriate constants.
Mathematical Model
We first consider the constraints that must be satisfied for the decision
variables of product price, warranty time, and warranty usage limit.
A manufacturer having knowledge of the unit cost of product and RD
expenditures, and a desirable profit margin, can usually identify a minimum
price, below which it would not be feasible to sell the product. Similarly,
knowing the competition, it has a notion of the maximum price that
the product should be priced at. Using a similar rationale, a manufacturer
might be able to specify minimum and maximum bounds on the warranty
time and usage limit to be offered with the product. Furthermore, the
organization will have some knowledge to set minimum and maximum
bounds on the unit RD expenditures. So, the constraints on the policy
parameters are
c1 c c2;
W1 W W2;
U1 U U2;
d1 RD d2;
(13)

where c1 is the minimum product price, c2 the maximum product price, W1
the minimum warranty period, W2 the maximum warranty period, U1
the minimum usage limit, U2 the maximum usage limit, and d1 and d2 the
minimum and maximum bound on RD, respectively.
The objective function, to minimize, is the sum of the expected warranty
costs and RD expenses per unit sales. Hence, the model becomes
Minimize ðECU þ RDÞ, (14)
subject to the set of constraints given by (13).
RESULTS
The application of the proposed model is demonstrated through some
sample results using selected values of the model parameters. The
complexity of calculating E[N(W,U)], given by Eq. (7), inﬂuences the
calculation of ECU, given by Eq. (9), which ultimately impacts the objective
function given by Eq. (14). Closed form solutions for E[N(W,U)], in general
cases, are usually not feasible. Hence, numerical integration methods
are used. Further, the optimal values of the objective function are not
guaranteed to be globally optimum.
Two distributions are selected for the usage rate, R. One being the
uniform distribution between (0,6), while the second being the gamma
distribution with parameter p ¼ 2, 4. For the failure rate intensity function,
conditional on R, the selected parameters are y0 ¼ 0.005; y1 ¼ 2, 5;
y2 ¼ 0.05; y3 ¼ 0.05. Based on the chosen value of y1, the value of the
parameter a5, which demonstrates the impact of RD on the failure rate, is
selected accordingly. For y1 ¼ 2, a5 is selected to be 1.9; while for y1 ¼ 5, a5
is selected to be 4.9. Note that the failure rate cannot be negative, hence
an appropriate constraint is placed when determining feasible solutions.
To study the stationary case, y2 and y3 are selected to be 0.
The unit product price, based on the average failure rate, is found using
the parameter values of a4 ¼ 1.0 and b4 ¼ 0.02. Similarly, the unit cost of
repair or replacement is found using a3 ¼ 0.25 and b3 ¼ 0.2. Bounds on the
warranty policy parameters are as follows: unit product price between
$10,000 and $40,000 (c1 ¼ 1, c2 ¼ 4); warranty period between 2 and 10
years (w1 ¼ 2, w2 ¼ 10); and usage limit between 50,000 and 120,000 miles
(U1 ¼ 5, U2 ¼ 12). For the unit expenditures on RD (RD) per unit sales,
the bounds are selected as 0.01 and 2 (d1 ¼ 0.01, d2 ¼ 2), respectively.
14

The behavior of the average failure rate (lave) as a function of the usage
limit (U) and the warranty time limit (W), for a given unit RD expenditures
per unit sales (RD) is shown in Fig. 2. The distribution of the usage rate is
assumed to be uniform with the failure rate being stationary, and RD ¼ 0.1.
As expected, lave increases with U, for a given W. Further, the average failure
rate for large values of W dominates those for smaller values of W. For large
values of W (W ¼ 10, 8), the average failure rate increases by more than two-
fold, over the range of U. For small values of W (W ¼ 2), the increase is less
than 50%. In the chosen range of U, lave appears to increase linearly for
large values of W. However, for small values of W, lave tapers off for large
values of U. A similar behavior is observed in Fig. 3, where the distribution
of the usage rate is gamma, the failure rate is stationary, and RD ¼ 0.1.
However, in this situation, the increase in the average failure rate is not as
much, relative to the uniform distribution of usage rate. For small values of
W (W ¼ 2), the increase in the average failure rate is minimal and it
approaches its asymptotic value, as a function of U, rather quickly.
The ECU function is also studied as a function of the warranty
parameters W and U and the unit RD expenditures per unit sales (RD).
Fig. 2. Lambda Average (lave) Versus U for Different Values of W for Uniform
Distribution of R.

Fig. 4 shows the ECU function for various values of W, for RD ¼ 0.5. The
distribution of the usage rate is uniform with the failure rate being
stationary. As expected, ECU increases with U, for a given W. For large
values of W (W ¼ 10, 8, 6), certain small values of U are not feasible.
Fig. 3. Lambda Average (lave) Versus U for Different Values of W for Gamma
Distribution of R.
Fig. 4. Expected Warranty Costs per Unit Sales for Uniform Distribution of R.
16

Also, ECU for large values of W dominates those for smaller values of W.
For large values of W, ECU increases by more than two-fold, over the
range of U. For small values of W (W ¼ 2), the increase in ECU is about
33%. In the selected range of U, ECU seems to increase linearly for large
values of W. However, for small values of W, increase in ECU tapers
off with an increase in U. A similar behavior is observed in Fig. 5, where the
distribution of the usage rate is gamma (p ¼ 2), the failure rate is stationary,
and RD ¼ 0.5. The increase in the ECU function over the chosen rage of U
is smaller than that compared with the usage rate distribution being uniform
with a stationary failure rate. The increase in the ECU function is more
asymptotic than linear, for large values of W, as observed in Fig. 4. Further,
for small values of W (W ¼ 2), the rate of increase is much smaller than
that compared with the usage rate distribution being uniform. This suggests
that, depending on the type of consumer (as estimated by the usage rate
distribution), the manufacturer could offer differing levels of the warranty
parameters (U and W), while maintaining the expected warranty costs per
unit sales to be restricted within certain bounds.
Fig. 6 shows the ECU values as a function of U for W ¼ 2, for different
values of RD. The chosen distribution of usage rate is uniform with the
failure rate being stationary. The impact of the variable RD can be
characterized from this graph. Obviously, for larger values of RD, ECU is
smaller compared with smaller values of RD over the entire range of the
warranty parameters. Interestingly, the ECU values taper off asymptotically
for large values of U, for all chosen values of RD. For large values
Fig. 5. Expected Warranty Costs per Unit Sales for Gamma Distribution of R.

of RD (RD ¼ 2.0), the increase in ECU is marginal, as a function of U.
When considering the total objective function of (ECU þ RD), it can be seen
that this function could be smaller for large values of RD (say RD ¼ 2.0),
when the total objective function approaches a value slightly below 4.0, even
for large values of W. However, for small values of RD (say RD ¼ 0.01),
the total objective function approaches a value above 5.0.
Table 1 shows some results on the optimal warranty policy parameters of
unit price, warranty time, and usage limit as well as RD expenditures per
unit sales. The objective function value of the sum of expected warranty
costs and RD costs, per unit sales, is also shown. The parameter values
discussed previously are used, with y1 ¼ 2 and a5 ¼ 1.9.
From Table 1, it is observed that spending the maximum permissible
amount on RD expenditures per unit sales leads to minimization of the
Fig. 6. Expected Warranty Costs per Unit Sales for Uniform Distribution of R and
Various values of RD.
Table 1. Optimal Warranty Policy Parameters.
Distribution of U Failure Rate c W U RD ECU þ RD
Uniform Stationary 1.022 2.000 5.000 2.000 2.877
Uniform Nonstationary 1.009 2.000 5.000 2.000 2.970
Gamma (p ¼ 2) Stationary 1.401 2.000 7.623 2.000 2.016
Gamma (p ¼ 2) Nonstationary 1.062 2.000 7.642 2.000 2.139
18

total warranty and RD expenditures per unit sales. Obviously, the choice
of the selected model parameters will inﬂuence this decision. Further, of the
three warranty policy parameters of unit price, warranty, and usage limit,
it seems that unit price and warranty time are more sensitive to the impact
on the objective function. With the goal being to minimize the objective
function, the optimal values of unit price and warranty time are close to
their respective lower bounds. Some ﬂexibility is observed in the optimal
values of the usage limit.
CONCLUSIONS
A two-dimensional warranty has been considered. With the concept of
product development in mind, the impact of unit RD expenditures has been
incorporated in a model. The policy parameters are the warranty time, usage
limit, unit product price, as well as the unit RD expenditures per unit sales.
It is well known that expected warranty costs increase with the parameters
of warranty time and usage limit. However, through expenditures on RD,
the failure rate of the product may be reduced. Such a reduction in the failure
rate may reduce the expected warranty costs per unit sales. Hence, the
objective function that is considered is the sum of the expected warranty costs
and the RD expenditures, per unit sales. It is desirable to minimize this
combined objective function subject to constraints on the policy parameters.
Several possibilities exist for future research in this area. One could involve
estimation of the distribution of usage rate of customers, based on the
availability of data from prior customers. Second, the impact of simultaneous
product development of competitors could also be an avenue for exploration.
The manufacturer could be impacted by the degree of product improve-
ment offered by competitors. This, in turn, may force the manufacturer
to accomplish certain desired features of the product. For example, the
manufacturer may have to improve the average failure rate of the product
to below a chosen level. The problem then becomes determination of the
unit RD expenditures, along with warranty policy parameters, to offer a
competitive product as well as a competitive warranty policy.
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22

FORECASTING THE USE OF
SEASONED EQUITY OFFERINGS
Rebecca Abraham and Charles Harrington
ABSTRACT
Seasoned equity offerings (SEOs) are sales of stock after the initial
public offering. They are a means to raise funds through the sale of stock
rather than the issuance of additional debt. We propose a method to
predict the characteristics of firms that undertake this form of financing.
Our procedure is based on logistic regression where firm-specific variables
are obtained from the perspective of the firm’s need to raise cash such as
high debt ratios, high current liabilities, reduction and changes in current
debt, significant increase in capital expenditure, and cash flows in terms of
cash as a percentage of assets.
Seasoned equity offerings (SEOs), more descriptively termed secondary
equity offerings, are the issue of stock by a firm that has already completed a
primary issue. From a capital structure perspective, a firm can raise long-
term funds by using internal financing if it has the funds available. Given
the likelihood that internal funds may be insufficient to meet long-term
needs for new product development, expansion of facilities, or research
and development investment, all of which require significant amounts of
capital, raising funds, from external sources becomes the only viable
alternative. This may take the form of borrowing from financial institutions
ISSN: 1477-4070/doi:10.1108/S1477-4070(2010)0000007005
23

(acquiring debt), or issuing common stock through a seasoned equity
offering to existing or new shareholders (selling equity). This chapter
is directed toward forecasting the likelihood that a firm would choose
equity.
The SEO research is limited. Only a few studies (Masulis Korwar, 1986;
Mikkelson Partch, 1986) investigate the reasons for using SEOs as a
means of external funding. Others focus on a the single variable as a
determinant of the SEO alternative. For example, Hull and Moellenberndt
(1994) examined bank debt reductions, Hull (1999) the failure to meet
industry debt standards, and Johnson, Serrano, and Thompson (1996) the
ability to capitalize on investment opportunities. We suggest that it is
a complex interplay of factors that determine the SEO choice decision,
particularly the availability of debt, current cash flow, and investment
opportunities so that any analysis must consider the simultaneous effect of
all three groups of variables. Cash flow considerations, in particular, have
been omitted from the above studies.
Why would a firm choose equity over debt? The tax deductibility of the
interest on debt renders debt the cheaper source of capital and does not
result in the dilution of ownership as would be the case if additional shares
are issued to new stockholders. Myers and Majluf (1984) theorized that
managers have privileged information about the firm. They are aware
of its cash flows, its retention of earnings, sales prospects and the need
for capital and research expenditure. If managers act rationally and have
the firm’s best interests at heart, they will invest in positive NPV projects
and raise firm value. The amount of capital for investment in these
projects may have to be obtained externally; excessive debt may alarm
existing shareholders given that the tax deductibility of interest on debt is
substantially offset by the risk of financial distress and bankruptcy in the
event that the firm’s future cash flows are insufficient to meet fixed payments
of principal and interest. That future cash flows may be insufficient is a
real concern given the uncertainty of the current economic environment.
In other words, multiple signals influence the choice of financing, negative
signals from the escalation of the risk of financial distress from use of
debt, positive signals from the tax benefit of debt and the lack of dilution
of ownership, positive signals from management’s prudent undertaking
of projects, and negative signals from management submitting to pressure
from existing shareholders not to issue stock. Ambarish, John, and
Williams (1987) concluded that positive signals dominate in favor of issuing
additional debt, empirically documenting positive announcement effects
from seasoned equity issues.
REBECCA ABRAHAM AND CHARLES HARRINGTON
24

REVIEW OF THE LITERATURE
Information asymmetry is at the cornerstone of the financing decision.
By definition, it is the examination of transactions in which there is an
imbalance of information, with one party to the transaction having more
valuable information that has the potential to influence the outcome.
Managers have inside information on day-to-day performance which
motivates them to select the optimal method of financing. The question
becomes, how the information advantage may be gleaned by outsiders. Such
denouement of management intentions was referred to by Stigler (1960), the
originator of the concept, as screening. The uninformed party (investors and
us, in this case) may use observations of the behavior of the informed party to
close the imbalance in information by evaluating the choices of managers,
which were based on their private information. Walker and Yost (2008)
attempted to accomplish this goal by observing the financial performance
of firms following SEO announcement. Like us, they recognized the need to
incorporate variables that measure diverse motivations for selecting SEOs,
namely, debt reduction, capitalizing on investment opportunities, and general
operational reasons, particularly declining performance. However, they
measured these effects on an ex ante basis in terms of future SEO performance
after announcement, in terms of both financial statement information and
statements made by management at announcement. This study measures SEO
motivations ex post, before announcement takes place using financial
statements only as we maintain that there are issues of response bias in self-
report measures. We also wish to update and extend their sample which
consisted of 2 years of pre-2001 data during a term rapid economic expansion
to suit the slower growth of the current era. We approach the issue from
a forecasting perspective in which we use a large sample based on the
entire Compustat database that meets our criteria, instead of confining our
analysis to just firms that made SEO announcements as we wish to use firm
characteristics to predict the likelihood of SEO offering.
Walker and Yost (2008) observed that expansion was the dominant goal
for firms so that those with high levels of debt concentrated on capitalizing
on growth opportunities rather than debt reduction. Any debt retirement
consisted of paying off old debt contracts and acquiring significant levels
of new debt of up to 50–90% of total capital. Both operating cash flow and
liquidity declined in the two years following SEO announcement, suggesting
that internal operational factors may have played a role in motivating
management to select SEOs. However, as the data was obtained ex ante it is
possible that prevailing conditions following announcement confounded the
Forecasting the Use of Seasoned Equity Offerings 25

results so that business conditions after announcement made expansion the
primary objective over debt reduction or that a sudden decline in operating
performance could have occurred independently of the SEO financing
decision. Operating cash flow was measured by operating income before
depreciation. As depreciation tax shields provide a major impetus to firms
seeking the purchase of new capital equipment, thereby increasing the level
of investment in equipment, their exclusion could lead to the overstatement
of operating income. Overstatements of operating income lessen the
likelihood of SEO choice as general financial health of the firm appears
unduly optimistic. Liquidity was measured by the ratio of net working
capital to total assets. The rationale was that net working capital or the
extra funds from liquid sources after payment of current debts declined
following announcement so that such firms use lack of liquidity as a
criterion in their choice of SEOs. We prefer to focus on cash flow mainly as
cash is the most liquid of all current assets. Net working capital includes
accounts receivable and inventory, which are less liquid assets than cash.
Accounts receivable typically takes 90 days to be liquidated, if liquidated
in less time it is due to factoring which involves significant losses. Inventory
is the least liquid of the current assets with goods remaining unsold for
months, so that their ultimate conversion to cash is certainly not timely,
but may even be questionable. Further, we take the position that multiple
measures of liquidity are necessary as they reveal different aspects of
cash flow, and provide a fuller picture of a firm’s liquidity position.
We supplement overall cash flow measures with cash flow investing to cover
unexpected expenses during expansion, and cash flow financing to explain
reductions in cash flow to cover dividend payouts.
HYPOTHESIS DEVELOPMENT
If a firm needs to raise additional funds, it is apparent that this need emerges
from a perceived need for cash in the immediate future. Therefore, the first
group of variables are cash flow variables.
Cash Flow
The first source of cash flow is income, which is the net profit of the business
after payment of all expenses, interest, and taxes. If the firm generates
sufficient income, it would have the funds needed to meet all of its current
26

expenses and reinvest retained earnings in the firm. Therefore, the change in
retained earnings would forecast the need to generate funds externally.
If retained earnings continue to increase in conjunction with debt, it appears
that the firm has exhausted its internal source of funds and needs a seasoned
equity offering.
Cash Flow Investing
If the firm has rapidly rising capital expenditures, it may be involved
in a major expansion. This could take the form of investing in foreign
markets, expanding production for the domestic market, or new product
development for either market. The change in capital expenditure should act
as an explanatory variable in determining the likelihood of seasoned equity
offerings.
Cash Flow Financing
Cash flow financing refers to the methods of disbursement of idle cash
generated by business operations. The first payout is dividends. Initial and
subsequent dividend announcements send a strong positive signal about
the financial health of the firm in that they disseminate information to
the investing public that the firm is financially strong enough to sustain
the distribution of cash to its shareholders, and that it wishes shareholders
to benefit from the continued success of the firm (John, Koticha,
Narayanan, Subrahmanyam, 2000). Rising dividend payouts during
economic prosperity and the maintenance of dividends at a stable level
during economic downturns bolster investor confidence are likely to be
employed by firms who feel that investors have the confidence to continue
investing through seasoned equity offerings.
Long-Term Debt Reduction
Our position is that firms that engage in a plan of long-term debt reduction
to reduce the threat of financial distress and bankruptcy. Such firms do
not wish to return to dependence of debt and may therefore be likely to seek
additional funding from equity sources.

Changes in Current Debt
Coupled with long-term debt reduction are changes in current debt. Falling
current debt indicates the desire to forego debt as a source of financing.
Given that internal financing may be insufficient, equity becomes the only
alternative.
BALANCE SHEET VARIABLES
The balance sheet, by definition, indicates the financial position of a firm at
a particular point in time. The most important variable may be total assets.
Given that a seasoned equity offering will only be attractive to investors
who have sufficient confidence that their funds will be used wisely, it is
highly plausible that they will seek large, visible firms who will disseminate
sufficient information about their future expansion and investment plans.
Only such firms will have stock that is liquid enough to be traded regularly
and in sufficient quantities to enable funds to be raised for significant capital
expenditures. Small firms have little collateral value and cannot raise
funds easily through equity due to high issuance costs and lack of credibility
(Myers Majluf, 1984). If any funds are raised through equity, it is due to
their inability to obtain sources of debt funding as documented by Fama
and French (2002). We will use total assets as a discriminator by excluding
the lowest 75 percent of firms as being unable to raise funds due to lack of
perceived liquidity. Other balance sheet variables that merit consideration
include cash and short-term investments, investment and advances, current
liabilities, and long-term debt.
Cash and Short-Term Investments
Cash and short-term investments refers to the cash balance in a demand
deposit account as well as investments in marketable securities which
consist of short-term bills and stocks held for a 1–3 month duration that act
as interest-earning repositories for idle cash. Declining levels of cash as a
percentage of total assets indicate short-term needs for cash usually to meet
high interest or other fixed payments such as leases of capital equipment or
debt repayment. Such firms are less likely to increase fixed payments
through increased dependence on debt and would opt for equity financing.
28

Long-Term Debt
An annual increase in long-term debt would be detrimental to the firm from
the perspective of controlling risk. Debt is inherently risky in that it imposes
restrictions of the use of future cash flows. Firms that show rapid increases
in debt are less likely to choose further debt financing and will choose
seasoned equity offerings.
Common Equity
Common equity acts as a proxy for retained earnings. As common equity
includes both capital stock and retained earnings. An increase in retained
earnings could mean that more funds are being generated by the business
and possibly there is less need for external funding in the form of an SEO
offering. However, it is more realistic to consider an increase in retained
earnings as an indicator of greater reinvestment capability and more interest
by management to promote the growth and future development of the
enterprise. In such cases, more ambitious capital investment projects will be
undertaken, possibly those that involve the creation of new products and
markets. Such projects may be too risky for traditional financial institutions
limiting the amount of capital to be raised through debt. In such cases,
equity becomes the preferred investment choice. The final category consists
of income statement variables. Income statement variables may not be as
useful as balance sheet variables in gauging external funding sources as they
tend to have a short-term focus on quarterly rather than long-term results.
However, the case can be made for the value of examining net income and
capital expenditure.
Net income
This is the single measure of final profitability of the firm. Firms with rising
net incomes are successful firms with products that continue to find
customers and managers who are committed to the long-term success of
the enterprise. They do not engage in agency conflicting behaviors that
promote individual self-interest at the expense of the firm’s prospects,
therefore, such firms continue to be profitable year after year, so that any
expansions that they undertake from external funding are fully justifiable
to shareholders and the public. Such firms would not wish to see a decline in

income by raising funds through debt as interest expense would reverse
the trend of rising net income. Further, foregoing potentially profitable
products would not be a choice as such managers are focused on continually
raising profits.
Capital Expenditures
An increase in capital expenditures represents an increasing in funding
new equipment, research expenditure, new product development, and new
market expansion. In keeping with Walker and Yost (2008), we employ
the measure of capital expenditure/total assets which includes research
expenditure. Rising capital expenditures mandate the need for significant
capital spending on new projects with uncertain potential. Financial
institutions may be reluctant to finance such projects so that SEOs become
the major source of investment capital.
The above discussion leads to the following hypotheses: The probability
of use of seasoned equity offerings increases with
H1. The combined effect of a rise in retained earnings and debt,
H2. An increase in capital expenditure,
H3. An increase in dividends,
H4. Long-term debt reduction,
H5. The decrease in current debt,
H6. The decline in levels of cash and short-term investments,
H7. The increase in long-term debt: This hypothesis is the alternative
to H4,
H8. The rise in net income.
METHODOLOGY
The entire Computstat North America database of 10,000 stocks was
screened to arrive at a sample of stocks with SEO potential. Using total
assets as the discriminator, firms that had total assets in the 95th percentile
were isolated. As stated only large, visible firms were considered to be
30

possible SEO candidates. Four years of annual financial statement data for
each of these firms was extracted including data from 2002 to 2005. This
ensured predictive accuracy based upon the effect of normal market
conditions without the confounding effect of the economic downturn
of 2007–2009. They included retained earnings, long-term debt, capital
expenditure, dividends, long-term debt reduction, change in current debt,
cash and short-term investment, net income, interest expense, and operating
income after depreciation. Each variable was scaled by total assets to
account for variations in size of the firm. Asset size was used to estimate the
probability of SEO offering, with a dichotomous variable taking on values
of 0 and 1 being used to indicate if the firm had a probability of SEO
offering (score of 1) or no probability of SEO offering (score of 0). The data
was subjected to the following logistic regression:
PðSEO offeringÞ ¼ a þ b1RE þ b2LTD þ b3CE þ b4D þ b5DR
þb6CD þ b7C þ b8NI
(1)
where RE is the retained earnings measured by common equity, CE the
capital expenditure, LTD the long-term debt, D the dividends, DR the debt
reduction, CD the current debt, C the cash and short-term investments,
NI the net income, and the P(SEO offering) a dichotomous variable based
on asset size. Firms which had asset sizes greater than the mean were
designated values of ‘‘1’’ while those with asset sizes less than the mean were
assigned values of ‘‘0.’’
RESULTS
Annual observations over years 2002–2005 for 300 separate stocks in the
final sample with the highest likelihood of being selected for seasoned equity
offerings were subjected to a logistic regression with the probability
of selection as dependent variable and capital expenditure, cash and
short-term investments, debt reduction, current debt, dividends, long-term
debt, and net income as independent variables. The final model used 1228
observations with 1031 correct cases thereby accurately predicting the
probability of SEO offerings with 83.96 percent accuracy. As shown by
Table 1, Hypothesis 1 was partly supported with the decline in both
common equity but no significant reduction in debt as the coefficient for
change in common equity was a significant 2.07 105
, po.01 and that
for debt reduction was a non significant 1.697 105
, pW.1. Hypothesis 2

was supported contrary to the hypothesized direction as the reduction in
capital expenditure led to an increased probability of choosing SEOs as a
method of financing (coefficient ¼ 2.388 104
, po.001). Hypothesis 3
was not supported. Firms that pay higher dividends as a percentage of assets
are unlikely to seek SEOs as a method of financing (b ¼ 1.495 104
,
pW.1). Hypothesis 4 was not supported; there was no significant reduction
in debt (coefficient of 1.697 105
, pW.1). We may conclude that long-
term debt reduction does not significantly influence the selection of firms
for seasoned equity offerings. Hypothesis 5 was supported at the .1 level
of significance (b ¼ 4.61 106
, po.1), though not at the more stringent
.05 level of significance (b ¼ 4.61 106
, p ¼ .07). The reduction in current
debt marginally increases the likelihood of selection for seasoned equity
offerings. Hypothesis 6 was supported contrary to the hypothesized
direction. Rising levels of cash and short-term investments, or a strong
liquidity position, was associated with the likelihood of opting for
seasoned equity offerings as the preferred method of financing
(coefficient ¼ 1.107 105
, po.01). Hypothesis 7 was not supported; as
Hypothesis 7 is the alternative to Hypothesis 4, the question is which of
them is supported, a decrease (Hypothesis 4) or an increase (Hypothesis 7)
to which the response is neither as there was no significant effect of the
reduction in debt on the probability of selection for an SEO. The increase
in net income was associated strongly with the choice of seasoned equity
offerings (coefficient ¼ 2.874 104
, po.001) supporting Hypothesis 8
(Table 2).
Table 1. Results of Logistic Regression of the Probability of Selecting
Seasoned Equity Offerings on Firm Characteristics.
Variable Coefficient t-Ratio
Capital expenditure 2.388 10
4 4.53, p ¼ .0000
Common equity 2.079 105 2.73, p ¼ .006
Cash and short-term investments 1.107 105 2.69, p ¼ .007
Debt reduction 1.697 105
1.56, p ¼ .117
Current debt 4.612 106
1.78, p ¼ .074
Dividends 1.495 104
1.33, p ¼ .184
Long-term debt 1.378 104 9.28, p ¼ .00
Net income 2.874 104 8.29, p ¼ .00
Percent accuracy 83.96
Average likelihood 0.576
Pseudo R2
0.225
po.05, po.01, po.001.
32

Table 2. Descriptive Statistics for Firm Characteristics.
Capital Expenditure (N ¼ 1228)
Mean 1461 Skewness 4.98
Variance 824404.00 Kurtosis 37.70
25th percentile 0
Median 444.5
75th percentile 1608.25
Maximum 33274
Minimum 0
Common equity (N ¼ 1228)
Mean 11085 Skewness 3.12
Variance 2.4904 108
Kurtosis 12.18
25th percentile 1911
Median 6445
Maximum 111412
Minimum 0
Cash and short-term investments (N ¼ 1228)
Mean 9250.59 Skewness 6.33
Variance 9.113 108
Kurtosis 47.44
25th Percentile 207.75
Median 1462.5
75th Percentile 4612.25
Maximum 339136
Minimum 0
Debt reduction (N ¼ 1228)
Variance 3.21 108
Kurtosis 120.78
25th percentile 0
Median 617
Maximum 280684
Minimum 0
Current debt (N ¼ 1228)
Variance 2.94 109
Kurtosis 43.79
Median 5626
Maximum 542569
Minimum 0

CONCLUSIONS AND RECOMMENDATIONS
FOR FUTURE RESEARCH
The sum total of all of the hypotheses indicates that firms are strong
fundamentally are more likely to select seasoned equity offerings as a
method of financing. Such firms have rising net incomes suggesting that they
produce profitable products targeted at growing markets, either domes-
tically or internationally. They do not necessarily pay high dividends and do
not use a large amount of common equity to fund expansion. As common
equity declines, they rely to an increasing extent on retained earnings or
internal financing. They are averse to relying on financial leverage to fund
expansion. The attitude toward debt is apparent in that they have declining
levels of existing debt, or old debt that is in the process of being retired,
without a firm policy of debt reduction, whereby they aggressively pay-off
Table 2. (Continued )
Capital Expenditure (N ¼ 1228)
Dividends (N ¼ 1228)
25th Percentile 0
Median 107
75th Percentile 501
Maximum 9352
Minimum 0
Long-Term Debt (N ¼ 1228)
25th percentile 0
Median 0
Maximum 105502
Minimum –24615
Net income (N ¼ 1228)
25th Percentile 0
Median 623
75th Percentile 1743
Maximum 24521
Minimum –25780
34

existing debt. They maintain high and strengthening cash balances which
reduce exposure in uncertain economic times and provide a cushion of
capital in an economic downturn. This suggests a high level of conservatism
even prior to the economic downturn of 2007–2009. Another relevant result
is the decline in capital expenditures being associated with the probability
of selection for seasoned equity offerings. At first glance, this may seem
puzzling, given the implicit assumption that firms seek more expensive
equity funding to finance capital projects. However, we need to be aware of
the fact that our measure is of current capital expenditure. Perhaps these
firms have reached their limit and are facing diminishing returns on current
capital investment projects. Given their rising net incomes, it is likely that
they wish to fund new, innovative projects with uncertain profit potential so
that they do not wish to raise debt and choose equity as the optimal method
of financing.
This study adds to the existing body of literature on the characteristics
of firms that undertake seasoned equity offerings. Together with Walker and
Yost (2008), it provides the only body of knowledge that seeks multiple
characteristics to explain the choice of seasoned equity for financing.
In addition, it is both contemporary and complete. The data set is very
current using data from the post-2002 time period. It provides for a longer
span of data than Walker and Yost (2008) who employed two years of data
versus four in this study. Our examination of the entire Compustat database
with a full 10,000 list of stocks makes this study uniquely comprehensive.
Future research should consider operating performance as a determinant
of seasoned equity offerings. The particularly relevant variable in this case
is operating income after depreciation. Firms that invest in research and
development by purchasing new equipment are able to write off significant
amounts of this new cost as depreciation expense. This depresses their
operating income after depreciation. As research and development expendi-
tures continue to rise, it is likely that there will come a point at which a rapidly
expanding firm will be unable to meet its research and development
expenditures from internal funds. Debt would reduce the level of internal
funding, so that equity financing in the form of SEOs offers the more attractive
alternative. Another method of confirming the growing trend toward
foregoing debt as a means of financing would be to use interest expense as
a determinant of SEO offerings. The arguments against the use of debt apply
to raising interest expense. Interest expense places a burden on operations
and pressure on managers to generate sufficient income from operations to
meet fixed payments. Declining interest expense is an indicator of declining
dependence on debt and the increasing probability of relying upon new equity.

In summary, this chapter adds to the literature on capital structure
by focusing on the an area in which there is a paucity of research, i.e., on
the firm characteristics that underlie the selection of stocks for seasoned
equity offerings by offering a comprehensive approach to forecasting the
prevalence of such offerings.
REFERENCES
Ambarish, R., John, K., Williams, J. (1987). Efficient signaling with dividends and
investments. Journal of Finance, 42, 321–344.
Fama, E., French, K. (2002). Testing trade-off and pecking order predictions about dividends
and debt. Review of Financial Studies, 15, 1–33.
Hull, R. (1999). Leverage ratios, industry norm, and stock price reaction: An empirical
investigation. Financial Management, 28, 32–45.
Hull, R., Moellenberndt, R. (1994). Bank debt reduction announcements and negative
signaling. Financial Management, 23, 21–30.
John, K., Koticha, A., Narayanan, R., Subrahmanyam, M. (2000). Margin rules, informed
trading in derivatives, and price dynamics. Working Paper, New York University.
Johnson, D., Serrano, J., Thompson, G. (1996). Seasoned equity offerings for new
investments. The Journal of Financial Research, 19, 91–103.
Masulis, R., Korwar, A. (1986). Seasoned equity offerings: An empirical investigation.
Journal of Financial Economics, 15, 31–60.
Mikkelson, W., Partch, M. (1986). Valuation effects of security offerings and the issuance
process. Journal of Financial Economics, 15, 31–60.
Myers, S., Majluf, N. (1984). Corporate financing and investment decisions when firms have
information that investors do not have. Journal of Financial Economics, 13, 187–221.
Stigler, G. J. (1960). The economics of information. Journal of Political Economy, 69, 213–225.
Walker, M. D., Yost, K. (2008). Seasoned equity offerings: What firms say, do, and how the
market reacts. Journal of Corporate Finance, 14, 376–386.
36

THE IMPACT OF LIFE CYCLE
ON THE VALUE RELEVANCE
OF FINANCIAL PERFORMANCE
MEASURES
Shaw K. Chen, Yu-Lin Chang and Chung-Jen Fu
ABSTRACT
The components of earnings or cash flows have different implications for
the assessment of the firm’s value. We extend the research for value-
relevant fundamentals to examine which financial performance measures
convey more information to help investors evaluate the performance and
value for firms in different life cycle stages in the high-tech industry.
Six financial performance measures are utilized to explain the difference
between market value and book value. Cross-sectional data from firms in
Taiwanese information electronics industry are used. We find all the six
performance measures which are taken from Income Statement and Cash
Flow Statement are important value indicators but the relative degrees
of value relevance of various performance measures are different across
the firm’s life cycle stages. The empirical results support that capital
markets react to various financial performance measures in different life
cycle stages and are reflected on the stock price.
ISSN: 1477-4070/doi:10.1108/S1477-4070(2010)0000007006
37

INTRODUCTION
Any financial variable is considered to be value relevant if it has a predictable
association with market values of equity. A sizable literature suggests that
financial measures can provide value-relevant information for investors and
that the components of earnings or cash flows have different implications
for the assessment of firm value. On the other hand, different life cycle
stages constitute an important contingency factor in the development of the
organizational theory of companies (Koberg, Uhlenbruck, Sarason, 1996).
Firms in different life cycle stages have different economic characteristics
that may affect the usefulness and value relevance of financial performance
measures (Black, 1998; Baginski, Lorek, Branson, 1999). Thus, it is
important to consider the impact of the life cycle stage on the value relevance
of the components of earnings and cash flows.
Impacts of different life cycle stages are critical for evaluating
performance (Hofer, 1975; Robinson, 1998; Pashley Philippatos, 1990;
Robinson McDougall, 2001). Jorion and Talmor (2001) state that
although generally accepted accounting principles (GAAP) are designed for
all companies to provide comparable financial reports, the usefulness of
accounting information may vary according to the changes in production
function and activities of firms. Porter (1980) suggests that regardless of
a firm’s strategies (e.g., sales growth or utilization of capital capacity), the
impacts of the life cycle stage of the company should be considered.
Robinson (1998) shows that the financial performance of companies that
enter a market in the start-up stage is better than the companies that enter a
market in the mature stage. His results support the proposition that it is very
important to consider the impact of life cycle when evaluating the financial
performance measures of firms. Fairfield, Sweeney, and Yohn (1996) suggest
that reported earnings alone may not transmit all the information in
accounting data for evaluating firm profitability. Black (1998) further
analyzes the life cycle impacts on the incremental value relevance of earnings
and cash flow measures.
Because the components of earnings or cash flows have different
implications for the assessment of firm value, this study extends the research
for value-relevant fundamentals by examining which financial performance
measures convey more information when evaluating. We use cross-sectional
data over twelve years yields from a total of 4,862 firm-year observations
to examine six financial performance measures for firms of different life
cycle stages in the Taiwanese high-tech industry. The earning measures
are decomposed into research and development expense (RD), operating
SHAW K. CHEN ET AL.
38

income (OI), and adjusted non-operating income (ANOI). The cash flow
measures are decomposed into cash flows from operating (CFO), cash flows
from investing (CFI), and cash flows from financing (CFF).
We find all the six performance measures are important value indicators
but the relative degrees of value relevance are different across firm life cycle
stages. For earnings-related measures, RD and ANOI are the best value-
relevant indicators in the growth stage. OI is more value-relevant in the
mature than in the decline stage. On the other hand, for cash flow measures,
CFI and CFF are both better value indicators in the decline stage compared
with the growth stage. This implies that the market does concern itself with
the various financial performance measures in different life cycle stages and
reflects it on the stock price.
Our result supports the Financial Accounting Standard Board (FASB)
suggestion that present and potential investors can rely on accounting
information to improve investment, credit, and similar predictive decisions.
Specifically, our findings detail the value relevance of different financial
performance measures across life cycle stages of information in electronic
firms, a critical and highly competitive industry for Taiwan’s economy.
The remainder of this chapter is organized as follows. The second section
presents the literature review and derives hypotheses from past research
and the third section shows our sample selection procedure, life cycle
classification, definition and measurement of the variables, and the
valuation model. The empirical results and analyses are discussed in the
fourth section. Further discussion on our finding and a brief conclusion are
provided in the final section.
LITERATURE REVIEW AND HYPOTHESES
Financial performance measures have been most widely used to evaluate the
organizational health of a firm. However, the opportunities, pressures, and
threats in both the external and internal environment of an organization vary
with the stages of life cycle (Anderson Zeithaml, 1984; Jawahar
Mclaughlin, 2001). Myers (1977) asserts that firm value can be analyzed from
two components: assets in place and future growth opportunities. In early life
cycle stages, growth opportunities constitute a larger component of firm
value; but in the later life cycle stages, assets in place become the larger
component. The information conveyed by the financial performance
measures is expected to be different for each component. Since the
proportion of these two value components differs in each life cycle stage,
The Value Relevance of Financial Performance Measures 39

the value relevance of financial performance measures is expected to vary by
stages (Anthony Ramesh, 1992; Black, 1998; Hand, 2005). Due to the
change in the combinations of activities and investments, there is a shift in
the value relevance of certain financial statements line items (Jorion
Talmor, 2001). Penman (2001) also indicates that information transmitted by
various cash flows typically varies over the life cycle of the firm. We expect
the information conveyed by the financial performance measures is expected
to be positively associated with firm value in different life cycle stages and
then develop related hypotheses across the different life cycle stages.
The Value Relevance of Financial Performance
Measures in the Start-Up Stage
Prior literature states that the start-up stage is characterized by market
growth, less intense competition, heavy capital investment requirement,
new technology development, and high prices. Dodge, Fullerton, and
Robbins (1994) and Jawahar and Mclaughlin (2001) indicate that financing
and marketing problems are perceived as crucial for organizational
survival. Thus, a firm’s important concerns are obtaining the initial capital
to solve financing problems and enter the market in this stage. Anderson
and Zeithaml (1984) indicate that during this stage, primary demand for
the product begins to grow, and products are unfamiliar for potential
customers. Robinson (1998) and Robinson and McDougall (2001) suggests
that sales growth is more appropriate than the market share as a per-
formance measure in the start-up stage. Therefore, sales growth is necessary
for firms to survive. As sales growth increases, the value of the firm will
increase in the start-up stage.1
Measures in the Growth Stage
RD is a critical element in the production function of information
electronic firms. Booth (1998) and Hand (2003, 2005) find that a firm with
continuous research and development will have a higher ratio of hidden
value in its firm value and supports the proposition that RD is beneficial
to the future development of the firm. With regard to a research-intensive
firm, Joos (2002) finds that when RD increases, return-on-equity (ROE)
will also increase. Relative to the later two life cycle stages, firms in the
SHAW K. CHEN ET AL.
40

growth stage will spend more on RD leading to future profit-generating
opportunities and increase firm value. This discussion leads to the following
hypothesis:
H1a. Relative to the mature and decline stages, RD is more positively
associated with firm value for firms in the growth stage.
In the growth stage, most firms can’t generate much income from core
operating activities. Those who can obtain more income from nonoperating
activities will create more value for shareholders. Fairfield et al. (1996)
suggest that nonoperating income has incremental predictive content of
future profitability. Therefore, in this stage, the firm’s adjusted nonoperat-
ing income (ANOI) is positively associated with firm value and we propose
the following hypothesis:
H1b. Relative to the mature and decline stages, ANOI is more positively
associated with firm value for firms in the growth stage.
Measures in the Mature Stage
Robinson (1998) indicates that operating income (OI) is a superior measure
to reflect a firm’s ability to sell its products and to evaluate operational
performance. Relative to the growth and decline stages, OI is a more
important earnings item; for firms in the mature stage would alter its focus
from increasing sales growth to increasing OI. As OI increases, the value of
the firm will increase. Thus we test the following hypothesis:
H2a. Relative to the growth and decline stages, OI is more positively
associated with firm value for firms in the mature stage.
Klein and Marquardt (2006) views CFO as a financial measure of the
firm’s real performance. In the mature stage, firms are often characterized
by generating sufficient cash flows, without particularly attractive invest-
ment opportunities (Jawahar Mclaughlin, 2001; Penman 2001). Black
(1998) also finds that CFO is positively associated with market value of the
firm in the mature stage. Therefore, as CFO increases, the value of the firm
will increase, and leads to our next hypothesis:
H2b. Relative to the growth and decline stages, CFO is more positively
associated with firm value for firms in the mature stage.

Measures in the Decline Stage
Business risk is high when firms move into the decline stage. When demand
for an organization’s traditional products and services are reduced, less
efficient firms are forced out of industries and market (Konrath, 1990;
Pashley Philippatos, 1990). Following the BCG (Boston Consulting
Group) model, when companies step into the decline stage, the cash generate
ability becomes a more important value driver for those companies or
divisions in the decline stages. The ability to generate funds from the outside
affects the opportunity for firms’ continuous operations and improvement.
Therefore, as CFF increases, the value of the firm will increase, and leads to
our next hypothesis:
H3a. Relative to the growth and mature stages, CFF is more positively
associated with firm value for firms in the decline stage.
Declining firms do not necessarily fail.2
Some firms are forced to consider
investment and develop new products and technology to ensure organiza-
tional survival (Kazanjian, 1988; Jawahar Mclaughlin, 2001; Zoltners,
Sinha, Lorimer, 2006). Black (1998) points out that firms can regenerate
by investing in new production facilities and innovative technology and
goes back into the growth or mature stage, prevent failure for many years.
CFI is expected to be positively correlated with firm value during decline
(Black, 1998). Pashley and Philippatos (1990) also have a similar conclusion.
Therefore, we develop the following hypothesis:
H3b. Relative to the growth and mature stages, CFI is more positively
associated with firm value for firms in the decline stage.
RESEARCH DESIGN AND METHODOLOGY
Sample Selection
We selected publicly listed information electronics companies from the
Taiwan Stock Exchange (TSE) and Gre Tai Securities Market (Taiwan OTC
market). The companies’ financial data and the equity market value data
are obtained from the Financial Data of Company Profile of the Taiwan
Economic Journal (TEJ) Data Bank. A total of 4862 firm-year observations
over twelve years from 1997 to 2008 are collected.
SHAW K. CHEN ET AL.
42

The criteria for sample selection are: (1) Sample firms are limited to
information electronics industries; (2) Companies with any missing
stock price or financial data are excluded; and (3) Companies subject
to full-delivery settlements and the de-listed companies are excluded. We
focus our attention on the information electronics industry for two reasons:
(1) we hope to derive less noisy competitive structure variables (such as
barrier-to-entry, concentration, and market share) (Joos, 2002) to mitigate
some problems caused by using cross-sectional studies (Ittner, Larcker,
Randall, 2003) and (2) the information electronic industry is a strategically
critical sector for Taiwan’s economic prosperity and growth.
Life Cycle Classification
Classifying companies into different life cycle stages is a challenging task.
This study uses a tailored classification method similar to Anthony and
Ramesh (1992) and Black (1998). A multivariate classification method is
used to classify observations into three life cycle stages.
The procedure of life cycle classification is as follows. First, we choose sales
growth, capital expenditures, dividend payout, and firm age as the classifica-
tion indicators. Second, sales growth and capital expenditure are sorted from
highest to lowest, while dividend payout and firm age are sorted from lowest
to highest by rank. The indicators are given a score of 0, 1, or 2 based on their
ranking. The firm with the highest sales growth or capital expenditures is
given a score 0; or else, the firm with the highest dividend payout or firm age
is given a score 2. The scores of the four classification indicators are then sum-
med together giving a composite score that ranges from zero to eight. Finally,
firm years are assigned to one of the three groups based on the composite
score. Firm-year observations with composite score equal or less than 2 are
assigned to the growth stage. Firm years with a composite score three, four,
or five are assigned to the mature stage. And, firm-year observations with
composite score equal or more than 6 are assigned to the decline stage.
At last, our final sample retains 1070 firm-year observations in growth
stage, 2730 firm-year observations in mature stage, and 1062 firm-year
observations in decline stage.
Empirical Model
We extend Ohlson’s (1995) valuation model to examine the relationship
between equity market value and the various financial performance

measures in each life cycle stage. We add a dummy variable (STAGE) based
on the life cycle stage and build two-way interaction terms among various
financial variables to test our hypotheses. Definition and measurement of
variables are given in Table 1. The extended empirical model is as follows.
MVi ¼ b0 þ b1BVCi þ b2CFOi þ b3CFOi STAGEi þ b4CFIi
þ b5CFIi STAGEi þ b6CFFi þ b7CFFi STAGEi
þ b8RDi þ b9RDi STAGEi þ b10OIi þ b11OIi STAGEi
þ b12ANOIi þ b13ANOIi SATGEi þ i
where MV is the market value of equity, BVC the book value of net assets
except for cash, CFO the cash flows from operating, CFI the cash flows
from investing, CFF the cash flows from financing, RD the RD expense,
OI the operating income, ANOI the djusted nonoperating income,
BVCSTAGE the interaction term for BVC and STAGE, CFOSTAGE
the interaction term for cash flows from operating and STAGE,
CFISTAGE the interaction term for cash flows from investing and
STAGE, CFFSTAGE the interaction term for Cash flows from financing
and STAGE, RDSTAGE the interaction term for RD expense and
STAGE, OISTAGE the interaction term for operating income and
STAGE, ANOISTAGE the interaction term for adjusted nonoperating
income and STAGE, and STAGE the life cycle stage.
ANALYSIS OF EMPIRICAL RESULTS
Descriptive Statistics and Correlation Analysis
Table 2 provides the descriptive information on the variables of different
life cycle stages. As shown in Table 2, the mean of MV is 22,280,000,
17,983,380, and 11,049,000 thousand New Taiwanese Dollars (NTD),
respectively. The mean of RD decreases from 309,501 to 256,245 thousand
NTD. This implies that firms generally reduce research and development
expenditures as they decline over time. The mean of CFI (cash outflows)
decreases from 2,850,576 to 528,939 thousand NTD and is consistent
with firm’s investment opportunity sets becoming smaller as firms decline.
CFF provides information about the ability of a firm’s asset in place to
generate cash to pay-off existing debt, or acquire additional funds for the
firm (Pashley Philippatos, 1990). The mean of CFF also decreases from
SHAW K. CHEN ET AL.
44

1,439,503 to 652,183 thousand NTD. This is also consistent with our
inference that firms require more external funds during the decline stage.
Table 3 shows the interrelations among the various financial performance
measures and MV in different life cycle stages. We find correlation among
variables is significant. For example, in the growth stage, MV is highly
positively correlated with RD (Pearson r ¼ 0.361; po0.01), in the mature
stage, MV is highly positively correlated with CFO (Pearson r ¼ 0.338;
po0.01), and in the decline stage, MV is highly positively correlated with
Table 1. Definition and Measurement of Variables.
Variables Measurement
A. Life cycle classification indicator variables
Sales growth (SGit) 100(salestsalest1)/salest1
Dividend payout (DPit) 100annual dividend of common stock/annual income
Capital expenditures (CEit) 100(purchase fixed assets – reevaluated fixed assets of firm i at
time t)/AVt1
Firm age The difference between the current year and the year which the
firm was originally formed
Life cycle stage (STAGEit) Dummy variable in the three groups (growth stage compared
with mature stage; mature stage compared with decline stage;
and decline stage compared with growth stage) and take on
the value of 1 for the former life cycle stage and 0 for the
latter life cycle stage,
B. Variables of the empirical model
Market value of equity
(MVit)
The market value of equity of firm i at time t/AVt1
Cash flows from operating
(CFOit)
Cash flows from operating activities of firm i at time t/AVt1
Cash flows from investing
(CFIit)
Cash flows from investing activities of firm i at time t/AVt1
Cash flows from financing
(CFFit)
Cash flows from financing activities of firm i at time t/AVt1
RD expense (RDit) RD expense of the firm i at time t/AVt1
Operating income (OIit) (Gross profit – operating expenses ) of firms i at time t/AVt1
Net income (NIit) The net income of firms i at time t/AVt1
Adjusted nonoperating
income (ANOIit)
(NIitOIitRDit)/AVt1
Control variable
Book value of net assets
except for cash (BVCit)
The book value of equity less the change in the cash account of
firm i at time t/AVt1 (Black, 1998)
Notes: All of the variables are deflated by each year by the book value of assets at the end of
year t1(AVt1). All of the financial variables are measured in thousand dollars.

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