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Working Paper 76-2
THE NOTIVATION FOR BANK HOLDING COMPANY ACQUISITIONS
Walter A. Varvel
Federal Reserve Bank of Richmond
February 1976
The views expressed here are solely those of
the author and do not necessarily reflect the
views of the Federal Reserve Bank of Richmond.
THE MOTIVATION FOR BANK HOLDING COMPANY ACQUISITIONS
Walter A. Varvel*
I.
Introduction
The commercial banking system in this country has undergone an
unparalleled consolidation movement since the mid-1960's.
Bank holding
companies (BHCS) have been active since the turn of the century, yet
they have become an important force in the banking structure only since
1965
l
The phenomenal growth in the number of corporations that hold
stock in one or more banks and the increased concentration of banking
resources in such entities have prompted much discussion and a wealth
of analytical studies of the potential impact of this development on
the nation's financial system.
Central to many of these studies has
been the question of how acquisition by a holding company may affect
the performance of an acquired commercial bank.
Related to this issue,
and often confused with it, is the question of the motivation for
such acquisitions.
The latter question has yet to be adequately answered.
Most efforts to explain the economic basis for bank holding company
acquisitions have evolved from a framework designed to measure the
resulting impact on the community served by an acquired bank.
Attention
has been centered on the consistent findings that the profitability of
a bank has not been improved, relative to similarly situated independent
banks, through acquisition to an extent that would clearly justify
*This paper is based on the author's unpublished Ph.D. dissertation,
"The Acquisition of Commercial Banks by Bank Holding Companies: A Valuation
Approach," Texas A & N University, 1975.
acquisition by a wealth-maximizing bank holding company.
But conclu-
sions based on measurements of bank profitability alone ignore the
possibility that owners' claims oneamings
streams are altered signi-
ficantly by the transaction.
This paper examines the hypothesis that the incentives for acquisition lie primarily in potential benefits accruing to owners, i.e.,
shareholders, who have claims on the earnings streams of the two firms
involved.
The framework for the analysis centers on a comparison of
the valuation of expected future earnings streams for both sets of
stockholders under the alternative assumptions, first, that the acquisition is not consummated and second, that it is consummated.
Rational
behavior implies that owners will exchange claims to earnings only..if
they value those received'more than those released.
Subsequent sections
will investigate the motivation for acquisition from both theoretical
and empirical constructs.
Some Previous Evidence
Among efforts to establish the existence of a "valuation disparity"
sufficient to justify a BHC acquisition have been those by Thomas Piper
and Steven Weiss. '
In a study of acquisitions during the period 1947
through 1967, Piper argued that the economic incentives for acquisitions
of banks "center on the resultant changes, both in the cash flows and
earnings of the acquired banks and in the valuation of these cash flows"
[14, p. 981. He emphasized the importance of comparing the value of
$iper's analysis of bank acquisitions [14] and his subsequent work
with Weiss [15] clearly recognized that an alteration in ownership positions resulted from acquisitions. Their consideration of this point was
an important shift from concentration on bank performance alone.
.
3
alternative ownership interests.
For the acquisitions studied, Piper
compared the value received by the stockholders of the bank being
acquired with the value they relinquished and found that the value of
the claims bank stockholders obtained was significantly greater than
their previously held claims on the bank.
2
In fact, the ratio at
which the holding company stock was exchanged for that of the bank was
so favorable to the bank's shareholders that a careful examination of
possible earnings differentials between the firms was not necessary.
The
market values of the stocks have been an adequate (albeit imperfect)
gauge of this differential.
A much closer look, however, is necessary
when trying to explain why BHCs have been willing to pay such premiums.
Piper's original study and his later work with Weiss shifted
emphasis from the valuation of the stocks traded in the acquisition
to the profitability of acquisitions to the stockholders of the parent
holding company.
Each study concluded that, due to the high premiums
paid for bank stock, acquisitions have failed to improve the earnings
of the holding companies.
The shift from valuation to profitability,
however, begs questions concerning the manner in which owners value a
given income stream.
A valuation framework that includes a constant discount rate,
adjusted for expectations of risk, rules out any possibility that the
manner in which earnings are valued may change in response to the
operating policies and earnings performance of the firm.
While such
2Piper's results showed that the market value of BHC stock received
exceeded the book value of the bank by 30 percent. In his later study
with Weiss, comparing the claims on holding company earnings received
by former stockholders of the acquired bank relative to earnings of the
bank stock, the median premium was found to be 16 percent.
4
an assumption greatly simplifies the analysis, it ignores a potentially
important source of the valuation disparity underlying the incentives
for the acquisition of commercial banks.by BHCs; i.e., changes in owners'
discount rates due to their evaluation of risk.3
Valuation Via A Risk-Adjusted Discount Rate
The most widely used model for valuing risky, multiperiod earnings
streams is.the risk-adjusted discount rate.
Through this technique, a
measure of the magnitude of the earnings flow, usually expected value,
is evaluated by a-discount rate that takes into account the rate of
time preference and some measure of the degree of riskiness associated
with an earnings flow.
Individuals must make estimates of future
earnings and apply a subjectively determined discount rate to them.
Since this approach is not based on any specific assumption as
to what constitutes the risk associated with expected earnings, it
has serious shortcomings.
Unless a specific, dynamic measure of risk
is incorporated within the framework, the detection of differences in
valuation due to differences in risk is not possible.
In order to
measure the effect on valuation of an acquisition, knowledge of the
pre-acquisition capitalization rate and the response of that rate to
the acquisition is required.
It is entirely possible that the addition
of another income stream with a different discount rate may alter owners'
capitalization rates in subsequent periods.
31f owners are concerned with more than just the mean level of
earnings, and a measure of risk does affect their discount factor(s),
a reduction in the risk associated with a given earnings distribution
will reduce the discount factor if owners are risk averse and result
in a higher valuation of those earnings. Comparison of earnings
means alone will not detect this disparity.
5
A specific present value of earnings cannot, however, be derived
without information concerning owners' attitudes toward risk and the
trade-off they are willing to make between risk and return.
This
becomes a serious stumbling block in the search for the motivation for
acquisition, but it need not be insurmountable.
sets of investors involved in any acquisition:
shareholders and those of the BHC.
There are two distinct
the independent bank
Each group obtains a claim on an
earnings stream that is somewhat altered from its previous holdings.
The acquisition is beneficial if the capitalized value of the transformed
earnings stream is greater than that the stockholders perceive would
have been available through holding on to their existing claims.
A
change in this valuation through a shift in capitalization rates, then,
could result from either a shift in the investor's measure of risk
following the acquisition or the manner in which a given change in
risk'affects his capitalization rate.
Since the individuals making
the valuation comparisons have not changed, it seems reasonable to
assume, for simplicity, that the exact form of the capitalization rate
function in terms of risk does not change.4
As long as an increase
(decrease) in the measure of risk faced by owners is reflected in an
increase (decrease) in the discount factor used to evaluate an earnings stream, emphasis may be placed on the expected behavior of risk
under alternative situations.
If it is assumed that a detected
4For a discussion of the dependence of the form of an individual's
capitalization rate function in the presence of uncertainty on the form
of his underlying utility function, see Douglas Vickers, Chapters 2
and 4. Vickers suggests that the capitalization rate function is nonlinear in the coefficient of variation of net income and concave upward.
6
difference in the measure of risk results in different capitalization
rates, valuation disparities may be sought by comparing alternative
earnings performances and 'measures of risk.
I
These comparisons are made
in Section IV of this paper.
The Basis For Acquisition
The suggested approach for analysis of the economic basis for
acquisition is founded upon the premise that the firm that engages in
banking determines its operating and organizational structure on the
basis of optimization of the economic value of the ownership of the
firm, i.e., the owners' wealth position.
Owners' wealth is perceived
*as the capitalized value of the expected future earnings stream.
Since
the objective to be maxim$zed is in value terms, specific attention
must be given to its components.
In general terms, V = IT/P,where V,
TT,and p represent, respectively, value, profit, and the owners'
capitalization rate (which is adjusted for considerations of time
preference and risk).
The essential consideration of the analysis for bank owners is
the difference in the valuation of their ownership position if they
(a) continue their present structure of organization and production as
opposed to (b) trading thefr bank stock for partial interest in a .
holding company.
For BHC owners, it is the difference in the valuation
of their ownership claims perceived through (a) the present BHC structure and (b) the expanded organization created through acquisition.
The
first disparity provides an incentive for the present bank owners to
make the transaction, while the second provides the incentive for holding
7
company acquisition activity.
The purchase price of the bank stock,
usually in terms of a stock-exchange ratio, is then determined by
the relative bargaining power of the buyer and sellers and the degree
of competition in the buying and selling of bank equity.
Regardless of the measure of risk utilized, acceptance of the
proposition that owners' conceptions of risk may change over time and
may be altered by specific actions of the firm has important implications for the risk-adjusted discount rate and may significantly alter
valuation of the earnings accruing to owners.
The provision of a
dynamic capitalization rate (p), which is a function of the risk
associated with a given earnings stream, provides a valuation framework that considers both the earnings experience and the behavior of
the d&scounting function used by owners in evaluating their ownership
position.
(1)
In present value terms,
H
v3
c =t
t-l Pt
where V is the present value of the future earnings stream to owners,
rt is net earnings on owners' equity in period t, pt is the owners'
capitalizationrate
applied to earnings in period t, and H is the economic
horizon of ownership in the firm.
In this framework, valuation disparities
may be sought for both sets of participants in the transaction--the bank
stockholder and the shareholder of the BHC.
5The owners' discount rate in period t (pt) may be further specified:
= (l+rl) (l+rZ) . . . (l+rt-1) (l+rt), where rt is dependent on the
Pt
owners' time preference pattern i (assumed constant) and an appropriate
measure of risk, e.g., the coefficient of variation of net income (Vn),
which is the standard deviation of the probability distribution of expected
net incomes divided by the mean of the probability distribution function.
p, then, may also be expressed as functionally dependent on these same
variables: p = p(i,
Vn).
8
Bank owners will have an incentive to trade their stock only if
a valuation disparity is established between the capitalized value of
the stream of bank profits accruing to owners through continued ownership in the bank and that,realizable from gaining an ownership interest
in the holding company.
Specifically, they have an incentive to trade
their stock for that of a holding company only if:
cvHC
where VB is the ownership valuation of the bank, c1is the share in the
total ownership of the holding company obtainable by bank owners, and
VHC is the total ownership valuation of the BHC.
The bank owners'
valuation of their portion of holding company earnings will, in this
case, be greater than their valuation of expected bank earnings.
Pre-
vious findings, in terms of this framework, suggest that CLhas been
large enough to assure the necessary disparity in valuation of earnings.
Similarly, an incentLve for holding company acquisitions exists
on the demand side ,for bank stock only if present company stockholders
view a similar valuation 'disparity. In particular, only if the acquisition of a commercial bank improves the capitalized value of owners'
earnings over that perceived without acquisition will present owners
move to acquire the bank, i.e., only if:
(3)
(vH&~
= t&t/P
t>-B
<
&(++)B
= B(vHC)B
9
where(VHc)-Bis the ownership valuation of the holding company without
acquiring the bank, B is the proportion of ownership interest in the
company retained by present owners (B = l-a), and (VHc)B is the capitalized
value of the earnings stream of the holding company including the proposed
acquired bank.
Even though their percentage ownership (13)falls with an
acquisition, present owners may still benefit if earnings increase significantly -- if risk, and, therefore, the vector of owners' capitalizaor
tion rates following acquisition - reduced.
is
For an acquisition to occur, then, both valuation disparities must
exist.
The present owners of an independent bank and of a holding company
will agree to participate in an exchange of stock if each group perceives
a positive shift in its ownership valuation resulting from the transaction.
Equations (2) and (3) represent the conditions necessary for consummation
of an acquisition agreement.
nowhere in
Of particular interest is the fact that
(3) is there any implication that the bank's.profitability must
be increased following acquisition.
If the owners are assumed to maximize
the value of their ownership position, they will be concerned with the
valuation of their share of the holding company rather than that of a
single subsidiary.
It may be that factors such as the structure of
organization, production considerations, and costs that optimize the
economic valuation of the consolidated company's earnings stream conflict
with the attainment of the maximization of one of its subsidiaries'
returns.
Such an hypothesis is consistent with empirical results here-
tofore obtained that suggest that bank profitability is not significantly
enhanced through holding company affiliation.
10
In fact, if it is recognized that the acquisition of a bank may
have a positive impact on the level and/or stability of earnings of
.
other subsidiaries within a BHC organization, consideration of changes
in bank profitability is an inadequate tool with which to examine the
economic basis for acquisition.
It is essential that the analysis con-
sider both the earnings experience and associated expectations of risk
of each ownership position.
An examination of both levels of alternative
earnings and the manner in which those earnings are valued is necessary
before conclusions may be reached.
II.
Components of the Valuation Framework
Within our generalized valuation framework (V = r/p),
it is essential
to carefully specify each of its components, i.e., (a) the firm's profit
function, and (b) the capitalization rate function as perceived by the
firm's stockholders.
Profit Function
Each period's profits are determined by the difference between
revenue generated form the firms
product markets and the costs asso-
ciated with their production.
Revenue
To allow for varying degrees of demand elasticity,
then, the demand conditions in the ith product market are represented
by Pi = P (qi); i = 1, 2,
product markets.
. . ., n; n is the number of distinguishable
These show the relation between the alternative
11
supplies of output and the price the firm can charge.
The firm can
influence the price of at least some of its products by varying its
production.
With negatively sloped demand curves, the firm can only
sell more of a good by lowering its price.
Hence, dPi/dqi < 0;
except
in those markets that may be represented by pure competition.
Revenue is defined as
(qi)41 , and marginal revenue is the change
in revenue as output changes:
MRi = (dPi/dqi)qi. Marginal revenue is,
for all but the perfectly elastic demand curves, less than price.
The
purely competitive product markets are special cases of the more general
representation.
The revenue function of independent banks and holding companies can
be expected to differ.
Banks are effectively limited to several specific
loan, investment, and service categories and frequently further restricted
to geographic markets.
A holding company has a much wider, diverse
scope of product and geographic markets in which it may operate.
Cost Conditions
The firm (bank or holding company) purchases the
services of fixed assets (building, equipment, etc.) and incurs the
direct costs of labor services (salaries). In addition, it must pay
interest costs on the various forms of money capital (funds) obtained.
These include debt capital (Kd), equity capital (K,), demand deposits
(DD)--paid in the form of services rendered, time and savings deposits
(TD), and other borrowing sources (B) such as the Federal Reserve
discount window, federal funds, etc.
The interest cost on equity is
in the form of net earnings accruing to owners.
12
In addition, the firm must bear other costs that
under an administrative cost heading.
may be summarized
Within this category, we include
expenditures on the replacement of management (search costs, direct
training or orientation costs, and the loss of realizable returns or
foregone earnings incurred during the training period).
Also, the
delegation of authority from owners to a smaller management group that
arises under the corporate structure requires stockholders to incur
costs to insure that management is acting in the owners' best interests.
These "monitoring costs" result from "team production" where the marginal
products of cooperating inputs are not separably observable.
Alchian
and Demsetz argued that this phenomenon allows input "shirking" that
can be detected only by observing the behavior of individual inputs-which is not costless.
The search costs (Cg) for management replacements are a function
of the number of replacements that must be found (R) and the expenditure
on information on candidate capabilities (I,) necessary before the
choice may be made.
There will be some direct training cost (CT) involved
with a new employee as well as indirect costs associated with on-the-job
training that may be represented by the foregone earnings (Ef) that
could have been realized during the training,period had the original
employee not left.
Each of these is dependent on the number of replacements
necessary (R) and the level of firm production (Q). During this period
of training it should be expected that the marginal productivity of labor
will be diminished somewhat.
Monitoring costs (CM) are a function of
the number of employee replacements (R) it is necessary for owners to
supervise, the information on management capabilities available to the
13
owners (I,), the degree the incentives of management (TM) have been made
to correspond with that of the owners--i.e., the degree to which management returns are linked to the returns to the firm (salary, bonuses,
fringe benefits, stock options, etc.), and the aggregate level of firm
production (Q). The administrative cost function (0) may be represented,
then, as follows:
(4)
0
=
8 [Cs(R, I,>,
CT@,
Q) , Ef (R, 9) , C&
I,, IM, Q) 1
where ae/ac,, ae/ac,, ae/aEf, ae/ac, > 0; acS/aR, ac,/az, > 0;
acT/aR, acT/aQ > 0; aEf/aR, aE,/aQ > 0; acM/aIc9 acM/aIM < 0; and
as/a&
acM/aQ > 0.
To complete the representation of the firm's cost function, it is
necessary to include expenditures on the provision of various supportive
business services (C,) and costs of providing additional labor support
programs or fringe benefits (C,) incurred by the firm.
Many independent
banks must rely on other banks or firms to provide such items as computer facilities, data processing and analysis, investment counseling,
and other management services.
These are frequently provided through a
correspondent relationship with a large bank.
In addition to explicit
payments for some services, the bank maintains correspondent balances
on deposit with other banks.
These funds are not available to generate
loans and investments for the original bank but can be used by the correspondent as any of its other deposits.
A full account of expenditures
on these business services, then, must include the opportunity cost (in
the form of reduced revenue) associated with their provision.
Such
expenditures are assumed dependent on the bank's level of 'production,Q.
14
A holding company, on the other hand, usually provides these services internally.
The parent company, either itself or through one of
its subsidiaries, will meet the different needs of the organization
and its affiliates.
these services.
Typically, the bank will be charged directly for
What is unique about the holding company, however, is
that what is a cost for the user of these services is a revenue for
another subsidiary.
The payment for these services is not lost, there-
fore, but merely transferred within the company.
As is frequently the.case, established holding companies operate
at a scale where such services are already produced within the company
structure (by one of its large banks or nonbank affiliates).
The
large initial costs of establishing these services (computer facilities,
research staff, building, etc.) have already been sunk.
The decision
criterion becomes the marginal cost of providing such services to one
more customer.
If this is less than the price of purchase from an
outsider, the holding company's earnings are enhanced.
Most previous studies of holding company acquisitions and investigations of bank profitability ignore the fact that these payments
are simply a transfer from one subsidiary to another and, therefore,
do not affect the ownership valuation of the holding company itself.
These transfers allow potential cost savings from internal provision
of business services.
The level of expenditures on fringe benefits for employees (insurance programs, retirement plans, conveniences, etc.) is considered to
be a variable under the control of the owners and subject to their
15
manipulation and perception of what its appropriate level should be.
It
will be argued that owners authorize expenditures in these areas in an
effort to increase the retention of present employees (and thereby reduce
necessary search and training costs and foregone earnings associated with
replacing personnel) and to increase management loyalty to owners (reducing
owners' monitoring costs).
Specifically, it will be posited that, optimally,
owners will incur these costs until the value of these expenditures is
just offset by the value of the expenditures saved in the above areas.
Labor is very much concerned with the explicit payment for its services.
If labor is also assumed to maximize the present value of its
future earnings (wage and benefits stream), the chance for advancement
to higher paying jobs must affect labor's behavior,
The holding company,
through its usual policy of promoting from within, offers a wide range
of higher paying positions with increased responsibility that
add lustre
to the organization.
The small independent bank cannot do the same.
There are relatively
few top positions attainable through the process of management succession.
As a consequence, banks frequently have trouble securing and retaining
qualified people.
They have no comparable incentive to provide extensive
fringe benefits as do larger holding companies.
Such expenditures may
not significantly enhance the retention of personnel.
The cost function of the firm for each period, then, may be represented by:
(5)
c
=
ylF + y2N + rd (Kd/K,, G) Kd + rDDDD i- rTDTD + rgB
+ e[Cs(R, ICI + CT@,
+ ‘+(Q) + CF
Q) + Ef(R, Q) + CM@,
I,, IM, Q)I
b
16
where:
Yl' Y2¶ rDD' rTD, and rB are the direct costs associated with
fixed assets (F), labor services (N), demand deposits (DD), time and
savings deposits (TD), and other borrowings (B), respectively.
They
are assumed exogenously determined either in competitive markets or
by regulatory authority. rKdis the
COSt
Of
debt capital (Kd), a function
of the debt/equity ratio (Rd/R,) and of a measure of the.degree of product
and geographic diversification (G) attained by the firm.
Combining the firm's revenue and cost functions, then, gives the
profits generated during each period:
(6)
n
=
izlP (Qi) Qi - C
where n is the number of distinguishable product markets in which the
firm operates.
The Capitalization Rate Function
The firm's capitalization rate is a function of both the time
preference pattern of owners and the level of risk that owners associate
with any given stream of earnings.
In examining this capitalization
rate function, it will be assumed that owners' time preference patterns
are identical and constant.
Any change in capitalization rates, there-
fore, must result from shifts in owners' evaluation of risk conditions
following a holding company acquisition.
As a measure of the level of risk perceived by the firm, this study
utilizes the coefficient of variation (V,) of net income expectations.
This measure is computed by dividing the standard deviation of the
17
distribution of net incomes by its expected value.
It is a ratio, there-
fore, describing the relative variability of a set of numbers.
.
the risk due to variability of earnings flows.
V, measures
From the definition of
the coefficient of variation, V, = an/E(N); or, since net income (NJ equals
net operating income (0) minus the total interest paid on debt capital
(rKdKd)' andassuming on = ~0:
(7)
v,
=
a0
E (0)-qKd
where E(0) is the expected value of net operating income and a0 is the
standard deviation of net operating income.
The coefficient of variation is dependent on the elements on the
right hand side of (7). The debt capital supply cost will be assumed
to be a function of both the debt/equity ratio @d/K,) and a proxy for
the level of product and geographic diversification (G) of the firm:
(8)
%d
= rKd
(Q/K,, G)
where arKd/a(Kd/Ke) > 0 and aq,/ac
c 0, that is, as the debt/equity
ratio rises so does the interest cost of debt capital and as the measure
of diversification of the firm's product market increases, the cost of
debt capital falls.
This last result assumes that potential lenders view the risk associated
with the placement of debt capital to be reduced if the firm expands the
scope or location of its operations.
A holding company structure, with
production in a wider range of product markets than allowed commercial
banks and, except possibly where statewide branching is allowed, a
greater geographic dispersion of activities,may expose the total organization to less risk.
Earnings variations at individual banks and nonbank
18
subsidiaries tend to cancel out unless a strong positive correlation
exists between profit performances.
Profit variability between a com-
pany's bank affiliates may offset each other due to the extension of
loans across a wide geographic area or to a wide range of borrowers.
The variance of the profits associated with combining activities
a and b may be representedby:ai+b
= ai + 62 + 2ro,cb; where r is the
correlation coefficient (-1 5 r 5 1).
This equation states that the
variance of the firm's profits is equal to the sum of the variance of
the profits of the separate activities plus the covariance between
them.
As Hall suggested, the-combination of disparate.activities
leads to less total variance and thereby to less total risk.
This
'reduced risk through risk-spreading' can be expected to occur unless
a strong positive correlation between the profits exists.
or negative correlations will reduce variance. 6
Independence
Hall does, however,
caution that the closer the 'linkages among activities--the less important
are the advantages of risk spreading.
The functional representation of the coefficient of variation is
given by:
(9)
vn
=
Vn (00
E(O) 9qd(Kd/Kes G))
where avn/aao > 0, av,/aE(o) <-0, avn/a(Kd/Ke> > 0, aV,/aG c 0.
6Adleman argued that additional profit centers resulted in larger
samples and greater stability of profits. A perfect negative correlation
between two activities (1:= -1) would completely eliminate variability
(assuming CJ$= CJ~and n1 = "2) while zero correlation would result in a
reduction in the standard error of the mean from a;; to ax*
1
19
The capitalization rate is, therefore, also seen to be a function
of the standard deviation of net operating income, the expected value
of net operating income, the level of the debt/equity ratio (or leveraging)
of the firm, and the degree of diversification of the firm's activities.
(10)
=
P
P(i,
Vn>;
i
=
ii
P =
P(Ts
00,
E(O),
Kd/Ke,
G)
where ap/aco > 0, ap/aE(o) c 0, ap/aKd/K, > 0, ap/aG < 0.
For convenience, assume that bank owners' patterns of time preferences
are identical with each other and with those of holding company stockholders.
Therefore, any change in the coefficient of variation of net income will
have a positive impact on the owners' capitalization rate and will affect
the owners' valuation of the firm's earnings stream.
An increase in the degree that the firm is diversified may have an
important impact on the capitalization rate.
Specifically, at a constant
debt/equity ratio, increased G may reduce the coefficient of variation
(through
effect onrKd or uO),which should reduce p.
its
Increased diversi-
fication may, on the other hand, allow the firm to make greater use of
debt without adversely affecting its capitalization rate and offsetting
potential gains from financial leveraging.
The determinants of the coefficient of variation of net income as
postulated provide insight into this question:
V, = V,(uO, E(O), Kd/Ke, G).
Totally differentiating yields:
%
(11)
dV,
=
e"
aVn
+ aE(O)'(')
avn
ava
+ a(Kd,Ke)d(Kd'Ke) + 2'
-
20
For the moment, assuming that the expected value and standard deviation of net operating income are held constant, we may see the relationship between the debt/equity ratio and measure of diversification that
must hold for any given value of the coefficient of variation of net
income.
For dx,
dE(O), dag:
aV,/aG
> 0; since
aVn/a(Kd/Ke)
This positive relationship is reflected
d(K$d
av,/aG c 0 and aVn/a(Kd/Ke) > 0.
3 -
in Figure 1.
The acquisition of a commercial bank by a holding company will increase
the firm's degree of diversification from G0 to Gl.
The acquisition it-
self (through.an exchange of stock) adds equity capital and immediately
reduces the firm's debt/equity ratio to (Kd/Ke)l.
only at a reduced value for V, (Vi).
This is maintainable
If the firm decides to expand its
use of debt capital to the original debt/equity ratio, it still must be
accompanied by a lower Vn (Vi) than the original position.
Unless the
impact of increased diversification is offset by either an increased
standard deviation associated with net operating income (u0~$)
or a
decreased expected value of operating income (E(O)CE(O>~), the coefficient
of variation (V,) and, therefore, the firm's capitalization rate (p)
should decline through the acquisition activity.
It is evident that
increased diversification may allow the firm to utilize a much higher
debt/equity ratio, to(Kd/K,)',atthe
original values of Vn, uo, and E(0)
and, therefore, p.
This opportunity is not available to bank owners.
Since commercial
banks are restricted by-regulation in the degree of diversification into
0
.
additional product and geographic markets they may attain, they may
(e
(
m--m--
.-----Be---
/
.---------
/
/
------
--
m-------
/
/
FIGURE
1.
FINANCIAL LEVERAGE, DIVERSIFICATION, AND THE
COEFFICIENT OF VARIATION OF NET INCOME
21
realize a similar decline in Vn only through a direct reduction in
along GoGo, reduced uo, or an increase in E(0).
Q/K,
Another useful relationship to be examined within this context
is that between G and uo.
duo/dG
=
- aV,/aG
aV, aa0
,
o
For dTn, dE(O), and d(Kd/Ke):
--
1
/
As mentioned previously, the acquisition of a commercial bank by'a
holding company increases the firm's measure of diversification (Go to G1
in Figure 2).
in u0'
It is unlikely, however, that this results in an increase
As a matter of fact, it may reduce uo.
coefficient of variation is reduced (to Vi).
an independent bank restricted to Go.
Even at ui,. though, the
This is not attainable by
Given these results and previous
assumptions, the firm's capitalization rate should be reduced through
diversification.
A firm limited to Go that
tries to use more debt capital is faced with
an increased coefficient of variation of net income unless it can reduce a0
or increase E(0).
The use of additional leverage does not necessarily in-
crease the coefficient of variation of net income.
Given a0
and Go, an
increase in operating income induced by a larger debt/equity ratio may result
in the initial value for V,.
If increased leverage does have a positive
impact on "net earnings on equity" as proposed by Lintner7 and Robichek and
gFor a discussion of the competing theories on the effect of leverage on
equity values, see John Lintner. The "entity value" theory (as represented
by Modigliani and Miller) holds that the net operating income of the corporation
as a whole (sum of debt and equity values) is capitalized and is reduced by
the market value of outstanding debt to determine the market value of the
corporate equity. Since the "entity value" is held independent of the proportion of debt in total capital, the sum of the market values of equity and debt
is a constant. An addition to debt will reduce net earnings due to additional
interest and increase the discount rate due to added risk on equity--together
reducing equity values in an amount equal to the value of the debt issued.
The "net earnings" theory, in contrast, values corporate equity as determined
.
l
Vi,E(o)‘,
(K,/K,)
/
------
/
------
----.
v,l,~(4 ( K,/K,)~
/
/
/
/
GO
FIGURE 2.
:I
G
DIVERSIFICATION, VARIABILITY OF EARNINGS, AND THE
COEFFICIENT OF VARIATION OF NET INCOME
22
Myers, the attainment of greater earnings at no higher coefficient of variation reveals that leverage may improve ownership valuation substantially,
,
The representation of the coefficient of variation in functional form,
then, aids in the understanding of the factors that determine its value.
It is not realistic to assume that additional use of debt automatically
increases the firm's concept of uncertainty associated with its earnings
stream.
This effect may be offset or even dominated by increased operating
income and/or diversification.
Recognizing this functional dependency,
it is feasible that firms adhering to different operating policies may
experience different values for the coefficient of variation of net income.
It is also true that the alteration of a firm's organizational structure,
which changes its ability to use financial leverage and diversification, may
alter the behavior of owners' risk-adjusted discount rates.
The acquisition of a bank by a BHC presents such a possibility.
Each
participating owner alters the structure of the claims on earnings he holds.
The independent banker gains partial claim on BHC earnings in exchange for
bank stock, while the holding company shareholder attains interest in the
bank in return for partial interest in the expanded BHC's future earnings.
by the capitalization of net earnings (after depreciation, taxes, and
interest). Equity values, therefore, represent the direct capitalization
of "net earnings on equity." The debt-equity ratio may have an impact on
market values in this approach. Solomon and Kuh are representative of
this approach. Lintner endorsed the net earnings approach in hisconelusion: "The sum of the market values of the corporate equity and debt
will not be invariant to changes in the finance mix (as asserted in the
entity value theory)--in particular stock values will not be equal to
equity value less corporate debt--except under fully idealized conditions
of certainty. Moreover, with uncertainty admitted, the earnings yield is
)‘
a continuously rising (and non-linear) function of corporate leverage-at least beyond some initial range--and not a declining function of leverage
beyond some point as inferred from the entity value theory" (p. 268).
The analysis in the present study incorporates the net earnings approach.
23
The acquisition drastically expands the measure of diversification and
extent of leveraging associated with the claims of the original bank
owners while.more moderate changes are experienced by the BHC shareholders.
It is entirely possible that the behavior of the coefficients of variation
of net income (and thus owners' capitalization rates) may be affected by
the transaction.
Production Function
Before these concepts are combined to describe the valuation framework
owners use in determining acquisition activity, the production function
must be described briefly.
Basically, the banking or financially-related
firm is dependent for its production on three classes of factor inputs-fixed assets (F), labor resources (N), and money capital (M).
assets represent bank premises, equipment, etc.
utilized in the productive process.
Fixed
N is the labor input
Money capital is the amount.of
funds actually available to the firm to place into the production of its
various loan and investment categories.
Additions to M evolve from ex-
pansions of equity capital, debt capital, deposits (demand or time and
savings), or other borrowing sources (B) such as Federal funds or the
Federal Reserve discount window.
The firm's level of production in any
period t, therefore, may be represented in general form by:
Qt = f(Ft, Nt, M,
24
III.
THE MODEL
Now that each of its components has been discussed, the valuation
framework on which owners base their decisions may be more completely
specified.
Substituting the production function into the revenue func-
tion and discounting the firms' future earnings stream in accord with
owners' time preferences and the degree of risk perceived (represented
by p) yields:
(12)
v=
c-
' Pit(qit)f(Ft, Nt, Mt) - YltFt
- 'f(d, ((z)ts
- YZtN,
Gt) Kdt - 'DDtDDt - rlDtTDt- rgtBt
..
- e{c+
Ict)
- cB,(Qt) - cq
+ CT,(Rt,
Q,) + $f,(Rt, Ict, IQ, Qt)\
1
The expression within the brackets is the profit function across the
firm's horizon,
Foregone earnings (Ef) are included within training
costs (CT> for simplification.
To create the valuation disparities posited essential for acquisitions to occur, (12) must be specified further to represent the firm
under alternative organizational structures.
(12a - 12b) and (12~ - 12d)
represent, respectively, the valuation frameworks that a set of owners
may use to determine whether the decision to trade stock with a holding
company (in the case of independent banks) or to acquire an additional
bank (for a present holding company) is in their economic interest.
25
.Both disparities must favor acquisition before the transaction will
take place.
For the bank owners' decision, the relevant functions are:
Wd
: Pit(qit>f(F t' N,, Mt) - Y1,Ft - yztNt
i='l
- %dt
(($
- 8 (Cst(Q,
- C@t)
't) Qt
- 'DDtDDt - r+%
Ict) + cq(Rt,
- CF,
Qt) + CMt(%
- 'BtBt
$9
IMt* Q,)t
1
B
and
Pit(sit>f(F t' NO
(lib)
- rKdt((z)ts
Mt) 7 YltFt - yz,N,
Gt) Kdt - rDDtDDt - 'TDt - mt
- rBtBt
- 0 {Cst(Rt, Ict) + CTt(Rts Qt) + CMt(Rt' Ict' *Mt' Qt)i
1
- CBt(Qt) - CFt
HC
where a is the percentage of holding company ownership offered to bank
owners in exchange for their stock, and pBt
and PHC
t
are the effective
capitalization rates of original bank owners applicable to period t under
assumptions of (a) continued ownership in the bank or (b) obtaining
interest in a holding company, respectively.
Holding company stockholders view the transaction by comparing ownership valuations of continued operation without acquiring the bank (i2c)
and that thought obtainable with the addition of the bank (12d).
26
c
pit(qit)f(Ft 9 N, 9 Mt) - YltFt - YztNt
- 'Kdt ((2)
' 't) Kdt - rDDtDDt - rmtTDt
- rBtBt
t
- 8 {Cs (Rt,
t
- Cg,(Qt)
Ict)
+ c+,
Qt) + $$rt,
+
IMt'
Qdt
1
- CFt
HC
(12d)
H
c
'HE = t=l (811
P&
n
c Pit(qit)f(Ft, Nt, Mt) - YltFt - YztNt
[i=l
- rKdt ((?k) ts Cy) Kdt - rDDtDD, - rqTDt
- 8 {C+
Ict) + $tRt,
- CBt(Qt) - cF
t
Qt) + %it(Rt,
- rBtBt
Ict’
IMts Q$t
1
H%'
where B is the proportion of ownership in the holding company retained
by original stockholders (B = 1 - a), and pHCt and pHgtare the perceived effective capitalization rates applied to each period's earnings
for holding company owners (a) under continued operation without purchasing the bank and (b) incorporating the bank within the company structure, respectively.
For any acquisition to occur, economic incentives must be established
for both participants.
12a - 12b)
Specifically, VHC must be greater than VB (in
and VHE must be larger than VHC (in 12c - 12d).
Insight into the comparative magnitudes of these measures may be
gained by viewing the relative responses of these functions following shifts
in owners' relevant decision variables.
There are several variables
27
that. will affect the paths of ownership valuation of the firm.
The
crucial factor within the present context, however, is the impact
shifts in each have on the capitalized value of future earnings streams
under the alternative banking organizations.
Of particular interest in this respect are expansion of debt and
equity capital, increased deposits, the emergence of the need to make
replacements in the managerial staff, and the opportunity to diversify
the firm's activities into new product and/or geographic markets.
In
addition, advantages for holding companies will result from familiarity
with employees' abilities and extensive provision of fringe benefits to
their staffs.
Each of the above will be examined in more detail.
The
analysis will first concentrate on determining whether bank owners have
an economic incentive to enter the transaction before the holding company's position is inspected.
The valuation schema, as posited above, places dual emphasis on
profit and risk expectations (embodied in p) in the effort to explain
the incentives present for bank holding company acquisitions to occur.
Since the significance of a greater earnings flow for one organization
concerning this motivation is obvious, the present analysis will inquire
into the possibility that owners foresee different capacities for dealing
with risk under the alternative ownership structures.
If this phenomenon
is present, a valuation disparity is established even if expected earnings
flows of the two are judged equivalent (which will be assumed for the
present).
Differences in the responses of the valuation ofearnings streams
(by bank or BHC stockholders viewing alternative structures) provide an
28
important incentive for owners to enter into acquisition negotiations.
Time preference patterns are assumed identical and constant, and for convenience, the time subscript will be suppressed in the following presentation.
The Bank Stockholder
For a bank to facilitateanexpansion
Expansion of Equity
of pro-
duction (loans, investments, other services) it must eventually expand
its capital base to meet regulatory demands.
In their ownership decisions,
bank owners view the comparative impacts on ownership valuation between
the different organizational structures as the use of equity capital increases.
The maximizing behavior of the independent bank is represented
by:
aoB
aK,
= - -
1
(TB) + PB
%d
aK,
Kd
aK, )I
rKd
+ aKd
=O
or
(14)
QB
z
(rB)
e
PB
i
[(
ar
Kd Kd + aKd rK
aK,
cl
aKe
(14) states that the change in the valuation of the firm's earnings
resulting from the impact of an increase in the use of equity on the
capitalization rate must equal the additional net marginal revenue
LJ
product (i.e., MRP less the net change in the level of interest payments
on debt capital) for ownership wealth maximization to occur.
In the
case of banks with total deposits of less than $30 million, a strong
tendency to use only equity capital in their capital structure has been
observed.8
If the bank does not use debt capital, no change in debt
interest payments will occur and the change in valuation induced by a
change in the capitalization rate will equalthefull
marginal revenue product of more equity.
sin&
WK,
measure of the
may normally be
considered positive, and since oB and ITBare both positive, 3PB is also
=G
positive for the independent banker in this case.
In other words, the
marginal revenue product of additional equity is equal to the required
return to investors to compensate them for the use of their funds.
On the other hand, if the firm does make use of debt capital.to some
extent, the magnitude of the change in ownership valuation (that portion
due.to a changed capitalization rate) is dependent on the relative sizes
of the components on the right-hand side of (14). The net change in
debt interest payments caused by expanded equity has two components:
(1) a reduction resulting from a decreased rate of interest on debt capital as lenders view an improved equity position; and (2) an increase
resulting from the use of more debt induced by a reduced debt/equity
ratio.
It is quite conceivable that an increase in equity may elicit
a strong enough increase in the use of debt capital to actually increase
the total interest payments on debt.
In such a case, the change in
ownership valuation resulting from a changed capitalization rate will be
8See Piper, p. 121.
30
less than the marginal revenue product of equity, i.e.,
(aPB/aK,hB
<
PB
MRp
‘e*
The increase in the capitalization rate for firms that do use debt
capital to this extent will be less, therefore, than the identical firm
would experience without the use of debt capital.
Identical profit per-
formances would result in a greater ownership valuation for the debt
users.
This is an advantage holding company organizations may provide to
owners.
The expansion of a firm's equity base may allow a reduction in
the interest rate it must pay on its debt.
A BHC may, however, expand
debt capital significantly in response to the decreased cost and the
decline in its debt/equity ratio.
As debt increases, the public will
re-evaluate the firm's debt instruments and adjust their required rates
of return upward.
If this process continues to the point where net inter-
est payments are increased, the required change in the owners' capitalization rate to assure valuation maximization becomes less than the marginal
revenue product realized from the investment of additional equity.
From
(14) it is evident that between two firms with equivalent profit performances the firm that makes greater use of debt capital can realize a
greater valuation of those earnings than, say, a firm that
or no use of debt.
dom
makes little
If that same firm has the further advantage of free-
of diversification (through acquisition) it may make use of even more
debt without disturbing the rate it pays on debt capital.
This may allow
an even greater disparity in valuation of equivalent earnings flows.
31
Diversification
Bank holding company acquisitions, in effect, pro-
vide owners with an additional way to expand equity that is not available
to independent banks.
The acquisition itself brings increased diversifica-
tion to the firm's operations as well.
This may have a further impact
on the availability of debt capital and the valuation of the firm's
earnings.
This is made clearer by examining the effect on ownership
valuation of expanding equity through an acquisition that
also increases
the firm's diversity in product and/or geographic markets (G).
aPHC
- CLx.("HC)
(15)
av,,=
a&
aqi
-+qi-aKe
2
pHC
api aqi
391 XC,
Kd2 rb)J
+’
Pi&
1
=O
Rearranging (4.6) and multiplying and dividing through by -%- gives:
PHC
aoHC
aPflC (A&
(rHC>
(16)
aKe
+ aG
= [=h
- {[zk
+zrKd)
oHC
'HC
ar% aKd
+
aG
Kd +rrKd
The combined effect, 'then, of increased equity and diversification
on the capitalization rate is extended to include the net change in debt
interest payments allowed by an increase in G.
of two components:
This change also consists
(1) a decrease as a result of reduced rates as lenders
view the increased scope 'of the firm's operations, and (2) an increase
..I&
due to an expansion in usage of debt.
The firm
that is afforded the
use of additional debt capital to the extent that total interest payments
increase as a result of an increase in the firm's degree of diversification will actually realize a smaller increase in the owner's capitalization rate than a bank that is not allowed to diversify to such an extent.
For firms with identical profits and originally identical p's, this will
result in greater valuation for the diversified debt user.
As long as
the net effect of diversification on interest payments is positive,
owners ' capitalization rates will be smaller than they would be without
diversification and debt usage.
Valuation advantages under a holding
company organization are, therefore, obvious for similar profit levels.
This is the situation of interest to us at present.
The original
bank owner, faced with alternative paths of his capitalization rate in
future time periods, will choose the path of lower o values if earnings
are expected to be roughly equivalent.
The motivation for owners of
small banks to choose to trade their interest in the bank for that of a
holding company is, therefore, enhanced if they view the prospect of
expanding the equity base of the firm by acquisition.
The above discussion has assumed that the independent bank and
holding company owners have equal access to additional equity capital.
It has ignored a very real problem facing smaller commercial banks in
recent years--the limited scope for expanding their equity base that
has placed an effective ceiling on growth potential.
The uncertainty
attached to the bank's future capital expansion capabilities, therefore,
could cause a further divergence between the capitalization rates of
bank owners and holding company owners that- (given profit performance)
33
will lead to a greater valuation of equivalent earnings through a BHC
than through an independent bank.
Expansion of Deposits
Commercial bank deposits is a variable that
most bankers can reasonably expect to increase as the economy expands,
To examine the impact deposit growth has on ownership valuation, (12a)
and (12b) must be differentiated with respect to deposits (time
for convenience).
deposits .
For the independent bank:
api
+ qi a qi
(17)
aqi
3TiF
-
?rD
aoB
_ ?i?tj(rB) =. C
1
pi
Rearranging we have:
(18)
MRp& - r!&
The equivalent term under the holding company structure is:
(19) =Fiir!E
- =
pHC
which reveals that the portion of the change in the valuation of the firm
attributable to the effect an increase in deposits has on the owners'
capitalization rate is equal to the difference between the marginal
revenue product of increased deposits and the marginal factor cost of
those funds.
If it is assumed that growth in deposits will not affect
the capitalization rate of the firm, the familiar results evolve that
each firm must expand its use of deposits until its marginal revenue
product equals marginal factor cost.
No information advantageous to the
holding company structure is discernible from this situation.
Even if
34
deposit growth does have an impact on p,
there appears to be no basis
for the argument that equivalent deposit increases would affect alternative organizational structures differently.
Personnel Replacements and Provision of Employee Benefits
Owners
realize that occasionally it will become necessary to fill employee
vacancies.
Whether it is due to death, retirement, or the resignation
of a staff member, the firm must make some expenditures on finding a
qualified replacement.
Retirement is predictable and gives the firm
enough notice where it can attempt to make the transition as smoothly
as possible.
Death and resignation, however, give little warning and
can greatly affect the total working efficiency of the firm's staff.
All require explicit expenditures of searching for and training a replacement.
They also involve the loss of potential earnings due to decreased
marginal productivity during the orientation and training period.
As has been suggested,' banks are often concerned with the lack of
an efficient and well defined program for management succession.
The
holding company organization provides a program that not only reduces the
costs involved with hiring and training a successor, but can often avoid
the loss of foregone earnings by promoting'or transferring an experienced,
competent person from within the company with little loss in productivity.
In addition, owners may experience a reduction in the costs of observing
or "monitoring" his performance in comparison with someone hired from
outside the company.
9
See Lawrence (19691, pp. 44-45.
35
Neither the holding company nor the independent bank can control
deaths or retirements.
The holding company, however, provides a means
.
to retain personnel by reducing the frequency of resignations.
The
corporate structure, with its several bank and nonbank subsidiaries,
provides an attractive network of possibilities for advancement for the
young executive--where the independent bank is limited in this respect.
Holding companies frequently initiate a centralized training program
that
provides a pool of management talent to the whole company.
'
Employees within each holding company system are usually given priority
when positions become available at subsidiary banks.
An employee's
chance for advancement to a position of added responsibility and
increased remuneration, therefore, is not limited to openings that
develop within a single bank.
The holding company also provides its subsidiaries with fringe benefits (health and accident insurance, retirement plans, etc.) that add to
the lustre and provide additional incentive for the employee to remain
with the company.
The combination of these factors suggests that,holding
companies may be more effective at retaining present employees than
smaller, less-diversified banks.
This undoubtedly has important impli-
cations for cost savings and owners' uncertainties connected with personnel replacement.
It becomes immediately apparent, however, that expenditures on
employee benefits have an impact on other components within the model.
Money capital (M) is diverted from production to provide these benefits-thus an opportunity cost in the form of foregone revenue is present.
On
the cost savings side, however, in addition to reduced search, training,
and monitoring costs associated with improved staff retention, training
36
costs and owners' monitoring costs are somewhat diminished by the
reduction in the level of production.
Monitoring costs are further
affected through a possible improved alignment of managements' motives
with owners' welfare.. As owners' trust in senior management increases,
they expend less time and worry over the need for supervision--freeing
them to attend to other matters.
Examination of these expenditures will not add directly to the
establishment of valuation disparities between the organizational frameworks,but it is anaspect
of the firm's behavior revealed by the model
and may lend support to the concerns for employee retention, managerial
succession, and owners' trust in management.
Differentiating (12) with
respect to CF yields:
ag -- aR
acs
acs aR acF
+qi---
(20)
+
39
zT
acT aQ=
aq aM acF
a0
ET
acT
-- aR
aR acF
+
Rearranging and dividing by p gives:
(21)
ae
a%
z
ax
&
aR
acM aR
--
--
l+mM’
a$
acF
)I
aR
acF
37
(21) reveals that the explicit cost of providing the,benefits to
employees plus the foregone revenue from decreased production is
exactly offset by the sum of the marginal savings from (a) reduced
search, training, and monitoring costs due to a reduction in R, (b)
reduced training, monitoring, and business services costs associated with
a reduction in production, and (c) reduced monitoring costs due to the
greater trust in management that owners experience.
This implies then that owners may be willing to make additional
explicit net expenditures if compensated by certain implicit cost
savings (e.g., marginal time savings for owners).
Expenditures on
employee benefits for banks and holding companies alike appear in the
. annualearningsreports
do not.
of each.
Reductions in owners' monitoring costs
If a monetary value were assigned to this time savings and
deducted from the cost side of the earnings statement, it could have a
significant impact on the reported earnings of the firm.
For this
reason, the earnings statement of the firm that experiences savings in
monitoring costs through its activities may be somewhat understated.
The BHC Stockholder
Holding company owners will decide to acquire a bank only if they
can similarly establish that the valuation of their earnings stream will
be enhanced as a result.
Company shareholders compare the ownership
positions attainable under the alternative organizational structures.
In the case of a proposed acquisition, the comparison is between the perceived performance of the BHC (inclusive of the bank) following the
acquisition of a banking subsidiary and that performance expected without its acquisition.
If the former is deemed superior to the latter,
38
the motivation for the company to pursue the acquisition is established.
The distinction between organizational structures will not be as
precise as the comparison provided independent bank owners.
Instead
of the alternatives presented in the choice between an independent bank
and the holding company organization, the present situation involves
whether or not an extension of the company structure will be positively
reflected in the ownership valuation of the firm.
The search for the
valuation disparity necessary for acquisition to occur must again focus
on both profit and risk considerations.
Equations (12~) and (12d)
(representing the alternative structures) will be differentiated with
respect to the variables of crucial importance to company stockholders.
The case for an extension of the company structure to include a$new
acquisition lies chiefly in the owners' views of the comparative effects
of expansion of equity capital, availabilityoand use of debt capital, and
an increased degree of product and/or geographic diversification on their
positions of ownership.
In addition, the importance of employee retention
and owners' monitoring costs will again be examined.
Increase in Equity Capital
The holding company
may increase
its equity position through retained earnings, the sale of stock on
the market, the purchase of additional shares by present owners, or
issuing new stock and trading for the stock of another firm (acquisition)..
The last method delivers a portion of the ownership of the holding
company to the bank owners with the original company stockholders retaining a smaller percentage ownership than before (6 =,l - cr)but of a
larger unit (holding company plus the newly acquired bank).
Searching
39
for a difference in ownership valuations, a comparison of the second and
fourth alternatives can be made--i.e., issuing new stock, selling it for
cash to outsiders, and maintaining the present company structure versus
trading those same new issues for the stock (and thus the assets) of a
bank.
Each method will leave the original company owners with B(0 < B ( 1)
of the ownership.
A comparison of the first and fourth or third and
fourth alternatives would be just as easy with present owners maintaining
total ownership (6 =l) in the first and third cases.
Differentiating (12~) and (12d) with respect to K, yields:
(22)
avHC
r
= e
aPHC
8aK, (rHC)
+B
pi&
'HC
a%
pi aK, + qi
K
-(
>I
and
a&l
B-aK, dc)
av&
(23)
a~,=
pii;
ar,,
-(
aKd
yKd+aK,rM
e
-- 0
P*
HC
ar,,
aKd
?
'd + -% 'Kd
aq
-aqi
1
=O
aqi
aK, >
=O
40
Rearranging and dividing through by 1
and B
, respectively, yields:
pHC
'HC
apHC ff
e
aKpiT)
(24)
=
[mKe-
($hd+&Kd)j
HC
and
(25)
As before, (24) and (25) represent the owners' wealth maximization
conditions that result from the expansion of equity capital through the
sale of stock and an acquisition through the transfer of new company
stock for that of the acquired firm, respectively.
The latter -method
may or may not have an increase in the firm's degree of diversification
associated with it.
For present purposes, it will be assumed that the
acquisition does introduce the company into a new product and/or geographical market represented by a simultaneous increase in G.
If the increased diversification (G) combined with the expansion of
equity resulting from the acquisition induces a greater usage of debt
capital (with resultant increased debt interest payments) than experienced
through an expansion of -equity with no diversification, and if (m&)Hi
is not any larger than (MRPIQHc,
than that of (24).
Therefore, the left-hand side of (25) is also smaller
than its counterpart in (24).
~PITIC
+ aPfiC<
aR,
T
aPHC
Ticg’
the right-hand side of (25) is less
If THC = 'rr&and if oHC = P;kC originally,
i.e., the acquisition method results in-smaller in-
crease in the owners' capitalization rate than the alternative method of
41
equity expansion.
Comparing equivalent profit expectations, company
shareholders will choose that organizational structure that provides the
smaller p value.
This action will maximize
the owners' valuation of
earnings.
Expansion of Debt Capital
Present company stockholders consider the
possible positive impact an acquisition may have on the future ability of
the firm to raise funds through the issuance of debt instruments.
This is
precisely the case just presented where(a) an expansion of equity may allow
the company to also increase its usage of debt, and/or(b) an increase in
the measure of diversification in production (G) further extends the company's debt capacity.
If the latter does not accompany the acquisition,
it is difficult to argue that owners anticipate lower p values than if the
acquisition did not take place.
The establishment of a valuation disparity
in favor of acquisition associated with the expanded use of debt capital
is then dependent upon distinguishable profit expectations.
Implicit Returns Through BHC Activity
If an extension of the holding
company structure (through,acquisition) results in an improvement for the
company in employee retention through increased opportunities for company
personnel-- thereby inducinigreductions in certain administrative costs
(search, training, monitoring) associated with replacements--over that.
possible without acquisition, a valuation disparity may be created.
Further,
if the additional opportunities for advancement and prosperity persuade
present employees that their future lies in the well-being of the company
and its owners rather than pursuing their own self-interests (i.e., causes
42
a shift from a management-interest oriented firm to an owner-interest
oriented firmlO> , owners may realize additional monitoring cost savings
through the reduced time spent in supervision of management.
Even if
the explicit'cost savings are not reflected in improved earnings performantes , implicit savings (not accounted for in earnings statements) may
form the basis for the necessary disparity in valuation if reported
earnings are equivalent.
Rather than attempting to quantify these implicit savings and adjusting earnings, they may be accounted for within the model by assuming that
they are reflected in the manner in which owners value reported earnings
flows.
Specifically, the owners' capitalization rate is adjusted to
reflect these developments.
The reduction in owners' monitoring costs
are in the form of less time and worry that owners must spend supervising
(a) the filling of personnel vacancies and (b) the behavior of management.
As owners gain additional confidence and trust in management and as the
frequency of necessary replacements declines, the owners' measure of
uncertainty accompanying a given income stream will likely be affected.
If this is reflected in a smaller value than would occur with greater
monitoring costs, a valuation disparity arising from extending the BHC
structure may appear.
For this purpose, equation (12) will again be
differentiated with respect to expenditures on employee benefits (CE).
Unlike in equation (18), however, it will presently be assumed that the
"For discussions of the effect of separation of ownership and control see Baumol, Cohen and Reid, and Monsen, Chiu, and Cooley. Each
argue that management-controlled firms may place less emphasis on profitassociated variables than owner-controlled firms, sacrificing them for
performance goals regarded as more consistent with management interest.
In a study.with Downs, Monsen suggests that management-controlled firms
may sacrifice profit rate and growth rate for reduced risk acceptance.
43
firm's capitalization rate is affected by the consequences.
This will
occur through an upward adjustment in the expected earnings of the firm
following improvements in both staff retention and owners' trust in
management.
Decreased monitoring of the replacement and productive pro-
cesses result in time savings to owners that may be as important as
expected dollar earnings.
Owners certainly would prefer an earnings
stream plus leisure time to equivalent earnings without leisure.
This
effect may be incorporated within the capitalization rate function by
redefining expected operating income E(0) to include an addition for
time savings E(t), i.e., E(O)* = E(0) + E(t).
tion of net income (V,) would then become:
p
Vt
The coefficient of varia=
00
[E(O)+E(t)I-qd(Kd/Ke,G)Kd
then becomes dependent on [E(O) + E(t)] rather than just E(0).
Further, as owners gain more faith that management will not seek
to cheat them or pursue non-owner goals, they may allocate more of their
time to other matters and less to the supervision of management.
This is
brought about through an improved alignment of management's motives with
stockholders' interests that may result from an addition to employee
benefits.
The reduced monitoring costs, therefore, are reflected in p
through an impact on E(t).
As E(t) increased (E(0) remaining constant),
the coefficient of variation (Vc) declines and, thus, p declines.
The
comparable expression to (18), adjusted to allow for this impact on p,
is given by (26).
'
44
3
,(26)
p I
ae
zT
l+mM-
acT
-aQ
a6
acF
)I
(26) implies that the ownership valuation maximizing firm will increase
expenditures on employee benefits until the change in ownership due to a
percentage decline in the owners' capitalization rate just equals the net
cost of such benefits.
The net cost is the explicit cost of the benefits
plus the marginal revenue product of the funds diverted from production
minus the explicit savings on search, training, and business services
expenditures
that result.
A shift in the capitalization rate from this
source could have very important implications for the valuation of earnings
streams.
It appears, therefore, that the firm
that provides additional bene-
fits to its employees (in the form of higher salaries, insurance and
retirement plans, stock options, attractive vacation plans, etc.) may
receive implicit returns that offset the loss in potential profits
caused by the diversion of funds from production to the provision of
fringe benefits.
These returns are present in the form of a solution to
the firm's management succession problem, reduced staff turnover, and
monitoring cost reductions.
This is frequently the experience of BHCs.
They provide extensive benefit programs to their employees and charge
each subsidiary directly.
Such increases in operating expenses have
often been cited as the primary reason why banks have not experienced
.
45
an improvement in profitability following acquisition.
Although operating
revenues "generally increased significantly after acquisition, . . .
,
revenue increases were typically matched by correspondingly large increases
in operating costs" (Piper and Weiss, p. 5).
BHC operating expenses may
similarly offset an improved revenue experience due to a shift in product
mix or efficiencies of the company structure.
However, the implicit (not
reported) returns thereby gained may cause the ownership valuation to be
significantly increased.
Though important, improved profitability is not
the only source of the valuation disparity sought to explain BHC acquisitions--that source may rest in the capitalization rates used to evaluate
a given income stream.
IV.
EMPIRICAL INVESTIGATION
The argument presented to this point suggests that a valuation framework, by taking expectations of future earnings and a measure of risk
associated with the pattern of future earnings into account, can explain
the economic motivation of both independent bank owners and BHC shareholders to negotiate an acquisition.
The remainder of this paper investi-
gates the gains accruing to holding company shareholders through acquisition.
A BHC's acquisition of a commercial bank involves the dilution of
its present ownership in an attempt to increase the present value of the
ownership retained.
This result is assured if the original BHC owners
believe that following the acquisition their earnings will be greater,
with equivalent or reduced risk, than they would be without acquisition.
46
This result could also occur, however, through a reduction in owners'
risk with equivalent or improved future earnings.
Any motivation for
acquisition arising from the combination of reduced earnings and reduced
risk or increased earnings and increased risk following acquisition is
entirely dependent on trade-offs between risk and return within individual
preference functions.
Since such information is not known, substantiation
of our hypothesis must rest on those cases where movements in risk and
return do not have conflicting effects on valuation.
The tendency in recent experience for multi-bank holding companies
to acquire numerous commercial banks, and at relatively short intervals,
seriously complicates the empirical task of isolating the impact of
individual bank acquisitions on BHC earnings performance.
The only
feasible empirical test has to involve the entire acquisition program of
the holding company and concerns itself with whether or not the policy of
expansion through acquisition improves the value of earnings accruing to
owners.
Benefits of acquisition may be explored by a direct comparison of
the trends in the earnings experienced over the post-acquisition period
under the alternative ownership positions.
The appropriate comparison
involves the values of earnings accruing to those owners holding stock
in a BHC at the time of acquisition--for they are the individuals contemplating the transaction.
A major problem with this approach is that
data that would reveal the earnings of a holding company had the acquisition not taken place, are not available.
47
Fortunately, however, this technique is applicable to one group of
acquisitions within the last decade.
Many of the acquisitions in the late
.1960's were facilitated by the simple reorganization of an independent
bank into another corporate form that was permitted to acquire additional
banks.
This was especially prevalent in states where mergers and/or
branching were prohibited or limited by state law.
The corporate trans-
formation often involved nothing more than the exchange of new BHC stock
for the stock of an existing bank.
At the same time, additional BHC
shares were issued in exchange for the stock of one or more additional
banks.
In other words, lead bank owners traded 100 percent ownership in
the bank for less than total ownership in an expanded banking organization.
Comparison of the earnings trend of that.specific set of owners following
reorganization with what they would have realized had they retained their
independent ownership in the bank provides a measure of the potential
benefits to owners via acquisition through a BHC organization.
Such a comparison is 'possible making use of previous empirical
results that have shown commercial bank profitability to be relatively
unaffected by acquisition.
11
This comparison was chosen because it pro-
vides the only appropriate data available that examine the incentives for
acquisition.
Reports of Income exist for the years following acquisition.
for the holding company on a consolidated basis and for the lead bank
separately.
valuation.
These provide the basis for the direct comparisons of owners'
There are no comparable data available that reveal the earnings
performance of a multi-bank holding company excluding any particular
acquired bank.
Benefits accruing to original owners of these lead banks
llThe reader is referred to Fischer, Lawrence (1967), Piper, Talley, and
Ware for a good sample of this literature.
48
through reorganization and acquisition, then, may be used as a subsample
to shed light on the economic incentives present in the larger population
.
of BHC acquisitions.
If bank earnings are not affected by acquisition,
the appropriate comparison to be made is between the trends of the ownership valuations of (a) the original bank owners' equity interest in the
bank and (b) the interest obtained by that same group of owners in the
expanded BHC organization through an exchange of stock.
This comparison, requiring complete knowledge of stock splits, dividends, and dilution of owners' percentage share of total earnings, began
the year immediately preceding the acquisition and continued for at least
five years after the time of acquisition.12
The sample was restricted
to those reorganizations occurring between 1962 and 1969, with all but
three occurring since 1966.
The average levels of earnings, average
growth rates in earnings, and coefficients of variation of levels and
growth rates of earnings (as measures of owners' risk) were computed
over the period for both of the ownership alternatives.
These sample
data permit mean difference tests to be performed on the arguments of
the valuation function.
Table I shows that the mean difference in average annual earnings
over the entire post-acquisition period was substantial.
Previous owners
of the lead banks realized an average improvement of $330,978 per year
through the reorganization.
This sum was not statistically significant,
12The sample consisted of 18 BHCs and associated lead banks located
in seven Federal Reserve Districts with data available for at least
five years after reorganization. The lead banks, all members of the
Federal Reserve System, ranged in deposit size from approximately $100
million to $650 million at the time of reorganization. The necessary
information was available for the sixth year for seven of these holding
companies and banks and was incorporated into the analysis. Earnings
accruing to original owners were computed by multiplying total net income
of the firm by their percentage ownership in the firm for each year.
TABLE 1
COMPARISON OF EARNINGS PERFORMANCES THROUGH BHC AND
CONTINUED OWNERSHIP IN LEAD BANK FOLLOWING REORGANIZATION
Banking
Firm
1
2
3
4
5
6
7
8
9
10
11
12
'13
14
15
Avg. Income
of Lead Bank
That Would
Have Accrued
to Owners of
Lead Bank
Avg. Income
of BHC Accruing to
Owners of
Lead Bank
$1,078,111
2,305,407
5,071,545
1,679,674
1,632,975
2,022,951
1,506,681
1,455,996
2,369,669
7,676,530
3,722,490
6,955,577
5,382,316
3,155,189
4,815,430
,$1,305,487
2,702,661
5,147,484
1,862,217
2,185,064
1,918,527
1,778,686
1,455,526
2,635,102
8,849,941
3,809,746
6,650,758
4,999,337
3,528,637
4,726,720
Difference
(BHC-Lead Bank)
$
227,376
397,254
75,939
182,543
552,089
- 104,424
272,005
470
265,433
1,173,411
87,256
- 304,819
- 382,979
373,448
- 88,710
Avg. Growth
Rate in Net
Income of
Lead Bank
Avg. Growth
Rate in Net
Income
Through BHC
Avg.
Difference
(BHC-Lead Bank)
12.55%
13.63
9.13
13.92
17.15
17.36
8.00
21.65
4.18
.9.22
8.11
10.99
13.58
16.92
7.93
16.02%
12.57
10.10
18.63
27.13
18.84
14.64
22.00
10.82
13.28
10.59
9.40
11.56
22.98
6.90
3.46%
- 1.06
0.97
4.71
9.97
1.48
6.64
0.35
6.64
4.07
2.48
- 1.60
- 2.02
6.07
- 1.02
TABLE
(continued)
16
17
18
,
Avg. Income
of Lead Bank
That Would
Have Accrued
to Owners of
Lead Bank
Avg. Income
of BHC Actruing to
Owners of
Lead Bank
Difference
(BHC-Lead Bank)
$2,300,507
3,387,176
1,775,490
Banking
FirlIl
Mean
1
$2,103,128
5,972,261
2,620,029
$- 197,379
2,585,085
844,539
$3,238,536
(568,712.187)
$3,569,512
(698,058.187)
$
330,978
Avg. Growth
Rate in Net
Income of
Lead Bank
35.11%
- 4.82
2.36
12.05%
(19.954346)
Avg. Growth
Rate in Net
Income
Through BHC
Avg.
Difference
(BHC-Lead Bank)
30.83%
6.35
16.34
15.50%
(16.037262)
*significant at the .20 level
Note:
Standard deviations given in parentheses
Sources: Moody's Bank and Finance Manual and internal records of seven Federal Reserve Banks.
-
4.28%
11.17
13.98
3.45X*
"t"=l.345
49
however, due largely to the considerable variance within sizes of firms
included in the sample.
The growth rates in net income did display a
significant difference, though only at the .20 level.
Specifically, the
growth rate in earnings through the BHC was an average of 3.45 percent
greater per year than would have been the case had the owners maintained
their interest in the bank alone.
Growth rates may be especially revealing
since they, at least partially, compensate for size discrepancies within
the sample.
At the same time there was no significant difference between
coefficients of variation of net income over the entire period.
The
coefficients of variation of growth rates of income, however, exhibited
a significant difference at the .05 level over the interval.
Specifically,
this .measure of risk was substantially reduced through the acquisition
program as reflected in Table 2.
A comparison of earnings experience over time, shown in Table 3,
indicates that holding company owners actually experienced reduced earnings
through reorganization and acquisition in the first year relative to the
experience of the bank alone.
This first-year reduction in earnings appears
attributable to the large premiums paid for bank stock.
Each year there-
after, however, earnings are progressively larger under the BHC structure.
This trend is also reflected in the difference in growth rates of earnings.
13
In general, therefore, it appears that earnings for the BHC not only increased faster on an absolute basis when compared to the bank but also on
a percentage basis, indicating that the difference between the two increases
over time.
131f BHC earnings are depressed in the immediate post-acquisition
. period, the experience of the third and fourth years.following reorganization is not surprising, since most of the BHCs in the sample made
additional acquisitions in those years.
TABLE
2
COMPARISON OF COEFFICIENTS OF VARIATION OF GROWTH RATES
OF NET INCOME THROUGH BHC AND LEAD BANK
FOLLOWING REORGANIZATION
Coefficient of Variation
of Income Growth Rates
For Lead Bank
Banking
Firm
Coefficient of Variation
of Income Growth Rates
Through BHC
Difference
(BHC;Bank)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
-
1.071895
2.645937
1.242849
1.130456
1.007689
1.248705
2.543271
1.649359
4.325461
3.987330
1.770638
0.605394
1.570596
1.196462
1.877712
0.729631
4.253756
3.889851
0.594423
1.851482
1.181919
0.234433
1.402617
1.160084
1.520361
1.323782
0.560705
0.941209
2.029515
0.795784
1.168754
0.772820
2.031342
0.571625
1.354321
0.564985
-0.477472
-0.794455
-0.060930
-0.896023
0.394928
-0.088621
-1.022910
-0.325577
-3.764756
-3.046121
0.258878
0.190390
-0.401842
-0.423642
0.153629
-0.158007
12.899434
-3.324865
Mean
2.041496
(1.260457)
1.114450
(0.530057)
-0.927045*
"t"=3.026
* significant at the .05 level
Note:
Standard deviations given in parentheses.
Sources:
See Table 1.
.
TABLE 3
COKPARISON EARNINGSTHROUGH BHC AND
O'F
LEAD BANK BY INDIVIDUAL YEAR
Years Following Reorganization
3 years
4 years
5 years
6 years
$3,936,692
$4,138,920
$5,004,592
3,268,524
3,520,821
3,545,288
3 247,005
180,031
260,829
416,144
593,632
1,757,589
21.49%
(17.635)
25.07%
(23.100)
9.27%
(12.966)
16.37%
(16.855)
6.11%
(9.427)
12.01%
(11.622)
26.08%
(25.869)
11.47%
(16.958)
10.92%
(16.048)
14.43%
(24.288)
0.93
(14.228)
- 0.86
(20.027)
- 4.59%
13.50"
"t"=1.999
5.18
12.87**
"t"=2.358
1 year
2 years
$2,659,982
$3,189,644
$3,529,352
Owners' Net Income
Through Lead Bank
2,867,316
3,009,613
Difference (BHC-Bank)
-.207,334
Growth Rate of Net
Income Through BHC
Growth Rate of Net
Income Through
Lead Bank
Owners' Net Income
Through BHC
Difference (BHC-Bank)
*
- 1.65
1.94
significant at the .lO level
**significant at the .05 level
Notes:
Sixth year data based on seven BCHs and associated lead banks.
of 18. Standard deviations given in parentheses.
Sources:
See Table 1.
Other years based on sample size
50
If owners are aware of this trend, they may willingly accept losses
in the first year after acquisition in order to receive claims on increasingly
improved earnings in later years.
If primary interest is placed on later
years by omitting the first year's results from the analysis, the inference
is altered somewhat (see Table 4).
The average annual difference in
net income increases to $444,784 while the difference in coefficients of
variation of net income remains slightly negative.
still not significant, however.
These differences are
The difference in average income growth
rates increases to 5.27 percent, significant now at the .lO level, while
the difference in coefficients of variation of income growth rates widened,
i.e., became more negative.
This difference remained significant at the
.05 level.
V.
SUMMARY AND CONCLUSIONS
Trends are established within the first few years following acquisition, therefore, that improve the present value of earnings flowing to
owners relative to that attainable without reorganization.
Owners have
experienced improvements in the level of earnings to which they hold
claims and, apparently, this improvement grows over time.
Figures 3 and
4 chart the relative experiences in mean earnings and income growth rates
for the alternative ownership positions, respectively.
In addition, to
the extent that the owners' conception of risk is accurately measured by
the coefficient of variation of income growth rates, risk was reduced
through the acquisition program.
If, as assumed, this is reflected in
lower capitalization rates associated with the expanded banking organization, a basis for disparity in both the numerator and denominator of the
TABLE 4
COMPARISON OF EARNINGS PERFORMANCES THROUGH BHC AND LEAD BANK
DELETING FIRST YEAR FOLLOWING REORGANIZATION
Mean Difference in
Average Annual
Net Incomes
(BHC-Lead Bank)
Mean Difference in
Coefficients of
Variation of Net
Incomes
$444,784
-.005253
*significant at the .lO level
**significant at the .05 level
Mean Difference in
Average Income
Growth Rates
Mean Difference in
Coefficients of
Varfation.of
Income Growth Rates
5.27%*
-1.708652**
Net Income
($ millions)
6
1
O-
I
1
I
2
I
3
I
4
I
5
I
6
Years After Acquisition
FIGURE 3.
LEVELS OF EARNINGS THROUGH BHC AND LEAD BANK
Income Growth
Rates (X)
28
24
16
12
8
4
\\v
\\
F
0
I
-4.
I
1
I
2
I
3
I
4
I
5
I
6
Years After Acquisition
FIGURE 4.
INCOME GROWTH RATES THROUGH BHC AND LEAD BANK
51
valuation framework (V = IT/~)is present.
The existence of significant disparities in either or both of the
variables specified does not guarantee a significant valuation disparity
in favor of acquisition.
Without specific information of underlying
utility functions (e.g., how risk affects the capitalization rate function
or the relative importance of earnings and uncertainty in the valuation
function), all that can be determined is an ordinal ranking of alternative
ownership valuation positions--much as described in Figure 5.
If owners
are risk averse, they prefer a position with greater income (IT~>~o)and
no increase in p.
The same result may be obtained with equivalent earnings
and a reduced capitalization rate function (increase from 1 to
where
PO
p. and pl represent vectors of expected capitalization rates in future
periods and p. > ~1.
VI is preferred to VC and owners choose the value
of the earnings stream associated with the expanded BHC structure.
Since
the exact shape of the owners' preference pattern is not known, we can
only be sure that positions between and including points A and B are preferred to point C.
Points to the left of AC (such as D) and below BC (E)
involve movements in ITand p that have conflicting effects on valuation
and may not legitimately be compared to point C.
These results become even more meaningful when it is realized that
earnings streams attained through a BHC structure may be somewhat depressed
by subsequent acquisitions during the period of analysis.
This tendency
would decrease the difference in earnings performance when comparisons are
made over
a
short post-acquisition interval and with firms that acquired
other institutions after the time of the original acquisition.
Victor of
Expected Earnings
n
Positions Preferred to Point C
IIP
(l/P),
(I/P),
Inverse of Vector of Expected Capitalization Rates
FIGURE 5.
VALUATION INDIFFERENCE CURVES:
TRADE-OFF
BETWEEN RETURN AND RISK (OWNERS ASSUMED RISK AVERSE)
52
A note of caution should be injected, however,
The sample used
represents a special class and a very small proportion of the total population of acquisitions taking place.
Whether or not measuring benefits
to lead bank owners who formed holding companies to acquire other firms
is representative of the benefits accruing to stockholders of established
BHCs through acquisition may be questioned.
It does, however, provide a
rational explanation for the formation of many BHCs that is consistent
with the theory of wealth maximization.
53
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M. Adelman, "The Antimerger Act, 1950-60," American Economic Review,
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A. Alchian and H. Demsetz, "Production, Information Costs and Economic
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w. Baumol, Portfolio Theory:
town, N.J. 1970.
The Selection of Asset Combinations, Morris-
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6.
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Part I," Staff
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54
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A. Robichek and S. Myers, "Problems in the Theory of Optimal Capital
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