litigation costs and the underpricing of initial public offerings

MANAGERIAL AND DECISION ECONOMICS, VOL. 16,111-128 (1995)

Litigation Costs and the Underpricing of Initial

Public Offerings Douglas A. Hensler

University of Texas at Arlington, Arlington, TX, USA

This paper examines a risk-averse entrepreneur’s motivation to underprice an initial public offering of equity where the entrepreneur faces the threat of litigation by outside investors. Outside investors have an incentive to seek compensation via tort law and the Securities Act of 1933 should the stock price fall subsequent to their purchase of the IPO. Potential litigation costs motivate the entrepreneur to underprice the IPO in a tradeoff between the litigation cost and the up-front opportunity loss of underpricing. In a single-period model, this paper formalizes the entrepreneur‘s pricing and retained ownership decisions resulting in ten testable hypotheses.

INTRODUCTION

Financial economists have long been perplexed by the underpricing of initial public offerings (IPOs) of equity securities. Reilly and Hatfield (1969), Ibbotson (1979, Ritter (1984a1, and others’ docu- ment underpricing in a range of 11.4% to 52.0% (for a summary see Smith, 1986) depending on the period of study and the type of investment banking contract. One exception in the IPO literature is that of Peavy (19901, who finds that IPO underpricing does not exist in the market for closed-end funds. Ruud (1993) and Hanley, et al. (1993) challenge the existence of average underpricing, arguing that price support by underwriters eliminates the negative tail of first-day returns.

Why do entrepreneurs leave money on the table when they issue equity securities? This study offers an answer to this question. Using a single- period model, I analyze the problem facing a risk-averse entrepreneur issing stock for the first time. The entrepreneur prices the stock knowing that investors have an incentive to sue if the subsequent aftermarket price falls below the offering price. This potential litigation imposes a cost which decreases the entrepreneur’s wealth. As an example of the occurrence of litigation, PC WEEK reported on 2 November 1986:

Kaypro Corp. has agreed in principle to pay

CCC 0143-6570/95/020111-18 0 1995 by John Wiley & Sons, Ltd.

shareholders $9.25 million to settle a 1984 class-action lawsuit arising from its initial public offering of stock ... The suit was filed by several Kaypro shareholder groups after Kaypro stock, which had sold for $10 a share at a time of the offering, fell in price during 1984 and 1985, reflecting a drop in the company’s revenue and profits, according to a Kaypro spokeswoman.

The entrepreneur will underprice the stock if the litigation cost is mitigated, but underpricing also imposes a cost . T h e risk-averse entrepreneur’s problem is one of maximizing the utility of wealth in a tradeoff between the reduction of potential litigation costs and the increase in the opportunity cost represented by underpricing.2

This study proceeds as follows. The next section discusses the study’s relationship to the literature. The third section describes the setting in which the entrepreneur is selling stock and presents an analysis of the litigation costs. The fourth section presents the formal model statement. The fifth section presents the results of simulations which substitute for the direct analysis of the entrepreneur’s expected utility function. The model developed in the fourth section does not yield a closed form solution. The fifth section also presents a comparison with previous work. The final section concludes this study.

112 DOUGLAS A. HENSLER

REVIEW OF RECENT LITERATURE

Theoretical Literature

In a signaling model, Hughes (1986) extends the work of Leland and Pyle (1977) by requiring the entrepreneur to signal both the expected value and the standard deviation of a single-period project. Hughes uses an ex post constant litigation cost to induce truthful signaling by an entrepreneur. While the present study is not a signaling model, it extends the work of Hughes in two ways. First, it specifies that the offering price reflects underpricing and not the intrinsic value of the stock. Second, this study explicitly models the stochastic nature of the litigation cost. While Hughes uses a constant litigation cost to induce truthful signaling, this study uses a stochastic litigation cost to explain IPO underpricing.

Previous explanations of IPO underpricing rely on information asymmetries between informed investors and uninformed investors and/or the issuer, see Ritter (1984a,b), Chalk and Peavy (19901, Rock (1986), Beatty and Ritter (19861, Benveniste and Spindt (1989), Carter and Manaster (1990), or, in the case of Baron (19821, between issuers and investment banker^.^ In general, these models either ignore the issuer’s rational decision making process or appeal to a process in which the issuer passes the decision on to an investment banker. A more recent set of explanations treats underpricing either as insurance against litigation4 (Tinic, 1988, or as a signal of firm value or relative quality (Allen and Faul- haber, 1989; Grinblatt and Hwang, 1989; and Welch, 1989).

Hughes and Thakor (1991) develop a theory of IPO underpricing which offers an explanation similar to this paper. In a single-period market characterized by risk-neutrality, Hughes and Thakor specify sufficient conditions under which underpricing occurs in a ‘perfect sequential equi- librium’. In their paper, the investment banker determines the offering price in a tradeoff between current revenue and the risk of litigation.

Empirical Literature

Tinic (1988) argues that the entrepreneur pur- chases an insurance policy against litigation by underpricing and asserts that offerings made prior to the Securities Act of 1933 are less vulnerable

to investor litigation than offerings made after the Act and, therefore, should be less deeply underpriced. In an intertemporal study, Tinic finds that offerings made during the 1923-30 time period were less deeply underpriced than those in the 1966-71 time period.

Drake and Vetsuypens (1993) investigate the characteristics of IPOs which subsequently are sued within three years of their offerings. They argue that their descriptive statistics of lawsuits show that potential litigation cannot explain the underpricing of IPOs.

Ruud (1993) and Hanley, et al. (1993) show that after price support or stabilization of initial prices is abandoned, prices of new issues fall. While their results suggest that IPO average underpricing may be overstated, they also indicate that there is strong concern by underwriters for the implications of falling prices in the aftermarket. These implications relate to underwriter reputation and to lawsuit avoidance.

Narasimhan, et al. (1993) investigate the relationship between underpricing and subsequent seasoned offerings. They find that there is a positive relationship between IPO underpricing and the probability and size of subsequent seasoned offerings. One implication of the Narasimhan, et af. results is that increased underpricing also pre- cludes future litigation which would interfere with later offerings of seasoned stock.

Schultz (1993) examines the characteristics of firms which issue unit IPOs and finds that they tend to be the smaller, younger, and riskier IPOs and shows that unit IPOs have a higher probability of failure. An interpretation of Schultz’s results is that issuers of units do so to increase the payoff of the positive outcome and in a tradeoff with even deeper underpricing.

Hanley (1993) examines the relationship of IPO underpricing to the offering price adjustment from the Red Herring prospectus price range and finds that offerings which exceed the upper boundary of the range yield greater underpricing. Hanley interprets this to mean that, rather than capitalize on the unconstrained demand for the IPO by issuing more shares and diluting their retained ownership, issuers prefer to underprice more deeply than otherwise.

In a study of the Finnish market, Keloharju (1993) finds that IPO underpricing exists in a market unfettered by federal laws prohibiting fradulent or misleading prospecti. However, Keloharju also notes that the average underpric-

LITIGATION, COSTS AND THE UNDERPRICING OF INITIAL PUBLIC OFFERINGS 113

ing is lower in Finland (8.7% - 1960-92) than in the United States (16.4% - 1960-87).

While some of the theoretical papers cited, most notably Hughes and Thakor, include the role of the investment banker (underwriters), I do not directly include that role in this study. Three arguments support this abstraction. First, in issuing IPOs, investment bankers form syndicates which distribute risk across several underwriters. Beyond the due diligence requirements of the Securities Act 1933, the distribution of risk moves underwriters toward a state of acting in a risk- neutral fashion with respect to the pricing of IPOs. Ultimate liability lies with the issuer as investment bankers are not liable once they demonstrate that due diligence was performed in issuing the IPO. Second, the typical offering prospectus includes an indemnification clause on the cover page which transfers liability from the investment banker to the issuer. Third, in contra- diction to Baron (19821, Muscarella and Vet- suypens (1989) show that investment bankers do not necessarily have superior information to issuers, therefore modeling the investment banker in a significant price setting role may not have empirical support.

The present study contributes to the underpricing literature in the following ways. First, it models the litigation cost explanation for underpricing. While Ibbotson conjectures this explanation as a possibility and Tinic provides some empirical verification, neither formally motivates the explanation in the context of rational economic behavior on the part of a risk-averse entrepreneur. The formal development of the litigation costs explanation yields a rich set of testable hypotheses. Excepting Grinblatt and Hwang (19891, previous theoretical studies yield few predictions about the behavior of entrepreneurs who are issuing stock for the first time. Grinblatt and Hwang develop nine hypotheses under a signaling theory. The present study yields ten hypotheses, two of which compete with those of Grinblatt and Hwang, and one of which is new. Second, this study contributes by providing an alternative explanation that partially helps explain the underpricing puz- ~ l e . ~

LIGITATION COSTS

In the setting of this study, the risk-averse entrepreneur maximizes his or her expected utility

of end-of-period wealth, which the entrepreneur derives from investments in his endowed tech- nology (the project in which the entrepreneur desires to invest) and the risk-free asset.6 Project execution requires an investment of I dollars and yields an uncertain end-of-period cash flow, i , where i -Jul p, a’). The entrepreneur sells stock at an offering price of Po. Upon placement of the shares in the secondary market, the price be- comes P, (a, Po), where a is the fraction of share retained by the entrepreneur. I assume that the market efficiently prices the stock at its intrinsic value, P*, therefore P, (a, Po) = P*.’ The stock’s intrinsic value, P*, is the expected cash flow discounted one period and diluted by the number of shares outstanding, p/(N(1 + r ) ) , where r is the risk-free rate. At the end-of-period, the entrepreneur and investors realize the cash flow i and its associated stock price, P , , which is i / N if i 2 0 and 0 if i < 0, where N is the total number of shares outstanding. The en- terepreneur’s share of the cash flow is a i where a = ( N - n ) / N and n is the number of shares the entrepreneur sells to outsiders.

The entrepreneur faces the threat of litigation by outside investors which poses a potential reduction in the entreprenuer’s end-qf-period wealth in the form of a litigation cost, L. Along with tort law, the Securities Act 1933 provides legal bases for investors to recover losses if the registration statement was deceptive.’ The courts award damages contingent on proof that a material misstatement or omission was made. Whether investors actually read the prospectus is immate- rial to their ability to recover and all investors can participate in loss recovery.’ The Securities Act stipulates that the maximum recovery awarded is the difference between the offering price and the current market price.” The entrepreneur also incurs an administrative cost consisting of lost managerial time, attorneys’ fees, accountants’ fees, etc.

The central focus of this study is the entrepreneur’s underpricing of his or her initial public offering as a mechanism for reducing the potential litigation cost.” The litigation cost consists of a repurchase cost, R, and an administrative cost, A. The repurchase cost, which represents the repurchase of outside shares, is the product of the number of outside shares and the difference between the offering price and the end-of-period price, n( Po - P, 1. If incurred, the administrative cost consists of attorney fees, ac-


counting fees, lost managerial time, etc., the sum of which I assume to be fixed at C. The probability of incurring C varies with the offering price and therefore the administrative cost, A, is stochastic. Underpricing the offering carries with it an opportunity cost which is the product of the number of shares sold and underpricing discount per share, n( P* - Po>.

There are few data about the nature of the court’s decision process in cases where investors are suing the firm because the stock price has fallen. I characterize the court’s decision process as one where the court finds in favor of the plaintiffs, the investors, if the end-of-period price, PI, is equal to or below an arbitrary trigger price, P,. If the end-of-period price is less than or equal to the trigger price, PI s P T , the entrepreneur incurs both the repurchase cost and the administrative cost.I2

To characterize the nature of the court’s trigger price determination, I assume that the court in- vestigates two price differences. First, the court observes the difference between the first aftermarket price and the offering price, P, (a, Po> - Po = P* -Po . Second, the court observes the difference between the end-of-period price and the offering price, PI -Po. I assume that the court requires the entrepreneur to repurchase the stock only when the end-of-period falls below the offering price by an amount equal to or more than the average of the initial price difference and the end-of-periodprice difference, PT = Po - 0.5 (P* -Po> - 0.5 (PI -Po) . The trigger price is increasing in the offering price and decreasing in the intrinsic price and end-of-period price.

Table 1 summarizes three examples which demonstrate the nature of the trigger price model. In all three examples, the intrinsic value of the

stock is $12. First, consider the case where the entrepreneur underprices the stock at $9 and the end-of-period price is $10. The court sets the trigger price at $7 and the entrepreneur does not incur a litigation cost as long as the end-of-period price is above the trigger price. Second, the entrepreneur again underprices the stock at $9, but the end-of-period price is $6. In this case, the court sets the trigger price at $9 and the entrepreneur incurs the repurchase cost and the administrative costs. Third, the entrepreneur underprices more deeply at $7 and the end-of-period price is $6. In this case the court sets the trigger price at $5 and the entrepreneur does not incur litigation costs.

For a fixed retained ownership fraction, a, the entrepreneur can reduce the expected litigation costs by reducing the offering price.I3 The cost of reducing the offering price is the loss of funds from selling stock, the up-front opportunity cost. In the context of a cost-minimization goal, at some point this loss exceeds the reduction in expected litigation costs and the entrepreneur will not reduce the offering price further. That is, the marginal cost of decreasing the offering price just equals the marginal benefit.I4 From the perspective of trading off the up-front opportunity cost for the litigation cost, the expected total cost of the offering is the sum of the expected repurchase cost, the expected administrative cost, and the opportunity cost, R +A+ n(P* -Po>.

The appendix presents the derivation of the expected repurchase cost, R, and the expected administrative cost, A. The expected repurchase cost is

Table 1. Trigger Price Examples

Trigger price (PT) versus offering price (Po) , first aftermarket price (P, = P* ), and end-of-period price (PI)

The intrinsic price is $12

PT = Po - O S P * - P o ) - O . S ( P 1 - Po)

Offering First aftermarket End-of-period Trigger Investors Price Price Price Price Sue and win

$9 $12 $10 $7 No $9 $12 $6 $9 Yes $7 $12 $6 $5 No


and the expected administrative cost is

A = C @ ( - 4 ( p - N P 0 ) / 3 u ) , (2)

where a(.) is the cumulative normal distribution. The total expected cost, including the repurchase cost, the administrative cost and the opportunity cost is

To demonstrate the cost tradeoff at work, Fig. 1 plots Eqn (3 ) for ten levels of entrepreneurial fractional ownership ranging from 0.0 to 0.9. The

input variables are: p = $2200000; u = $500000; r = 0 % ; N=1000000; C=$1000000. Figure 1 shows that for each a there exists an offering price and an underpricing ratio, P,/P*, which yields a minimum expected total cost. The figure also shows that, given P*, as the entrepreneur’s retained ownership fraction increases, the optimal offering price decreases. One explanation of this result is that at the lower levels of outside ownership the administrative costs are distributed over fewer outside shares.

THE MODEL

The risk-averse entrepreneur seeks to maximize the expected utility of his or her end-of-period wealth. The entrepreneur divides his initial wealth, W,, between ownership in his firm and the risk-free asset and achieves his objective by simultaneously choosing the optimal offering price and his optimal retained ownership fraction. His end-of-period wealth derives from the project’s cash flow outcome and the risk-free asset investment, less the litigation cost if the cash flow outcome falls far enough.

0.2 0.4 0.6 0.8 1 .o 1.2

Po/P*, Underpricing Ratio Figure 1. Expected total cost versus underpricing ratio, P,/P*, for a = 0.0 through 0.9. Top line is a = 0.0, descending across lines at 0.1 increasing increments of a. Expected cash flow ( p ) = $2 200000; cash flow standard deviation ( 0 ) = $500000; intrinsic price ( P * ) = $2.20; total number of shares ( N ) = 1 OOOOOO; risk-free rate

( r ) = 0%; litigation administrative cost (C) = $1 OOOOOO.


Equations (4) through (9) formalize the en- = number of shares sold to outside in- trepreneur’s objective and the constraints the entrepreneur faces: N = total number of shares outstanding,

n vestors,

where

or

and

W, = initial wealth of the entrepreneur. (4)

To make the model tractable, assume the following:

Max a , P , E( u( k,))

(1) The end-of-period cash flow is uncorrelated

(2) The repurchase cost and the administrative cost are uncorrelated with the market port-

k l = a x ’ + ( l + r ) Y - i . with the market portfolio

folio (3) The entrepreneur has a negative exponential

FP, = ax’ + (1 + r )Y - R -A ( 5 )

utility function (4) All securities’ cash flows are normally dis-

tributed R = - / n ( P o - F 1 ) O I F , I P , (6) ( 5 ) The risk-free rate is zero.

otherwise To characterize the entrepreneur’s risk aver- 1 O

c O I F , I P , sion, I assume the entrepreneur has a negative

A= { exponential utility function, U ( F P ~ > = - e - b W I , 0 otherwise where b is the entrepreneur’s risk-aversion

(7)

and where

a k C

Po = the offering price, P1 = the end-of-period price, FT = the trigger price, r = risk-free rate of return, R = repurchase costs from underpricing, Wl = entrepreneur’s end-of-period wealth, x’ = the project cash flow outcome, and Y = dollars invested in the risk-free asset.

= entrepreneur’s fraction of the firm, = administrative costs from litigation, = the administrative cost constant, = R +A, end-of-period litigation cost,

This objective function is subject to the budget constraint:

W, + nP, - I - Y = 0 (8)

or

w, + (1 - (Y )NP, - I - Y = 0 (9)

where

1 - a = outside investors’ fraction of the firm,

I n/N,

= investment in the project,

parameter. Given a negative exponential utility function and normally distributed securities cash flows,

Therefore, Eqn (4) can be written as

Letting

(11)

(12)

and using Eqn (lo), the entrepreneur’s objective function can be reduced to maxmizing H over (Y

and Po. To solve the problem stated in Eqns (4) through

(9) using Eqn (121, solve for Y in Eqn (9) and substitute into Eqn (5 ) to get

Ct, = ax’ + ( 1 - (Y ) NP, - R - A + W, - I ( 13)

where the positive signed terms are cash inflows (Wo is actually the entrepreneur’s initial wealth)

LITIGATION. COSTS AND THE UNDERPRICING OF INITIAL PUBLIC OFFERINGS 117

and the negative signed terms are cash outflows. The expected value and variance of kl are

Wl = ( ~ p + (1 - (Y ) NP, - R - A - W, - I (14)

and

a; = a2u2 + a;+ 0-2 - 2aCov( i ,d )

expected value of the project cash flow, standard deviation of the project cash flow, variance of the end-of-period repurchase cost, variance of the end-of-period administrative cost, covariance of the end-of-period cash flow and the repurchase cost, covariance of the end-of-period cash flow and the administrative cost, and covariance of the repurchase cost and the adminstrative cost.

+ baCov(i , k ) + baCov(i , 2) - bCov(A’, A) (16)

where R is the expected end-of-period repurchase cost and is the expected end-of-period administrataive cost as defined in Eqns (1) and (21, respectively. First-order conditions are

and

An explicit solution for this pair of first-order conditions is not attainable. To characterize the entrepreneur’s behavior, we use simulation to analyze the problem.

SIMULATION

Method

While simulation lacks the specificity of a direct solution for the optimal choice variables, a* and P,*, it does yield descriptive information about the partials of a* and P,* with respect to ex- ogenous variables, p and u, and with respect to each other. The following describes the computer-intensive simulation method used to find the partials of the optimal underpricing ratio, P,*/P*,” and the optimal retained ownership fraction, a* , and with respect to the expected cash flow and the cash flow standard deviation. GAUSS,, provides the environment for program development and execution. GAUSS is a high- speed numerical analysis program based on linear algebra and executes in the Microsoft DOS oper- ating environment.16

Figure 2 shows a representation of the expected utility function based on Eqn (16) which represents the transformation across the negative exponential utility function. The program which plots this ‘picture’ also finds the global maximum, H ( a * , P*), at a* = 0.7 and P,/P* = 0.625 for the input variables specified.

The model simulation uses Eqns (4) and (13):

where

kl = a i + (1 - a ) NP, - R - A + ( W, - I ) (13)

and the negataive exponential utility function,


H(oc,Po) v s a AND Po/P*

GLOBAL MAXIMUM AT a* =0.70 and Po*/P*=O .625

Figure 2. Expected utility as represented by Eqn (16) versus underpricing ratio and retained ownership fraction. Expected cash flow ( p ) = $8, cash flow standard deviation (u) = $1.5, total number of shares (N) = 100, risk-free rate ( r ) = 0%, initial wealth (W,) = $1, project investment ( I ) = $2, risk aversion parameter ( b ) = 2, litigation

administrative cost ( C ) = $1.

U(l@,;> = - e - b ~ l , describes the entrepreneur’s utility of end-of-period wealth.

The details of one of the simulation programs are as follows. At a specified offering price, given a fixed expected cash flow, and for a vector of cash flow standard deviations, the program selects another vector of 1000 random numbers from the standard normal distribution. From these two vectors the program calculates a matrix of cash flows, a cash flow distribution vector for each cash flow standard deviation. The matrix contains 26 000 end-of-period cash flow outcomes, 1000 for each of 26 cash flow standard deviations. The matrix of cash flow outcomes is transformed into an end-of-period price matrix, limited liability included, from which a trigger price is determined. In similar programs, the cash flow standard devia-

tion is fixed and the matrix has 20 columns repre- senting 20 different expected cash flow levels.

From the end-of-period price matrix, the program calculates matrices of the repurchase cost and the administrative cost for each instance where the end-of-period price is at or below the trigger price. These combine with the scalars rep- resenting the cash flow from the sale of stock, the entrepreneur’s initial wealth, and the required investment to yield an end-of-period wealth matrix. From the end-of-period wealth matrix the program calculates a matrix in which each column represents a distribution of utility of end-of-period wealth for each different cash flow standard deviation. The program then calculates an expected utility of end-of-period wealth across each column. This final vector is the expected utility of end-of-


period wealth at each cash flow standard deviation, given an offering price (underpricing ratio).

The preceding description represents the program calculations for one combination of retained ownership fraction and offering price. The program repeats the calculation for an outer loop of entrepreneurial ownership fraction ranging from zero to 0.95 at 0.05 intervals and an inner loop of offering prices from $0.001 to $0.030 at $0.001 intervals. The entrepreneur’s initial wealth, W,, is $1; project’s required investment, I , is $2; the entrepreneur’s risk aversion parameter, b, is 2; the risk-free rate, r , is zero; and the administrative cost of litigation, C , is $1.’’

For each entrepreneurial ownership fraction, the program produces a table of expected utility/offering price combinations for each cash flow standard deviation. The program then searches the table for the maximum expected utility and records it and the associated optimal offering price, along with the respective cash flow standard deviations, into another table. This is repeated for each fractional ownership level resulting in 20 tables of data for graphing purposes.

The program contains over 250 000 000 calculations. With changes in input constants to check for qualitative consistency, the simulation effort performs over 2 billion calculations. The entire simulation analysis includes three other program sets of similar complexity and calculation inten- sity.

Results

Figures 3 through 6 show representative results for the four sets of simulations as follows:

Optimal underpricing ratio as a function of project risk (cash flow standard deviation) Optimal entrepreneurial ownership fraction as a function of project risk Optimal underpricing ratio as a function of project expected cash flow Optimal entrepreneurial ownership fraction as function of expected cash flow.

Table 2 summarizes the following comparative statics results represented in Figs 3 through 6.

Figure 3 presents the optimal underpricing ratio as measured by the ratio of the optimal offering price to the intrinsic price, P,*/P*, versus project risk as measured by the cash flow standard deviation for a retained ownership fraction of 0.70 (70%) and an expected cash flow, p , of $2.2. The graph shows that, as the standard deviation of the project cash flow increases, the entrepreneur’s expected utility-maximizing offering price decreases, [ d P , * / P * ) / d a < O l a ] . That is, since higher project risk produces greater expected litigation cost, the entrepreneur lowers the offering price to mitigate some of the increased litigation cost.

Table 2. Comparative Statics Results

Partial Constant Sign Figure

3

U + 3

- dP,* /P*

dP,*/P* dcr

a d u

da * dU -

da * dP

dP,:/P* dP

dP,:/P*

dP,* /P*

~

dU

da da * dl* da * -

a

P

4

+ 4

+ 5

5

5

+ 6

6

6

-

-

-

-

-


OPTIMAL UNDERPRICING RATIO, Po*/P* vs

PROJECT R I S K , 0

a=0.70 p=2.2 b=2 r = O . O

PI 0

a \ 0

4 l

a

(D :I 0 cv 0

s- 0.0 0.2 0.4 0.6 0.8 1 .o 1.2

0 , Cash Flow Standard Deviation Figure 3. Optimal underpricing ratio versus project risk for a = 0.70. Expected cash flow ( p ) = $2.2, total number of shares ( N ) = 100, risk-free rate ( r ) = 0%, initial wealth (W,) = $1, project investment ( I ) = $2, risk aversion

parameter ( b ) = 2, litigation administrative cost ( C ) = $1.

Extending the analysis across varying levels of retained ownership yields no qualitative change in the relationship. Additional simulations for conditions of positive risk-free rates of return yield similar results. However, simulations performed with larger expected cash flows, standard deviation constant, yield larger underpricing ratios, [ d( PJP* ) /dp > 01 1. Since the entrepreneur an- ticipates greater expected end-of-period wealth for a higher expected cash flow, he is better prepared for the threat of litigation. Therefore, the entrepreneur offers the stock at a higher relative price.

Figure 4 presents the optimal entrepreneurial fractional ownership versus project risk for an underpricing ratio, P, /P*, of 0.70 and an expected cash flow of $2.2. The graph shows that, as project risk increases, there is a threshold below which the entrepreneur retains 100% of the firm.” Once the threshold is reached, the entrepreneur’s

optimal ownership fraction drops as project risk increases, [ d a * / d u < OIpo,p* ] . If the project risk is low enough the risk averse entrepreneur attains higher expected utility by retaining 100% of the firm. Above a certain project risk level the entrepreneur decreases his fractional holdings as the project’s risk increases in order to diversify away from the project’s risk.

Extending the analysis across varying underpricing ratios reveals that, as the underpricing ratio increases (the degree of underpricing decreases), the threshold and the rate of decrease in a* with increases in cash flow standard deviation are vir- tually unaffected. In simulations with higher expected cash flows, the threshold point shifts to the right (higher project risk). Therefore, given the cash flow standard deviation, the greater the expected cash flow, the greater the entrepreneur’s optimal ownership fraction, [ d a * / d p > O l u l . Given the project’s risk, the greater expected cash

LITIGATION, COSTS AND THE UNDERPRICING OF INITIAL PUBLIC OFFERINGS

0 d

CD 0 -

rL, 0 -

* 0 -

02 0 -

0 -

121

I I I I I

I I I I I

OPTIMAL OWNERSHIP FRACTION, a* vs

PROJECT RISK, 0

Po/P*=0.700 p=2.2 b= 2 r = O . O

3 . 0 0.2 0.4 0.6 0.8 1 .o 1.2

0 , Cash Flow Standard Deviation Figure 4. Optimal entrepreneurial ownership fraction versus project risk for P,/P* = 0.70. Expected cash flow ( /L) = $2.2, total number of shares ( N ) = 100, risk-free rate ( r ) = 0%, initial wealth (W,) = $1, project investment

( I ) = $2, risk aversion parameter ( b ) = 2, litigation administrative cost (C) = $1.

flow makes the project more desirable from a risk/return perspective and, therefore, the entrepreneur retains a greater fraction of the firm.

Figure 5 presents the optimal underpricing ratio versus the expected cash flow for a retained ownership fraction of 0.70 (70%) and a cash flow standard deviation of $0.50. This graph shows that, as the expected cash flow increases, the optimal underpricing ratio increases at a decreasing rate, [d(P,*/P*)/dp > O l a ] . Given an ownership fraction, the entrepreneur attains greater expected end-of-period wealth when the project’s expected cash flow is higher. This fact enhances the entrepreneur’s ability to withstand litigation and the entrepreneur offers the stock at a higher relative price.

Additional simulations for conditions of positive risk-free rates and increases in the entrepreneur’s initial wealth do not qualitatively change the results. However, an increase in the cash flow stan-

dard deviation causes the optimal underpricing ratio to decrease, given the expected cash flow level, [d (P ,* /P*) /da < Ol,]. Given the expected cash flow, the entrepreneur will decrease the offering price when the risk of his project is higher because the increased risk produces a higher litigation cost.

Extending the analysis across varying retained ownership fractions reveals that, as the entrepreneur’s retained ownership fraction increases, the optimal underpricing ratio decreases at each expected cash flow [d(P,* /P*) /da < Ol,]. Given the expected cash flow, the entrepreneur gives up part of the value-per-share when the entrepreneur increases his ownership fraction. The entrepreneur does this because, even though at a higher ownership fraction the total litigation cost is lower, the entrepreneur can minimize the litigation cost at the higher ownership fraction by lowering the offering price.


OPTIMAL UNDERPRCING RATIO, Po+/P+ v s

EXPECTED CASH FLOW, p

cu=0.70 a=0.5 b=2 r = O . O

1, Expected Cash Flow Figure 5. Optimal underpricing ratio versus project expected cash flow for a = 0.70. Cash flow standard deviation ((r) = $0.5, total number of shares ( N ) = 100, risk-rate free ( r ) = 0%, initial wealth (W,) = $1, project investment

( 1 ) = $2, risk aversion parameter ( b ) = 2, litigation administrative cost ( C ) = $1.

Figure 6 presents the optimal entrepreneurial fractional ownership versus expected cash flow for an offering price, Po, of $0.014 and a cash flow standard deviation of $0.50. This simulation uses the offering price instead of the underpricing ratio, P,,/P* , because the underpricing ratio cannot be held constant when the expected cash flow varies. This graph shows that, as the project's expected cash flow increases, the entrepreneur's optimal ownership fraction increases until it reaches a maximum of 100% (extrapolating beyond the 95% level shown), [ d a * / d p > Olpo]. In this case, when the expected cash flow is increasing (decreasing) for the constant offering price, the degree of underpricing is increasing (decreasing). Given the offering price, a larger expected cash flow means the entrepreneur yields more value-per-share to outside investors. To offset this effect the entrepreneur retains a greater fraction of the firm in order to maximize his expected utility of end-of-period wealth.

Additional simulations for conditions of increased project risk indicates that the optimal retained ownership fraction decreases at any given expected cash flow. That is, given the expected cash flow, the entrepreneur's optimal ownership fraction is negatively related to project risk, [ d a * / d a < Ol,]. Given the project's expected cash flow, the entrepreneur decreases his fractional holdings as the project's risk increases because the entrepreneur desires to lower the risk associated with investment in his firm's project.

Extending the analysis across varying offering prices reveals that, as the offering price increases at any given expected cash flow, the entrepreneur's optimal ownership fraction decreases, [ d a * / d ( P , / P * ) < Ol,]. Given the expected cash flow, the entrepreneur increases his up-front loss when he decreases the offering price. This motivates the entrepreneur to increase his holding in the firm thereby obtaining a larger share of the project's expected cash flow.


a 0

* ei

OPTIMAL OWNERSHIP FRACTION, a'' vs

EXPECTED CASH FLOW, p

Po=0.014 a=0.5 b= 2 r = O . O

p, Expected Cash Flow Figure 6. Optimal entrepreneurial ownership fraction versus project expected cash flow for Po = $0.014. Cash flow standard deviation (u) = $0.5, total number of shares ( N ) = 100, risk-free rate ( r ) = %, initial wealth (W,) = $1,

project investment (I) = $2, risk aversion parameter ( b ) = 2, litigation administrative cost ( C ) = $1.

COMPARISON WITH PREVIOUS WORK

The following four hypotheses, the first three of which are consolidated in pairs from six of the comparative statics results above, are consistent with Grinblatt and Hwang (1989) and the first is consistent with Rock (1986):

(1) The negative relationship between the optimal underpricing ratio and the cash flow standard deviation.

(2) The negative relationship between the optimal retained ownership fraction and the cash flow standard deviation.

(3) The positive relationship between the optimal retained ownership fraction and the expected cash flow.

(4) The negative relationship between the optimal underpricing ratio and the retained ownership fraction,

The positive relationship between the underpricing ratio and the expected cash flow competes with Grinblatt and Hwang (1989). Grinblatt and Hwang argue that underpricing is a signal of firm value, i.e., ceteris paribus, deeper underpricing sig- nals the market that the firm has higher relative value. I argue that, ceterisparibus, the firm's value, represented in my model by the expected cash flow, determines the degree of underpricing. There exists a fundamental causality difference between the two models. Grinblatt and Hwang model investor's inference of firm value from the degree of underpricing whereas I model the degree of underpricing as a function of firm value. The negative relationship between the optimal retained ownership fraction and the underpricing ratio is unique to this study, but it is consistent with the inverse of the relationship noted in item 4 above.

Previous empirical work offers some support for the hypotheses developed here. Ritter (1984b)


and Downes and Heinkel (1982) provide evidence that supports the positive relationship between the optimal retained ownership fraction and the expected cash flow. In the theoretical development of this study, p represents the firm value. While stressing the signaling perspectve of IPOs, Ritter and Downes and Heinkel test causality where firm value is the dependent variable and the entrepreneur’s retained ownership fraction is the independent variable. Both use the total market value of equity after the initial offer as a proxy for firm value and both find a statistically significant positive relationship between firm value and the issuer’s retained ownership fraction. As with Grinblatt and Hwang, Rock and Downes and Heinkel analyze the problem from the perspective of the investor. The present study predicts the same positive relationship with the causality reversed.

Chalk and Peavy (1990) and Beatty and Ritter (1986) provide support for the negative relationship between the optimal underpricing ratio and the cash flow standard deviation. Chalk and Peavy provide the weaker support of the two which is extrapolated from the statistically significant finding that smaller offerings are more deeply underpriced. Researchers generally perceive that smaller offerings are riskier than larger ones. Extrapolating from Chalk and Peavy’s finding that the degree of underpricing and firm size are negatively related, since riskier offerings are associated with smaller offerings, a negative (positive) relationship exists between the underpricing ratio (degree of underpricing) and the degree of risk. Beatty and Ritter provide stronger support by using two proxies for ex ante uncertainty, log(1 + number of uses of proceeds) and the reciprocal of gross proceeds. Beatty and Ritter conclude that there is a negative (positive) relationship between the underpricing ratio (degree of underpricing) and ex ante uncertainty.

Chalk and Peavy also provide support for the positive relationship between the optimal underpricing ratio and the expected cash flow. They find that the larger the offering, the smaller the initial return. If the offering size is a proxy for firm value, Chalk and Peavy’s finding translates to a positive (negative) relationship between the underpricing ratio (degree of underpricing) and firm value. The interesting feature of this finding is its support for an alternative explanation to the em- pirically observed positive relationship between firm size and underpricing. As stated above, re-

searchers previously assigned the finding that smaller offerings are more deeply underpriced to the assertion that smaller offerings are riskier. This study controls for the risk of the offering and simultaneously predicts the negative relationship between the degree of underpricing and firm size. This appears to substantiate the litigation cost explanation for underpricing. Indeed, given the same probability of litigation, a constant administrative cost as imposed in the present study would be relatively more damaging to a smaller firm, thus inducing entrepreneurs of smaller firms to underprice more deeply. An interesting test of this hypothesis would be an empirical study of IPO pricing to ascertain whether or not ‘overpriced’ IPOs are dominated by the larger offerings.

Tinic (1988) proposes an intuitive insurance explanation for the underpricing of IPOs and con- trasts the degree of underpricing for firms going public prior to and after the Securities Act 1933. Tinic finds that firms which issued IPOs prior to the Securities Act were less deeply underpriced than those issuing after the Act. This finding provides general support for the theoretical basis of the present study. More specifically, Tinic’s empirical results provide indirect support for the negative relationship between the optimal underpricing ratio and the cash flow standard deviation and for the positive relationship between the optimal underpricing ratio and the expected cash flow.

The more recent work of Drake and Vet- suypens (1993) presents evidence which, they argue, contradicts the litigation costs hypothesis. They examine attributes of 93 IPOs offered from 1969 through 1990 which were subsequently sued for allegedly misstating company information in either the offering prospectus or the registration statement. Drake and Vetsuypens report that the mean underpricing of the subseqently sued IPOs, 9.18%, is similar to that for IPOs which did not get sued, 11.4% in the Ibbotson (1975) study and 8.6% in the Ibbotson et al. study.

Unfortunately, Drake and Vetsuypen’s analysis lack tests which include risk measures of the IPOs they study. Risk is a central consideration in the model herein, therefore, Drake and Vet- suypens’ results must be interpreted carefully. In a sample of sued IPOs representative of the population of IPOs in degree of underpricing, Drake and Vetsuypens show that the percentage of IPOs subsequently sued does not vary signifi-


cantly across underpricing regimes. They report that over 10% of IPOs underpriced more than 10% were sued, approximately 7% of IPOs underpriced between 0% and 10% were sued, and approximately 7% of IPOs which were overpriced were sued. This evidence does not preclude the insurance hypothesis for if entrepreneurs consider only the probability of being sued and price accordingly, then one would expect to find equal fractions of offerings resulting in lawsuits.

CONCLUSION

This study develops an expected utility-maximization model to analyze and explain a risk-averse entrepreneur's motivation for underpricing his initial public offering. In the model, the entrepreneur is subject to a litigation cost if the share price falls low enough after the stock is introduced to the secondary market. To mitigate the litigation cost, the entrepreneur underprices the offering which results in an up-front opportunity loss. The entrepreneur must balance the two costs while selecting a retained ownership fraction in a manner which maximizes his expected utility of end-of-period wealth.

Simulation analysis of the model yields ten testable hypotheses for which some empirical support exists. Most interesting are the two resulting hypotheses which state that there exists a positive (negative) relationship between the underpricing ratio (degree of underpricing) and the expected value of the firm. These compete with the opposite relationship which Grinblatt and Hwang (1989) derive. While Garfinkel (1993) provides indirect evidence refuting Grinblatt and Hwang's signaling hypothesis that the degree of underpricing and expected value are positively related, conclusive empirical verification of these two hypotheses, as well as the others, is left to future research.

APPENDIX DERIVATION OF THE EXPECTED LITIGATION COSTS

This appendix presents the derivation of the expected litigation cost discussed in the third section. The litigation cost consists of two parts: a repurchase cost, R , and an adminstrative cost, 2.

The entrepreneur incurs both the repurchase cost and the administrative cost if the end-of-

period price, Fl, is equal to or less than the litigation trigger price. In this single-period model, the end-of-period price is equal to the cash flow outcome divided by the number of shares outstanding, x'/N, where x' -4 p, a*). If the cash flow outcome is negative, the end-of-period price is zero due to limited liability. Thus, the repurchase cost must be evaluated over two subregions. The first subregion is that in which the cash flow outcome, i , falls between --03 and 0. In this subregion, the market price of the stock is zero so the repurchase cost is the product of the number of outside shares and the offering price, nPo. The second subregion is that in which the cash flow outcome falls between zero and that associated with the litigation trigger price. In this subregion, the market price is x'/N and the repurchase cost is the product of the number of outside shares and the difference between the offering price and end-of-period price, n( Po - Fl ). As modeled in the third section, the trigger

price is equal to the offering price less the simple average of the first market price less the offering price, P,,,(a,Po) - Po, and the end-of-period price less the offering price, -Po. Since I assume the market efficiently prices the stock upon entry to the secondary market at its intrinsic value, P*, the trigger price is

P, =Po - 0.5( P* - Po) - 0.5( Fl -Po) (Al.l)

The offering price is equal to the intrinsic value of the stock less an underpricing discount. As- suming the end-of-period cash flow is uncorrelated with the market portfolio, the intrinsic value is equal to p/(N(l + r ) ) , where p is the expected cash flow and r is the risk-free rate. The offering price is equal to this amount less the offering discount, defined here as D/N, where D is the product of the total number of shares and the per share discount, N(P* -Po> = p 7 NP,.

The expected repurchase cost IS

(Al.2)

where f ( x ) is the density function for the distribution of x' and PB is the upper boundaIy for the cash flow region which triggers litigation. The upper boundary is the point where the end-of-


period price equals the trigger price, or

P, = Po - 0.5( P* - Po) - 0.5( P, - Po) (Al.8)

Simplifying, R is the expected litigation cost when the stock is priced at ( p - D ) / N , with a trigger price of pT = 2P, - OSP* - 0.5F, = ( 1 . 5 ~ - 2 0 - 0.53/N.

Similarly, the administrative cost occurs when the cash flow outcome is at or below that represented by the trigger price. The expected adrninis- trative cost is

4 1 P, = 3Po - -P* 3 (A1.3)

Assuming a zero risk-free rate, P* = p / N and the upper boundary in terms of the end-of-period cash flow is p-4D/3 . Restating the expected repurchase cost in terms of the cash flow,

p - 4 D / 3 A= 1 C-f(x)dx) (A1.9) - m

Restating in terms of the standard normal,

. 2

Restating in terms of the standard normal,

-4D/3u -

A= C@(-4(p-NP0)/3u) (A1.12) Integrating,

R=r [ p - D ] @ ( - p / u ) Acknowledgements This paper is extracted from my PhD dissertation at the University of Washington. Receipt of the American Associa- tion of Individual Investor’s Award at the 1991 Midwest

) ( ~ 1 . 6 ) Finance Association Meetings is gratefully acknowledged. I am most grateful to my reading committee, Bill Alberts (Chairman), Pete Frost, and Eric Noreen, for their insightful and helpful comments. 1 am especially thankful to Janet Cooper Alexander, Patricia Hughes and Paul Malatesta and four anonymous referees for providing very useful suggestions. I wish to thank participants at presentations at the 1991 Midwest Finance Association meeting and at research svmuo-

“i - D [ @ ( - ~ D / ~ u ) - @ ( - p / ~ ) ]

) I U ( , - ; ( D / U ) * - , - f ( p / ~ ) *

JG Simplifying and restating to eliminate the discount term, D,

Y d .

siums at the University of Texas at Arlington, Syracuse Uni- versity, and Washington State University. An earlier version, = ( l - ){ p@( - p i u - D’( - 4D/3u )

\ entitlkd ‘Underprichg of initial public bfferings: a litigation cost explanation’ was presented at the 1990 Small Firm Finan- cial Research Symposium. Remaining errors are my own. (A1*7) u ( e - ; ( D / u ) * - e - f ( p / ~ ) ~ ) +- dG

NOTES or

1. McDonald and Fisher (1972), Logue (19731, Ibbot- son and Jaffe (1975), Reilly (19771, Chalk and Peavy (1987), and Tinic (1988).

2. Ibbotson (1975) suggests a similar explanation for


underpricing: ‘If the issuing corporation and underwriter perceive that underpricing constitutes a form of insurance against legal suits. For example, errors in the prospectus may be less likely to result in legal suits when the stock’s initial performance is positive.’

3. Sherman (1992) argues that the underpricing of best efforts new issues is compensation to investors for information gathering about the value of the firm. That is, entrepreneurs are unsure about the value of their stock and compensate outside investors via underpricing to expend resources to gather information so a value can be assigned.

4. This insurance hypothesis is equivalent to the litigation costs explanation for underpricing.

5. Another alternative explanation for IPO underpricing is differential tax-based incentives for the entrepreneur. Dandapani et d. (1992) have developed this alternative to the point of reaching corner solutions to the problem. Robinson and Robinson (1993) refine the development to reach interior solutions for the entrepreneur’s optimal underpricing and retained ownership fraction. Integration of the litigation costs explanation and the tax incentives explanation presents a future challenge to researchers.

6. This study initially included the market portfolio. However, as in Hughes (19861, the optimal selection of the market portfolio is independent of the optimal choice of retained fractional ownership and the degree of underpricing and vice versa. The independence of the optimal choice of investment in the market portfolio and the optimal choices of retained ownership and of offering price depends on the assumption, made here, that the project’s cash flow is uncorrelated with the market portfolio.

7. Ritter (1991) provides evidence that P,,,(rr,P,) may be greater than P*.

8. Sec. 11. (a). In case any part of the registration statement, when such part became effective, contained an untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary to make the statements therein not misleading, any person acquiring such security (un- less it is proved that at the time of such acquisition he knew of such untruth or omission) may, either at law or in equity, in any court of competent jurisdiction, sue - (1) every person who signed the registration statement; (2) every person who was a director of (or person performing similar functions) or partner in, the issuer at the time of the filing of the part of the registration statement with respect to which his ability is asserted; (3) every person who, with his consent, is named in the registration statement as being or about to become a director, person performing similar functions, or partner; (4) every accountant, engineer, or appraiser, or any person whose profession gives authority to a state-

ment made by him, who has with his consent been named as having prepared or certified any part of the registration statement, or as having prepared or statement, with respect to the statement in such registration statement, report, or valuation which purports to have been prepared or certified by him; ( 5 ) every underwriter with respect to such security. (73d Congress Sess. I. Ch. 38 27 May, 1933).

9. Alexander (1991) provides evidence that there is little relationship between securities class actions settlements and the merits of the cases. For a legal analysis of lawsuit avoidance theories see Alexan- der (1993).

The suit authorized under subchapter (a) may be either (1) to recover the consideration paid for such security with interest thereon, less the amount of any income received thereon, upon the tender of such security, or (2) for damages if the person suing no longer owns the security. Sec. 11. (g). In no case shall the amount receivable under this chapter exceed the price at which the security was offered to the public. (73d Congress Sess. I . Ch. 38 27 May, 1933).

11. For simplification purposes, this study ignores the mitigating influences of underwriter reputation, au- ditiors, and legal advisors.

12. IPO price support activity by underwriters can have an upward effect on the first aftermarket price, therefore, an opposite effect on the trigger price. Price support activity normally does not last beyond approximately ten trading days so it is unlikely that the end-of-period price is affected. For empirical examinations of price support activity see Ruud (1993) and Hanley (1993).

13. Given a fixed offering price, the entrepreneur can also reduce expected litigation costs by retaining a higher fraction of the firm.

14. If the entrepreneur is risk-neutral, this cost analysis comprises his pricing decision problem. The fourth section extends the analysis to expected utility maximization which includes risk.

15. All but one of the simulation programs use the partial of P,*/P* instead of the partial of P,* in order to ‘normalize’ the degree of underpricing with the expected cash flow parameter.

16. GAUSS is the product of Aptech Systems and Microsoft DOS is the product of Microsoft, Inc.

17. The described simulation uses the expected cash flow of $2.2 and an intrinsic stock value of $0.022. The selection of small numbers facilitates the use of the negative exponential utility function. Amounts to which one can relate more easily, such as an expected cash flow of $2 million, cause the negative exponential utility function to produce output numbers which exceed the floating point limits of the computer program.

18. The plots show a ceiling of 95% as underpricing is moot at a 100% entrepreneurial ownership. The assertion of the threshold is an extrapolation of the plots and of the structure of the model.

10. Sec. 11. (e).


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