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Journal of Financial Economics 28 (1990) 149-171. North-Holland Borrowing relationships, intermediation, and the cost of issuing public securities* Christopher James University of Florida, Gaines&e, FL 32611-2017, USA Peggy Wier University of Oregon, Eugene, OR 97403-1208, USA Received March 1990, final version received December 1990 This paper investigates how an established borrowing relationship affects the costs associated with initial public offerings of equity. Our model illustrates how the existence of a borrowing relationship reduces the ex ante uncertainty about the value of the issuing firm’s equity in the secondary market. If underpricing is related to uncertainty, a borrowing relationship can reduce underpricing. Empirically, we find that, other things equal, IPOs of firms with previously established borrowing relationships are underpriced substantially less than other IPOs. 1. Introduction Most analyses of capital acquisition and capital structure distinguish be- tween inside and outside claims on the firm. Inside claimants have access to information about the firm that is not available to the public, while outside claims are publicly traded among investors who rely on information available to all. Although the costs of informing and contracting with investors are generally higher for outside claims, economies of scale in these costs and in issuing expenses make publicly-traded securities economical for large corpo- rations. For smaller firms, inside claims such as bank debt can be less costly.’ *We received helpful comments from David Brown, Mark Flannery, Tom George, Scott Lummer, David Mayers, Mark Ryngaert, Jay Ritter (the referee), Clifford Smith (the editor), and participants of the finance workshops at the University of Florida, Georgetown University, Ohio State University, Tulane University, and Arizona State University. Jay Ritter kindly let us use his extensive IPO data. Thanks to Jon Garfinkel and Steve Cox for research assistance. ‘See Jensen and Meckling (19761, Fama and Jensen (19831, and Smith and Warner (1979) for a discussion of the distinctions between inside and outside debt and equity. Blackwell and Kidwell (1988) analyze the flotation costs associated with private and public placements of debt. 0304-405X/90/$03.50 0 1990-Elsevier Science Publishers B.V. (North-Holland)
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Page 1: Borrowing relationships, intermediation, and the cost of issuing public securities

Journal of Financial Economics 28 (1990) 149-171. North-Holland

Borrowing relationships, intermediation, and the cost of issuing public securities*

Christopher James University of Florida, Gaines&e, FL 32611-2017, USA

Peggy Wier University of Oregon, Eugene, OR 97403-1208, USA

Received March 1990, final version received December 1990

This paper investigates how an established borrowing relationship affects the costs associated with initial public offerings of equity. Our model illustrates how the existence of a borrowing relationship reduces the ex ante uncertainty about the value of the issuing firm’s equity in the secondary market. If underpricing is related to uncertainty, a borrowing relationship can reduce underpricing. Empirically, we find that, other things equal, IPOs of firms with previously established borrowing relationships are underpriced substantially less than other IPOs.

1. Introduction

Most analyses of capital acquisition and capital structure distinguish be- tween inside and outside claims on the firm. Inside claimants have access to information about the firm that is not available to the public, while outside claims are publicly traded among investors who rely on information available to all. Although the costs of informing and contracting with investors are generally higher for outside claims, economies of scale in these costs and in issuing expenses make publicly-traded securities economical for large corpo- rations. For smaller firms, inside claims such as bank debt can be less costly.’

*We received helpful comments from David Brown, Mark Flannery, Tom George, Scott Lummer, David Mayers, Mark Ryngaert, Jay Ritter (the referee), Clifford Smith (the editor), and participants of the finance workshops at the University of Florida, Georgetown University, Ohio State University, Tulane University, and Arizona State University. Jay Ritter kindly let us use his extensive IPO data. Thanks to Jon Garfinkel and Steve Cox for research assistance.

‘See Jensen and Meckling (19761, Fama and Jensen (19831, and Smith and Warner (1979) for a discussion of the distinctions between inside and outside debt and equity. Blackwell and Kidwell (1988) analyze the flotation costs associated with private and public placements of debt.

0304-405X/90/$03.50 0 1990-Elsevier Science Publishers B.V. (North-Holland)

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150 C. James and P. Wit-r, Borrowing relationships and the cost of IPO’s

The advantages of inside debt may go beyond issuing expenses, however. Myers and Majluf (1984) show that information asymmetries between man- agement and outside investors can induce managers to refrain from issuing new equity and forego positive net-present-value investments. Inside debt may be able to reduce those asymmetries. Campbell and Kracaw (1980) and Fama (1985) argue that borrowing from intermediaries can reduce informa- tion costs for all of a firm’s claimants by providing a credible signal about the firm’s creditworthiness.’ Finally, monitoring by intermediaries may reduce agency costs arising from conflicts among inside equity holders, outside claimants, and the managers of the firm.

The costs of informing potential investors about a firm’s prospects are likely to be highest when a firm makes its first public offering of securities. Indeed, Rock (1986) and Beatty and Ritter (1986) argue that investor uncertainty about the value of the firm causes substantial underpricing of initial public offerings of equity (IPOs). The benefits of existing inside debt should therefore be especially important when firms go public.

In this paper we investigate how an established relationship with an inside lender affects the costs associated with an IPO. We present and test a model that illustrates how the existence of a borrowing relationship can reduce the ex ante uncertainty about the value of the issuing firm’s equity in the secondary market and thereby reduce underpricing. The model therefore illustrates an advantage to borrowing that extends beyond the benefits of monitoring and certification by lenders. It also shows why some firms will choose not to establish a borrowing relationship before taking an IPO to market.

In developing the model, we assume that there are two types of firms, whose market values are drawn from distributions with the same means but different dispersions. In addition, we assume that firm owners know their firm’s type but not its true market value, and potential investors cannot costlessly discover a firm’s type. If a prospective lender makes an unbiased estimate of the firm’s value, then the probability that a loan request is rejected will be greater for high-dispersion firms. Since rejection establishes that the loan request exceeds the lender’s estimate of the firm’s value, the proceeds from a subsequent IPO will be lower than if the firm had not tried to borrow. If firm owners know their firm’s type, they can calculate ex ante the probability of rejection and, therefore, the expected benefit from applying for a loan. We show that low-dispersion firms expect positive benefits, but for high-dispersion firms the expected benefits can be negative and they there-

‘See James (1987) and Lummer and McConnell (1989) for empirical evidence on the valuation effects of announcements of bank-loan agreements.

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C. James and P. Wier, Borrowing relationships and the cost of IPO’s 151

fore will choose not to apply. As a result, a firm’s decision whether to apply for a loan before selling stock can identify firm type.

Our model is based on the simplifying assumption that the only benefit of borrowing is to signal information about the dispersion of the firm’s market value. However, our model can accommodate other benefits from borrowing. For example, monitoring by intermediaries may increase a firm’s value and this reduces the cost of signaling for low-dispersion firms (since they would find borrowing optimal without the benefits of signaling). If high-dispersion firms find that the cost of establishing a lending relationship before going public outweighs the monitoring benefits, the borrowing decision will still reveal firm type.

The model predicts that firms with inside debt will experience less severe underpricing when they go public. In fact, we observe that the average initial return for the 455 firms in our sample with previously established borrowing relationships is 9%, while the average for the remaining 94 firms without debt is 31%.

Another possible explanation for the association between borrowing and underpricing is that firms which rely to a significant extent on debt financing consist mostly of assets in place while equity-financed firms possess mostly growth options [Myers (1977) and Harris and Raviv (199O)l. If there is more uncertainty about the ex ante market value of growth firms, they will be more severely underpriced. As a result, the empirical relation between underpric- ing and borrowing could be due to the nature of the firm’s assets and not to the signal which borrowing provides. We explore this argument below.

2. The model

The model shows how issuing private debt claims before issuing stock to the public can reduce the degree of IPO underpricing for certain firms. In the spirit of Rock (1986) and Beatty and Ritter (19861, we assume that some underpricing is required to compensate uninformed investors for their antici- pated losses on overpriced issues and to ensure their continued participation in the market. The degree of underpricing is directly related to the ex ante uncertainty about the market value of the firm. In addition, we assume that there are two types of IPO firms with the Same expected value but different dispersions of possible market values. Potential investors cannot costlessly discover a firm’s type. Original owners know their firm’s type but cannot determine before going public what its market value will be. Since low-vari- ance firms get higher initial offer prices, it is in their interest to identify themselves if possible. We show that they can do so under certain circum- stances by borrowing from a lender that can make an unbiased estimate of the firm’s value.

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152 C. James and P. Wier, Borrowing relationships and the cost of IPOS

2.1. Assumptions

We assume a market for IPOs similar to the one described by Beatty and Ritter. Investors in this market are risk-neutral and the risk-free interest rate is zero. Owners of a firm do not know its true market value before going public. Investors are able to pay c dollars to become informed and learn prior to the offering the true value of the firm. Investors that choose to become informed will submit purchase orders only if the offer is not over- priced. In particular, if uJ denotes the true value of the firm and OP, represents the offer proceeds, then informed investors will submit purchase orders only if uJ 2 OP,. If the original owners do not sell all their shares, then informed investors will submit purchase orders only if u&l - IY) 2 OP,, where 1 - (Y is the proportion of the firm that new shareholders own. Like Beatty and Ritter we assume that underwriters have the same information as uninformed investors.

To analyze the role of borrowing relationships we modify Beatty and Ritter’s model in the following ways:

Assumptions about issuers

L type firms have greater dispersion in possible market values than H type firms. L firms, if identified, would receive lower IPO proceeds than H firms. Owners of a firm know its type but (as in Beatty and Ritter) not its true value. The proportions of L and H firms are h and 1 - A. The distributions of possible market values for each type of firm are uniform:

~~-U[a,,b,l, GH-U[a,,b,],

where a and b are the bounds of the distributions and

a,sa,, b,> b,.

We denote the common expected firm value as /1 and the realized value of a firm as U.

The proceeds of the offerings are used to reduce the owners’ stake and not for real investment.

Assumption about the market for IPOs

3. There are four dates of interest: t = 0: Owners can attempt to borrow D dollars, to be repaid at t = 2, and

use the proceeds to reduce their stake in the firm. This assumption

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C. James and I? Wier, Borrowing relationships and the cost of PO’s 1.53

assures that the unconditional expected market values of equity of both types of firms are the same. Owners make an IPO at t = 0 if a loan application is refused or if they decide not to apply for a loan and instead go directly to the equity market.

t = 1: Shares issued at t = 0 are traded in the secondary market. t = 2: Firms that borrowed at t = 0 make IPOs and use the proceeds to

repay their loans. If the proceeds are insufficient to repay the loan, lenders take control of the firm’s assets.

t = 3: Shares issued at t = 2 are traded in the secondary market.

Assumption about investors in IPOs

4. Investors know the probability density of Gt and cN and the proportion of L and H firms in the market but cannot classify ex ante individual firms by

type.

Assumptions about lenders

5. In the course of evaluating a potential borrower, a lender makes an unbiased estimate e’, of the borrower’s true value, where Z, = L’~ + ?jJ, E(ij,) = 0. However, the lender cannot credibly communicate this estimate directly to the market because the lender has an incentive to overstate the borrower’s value in order to raise the IPO proceeds used to retire the loan.

6. Lenders cannot participate in the IPO. This assumption is consistent with the restrictions on commercial bank equity investments imposed by the Glass Steagall Act of 1927.

7. Lending decisions are public information. This assumption simplifies the analysis and seems plausible since borrowing is reported in the firm’s financial statements. However, it is not essential for the model’s conclu- sions if there are costs associated with applying for a loan. We discuss relaxing the assumption of public information below.

2.2. Offer pricing

2.2.1. No borrowing

Assume for the moment that there is no borrowing. Since firms are indistinguishable to uninformed investors, all firms are pooled. Offer pro- ceeds for each type of firm will be the same. If firm types are known, Beatty and Ritter (1986) and Carter and Manaster (1989) show that equilibrium in

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154 C. James and P. wier, Borrowing relationships and the cost of IPO’S

the primary market would require

and

/,“( OP, - S,)f( iiu) dv, aH

+(l-~,)/~~[OP,-B,]f(6,)du, =O. H 1

(1)

OP, is the offer proceeds to firm type J. N is the number of informed investors; c is the cost per investor of becoming informed; and rTTJ is the proportion of firm J’s shares that are acquired by informed investors.

Eq. (1) states that in equilibrium the profits that informed investors receive from underpricing must equal the aggregate cost of becoming informed so that informed investors earn zero expected profits. Eq. (2) states that in equilibrium uninformed investors’ expected losses from overpricing offset their underpricing gains (see appendix of Beatty and Ritter).

We define OP, as the offer proceeds assuming that firm types are not observable ex ante to outsiders and that all types are pooled together. The expected values of both types of firms are the same but, because offer proceeds are decreasing in ex ante uncertainty,

OP, < OP, < OP, )

where

OP, = offer proceeds for known ex ante,

OP, = offer proceeds for known ex ante.

L (high-dispersion) firms, assuming firm types are

H (low-dispersion) firms, assuming firm types are

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C. James and P. Wier, Borrowing relationships and the cost of IPOS 155

That is, H firms would receive higher proceeds and L firms would receive lower proceeds if their types were known, because uninformed investors face greater adverse selection risk in purchasing shares of L firms and therefore require greater underpricing to participate.

2.2.2. Firm borrowing at t = 0

2.2.2.1. Lending decisions are revealed to investors

Assume first that firm types are known to investors. If D, the amount of borrowing, is set so that OP, < D 5 OP,, the total proceeds from the IPO will be insufficient to repay the loans of L firms, and therefore a given L firm will receive a loan only if the lender estimates that the value of the firm’s equity (assets) in the secondary market is greater than the amount of the borrowing (that is, eL > 0). Since D s OP,, H firms will always receive loans if they apply. Moreover, the owners of H firms will be indifferent between borrowing and issuing at time t = 2 or issuing at t = 0 and not borrowing. This result follows because regardless of the amount of borrowing, equity claims on assets with a market value of v at time t = 3 are sold to new shareholders at t = 2. Borrowing in our model only changes the identity of the recipient of the IPO proceeds from original owners to lenders. The distribution of firm value thus remains the same whether or not the firm borrows, so that borrowing does not affect investor uncertainty concerning the value of H firms.

Consider now the case in which firm types are not known and assume as before that the amount of borrowing is set so that OP, I D I OP,. We discuss later how the level of borrowing is determined. Lending will occur only if the lender’s estimate of the value of the firm or the offer proceeds are greater than D. If no L firms borrow, all loan applicants can be identified as H firms. Their offer proceeds will be OP, and they will all receive loans since D I OP,. Therefore, H firms will borrow if L firms do not, because their offer proceeds exceed the pooled equilibrium proceeds OP,.

Will L firms apply for loans? If they do, some will be rejected because the lender’s estimate of their value falls below D. Since owners know their firm’s type but not the lender’s estimate of the firm’s value, they cannot predict with certainty the outcome of the loan request. In determining whether to apply, L firms will compare the expected IPO proceeds if they do apply to the proceeds they will receive if they do not. A single L firm attempting to mimic an H firm by borrowing would face expected IPO proceeds OP,, such that

(3)

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156 C. James and P. Wier, Borrowing relationships and the cost of IPO’s

where

F,(D) = probability that the true value of an L firm is less than D, OP,, = offer proceeds for L firms conditional on being refused a loan of

size D.

(3) says that the expected offer proceeds are the proceeds if rejected times the probability of rejection plus the proceeds if accepted (and thus classified as an H firm) times the probability of acceptance.3 We show in the appendix that these expected proceeds (OP,) can be less than OP,, which are the proceeds if the L firm did not attempt to borrow.

Intuitively, if the lender’s decision is public information, then any firm that applies for a loan and is rejected is revealed to be a low-valued L firm (i.e., the estimated value of the firm is less than D). Moreover, L firms that receive loans have a higher expected value than the H firms that borrow because their values are distributed over the interval [D, bJ, with b, > b, and D 2 uH. However, they receive the same offer proceeds as H firms. Thus L firms bear all the costs of rejection but do not receive the full benefits of acceptance (i.e., identification as a firm with possible values over the interval [D, b,]). Because L firms that are approved for loans are pooled with H firms, expected offer proceeds for L firms that try to borrow are less than the offer proceeds associated with not borrowing. Therefore, if OP, <D I OP,, L firms will not find it advantageous to apply for loans.4

We now address the question of how the amount of borrowing is deter- mined. If OP, <D % OP,, the H firms are unambiguously better off if they borrow D and avoid the pooling equilibrium, and the L firms are worse off if they apply to borrow D. Suppose L firms apply for a loan in an amount different from D. The H firms will have no incentive to mimic this borrowing strategy since they are no better off and may be worse off if they are pooled with L firms. Moreover, since the lender’s credit decision is public knowl- edge, the L firms will reveal themselves by borrowing an amount different

3Expression (3) assumes that investors cannot distinguish L firms with loans from H firms with loans. They view all firms with loans as H firms. If investors assume that all L firms would apply, the expected proceeds would be:

F,(D)OP,,+{l-F,(D)}OPi, with OPi,=hOP,,+(l-h)OP,,

where OP, are the offer proceeds for firms with values distributed over interval [D, b,]. That is, market participants would assume that firms with loans are both L and H firms in proportions {l - F,(D)},4 and 1 - {l - F,_(D)},+. Note that in this case H firms receive offer proceeds higher than OP, because they are pooled with L firms that are accepted for borrowing.

4While we prove this only for the uniform distribution, we believe the result holds for any symmetric probability distribution that can be described by the first two moments of the distribution. For a distribution of this type, the probability of L firms (with the more disperse distribution) being rejected when OP, < D 5 OP, is greater than the probability of H firms being rejected.

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C. James and P. wier, Borrowing relationships and the cost of IPO’s 1.57

from D, which removes their incentive to borrow. (Once they are identified as L firms, the expected proceeds from a borrowing strategy are OP,).

2.2.2.2. Lending decisions are confidential

An important assumption in the preceding analysis is that the lender’s decision to accept or reject a loan application is public information. This assumption seems plausible when a loan is granted, since borrowing is reported in the prospectus, but rejection decisions are less reliably made public. Rejections may be reported under securities laws that require issuers to disclose information that may materially affect the offer price of the security [see Loss (1961)]. However, no firm in our sample reported a rejection in its prospectus. This is consistent both with the prediction of our model that firms facing rejection do not apply, as well as with the idea that rejections are not systematically reported.

If applying for a loan is costless and the outcome of the loan application is kept confidential, then borrowing will not separate firm types. In this case, an individual L firm will apply for a loan even though the expected proceeds for all L firms will decline. That is, an L firm’s owners will perceive no costs to applying for a loan if they assume that other L firms will not apply and investors will not know if their application is rejected. In this case L firms will expect offer proceeds of OP, if they are rejected. If all L firms make these assumptions, both L and H firms will try to borrow. In the resulting equilib- rium, H firms are unambiguously better off compared to the equilibrium in which no borrowing occurs, because they are pooled with borrowing L firms (see footnote 3). Nonborrowing firms will all be low-valued L firms with market values distributed over the interval [aL, D].

With positive loan-application costs, a separating equilibrium, in which only H firms borrow, is possible even if the rejection decision is not revealed. If 4i is defined as the cost of obtaining a loan of size D for signalingpurposes where D is set such that OP, <D 5 OP,, the conditions for a separating equilibrium are:

OP, - & > OP, (4)

(H firms find it profitable to borrow)

and

F(D)OP,+(l-F(D))OP,-&COP,

(L firms find borrowing unprofitable) .

(5)

Expressions (4) and (5) together imply that for a common cost of establish- ing credit (c$ = &, = &), separation requires (1 - F(D)XOP, - OP,) < 4 <

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158 C. James and P. Wier, Borrowing relationships and the cost of IPO’s

ACOP, - OPJ Thus the cost of borrowing required to separate firms by type will depend on the proportion of L firms in the population (h), the probabil- ity of being rejected U’(D)), and the difference in the offer proceeds between H and L firms.

Borrowing is a costly (dissipative) signal if it provides no other benefits besides signaling firm type. But suppose that monitoring by a lender raises a firm’s value by reducing agency costs, and that the cost of establishing a credit relationship is higher the greater is the ex ante uncertainty concerning the market value of the firm. In this case, H firms might borrow even in the absence of signaling benefits. Their cost of signaling firm type by borrowing [& in (4)] would be zero. If L firms face high costs of establishing a credit relationship, they may decide not to borrow prior to going public. This modification permits other benefits to borrowing while explaining why some firms choose not to apply for loans.

Our analysis yields several testable implications. First, our model predicts that the magnitude of underpricing will be less for firms with existing credit relationships than for firms with no borrowing history. Second, since the important information for outside investors is whether the issuing firm has been approved for a loan, only a loan commitment (not actual borrowing) is required to reveal firm type. Finally, since the level of borrowing necessary to separate firm types will vary across industries, our model predicts that in cross-sectional tests the existence of a borrowing relationship, and not the amount of borrowing, will be important in explaining underpricing.

2.3. Other explanations for the relation between borrowing and underpricing

Agency theory offers another explanation for the association between borrowing and underpricing. It suggests that inside lenders monitor a borrow- ing firm’s operations, thus reducing conflicts of interest among classes of claimants and increasing firm value. But borrowing also has costs - it can induce firms to forego profitable projects and undertake risky unprofitable ones. (The agency literature calls these the underinvestment and asset-sub- stitution problems.) Perverse investment incentives are especially trouble- some for firms with mostly intangible assets, or growth options, rather than assets in place [see Smith and Warner (1979) and Myers (197711. Growth firms are therefore likely to have little debt in their capital structure. If the market values of growth firms are viewed by investors as highly uncertain when they go public, their IPOs will be severely underpriced. Thus firms with debt will exhibit less underpricing than firms without debt because of the nature of the firm’s assets. We explore this explanation below.

Slovin and Young (1990) also examine the relation between underpricing and bank borrowing. They argue that a firm’s decision to establish a banking relationship can provide a credible signal concerning the quality of the firm.

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C. James and P. Wier, Borrowing relationships and the cost of IPO’s 159

Therefore, firms with favorable characteristics will choose to borrow from banks. Outside investors consequently view bank lending as a credible signal concerning firm value, which reduces IPO underpricing. Consistent with this argument Slovin and Young find that firms with banking relationships experi- ence less JPO underpricing than firms with no banking relationship.

However, there are several problems with this simple signaling story. If the issuing firm has bank loans outstanding, the bank is better off the greater the proceeds from the offering, so banks have an incentive to overstate the true value of the firm. If outsiders are aware of this incentive, bank borrowing cannot provide a credible signal.

The credibility of the bank or other private lender may be restored if the lender has reputational capital that will depreciate if the true value of the firm is misrepresented. Beatty and Ritter (1986) and Carter and Manaster (1990) argue that reputational capital is important in understanding the role of IPO underwrites, and Beatty (1989) provides evidence that auditor reputa- tion may be important as well. Reputational capital is less likely to be important in understanding the lender’s role because the bank or private lender’s livelihood is less directly linked than the underwriter’s to the securities-issuance process, since firms issuing securities for the first time are likely to be a smaller proportion of the business of a commercial bank or private lender than of an investment banking firm. Moreover, if the lender’s reputation is important we would expect the identity of the lender to be revealed in the prospectus (as are the names of the auditor and investment banker). However, only 1 percent of the borrowing firms in our sample provided the name of a lender in the prospectus.

A second problem with the simple signaling story is that it fails to explain why all firms do not establish credit relations before going public, since they have an incentive to do so if the existence of a credit relationship (and not the amount of borrowing) can reduce underpricing. Since all firms have positive expected offer proceeds, they would be accepted for some loan amount. In this case the existence of a borrowing relationship would lose its signaling value. Our model is intended to explain why borrowing can serve as a credible signal and why some firms rationally choose not to apply for loans.

3. Data

We test our model on a sample of initial public offerings of equity that occurred during the period January 1, 1980 through December 31, 1983. Our sample consists of firm commitment offers announced in the Investment Dealer’s Digest. We exclude stock offerings which incorporate warrants because we could not separate changes in warrant values from the stock-price effects we wish to examine. We also exclude offerings by financial corpora- tions, because their debt claims may be different from those issued by

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160 C. James and P. Wier, Borrowing relationships and the cost of IPO’s

nonfinancial firms and also because government guarantees may distort the decisions of banks and thrift institutions to issue debt. Our sample consists of 549 issues.

Information on the use of the proceeds and the firm’s financial characteris- tics, ownership composition, and age comes from the prospectus and from Moody’s OTC and Zndustrial Munuals. We calculate the initial returns for each IPO using the closing bid prices at the end of the offer month. These prices were obtained from the Financial Chronicle and from the Daily Stock Price Record. We also obtained initial returns based on the first day of trading from Ritter’s IPO data base.

Since Carter and Manaster and others find that the identity of the underwriter affects the degree of underpricing, we identified the lead under- writer from the Investment Dealer’s Digest and the ranking of underwriters from Carter and Manaster.

4. Empirical evidence

We identify a firm as having a borrowing relationship if its prospectus reports that prior to the IPO it had a bank loan, a credit commitment, or long-term debt from a source other than stockholders. We exclude capital- ized leases and mortgages from long-term debt because the value of the collateral is known. Since no firm indicated in its prospectus that it had publicly traded debt outstanding and there was no public debt listed in any of the firms’ Moody’s entries just after the offering, we assume that all of the debt outstanding for these firms is privately held and therefore constitutes inside debt.

Table 1 presents descriptive statistics for the firms in our sample. An initial return is the difference between the offer price and the price at the end of the offer month, divided by the offer price. The mean initial return for the offers is 13%, which is similar to the initial returns reported by others [see Carter and Manaster (1990) or Ritter (198911. The median is 3%. The average size of the offering is $15 million. The majority of the firms in our sample had some form of debt outstanding at the time of the offering - 76% had bank loans or bank-loan commitments, 74% had long-term debt out- standing, and a total of 83% had either bank loans or long-term debt. Of the 455 firms with borrowing relationships, 333 (73%) had both long-term debt and bank loans outstanding. Finally, the average ratio of book value of debt to total assets prior to the IPO is 31%, and debt as a proportion of offer proceeds is 42%.

We perform several tests of the hypothesis that a credit relationship can reduce the degree of underpricing. First, we examine the initial return differences between firms with bank loans or long-term debt outstanding and

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Table 1

Summary statistics for a sample of 549 initial public offerings of equity issued during the period 1980-1983.

Mean Median Minimum Maximum

Offer size (in thousandsY Assets of issuing firm

(in thousandsIb Sales of issuing firms

(in thousandsjb Age of firm (in years) Ratio of insider shares

to total shares offeredc Initial returnd Ratio of debt to assetse Ratio of debt to offer

proceeds

Percentage of firms with bank loans

Percentage of firms with long-term debt

Percentage of firms with bank loans and/or long-term debt

$15,116 $9,933 $1,400 $215,000 $20,116 $7,329 $52 $236,398

$33,102 $11,519 $716,397

8.94 0.19

5.2 0.04

13.32% 3.12% 0.31 0.19 0.42 0.15

0

0.08 0

- 44% 0 0

80 1.00

306% 4.45 8.89

76%

74%

83%

aOffer size is the offer price times the number of shares offered (including secondary shares issued). Number of shares offered includes shares provided underwriters through the over-allot- ment option. This is from the Znoestment Dealers Digest.

bAssets of the issuing firm and sales are from the prospectus. Sales are revenues for 12 months prior to the offering. Assets are the assets of the firm prior to the IPO.

‘Ratio of insiders’ shares is calculated by dividing secondary shares offered by total shares offered. This is from the Investment Dealers Digest.

dAn initial return is the difference between the offer price and the price at the end of the offer month divided by the offer price.

‘Debt is measured as the total of bank loans and long-term debt prior to the offering.

firms with no borrowing at the time of the offering. The mean initial return for the 455 firms with borrowing relations is 9% (the standard deviation of returns is 25%) and the median return is 2%. In contrast, the mean initial return for firms with no borrowing relationships is 31% (the standard deviation is 67%) and the median return is 13%. The difference between the means is significantly different from zero at the 0.01 level. The t-statistic for the difference in means test (assuming unequal variances) is -3.14. The difference in medians is significant at the 0.05 level. The X2-statistic for the medians test is 3.97.

The analysis in the previous section also implies that the variability in initial returns will be greater for the firms without borrowing relationships. The F-statistic associated with a test of the equality of sample variances is 7.18, which is significantly different from zero at the 0.01 level.

Page 14: Borrowing relationships, intermediation, and the cost of issuing public securities

162 C. James and P. Wier, Borrowing relationsh@s and the cost of IPO’s

Our second test involves examining the relation between initial returns and firm borrowing using a series of proxies to control for ex ante uncertainty. We constructed three dummy variables to indicate whether the firm had a borrowing relationship at the time of the offering. These dummy variables are defined as follows:

BankD = 1 if the firm has a bank-loan or bank-credit agreement outstand- ing, 0 otherwise.

LTdebtD = 1 if the firm has long-term debt outstanding other than bank debt, 0 otherwise.

DebtD = 1 if LTdebtD or BankD equals 1, 0 otherwise.

We use dummy variables for several reasons. First, our model predicts that the existence of a borrowing relationship and not the amount of borrowing provides a signal of firm type. Second, we expect that the amount of borrowing needed to separate firms by type varies across industries because of differences in ex ante uncertainty and differences in expected values across industries. We also examine the relation between underpricing and the amount of borrowing, since firms with more borrowing may have more tangible assets and less ex ante uncertainty.

Our tests use linear regression analysis. Since prior studies use other measures of uncertainty, we also include the following independent variables:

1. Rank of the underwriter (Rank): This is a measure of underwriter prestige obtained from Carter and Manaster (1990). Rankings range from 0 (least prestigious) to 9 (most prestigious). Carter and Manaster argue that prestigious underwriters are associated with offerings with low disper- sion in firm value. Their model predicts a negative relation between the initial return and underwriter rank.

2. Age of the firm (Age): This is the number of years since incorporation. Ritter (1989) argues that the age of the firms may proxy for the degree of ex ante uncertainty concerning the value of the firm. Ritter (1989) and Muscarella and Vetsuypens (1988) present evidence consistent with his argument.

3. Offering size (Offer Size): This is the initial offer price times the number of shares issued measured in millions of dollars. Barry and Brown (1984) suggest a positive relation between firm-specific information in the equity market and firm size.

4. Shares offered by insiders (Insider): This is the ratio of shares sold by owners of the firm (secondary shares offered) to total shares issued. Grinblatt and Hwang (1989) present a model which predicts that, given the variance in firm values, the initial return is directly related to the level of insider participation.

Page 15: Borrowing relationships, intermediation, and the cost of issuing public securities

C. James and P. Wier, Borrowing relationships and the cost of IPOS 163

Three regressions are reported in table 2. The standard errors and the t-statistics are computed using the procedure described in White (1980) to obtain consistent estimates of the variance-covariance matrix in the presence of heteroskedasticity. In the first regression we do not distinguish between bank borrowing and long-term debt. This specification assumes either that the long-term borrowing is also bank lending, but is not identified as such in the prospectus, or that the signal provided by borrowing does not depend on the identity of the lender. The results in row 1 of table 2 indicate a negative and statistically significant relation between the initial return and a dummy variable denoting borrowing, consistent with the predictions of our model. The estimated coefficient on DebtD indicates that, other things equal, the mean initial return for firms with borrowing relationships is 25 percent- age points lower than the mean return for firms without (t = 5.2).

Consistent with Muscarella and Vetsuypens (1988) and Ritter (19891, we find a negative relation between the initial return and the age of the corporation. However, unlike Carter and Manaster we find no significant relation between the initial return and the rank of the underwriter. One reason may be that our time period differs slightly from Carter and Manaster’s. Also, we exclude financial firms and include ‘penny stock’ offers where the offer price is less than a dollar. Finally, the rank of the undewriter may be highly correlated with other observable measures of ex ante uncer- tainty so that the identity of the underwriter provides no additional basis for sorting firm types according to uncertainty. When we regress underwriter rank on the other independent variables in table 2, the regression explains over 30% of the variability in rank of the underwriter.

Contrary to the prediction of Grinblatt and Hwang (1989), we fail to find any significant relation between underpricing and the proportion of insider shares sold.

In the second row of table 2, we estimate a regression in which bank loans are distinguished from other types of debt. Like Slovin and Young we find a negative relation between the initial return and the presence of bank debt (denoted by BankD). However, we also find a negative relation between the initial return and the existence of long-term debt. Moreover, we cannot reject the hypothesis that the effects of long-term debt and bank loans on iniital returns are the same (the t-statistic associated with the difference in regres- sion coefficients is 0.48). Our evidence does not support the hypothesis that bank loans play a unique role in reducing information costs for IPOs.

The last two rows of table 2 provide estimates of an underpricing model with no measure of borrowing history. Notice that the explanatory power of the model drops substantially. An F-test rejects at the 0.01 level the null hypothesis that borrowing history is an irrelevant variable (or that it adds no explanatory power other than through being correlated with the other mea- sures of ex ante uncertainty).

Page 16: Borrowing relationships, intermediation, and the cost of issuing public securities

Tab

le 2

Est

imat

es

of t

he r

elat

ion

betw

een

initi

al r

etur

ns

on I

POs,

iss

uer

borr

owin

g,

and

othe

r m

easu

res

of e

x an

te

unce

rtai

nty

conc

erni

ng

mar

ket

valu

e fo

r a

sam

ple

of 5

48 I

POs

in 1

980-

1983

(t-

stat

istic

s [h

eter

oske

dast

icity

co

rrec

ted]

ar

e in

par

enth

eses

).

Inte

rcep

t B

ankD

b L

tDeb

tDc

Deb

tDd

Ran

ke

Age

’ In

side

r 8

Off

er s

ize h

A

dj.

R2

F

(1)

50.4

37

- 0.

251

- 0.

004

- 0.

036

- 0.

040

- 3.

35E

-I

0.11

10

.63

(9.2

7)

(-5.

28)

(-

0.65

) (-

2.

45)

(-0.

61)

( - 0

.39)

(2)

0.38

1 -

0.08

5 -0

.114

-

0.00

5 -

0.03

9 -

0.02

4 -

5.07

E-7

0.

08

7.20

(8

.80)

(-

2.

21)

( - 2

.94)

(-

0.93

) (-

2.

62)

(-

0.36

) (-

0.59

)

(3)

0.27

3 -

0.01

0 -

0.05

3 -

0.01

6 -

5.31

E-7

0.

04

5.84

(7

.49)

(-

1.

68)

(-3.

67)

( - 0

.249

) (-

0.68

)

aThe

dep

ende

nt

vari

able

is

the

ini

tial

retu

rn

defi

ned

as t

he d

iffe

renc

e be

twee

n th

e of

fer

pric

e an

d th

e pr

ice

in t

he s

econ

dary

m

arke

t at

the

end

of

the

offe

r m

onth

di

vide

d by

the

off

er p

rice

. A

n in

itial

ret

urn

of 1

3 pe

rcen

t is

mea

sure

d as

0.1

3.

bBan

kD

is e

qual

to

1 if

the

is

suin

g fi

rm h

as b

ank

loan

s ou

tsta

ndin

g or

has

a b

ank-

cred

it ag

reem

ent,

0 ot

henv

ise.

‘L

tDeb

tD

equa

ls

1 if

the

fir

m h

as l

ong-

term

de

bt

outs

tand

ing

at t

he t

ime

of t

he o

ffer

ing,

0

othe

rwis

e.

dDeb

tD e

qual

s 1

if L

tdeb

tD

or B

ankD

eq

uals

1,

0 o

ther

wis

e.

eRan

k is

the

ran

k of

the

und

erw

rite

r w

hich

is

a di

scre

te

vari

able

th

at r

ange

s fr

om 9

to

0, w

here

9

is t

he h

ighe

st

pres

tige

unde

rwri

ter

grou

p. R

anks

ar

e fr

om C

arte

r an

d M

anas

ter

(199

0).

fAge

is

the

natu

ral

log

of t

he

num

ber

of y

ears

si

nce

the

foun

ding

of

the

is

suin

g fi

rm.

For

firm

s w

ith

age

less

th

an

1 ye

ar,

age

is m

easu

red

in

frac

tions

of

a y

ear.

gl

nsid

er

is t

he f

ract

ion

of t

otal

sha

res

issu

ed t

hat

wer

e he

ld b

y in

side

sh

areh

olde

rs

prio

r to

the

off

erin

g.

hOfi

r si

ze i

s th

e gr

oss

proc

eeds

fr

om t

he o

ffer

ing

in t

hous

ands

of

dol

lars

.

Page 17: Borrowing relationships, intermediation, and the cost of issuing public securities

C. James and P. Wier, Borrowing relationships and the cost of IPO’s 16.5

In the preceding empirical analysis we use a binary variable to test the effect of a borrowing relationship on underpricing. If underpricing is related to some unobservable firm characteristic that is in turn related to the cost of borrowing, we would observe a relation between initial returns and the amount of debt relative to the assets of the firm or the offer proceeds. To test whether the level of borrowing also affects the initial return we calculated the ratio of debt to total assets prior to the offering and the ratio of debt to total offer proceeds. We then estimated the relation between the initial return and other measures of RY ante uncertainty. These results (not reported here) reveal no statistically significant relation between the level of underpricing and the amount of borrowing.

Finally, the markup over prime or LIBOR is often reported in the prospectus of the issuing firm. To determine whether the initial return is related to the risk of the debt issued we estimated the relation between the degree of underpricing and the markup on the firm’s bank loans. We find no significant relation between underpricing and the terms of bank borrowing.

The third test involves examining the difference between the effect on underpricing of actual borrowing and agreements to borrow. We include a dummy variable, CreditD, in our regression analysis that takes on the value of 1 if the firm has a credit agreement with no borrowing (except possibly from original shareholders) and 0 otherwise. The results are presented in part A of table 3. We find a significant negative relation between underpricing and the existence of a credit commitment. Moreover, we cannot reject at the 0.10 level the hypothesis that the effect of a credit commitment on underpricing is the same as actual borrowing.

In part B of table 3 we provide the pairwise correlations between the initial return and firm characteristics as well as the correlations between pairs of independent variables. The independent variables (including the debt dummy) used to measure ex ante uncertainty are positively correlated. We would expect this result if borrowing sorts firms on the basis of the degree of ex ante uncertainty. Notice, however, that the initial return is more highly correlated with borrowing history than with the other measures of uncertainty. More- over, as reported in table 2, the explanatory power of the underpricing model is significantly lower when we exclude the borrowing history dummy.

One possible explanation for the lower underpricing for firms with borrow- ing relationships is that the cost of borrowing is related to asset characteris- tics that affect the degree of underpricing. This explanation is consistent with our model as long as it is borrowing and not asset characteristics that determines the degree of underpricing. We cannot distinguish empirically between borrowing or asset characteristics as the explanatory variable, but we can examine the data a bit further for additional evidence.

A firm that chooses not to borrow before going public may do so either to avoid the negative effects a rejection would have on the offer proceeds or to

Page 18: Borrowing relationships, intermediation, and the cost of issuing public securities

Tab

le

3

Part

A

: R

egre

ssio

n re

latin

g in

itial

re

turn

a to

fi

rm

char

acte

rist

ics

and

loan

co

mm

itmen

ts

for

a sa

mpl

e of

54

9 IP

Os

in

1980

-198

3 (t

-sta

tistic

s [h

eter

oske

dast

icity

co

rrec

ted]

ar

e in

par

enth

eses

)

Inte

rcep

t C

redi

tD h

B

orro

wD

C

Ran

kd

Age

e In

side

r *

OfS

er s

izeg

R

2 F

0.43

7 -

0.20

7 -

0.25

4 -

0.00

5 -

0.03

3 -

0.03

6 -

3.23

E-0

7 0.

10

8.91

(9

.32)

(

- 2.

33)

(-5.

36)

(-

0.79

) (-

2.31

) (-

0.

55)

(0.3

85)

Part

B

: C

orre

latio

ns

amon

g in

itial

re

turn

s an

d fi

rm

char

acte

rist

ics

Initi

al

retu

rn

Deb

tD

Ran

k A

ge

Insi

der

Off

er s

ize

Initi

al

retu

rn

1.00

0 D

ebtD

-

0.28

3 1.

000

Ran

k -

0.12

4 0.

225

1 .o

oo

Age

-0

.135

0.

277

0.20

0 1.

000

Insi

der

- 0.

091

0.07

8 0.

315

0.26

3 1.

000

Off

er s

ize

- 0.

063

0.11

3 0.

366

0.04

7 0.

233

1.00

0

aThe

de

pend

ent

vari

able

is

the

in

iital

re

turn

de

fine

d as

the

di

ffer

ence

be

twee

n th

e of

fer

pric

e an

d th

e pr

ice

in t

he

seco

ndar

y m

arke

t at

th

e en

d of

th

e of

fer

mon

th

divi

ded

by

the

offe

r pr

ice.

A

n in

itial

re

turn

of

13

per

cent

is

mea

sure

d as

0.

13.

‘Cre

ditD

=

1 i

f th

e fi

rm

has

an

unus

ed

cred

it lin

e an

d no

ot

her

debt

, 0

othe

rwis

e.

‘Bor

row

D

= 1

if

the

fum

ha

s lo

ng-t

erm

de

bt

or

bank

lo

ans

outs

tand

ing,

0

othe

rwis

e.

dRan

k is

the

ra

nk

of t

he

unde

rwri

ter

whi

ch

is a

dis

cret

e va

riab

le

that

ra

nges

fr

om

9 to

0.

Ran

ks

are

from

C

arte

r an

d M

anas

ter

(199

0).

eAge

is

the

natu

ral

log

of

the

num

ber

of y

ears

si

nce

the

foun

ding

of

th

e is

suin

g fi

rm.

‘hid

er

is t

he

frac

tion

of

tota

l sh

ares

is

sued

th

at

wer

e he

ld

by i

nsid

e sh

areh

olde

rs

prio

r to

th

e of

feri

ng.

gOfi

r si

ze

is t

he

gros

s pr

ocee

ds

from

th

e of

feri

ng

in t

hous

ands

of

do

llars

.

Page 19: Borrowing relationships, intermediation, and the cost of issuing public securities

C. James and P. Wier, Borrowing relationships and the cost of IPO’s 167

avoid high costs of borrowing. If the former explanation is correct, there is no reason to expect continued reliance on equity financing by the 94 nonborrow- ing firms after the IPO, because a market value has already been established. We examine the capital structure of these 94 firms at year-end following the IPO, using information from Moody’s manuals. In fact, only 13 of these 94 firms reported bank loans or long-term debt outstanding, suggesting that borrowing is costly. Therefore it appears that firms without credit relation- ships at the time of their IPO continue to rely primarily on equity financing. Of course, firms may not need additional external financing immediately following their IPO and therefore maintain their existing capital structure.

We also use a logit model to explore the relation between borrowing history and firm characteristics that may be associated with both the degree of underpricing and the cost of borrowing. The firm characteristics are: (1) the age of the company, (2) the ratio of plant and equipment to total assets, and (3) the sales of the company in the 12 months prior to the IPO.

We expect that firms with longer operating histories, higher levels of sales, and higher ratios of plant and equipment to total assets are more likely to have credit relationships at the time of their offering, either because it is easier for lenders to estimate their values or because these variables measure assets in place. The results are

DebtD = 0.99 + O.lOAge + 0.080Plant + 2.47E-OSales, (4.22) (3.18) (0.22) (2.50)

with asymptotic t-statistics in parentheses, log likelihood = - 168.54, and where

DebtD = 1 when there is a borrowing relationship, 0 otherwise, Age, = natural log of the age of the firm.

These results together with those reported in part B of table 3 are consistent with the hypothesis that debt is associated with firm characteristics that may affect the cost of borrowing (e.g., age and sales). However, if we include sales and plant and equipment directly in the underpricing regres- sion, they are insignificant both when borrowing history is included in the regression and when it is excluded; although when included, borrowing history continues to be significant. Therefore, while we cannot rule out the possibility that borrowing proxies for some asset characteristic related to underpricing, the characteristics we examine - age, sales, or asset composi- tion - do not explain underpricing.

We also examine whether firms that borrow before going public are concentrated in industries where there is less ex ante uncertainty concerning firm value. Ritter’s (1984, 1989) evidence that the degree of underpricing varies across industries raises this possibility. To determine whether the

Page 20: Borrowing relationships, intermediation, and the cost of issuing public securities

Tab

le 4

Mea

n ag

e, s

ales

, an

d pe

rcen

t of

fir

ms

with

ban

k lo

ans

and

debt

fo

r a

sam

ple

of 5

49 i

nitia

l pu

blic

off

ers

of e

quai

ty

in 1

980-

1983

, ca

tego

rize

d by

in

dust

ry.

Indu

stry

SI

C

Initi

al

cqde

s re

turn

a

Initi

al r

etur

n fo

r fi

rms

with

bor

row

ing

Num

ber

of

Ann

ual

offe

rs

sale

sb

Ass

etsC

A

ge o

f fi

rmd

% w

ith

% w

ith

bank

an

y lo

ans

debt

e

Com

pute

r M

anuf

actu

ring

C

omm

unic

atio

ns/

Ele

ctro

nics

O

il an

d G

as

351

17%

11

%

68

17.2

9 12

.78

5.35

86

%

12%

8%

58

12

.02

10.3

5 8.

90

76%

20

%

2%

39

32.1

1 19

.92

7.00

77

%

91%

366,

361

131,

138

, 29

1,67

9

82%

79

%

137

87%

381-

384 58

1 80

5-80

9

88%

10

0%

93%

Com

pute

r/D

ata

Proc

essi

ng

Serv

ices

9%

6%

39

18

.29

11.9

3 8.

25

74%

O

ptic

al,

Med

ical

, Sc

ient

ific

Ins

trum

ents

18

%

18%

40

6.

84

5.98

6.

85

75%

R

esta

uran

t C

hain

s 16

%

16%

18

26

.11

13.7

1 6.

61

77%

H

ealth

C

are

HM

O’s

6%

6%

1.

5 56

.65

28.4

1 5.

33

87%

D

rugs

/Gen

etic

E

ngin

eeri

ng

16%

6%

21

4.

57

6.84

4.

41

68%

M

isce

llane

ous

Bus

ines

ses

3%

0%

13

13.5

7 8.

46

5.39

61

%

All

Oth

er

9%

6%

309

46.5

7 27

.09

10.8

9 74

%

All

Firm

s 13

%

9%

549

33.1

0 20

.11

8.94

76

%

aIni

tial

retu

rn

is d

efin

ed

as t

he d

iffe

renc

e be

twee

n th

e of

fer

pric

e an

d th

e pr

ice

in t

he s

econ

dary

m

arke

t at

the

end

of

the

offe

r m

onth

di

vide

d by

th

e of

fer

pric

e.

bAnn

ual

sale

s ar

e fr

om t

he o

ffer

pro

spec

tus

and

is m

easu

red

in m

illio

ns o

f do

llars

. ‘A

sset

s ar

e th

e pr

e-of

fer

asse

ts o

f th

e fi

rm i

n m

illio

ns o

f do

llars

as

rep

orte

d in

the

off

erin

g pr

ospe

ctus

. dA

ge o

f th

e fi

rm i

s th

e nu

mbe

r of

yea

rs s

ince

inc

orpo

ratio

n (f

rom

off

erin

g pr

ospe

ctus

).

eAny

deb

t m

eans

ban

k lo

ans

or c

redi

t lin

es a

nd l

ong-

term

de

bt

(fro

m t

he p

rosp

ectu

s).

283

139

- -

82%

76

%

89%

88

%

Page 21: Borrowing relationships, intermediation, and the cost of issuing public securities

C. James and P. Wier, Borrowing relationships and the cost of PO’s 169

likelihood of a borrowing relationship is higher for certain industries and whether industry differences, rather than borrowing, account for differences in the initial returns, we calculated the proportion of firms with borrowing relationships by industry group. This information is reported in table 4. The proportion with borrowing relations ranges from 100% for restaurant chains to 76% for miscellaneous businesses. For most of the industry groups the percentage of firms with external debt is 80 to 90%. We find no pattern in the industry classifications to indicate that the lower initial returns for firms with debt outstanding result from a concentration of borrowing firms in a particu- lar set of industries.

Finally, we examine the relation between the degree of underpricing and use of the IPO proceeds. We find no significant relation between initial returns and a dummy variable that equals 1 if the proceeds are used to repay debt.

5. Conclusion

In this paper we present a model in which establishing a borrowing relationship prior to offering stock publicly can reduce investors’ uncertainty about the market value of the issuing firm and therefore can increase IPO proceeds. The model also shows why some firms choose to issue securities without having established a borrowing relationship.

We find that the IPOs of firms that have credit relationships with private lenders are less severely underpriced on average than firms without borrow- ing relationships. This result is consistent with the predictions of our model. However, we cannot rule out the possibility that the existence of a borrowing relationship is related to some other unobserved characteristic of the firm and that it is this characteristic that actually affects underpricing.

Appendix

We wish to show that a level of borrowing can be found such that OP, > OPLp, implying that L firms will not apply for loans. We show that the existence of a separating equilibrium will depend on the degree of underpric- ing. Let

0PI.R = offer proceeds for L firms whose loan application is rejected,

OP, = offer proceeds for H firms,

OPr_ = offer proceeds for L firms when no L firms borrow,

OPr_, = expected offer proceeds for L firms that apply for loans, F,(D) = probability that the true value of an L firm s less than D.

Page 22: Borrowing relationships, intermediation, and the cost of issuing public securities

170 C. James and P. Wier, Borrowing relationships and fhe cost of IPO’S

From the text,

OP,p=F,(D)OPL, + [l +QD)]OPH.

Separation requires:

or

OP, - OP,, > 0

OP,-(F,(D)OP,- [l -FL(D)]OPH} >o. (A-1)

Define pi as the expected value of firm type i and UPi as the dollar amount that type i firms are underpriced relative to their expected value. The offer proceeds for type i firms will be

pi - UPi. (A.2)

Substituting (2) into (1) and simplifying yields

The left-hand side of (3) is the difference between the expected value of L firms when they do not borrow and their expected value when they apply for loans multiplied by the probability that firm value is less than D. Separation requires that the difference in expected values [the left-hand side of (3)l exceed the difference in underpricing for L firms with no borrowing and with L firms applying for loans [the right-hand side of (3)I.

With no underpricing (3) will hold since the expected value of all L firms (pr) exceeds the expected value of L firms that are rejected (pLR).

To determine whether (3) holds with underpricing, consider the maximum degree of underpricing for L firms, L firms that are rejected, and H firms. These maximums are p., - aL, pr,, - a,_, and pCLH - au, respectively. Define l/m as the degree of underpricing relative to the maximum. Substituting the the actual underpricing relative to the theoretical maximum [(l/rn>(~~ - ai> into expression (3) and simplifying yields

~L(D)IPr_-PI,Rl( m - 1) > [I -&(D)](+r-UL), (A.37

since or - pLR = (b, - D)/2, and

J’,(D) =(D-ad/(&a-a.).

Page 23: Borrowing relationships, intermediation, and the cost of issuing public securities

C. James and l? Wier, Borrowing relationships and the cost of E’OS 171

(A.37 simplifies to

2

l>(;zyj (m-l)’ (A.3”)

Since D > aH, a sufficient condition for separation is m 2 3 (i.e., underpric- ing is less than or equal to one third the maximum).

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