6 Concluding Remarks

This paper develops a simple control theory of financial structure which generates a com-prehensive financial structure consisting of short-term senior debt, long-term covenanted debt, and equity with voting rights. As is well known from Modigliani and Miller (1958), the choice of financial structure, and therefore the design of securities, is irrelevant in fric-tionless markets. Security design is relevant in the present model because information, though costlessly observable to all, is non-verifiable and therefore cannot be contracted upon directly and because the presence of non-assignable entrepreneurial control rents create a non-alignment between the interests of the manager-entrepreneur and the in-terests of the firm's security holders. The contribution of the paper is to show that the financial structure needed to optimally allocate control rights and cash flow rights in this setting closely resembles the type of comprehensive financial structures observed in practice.

Appendix Proof of Proposition 1

(i) X E [12,XL). Then E(x+w) =X

<

Ds so that if choosing continuation the founder will be unable to raise enough cash to satisfy date O short-term lenders. Date O short term lenders will therefore take control, liquidate the firm and receive min(Ds, l) = Ds =XL.

(ii) X E [XL, XE]. In this case we must show (a) that the firm is able to raise enough cash to satisfy date O short-term lenders, (b) that expansion will not be profitable, and (c) that shareholders will refrain from forcing the firm to be liquidated (which is profitable for the firm's security holders for all X E (XL, l).

Condition (a) follows since the new claimis senior to existing claims and since E(x+w)

=

X > Ds

=

^{XL for all X E [XL, XE].}

Consider then condition (b). The date 1 value of equity under expansion is given by

E{max[J(x)

+

w - Dl - Dsl,

on ⁼

^{O. (1)}

Insert the expression for Dl = J(XE)

+

^{W -} Dsl into (1) to find that the date 1 equity value is

E{max[(J(x) - J(XE))

+

(w - w),

On,

which, since J(x) ~ J(XE) and w ~ w, is zero for all X E [XL, XE]

Consider finally condition (c). The face value Dl oflong-term debt is determined so that

J(XE) = Vz(J(XE), Dl (J(XE)))

+

Ds, (2)

where Vz(·,·) is the date 1 value of a long-term debt claim with face value Dl(·). Ds is similarly the date 1 value of a debt claim issued on date 1 with face value Dsl due on . date 2.

Let Ve(l) denote the cash received by shareholders if the firm is liquidated on date 1. We want to prove that Ve(l) =

o.

Suppose to the contrary that Ve(l) >

o.

^{Ifthe firm}

is liquidated, its liquidation proceeds l will be distributed to claimholders according to stated priority rules. By the assumption that Ve(l) > O, this implies that long-term lenders receive Dl and that short-term lenders receive Ds. Ve(l) is therefore the residual

value determined from

(3) The assumption that Ve(l) > Oimplies now that

or that

which, by the fact that Vi(·;·) < Dl, implies that l > J(XE), which, by the assumption that Xc is non-empty (i.e. XE > XL), must be incorrect. This implies that a contra-diction has been obtained and therefore that the initial assumption that Ve(l) > O was

wrong. We may therefore conclude that Ve(l) = O. O

Proof of Lemma 1

The result that Ds is decreasing in Q is seen directly from Ds

=

^XL

=

^{l - Q/a.}

The result that Dl is increasing in Q can be seen from the expression Dl = J(XE)

+

W - Ds1(J(XT)) and the first order condition J(XE) = XE

+

Q/a; a larger value of Q leads to a larger value ofXE (since J'(x) > 1), which leads to a greater J(XE), a lower Ds1(J(XE)) and thus higher Ds1(·).

To see that D = Ds

+

^Dl is increasing in Q, we note that D = l- Q/a

+

^J(XT)

+

w-Dsl(J(XT )). Taking the total derivative of D with respect to Q yields:

~~ =

^-l/a

+

J'(xT)[l - D~l(J(XT))]~~

=

^-l/a

+

J'(xT)[l- D~l(J(XT))]a[J'(x~) -1]

so that

~g

^{> Oif}

which is the fact since D~l (J(XE)) <

o.

o

Proof of Lemma 2 The proof of Lemma 2 follows the proof of Lemma 1 with the

exception that a takes the place of Q.

o

Proof of Lemma 3

The fact that Ds is increasing in l is seen directly from Ds =XL = l - Q. To see that Dl =J(XE)

+

^{W -} DsI(J(XE)) recall first that DsI(i(x)) is determined by

l

^DS1-i(X)

ie. (i(x)

+

w)g(w)dw

+

DsI(l - G(Dsl - i(x)))

=

^Ds

=

^{l -} Q/a,

from which it can be observed that a larger value of lleads to a larger value ofDsI. The larger Dsl can in turn be seen from Dl

=

^J(XE)

+

^{W -} DsI(J(XE)) to decrease Dl'

Finally, to see that D

=

^Dl

+

Ds is decreasing in l, differentiate D with respect to l:

dD = 1 _ dDsl = 1- 1 < O.

dl dl 1- G(Dsl - J(XE))

o

References

Aghion, P. and P. Bolton, 1992, "An Incomplete Contracts Approach to Bankruptcy and the Financial Structure of the Firm, Review of Economic Studies 59, 473 - 494.

Berglof, E., 1994, "A Control Theory of Venture Capital Finance," Journal of Law, Economics, f3 Organization 10, 247 - 267.

Berkovitch, E. and R. Israel, 1996, "The Design of Internal Control and Capital Struc-ture,"

.

Review of Financial Studies 9, 209 - 240.

Dewatripont, M. and J. Tirole, 1994, "A Theory of Debt and Equity: Diversity of Securities and Manager-Shareholder Congruence," Quarterly Journal of Economics, 1027 - 1054.

Diamond, D., 1993, "Seniority and Maturity of Debt Contracts," Journal of Financial Economics 33, 341 - 368.

Grossman, S. and O. Hart, 1986, "The Cost and Benefit of Ownership: A Theory of Vertical and Lateral Integration," Journal of Political Economy 94, 691 - 719.

Harris, M. and A. Raviv, 1990, "Capital Structure and the Informational Role of Debt,"

Journal of Finance 45, 321 - 350.

-, 1991, "The Theory of Captial Structure," Journal of Finance 46, 297 - 355.

Hart, O. and J. Moore, 1989, "Default and Renegotiation: A Dynamic Model of Debt,"

Working paper, Dept. of Economics, MIT.

-, 1995, "Debt and Seniority: An Analysis of the Role of Hard Claims in Constraining Management," American Economic Review 86, 567 - 585.

Israel, R., 1991, "Capital Structure and the Market for Corporate Control: The Defensive Role of Debt Financing," Journal of Finance 46, 1391 - 1409.

Modigliani, F. and M. Miller, 1958, "The Cost of Capital, Corporation Finance, and the Theory of Investment," American Economic Review 48,267 - 297.

Myers, S., 1977, "Determinants of Corporate Borrowing," Journal of Financial Eco-nomics 5, 147 - 175.

Stohs, M. S., and D. C. Mauer, 1996, "The Determinants of Corporate Debt Maturity Structure," Journal of Business, 69, 279 - 312.

Williamson, 0., 1988, "Corporate Finance and Corporate Governance," Journal of Fi-nance 43, 567 - 59l.

Zwiebel, J., 1996, "Dynamic Capital Structure under Managerial Entrenchment," Amer-ican Economic Review 86, 1197 - 1215.

CHAPTER 2

Costly State Verification: Outside Equity

In document Essays in corporate finance (sider 36-42)