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Financing investment with external funds Moyen, Nathalie 1999

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Financing Investment with External Funds by  Nathalie Moyen  B . S c . ( E c o n o m i e ) , U n i v e r s i t e de M o n c t o n M . A . ( E c o n o m i c s ) , Q u e e n ' s U n i v e r s i t y at K i n g s t o n  A thesis s u b m i t t e d i n p a r t i a l fulfillment of the requirements for the degree o f  D o c t o r of P h i l o s o p h y  in  the F a c u l t y of G r a d u a t e Studies the F a c u l t y of C o m m e r c e a n d B u s i n e s s A d m i n i s t r a t i o n  W e accept this thesis as c o n f o r m i n g to the required s t a n d a r d  T h e U n i v e r s i t y of B r i t i s h C o l u m b i a J u n e 1999 © N a t h a l i e M o y e n , 1999  In presenting this thesis i n p a r t i a l fulfillment of the requirements for an advanced degree at the U n i v e r s i t y of B r i t i s h C o l u m b i a , I agree that the L i b r a r y shall make it freely available for reference a n d study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his representatives. It is understood that copying or p u b l i c a t i o n of this thesis for financial gain shall not be allowed w i t h o u t my w r i t t e n permission.  Faculty of Business A d m i n i s t r a t i o n T h e U n i v e r s i t y of B r i t i s h C o l u m b i a Vancouver, C a n a d a  Abstract  This thesis presents various dynamic models of corporate decisions to address two main issues: investment distortions caused by debt financing and cash flow sensitivities. In the first chapter, four measures of investment distortion are computed. First, the effect of financing frictions is examined. The tax benefit of debt induces firms to increase their debt capacity and to invest beyond the first-best level on average. The cost of this investment distortion outweighs the tax benefit of debt. Second, Myers's (1977) debt overhang problem is examined in a dynamic framework. Debt overhang obtains on average, but not in low technology states. Third, there is no debt overhang problem in all technology states when debt is optimally put in place prior to the investment decision. Finally, the cost of choosing investment after the debt policy is examined. Equity claimants lose value by choosing to invest after their debt is optimally put in place because they do not consider the interaction between their investment choice and the debt financing conditions. The second chapter explores the impact of financial constraints on firms' cash flow sensitivities. In contrast to Fazzari, Hubbard, and Petersen (1988), cash flow sensitivities are found to be larger, rather than smaller, for unconstrained firms than for constrained firms. Then, why is investment sensitive to cash flow? In the two models examined in the second chapter, the underlying source of investment opportunities is highly correlated with cash flows. Investment may be sensitive to cash flow fluctuations simply because cash flows proxy for investment opportunities. This leaves two important questions. Can this chapter suggest a better measure of investment opportunities than Tobin's Q? Not a single measure for both the unconstrained and constrained firm models. Can this chapter suggest an easily observable measure of financial constraint? Yes: large and volatile dividend-to-income ratios.  ii  Table of Contents  Abstract  ii  L i s t of Tables  iv  L i s t of Figures  v  Acknowledgements  vi  1 Introduction  1  2 Investment D i s t o r t i o n s Caused by D e b t F i n a n c i n g  7  2.1 T h e M o d e l 2.2 D e s c r i p t i o n of S i m u l a t e d Series 2.3 Investment D i s t o r t i o n 2.3.1 D i s t o r t i o n Caused by F i n a n c i n g Frictions 2.3.2 D e b t O v e r h a n g 2.3.3 Debt O v e r h a n g w i t h O p t i m a l D e b t 2.3.4 D i s t o r t i o n Caused by Sequential Decisions 2.4 C o n c l u d i n g C o m m e n t s on Investment D i s t o r t i o n s  7 12 16 16 18 19 21 22  3 W h y is Investment Sensitive to C a s h F l o w ?  23  3.1 U n c o n s t r a i n e d F i r m s  24  3.2 C o n s t r a i n e d F i r m s 3.3 Results 3.4 C o n c l u d i n g C o m m e n t s on C a s h F l o w Sensitivities  29 29 32  References  33  4 Appendix  38  4.1 Effects of the F i r m ' s Decisions o n the F a i r - B o n d - P r i c i n g E q u a t i o n . . 38 4.2 D a t a a n d C a l i b r a t i o n  39  4.3 N u m e r i c a l M e t h o d  42  4.4 S i m u l a t i o n  43  iii  L i s t o f Tables 1 Calibration of the Revenues Function  44  2 Descriptive Statistics from the Compustat Sample  45  3 Descriptive Statistics Simulated from the Model  46  4 Investment Distortion Caused by Financing Frictions  47  5 Debt Overhang  48  6 Debt Overhang with Optimal Debt  49  7 Investment Distortion Caused by Sequential Decisions  50  8 Cash Flow Sensitivity Results of Fazzari, Hubbard, and Petersen (1988) 51 9 Cash Flow Sensitivities of Unconstrained Firms  52  10 Cash Flow Sensitivities of Constrained Firms  53  11 Main Results of the Cash Flow Sensitivity Literature  54  iv  List of Figures 1 P o l i c y Functions  55  2 M i n i m u m Beginning-of-the-Period Funds  56  3 Sensitivity A n a l y s i s  57  4 Investment D i s t o r t i o n C a u s e d by F i n a n c i n g Frictions  60  5 Debt O v e r h a n g  61  6 Debt Overhang w i t h O p t i m a l Debt  62  7 Investment D i s t o r t i o n C a u s e d by Sequential Decisions  63  8 P o l i c y Functions of U n c o n s t r a i n e d F i r m s  64  9 P o l i c y Functions of C o n s t r a i n e d F i r m s  65  v  Acknowledgements Wow! It's been a long road. I a m most grateful to m y travelling c o m p a n i o n , M a r t i n B o i l e a u . After three years of meeting each other, M a r t i n chose to follow me across the country o n a S S H R C post-doctoral fellowship for the first two years of my P h . D . program. He offered me his love a n d support, most of the closet space, a n d too many meaty dishes. H o w could I have done it w i t h o u t you? U p o n a r r i v i n g i n Vancouver, K h a n g M i n Lee and J i m Storey i m m e d i a t e l y included me i n their study group and their lives. T h e y are great friends and challenging colleagues: K h a n g M i n is perfect (even her c o m p u t a t i o n a l errors canceled out) and J i m understands the big picture. B u t w i t h o u t me, who w o u l d have reminded t h e m of the various statistical formulas? I a m also lucky to have met B r y a n Routledge, M u r r a y C a r l s o n , L i s a K r a m e r (great to see you alive and well), D a v i d Peterson, P a t r i c k Savaria, M a r y K e l l y , Joshua Slive, Lorenzo G a r l a p p i , and Y i n g h u L i u i n the program. R o b Heinkel and B u r t o n Hollifield have been wonderful thesis supervisors, always encouraging and c r i t i c a l . I a m inspired by your d e d i c a t i o n a n d constructive outlook. I also w i s h to thank G l e n D o n a l d s o n , G e r r y Garvey, R o n G i a m m a r i n o , Margaret Slade, R a m a n U p p a l a n d T a n W a n g for their support. I a m grateful to seminar participants at A S U , U B C , C M U , C U B o u l d e r , C o l u m b i a , M a r y l a n d , M c G i l l , Northwestern, P e n n State, Queen's, Toronto, U t a h , W a t e r l o o , Y o r k , a n d at the 1998 W F A meetings. I a m especially indebted to R i c k Green, Charles H i m m e l b e r g , M i c h a e l L e m m o n , D e b o r a h Lucas, Vojislav M a k s i m o v i c , and T o n y S m i t h for helpful discussions. F i n a n c i a l support from the U n i v e r s i t y of B r i t i s h C o l u m b i a G r a d u a t e Fellowship, the Social Sciences and H u m a n i t i e s Research C o u n c i l of C a n a d a , and the Fonds pour l a F o r m a t i o n de Chercheurs et l ' A i d e a l a Recherche is gratefully acknowledged. F i n a l l y , I thank m y family for accepting a n d encouraging m y academic pursuit i n a foreign land: Popsy, M o m s y , J u j u , et Pet, je vous aime beaucoup. For the same reason, I thank the B o i l e a u family.  vi  1  Introduction  T h e first chapter examines firms' investment decisions i n a d y n a m i c stochastic framework w i t h an interest tax deduction benefit a n d a deadweight default cost of debt financing. It begins by investigating the model's i m p l i cations regarding the cross-sectional and time-series properties of financial series, i n c l u d i n g investments, debt issues, revenues, d i v i d e n d s , equity returns, a n d interest rates. T h e series simulated from the m o d e l show that firms adjust their asset and debt levels to avoid default t h r o u g h time. A firm choosing a higher debt level today might not be able to repay debt claimants tomorrow, unless the firm also invests more today i n order to generate higher revenues tomorrow. Investments are thus h i g h l y correlated w i t h debt issues, consistent w i t h the observed series. G i v e n that the m o d e l compares well w i t h the data, investment distortions caused by the presence of debt i n a firm's c a p i t a l structure are measured. T h e firm's investment p o l i c y i n the benchmark m o d e l is compared to policies derived i n different economic environments. I n t u r n , the benchm a r k investment p o l i c y is compared w i t h the first-best p o l i c y derived from a M o d i g l i a n i a n d M i l l e r (1958) framework of no financing friction, w i t h the p o l i c y derived from a M y e r s (1977) framework where the levered firm m a x i mizes its equity value given the c a p i t a l structure already i n place, and w i t h the p o l i c y derived from a modified-Myers framework where the debt i n place is o p t i m a l l y chosen. Four conclusions o b t a i n from this c o m p a r i s o n of investment policies. F i r s t , financing frictions induce the firm to increase its debt capacity a n d to invest beyond the first-best level o n average. T h e presence of financing frictions leads to a n i m p o r t a n t r e d u c t i o n i n equity value. Second, M y e r s ' s debt overhang p r o b l e m obtains on average i n the d y n a m i c framework. T h a t is, equity claimants m a x i m i z e their o w n value by underinvesting i n the presence of risky debt already i n place. N o debt overhang obtains i n low technology states because equity claimants overinvest as a b i d to avoid default tomorrow. T h i r d , w h e n debt is o p t i m a l l y put is place p r i o r to the choice of investment, no debt overhang occurs: the investment level is first-best. F i n a l l y , equity claimants lose significant value by choosing to invest after their debt is i n place rather t h a n simultaneously choosing their investment and debt policies. W i t h sequential decisions, equity claimants ignore the effect of investment on the debt financing conditions. M o r e generally, the first chapter contributes to the literature on investment and financing decisions w h i c h began w i t h M o d i g l i a n i a n d M i l l e r (1958), who demonstrate that a firm's p r o d u c t i o n decisions are independent of its  1  financial decisions. T h e i r irrelevance result is consistent w i t h T o b i n ' s Q theory i n w h i c h a firm's investment decision is determined by m a x i m i z i n g its profits, regardless of its other sources a n d uses of funds. T h e r e also exist many studies of a firm's recapitalization decision that take the investment decision as given. D y n a m i c recapitalization studies include Fischer, Heinkel, a n d Zechner (1989), G o l d s t e i n , J u , a n d L e l a n d (1998), J u (1998), K a n e , M a r c u s , a n d M c D o n a l d (1984, 1985), and W i g g i n s (1990). M o d i g l i a n i and M i l l e r ' s (1958) irrelevancy result is derived i n an economic environment w i t h no financing frictions. Since then, the literature has e x a m i n e d more realistic environments, i n c l u d i n g frictions such as recapi t a l i z a t i o n costs, a s y m m e t r i c information, taxes, and a default cost of debt. W i t h these frictions, the investment decision of firms depends on their fin a n c i a l decisions. Papers discussing the impact of these frictions on the investment decision include Bernanke and Gertler (1989, 1990), B r e n n a n and Schwartz (1978), C a l o m i r i s and H u b b a r d (1990), D a m m o n and Senbet (1988), Decamps and F a u r e - G r i m a u d (1997), D o t a n and R a v i d (1985), F a i g a n d S h u m (1999), Froot, Scharfstein, and S t e i n (1993), L e l a n d (1994), L e l a n d a n d Toft (1996), Mayer (1986), M e l l a - B a r r a l and P e r r a u d i n (1997), a n d M y e r s a n d M a j l u f (1984) among others. These papers are developed w i t h i n a static framework, do not allow for changes i n the debt level t h r o u g h time, or do not solve for the endogenous claims prices. I n contrast, this chapter presents a m o d e l of investment i n the presence of the t r a d i t i o n a l debt fin a n c i n g frictions - a tax benefit and a default cost - that is d y n a m i c , allows for recapitalizations through time, and imposes consistent p r i c i n g . B r e n n a n a n d Schwartz (1984), Jensen and M e c k l i n g (1976), L e l a n d (1998), M a u e r a n d T r i a n t i s (1994), M e l l o a n d Parsons (1992), M y e r s (1977), a n d P a r r i n o and Weisbach (1997) focus their attention on the d i s t o r t i o n a r y effects of debt on firms' real decisions. T h e first chapter's m a i n contributions to this literature are two-fold. F i r s t , the m o d e l extends previous d y n a m i c studies by characterizing the investment scale decision. L e l a n d (1998) concludes his presidential address by stating: " D i v i d e n d (payout) policies and investment scale are treated as exogenous. [...] R e l a x i n g these assumptions remains a major challenge for future research." T h e m o d e l characterizes o p t i m a l d i v i d e n d policies and o p t i m a l investment scale policies t h r o u g h time. M o r e specifically, the m o d e l characterizes firms' investment decisions as they interact w i t h debt financing decisions t h r o u g h the p r o b a b i l i t y of default. T h e investment d i s t o r t i o n costs thereby obtained can be compared to the operating d i s t o r t i o n costs documented i n the literature. Second, the investment d i s t o r t i o n is quantified throughout various u n d e r l y i n g technol-  2  ogy states. For example, as discussed below, M y e r s ' s (1977) debt overhang p r o b l e m obtains on average, but not i n low technology states. M y e r s (1977) illustrates the debt overhang p r o b l e m according to w h i c h equity claimants invest less t h a n the t o t a l firm v a l u e - m a x i m i z i n g level w i t h risky debt i n place. E q u i t y claimants forgo positive net present value projects, because they m a x i m i z e their own levered value rather t h a n the t o t a l firm value. T h i s chapter shows that debt overhang occurs on average, b u t not i n low technology states and not when equity claimants o p t i m a l l y choose their debt i n place. B r e n n a n a n d Schwartz (1984) were the first to examine the interaction of firms' investment and financing decisions i n a d y n a m i c framework. T h e y develop a m o d e l of firm v a l u a t i o n i n the presence of b o n d indenture provisions that disallow asset sales, debt levels greater t h a n the asset base value, and debt levels v i o l a t i n g a specified interest coverage test. M a u e r and T r i a n t i s (1994) and M e l l o and Parsons (1992) examine the operating d i s t o r t i o n cost of debt i n the presence of a tax benefit a n d a default cost. I n b o t h papers, the operating p o l i c y is a b i n a r y function that depends on an u n d e r l y i n g price process related to the firm's cash flows. M e l l o and Parsons take the firm's c a p i t a l structure as given. A s such, they quantify M y e r s ' s (1977) debt overhang p r o b l e m i n a d y n a m i c framework. T h e debt overhang is measured as the difference between the firm value w i t h the firstbest operating p o l i c y and the firm value w i t h the operating p o l i c y that maximizes the levered equity value only. T h e y find that this agency cost is significant. T h e results obtained i n this chapter are consistent w i t h a large debt overhang cost. Conversely, M a u e r and T r i a n t i s allow for costly debt recapitalizations through time. T h e firm decides to produce or not and how m u c h debt to carry at each point i n time. T h e y find that changes i n the r e c a p i t a l i z a t i o n cost impact the debt level, but has very l i t t l e effect on the operating policy. T h a t is, the investment d i s t o r t i o n cost of debt frictions is not significant. W i t h o u t a real o p t i o n - p r i c i n g framework where there is value o f w a i t i n g to invest, the investment d i s t o r t i o n due to debt financing frictions is i m p o r t a n t . Jensen and M e c k l i n g (1976) discuss the asset s u b s t i t u t i o n p r o b l e m according to w h i c h equity claimants invest i n more risky projects w h e n debt is already i n place, thereby e x p r o p r i a t i n g value from debt claimants. O b viously, the asset s u b s t i t u t i o n p r o b l e m and the debt overhang p r o b l e m are closely related. T h e asset s u b s t i t u t i o n p r o b l e m refers to the variance distortion, while the debt overhang p r o b l e m refers to the mean d i s t o r t i o n . B o t h trigger agency costs because equity claimants choose a n investment p o l i c y 3  that m a x i m i z e s the equity value only, once debt is already i n place. L e l a n d (1998) allows the firm to change b o t h its risk strategy (low or high) a n d its debt structure through time. T h e d i s t o r t i o n cost is measured by the difference between the firm value w h e n b o t h the risk strategy a n d debt structure is chosen simultaneously a n d the firm value w h e n the risk strategy is chosen after debt is o p t i m a l l y put i n place. L e l a n d finds that the difference i n firm values is very s m a l l . P a r r i n o a n d Weisbach (1997) conduct M o n t e C a r l o experiments to quantify the magnitude of b o t h agency problems: debt overhang a n d asset subs t i t u t i o n . T h e y quantify the wealth transfer from equity claimants to debt claimants arising from the a d o p t i o n of low-risk positive-net-present-value projects, a n d the converse transfer arising from the a d o p t i o n of high-risk negative-net-present-value projects. T h e M o n t e C a r l o experiments suggest that these agency costs are unlikely to be i m p o r t a n t . I n contrast to the previous papers, P a r r i n o and Weisbach's investment and debt decisions are not obtained i n a v a l u e - m a x i m i z i n g framework, but are described by given rules. P r o x y i n g agency costs w i t h such rules may be misleading because the firm is not allowed to behave optimally. T h e second chapter is motivated by the e m p i r i c a l findings of F a z z a r i , H u b b a r d , and Petersen ( F H P , 1988). F H P present evidence o n the investment behavior of U . S . manufacturing firms d u r i n g the 1970-1984 p e r i o d . T h e y test the financing hierarchy hypothesis according to w h i c h equity and debt markets charge an i n f o r m a t i o n p r e m i u m to certain firms w i t h hard-toevaluate investment opportunities. F i r m s facing such i n f o r m a t i o n problems prefer to finance their investments w i t h retained earnings. Investments of these constrained firms (identified a p r i o r i as firms w i t h low dividend-toincome ratios) should be explained by their cash flows, w h i l e investments of less constrained firms (identified a p r i o r i as firms w i t h h i g h d i v i d e n d - t o income ratios) should be less sensitive to their cash flows. T h e e m p i r i c a l evidence is consistent w i t h this hypothesis: investments of l o w - d i v i d e n d firms are more sensitive to cash flow variations t h a n investments of h i g h - d i v i d e n d firms. F H P ' s results i n i t i a t e d an i m p o r t a n t and heated debate. O n the emp i r i c a l front, K a p l a n and Zingales ( K Z , 1997) took a different look at the subset of firms identified as most-financially-constrained by F H P . K Z consider various quantitative indicators of financial constraint a n d supplement this i n f o r m a t i o n w i t h manager's statements about the firm's l i q u i d i t y to b u i l d a new classification of financial constraint. K Z classify firms as constrained i f they are constrained from investing more w h i l e F H P view firms 4  as constrained i f they are constrained from o b t a i n i n g external funds to finance their investment. K Z find that, i n 85 percent o f firm-years, F H P ' s most-constrained firms were actually not constrained from investing more. T h i s suggests that the dividend-to-income ratio m a y not p r o x y well for investment-constrained firms. Moreover, K Z show that, according to their classification of investment-constraints, most-constrained firms have lower cash flow sensitivities t h a n least-constrained firms. T h i s result contrasts w i t h F H P ' s evidence that most-constrained firms e x h i b i t higher sensitivities t h a n least-constrained firms. T h e second chapter examines two models to assess the i m p a c t of financial constraints o n firms' cash flow sensitivities. C o n s t r a i n e d firms are modeled as firms w i t h o u t access to external markets while unconstrained firms are modeled as firms that can choose their o p t i m a l amount of external financing i n the presence of t a x a n d default frictions. I n contrast to F H P , cash flow sensitivities are larger, rather t h a n smaller, for unconstrained firms t h a n for constrained firms. M o r e i m p o r t a n t l y , the u n d e r l y i n g source of investment o p p o r t u n i t i e s i n the two models is found to be h i g h l y correlated w i t h cash flows. T h i s suggests that investment m a y be sensitive to cash flow fluctuations s i m p l y because cash flows p r o x y for investment opportunities. Unfortunately, the m o d e l does not suggest a single measure of investment o p p o r t u n i t i e s for b o t h unconstrained a n d constrained firms because the m a r g i n a l p r o d u c t of c a p i t a l i n these two models are too different. T h i s second chapter also suggests that F H P ' s identification of greater financial constraint w i t h low dividend-to-income ratios m a y be misleading. C o n s t r a i n e d firms are found to have higher dividend-to-income ratios t h a n unconstrained firms. Indeed, larger a n d more volatile dividend-to-income ratios p r o x y for a greater degree of financial constraint. F i r m s w i t h no financial flexibility cannot s m o o t h dividends b u t promise larger d i v i d e n d s to compensate equity claimants for the default risk they face. H o s h i , K a s h y a p , a n d Scharfstein (1991) provide e m p i r i c a l evidence i n support of F H P . T h e y d i v i d e Japanese firms into two groups using the natu r a l identification of financial constraint provided by the keiretsu i n s t i t u t i o n . A firm who belongs to a keiretsu has close ties to a m a i n bank. T h i s m a i n bank is likely to be well informed about the firm a n d is likely to be the p r i m a r y lender of funds to the firm. F i r m s are identified as less (more) constrained i f they (do not) belong to a keiretsu. H o s h i , K a s h y a p , a n d Scharfstein find that constrained firms have investment policies that are more sensitive to cash flow fluctuations than unconstrained firms. 5  F H P ' s e m p i r i c a l findings have generated interest i n conglomerates. L a mont (1997), R a j a n , Servaes, and Zingales ( R S Z , 1998), Scharfstein (1997), S h i n and P a r k (1998), and S h i n a n d Stulz (1998) examine the r e l a t i o n between internal funds transfers across divisions of diversified firms a n d their respective investment policies. A l l papers but R S Z use a n e m p i r i c a l specification similar to F H P a n d find that a d i v i s i o n ' s investment p o l i c y is sensitive to the cash flow fluctuations of another but not sensitive to its o w n investment opportunities. A number of s t r u c t u r a l estimations have been performed to test the presence of a b o r r o w i n g constraint. B o n d a n d M e g h i r (1994), H u b b a r d a n d K a s h y a p (1992), H u b b a r d , K a s h y a p , a n d W h i t e d (1995), a n d W h i t e d (1992) describe the investment decision using a m o d e l of p r o f i t - m a x i m i z i n g firms under the n u l l hypothesis of no b o r r o w i n g constraint a n d under the alternative of an exogenous b o r r o w i n g constraint. T h e y find that the former is consistent w i t h d a t a for unconstrained firms while the latter fits the d a t a for constrained firms. R a t h e r t h a n t a k i n g as given the presence of a given b o r r o w i n g l i m i t , Gross (1995) a n d P r a t a p and R e n d o n (1998) m o d e l the investment decision under an endogenous financing constraint defined by the p o s s i b i l i t y of l i q u i d a t i o n i f the firm's cash flow falls to zero at any point i n time. B o t h studies find that these cash flows are d y n a m i c a l l y managed to avoid l i q u i d a t i o n . I n that sense, a l l firms behave as i f they are constrained i n their investment decisions, w i t h constraint-binding firms being more sensitive to cash flow variations. Gross and P r a t a p and R e n d o n identify firms as constrained i f the cash flow constraint is b i n d i n g . T h i s is similar to K Z ' s identification of investment-constrained firms when firms are constrained from investing more. However, the theoretical results of Gross and P r a t a p a n d R e n d o n contrast w i t h K Z ' s e m p i r i c a l results that most-constrained firms are less sensitive to cash flow fluctuations. T h e chapter investigates whether Gross's and P r a t a p a n d R e n d o n ' s default definition is to blame. T h e i r default defini t i o n implies that a highly valuable firm w i t h a low cash flow i n a p a r t i c u l a r year must default: it cannot sell assets, issue equity, or raise new debt. I n this chapter, default is defined i n reference to the firm value rather t h a n the current cash flow. I n spite of this value-based default point, the results obtained are similar to Gross a n d P r a t a p a n d R e n d o n , inconsistent w i t h KZ. G i l c h r i s t and H i m m e l b e r g (1995) and C u m m i n s , Hasset, a n d O l i n e r (1997) e m p i r i c a l l y investigate the possibility that T o b i n ' s Q mismeasures i n vestment opportunities such that cash flow predicts investment o n l y because 6  it contains valuable information about investment opportunities. Gilchrist and Himmelberg construct an alternative measure of Tobin's Q based on Abel and Blanchard (1986) and they find that the cash flow sensitivity survives this alternative measure of Tobin's Q. Hence, mismeasurement of investment opportunities by Tobin's Q does not seem to explain the cash flow sensitivity. O n the other hand, Cummins, Hasset, and Oliner use analysts' earnings forecasts as a measure of a firm's opportunities. They find no cash flow sensitivity, suggesting, in contrast to Gilchrist and Himmelberg, that mismeasurement of investment opportunities by Tobin's Q explains the cash flow sensitivity. Gomes (1998) builds an investment model with exogenous financing costs where profit-maximizing firms also choose whether to exit at any point in time. Gomes shows that the real cash flow variable does not improve the fit of the investment regression when Tobin's Q is measured without error. The real cash flow variable only increases the fit of the investment regression when measurement error is introduced to Tobin's Q. Gomes lends support to Cummins, Hasset, and Oliner. The first chapter is organized as follows. The next section describes the model. Section 2.2 describes the financial series simulated from the model. Section 2.3 measures the amount and cost of investment distortions caused by debt. Section 2.4 concludes the chapter on investment distortions. The second chapter begins in Section 3.1 by describing the unconstrained firm model. Section 3.2 describes the constrained firm model. Section 3.3 presents the cash flow sensitivity results. Section 3.4 concludes the chapter on cash flow sensitivities.  2  Investment Distortions Caused by Debt Financing  This chapter examines firms' investment decisions in a dynamic stochastic framework with an interest tax deduction benefit and a deadweight default cost of debt financing.  2.1  The Model  Risk neutral claimants price the firm's equity according to p = BE[(p' + D')l ,> ], {v  7  Q)  (1)  where p is the ex-dividend equity price, j5 is the discount factor, D is the dividend, primed variables refer to tomorrow's beginning-of-the-period values, and is the no-default state (to be defined below). Equation (1) shows that today's equity price equals tomorrow's expected discounted payoff. The equity payoff consists of the price and dividend if the firm does not default. Substituting for the unlimited liability equity value, defined as V =p + D,  (2)  u  equation (1) becomes .V = D + BE U  [v;i( ,> ], V  0)  where V is the unlimited liability equity value and the no-default indicator function is 1 _ J" 11 I Iif V14 S> U0 0 otherwise. If no default occurs tomorrow, equity claims are valued at V^. Otherwise, equity claimants are protected from debt claimants by limited liability. Thus, default is defined to occur tomorrow when the equity value Fjl(yv>o) is nil, i.e., when the equity value with unlimited liability is less than zero. Clearly, by maximizing the unlimited liability equity value V , the firm also maximizes the limited liability equity value V l( y The dividend is defined by the firm's sources and uses of funds equation u  / o x  u  u  u  D = (1 - T )f(K; 6)-I f  Vu>0  + T 8K + B' - (1 + (1 - T )I)B, f  }  (4)  where r/ is the firm's tax rate, K is the asset base, 9 is the technology state describing the underlying economic conditions, (1 — Tf)f(K;9) is the after-tax operating income before depreciation, / is the investment, 5 is the depreciation rate, Tf5K is the capital cost allowance, B' is the new debt level, L is the interest rate, and (1 + (1 — Tf)i)B is the principal and taxdeductible interest payments. Although the debt B is modeled with a one-period maturity, the firm can decide at each time period to roll it over AB' = B' — B = 0, to make a new issue AB' > 0, or to retire a portion of its debt outstanding AB' < 0. The one-period maturity debt can thus be viewed as an infinite maturity debt with a floating rate. 1  For simplicity, the capital cost allowance rate is assumed equal to the true economic depreciation rate of the asset base. 1  8  The firm's operating income before depreciation is the difference between its revenues a n d expenses  f(K;9)  = 9K -F,  (5)  a  where the C o b b - D o u g l a s parameter a 6 (0,1) specifies decreasing returns to scale a n d F is a fixed cost representing labor a n d other expenses. F = 9.5 is chosen such that the mean of the debt-to-asset ratio B/K series generated from the m o d e l (0.4126) approximates the mean i n the d a t a (0.4031). 2  The asset base is subject to depreciation a n d takes time to b u i l d . evolves according to the a c c u m u l a t i o n equation K'  =  (1 - 5)K  It  (6)  + I.  T h e technology state is represented by the following first-order autoregressive process:  l n 0 ' = InA + plne + at',  (7)  where A is a constant a n d e ~ iid N(0,1). T h e persistence p of the technology shock provides a n exogenous source of dynamics. The firm chooses how much d i v i d e n d D to pay, how m u c h to invest K', a n d how m u c h debt to issue B' at w h i c h interest rate t'. T h e firm makes these decisions after observing the beginning-of-the-period value for the technology state 9 a n d last period's choices of asset base K, debt B, a n d interest rate i. T h e following summarizes the t i m i n g of these decisions:  the firm observes 9  the firm observes 9'  given K, B, t  given K', B', L'  it chooses D,K',B',L'  it chooses D', K", B", t"  W h e n m a k i n g its d i v i d e n d D, asset K', a n d debt financing (B , L') de1  cisions, the firm takes into account the p r i c i n g schedule at w h i c h the debt can be financed. R i s k neutral debt claimants require a n interest rate il such that the debt is fairly priced according to  BE (1 + (1 - r ) i ) 1 ^> ) + ( t  (  -gj  0  X j (1 -  1(^>0))  = 1,  (8) 2  The firm's labor demand decision is not modeled.  9  where r is the debt claimants' interest income tax rate a n d X is the deadweight default cost as a p r o p o r t i o n of the debt face value. E q u a t i o n (8) shows that debt claimants require an interest rate such that one unit of debt lent to the firm today equals tomorrow's expected discounted payoff. T h e payoff o n the debt c l a i m consists of the face value a n d the after-tax interest payment i f the firm does not default, or the net residual value i f the firm defaults. Default triggers an immediate reorganization process. T h e residual acc r u i n g to debt claimants u p o n default is the reorganized value of the firm V (K,0,0;9): the equity value w i t h assets K, no debt, no interest, a n d a technology state 9. Debt claimants may then recapitalize the firm i n an o p t i m a l manner. I n fact, V (K, 0,0; 9) takes into account the o p t i m a l rec a p i t a l i z a t i o n from that unlevered state. t  3  U  U  4  T h e firm does not choose whether to default or not. A l t h o u g h the firm positions itself to m i n i m i z e the possibility of default tomorrow, default could nevertheless h a p p e n as a result of today's decisions K',B', a n d i! when tomorrow's technology state 9' turns out to be m u c h lower t h a n expected. E q u a t i o n s (4), (5), (6), and (8) are the only constraints facing the firm. T h e l o g a r i t h m i c technology process restricts revenues 9K to be positive given that A > 0. T h e firm experiences operating losses before depreciation when expenses F exceed revenues 9K . W h e n net losses occur, the d i v i d e n d is increased by a tax subsidy, -Tf(f(K;9) - 8K - iB) > 0 . D i v i d e n d s D are not restricted to be non-negative. Negative dividends are interpreted as rights offers. E q u i t y claimants find it worthwhile to exercise these rights, otherwise default is triggered. I n fact, the firm optimizes w i t h respect to the d i v i d e n d policy. T h e firm decides on the amount of dividends or rights issues that is o p t i m a l . I n a d d i t i o n to dividends, investments / a n d debt a  a  5  This model does not distinguish between an informal reorganization process and a formal reorganization process through the bankruptcy court. It only specifies that reorganization is costly with a deadweight cost X and a one-period forgone tax benefit due to the reorganization (r/ — T )L . By definition, the residual accruing to debt claimants upon default (when V < 0) is always less than the principal and after-tax interest income 3  L  4  U  V {K,B,L;9)= U  V (K,O,O;0)~ U  YAWSl  (1 + (1 <(i  +  T f  (i-  )t)B T /  <  0  ) )<(l + (l-r00 t  because the corporate tax rate TJ is higher than the debt claimants' interest income tax rate T . Tax asymmetries such as limited carryback and carryforward provisions are not addressed. L  5  10  issues AB'  are not restricted to be non-negative. T h e firm is allowed to sell  its assets a n d to retire its debt. The B e l l m a n equation describing the firm's i n t e r t e m p o r a l p r o b l e m is max  V (K,B,L;9)= U  (3E \v (K',  D +  u  B',  L';6')1 , ] {V >0)  subject to equations (4), (5), (6),'and (8). T h e asset, debt, and c o u p o n decisions of the firm are characterized by the following equations:  + (1 - (1 - T )6)} l (v ,> 0) ] + \v ,  BE [{(1 - TfWaK"*-  1  BE[{l  K  f  = 1,  (9)  + (l-T )L')l, ,> ]=l-\v ,, f  v  0)  (10)  B  and E[(l-T )B'l ,> ] F  {v  =-Atv,  0)  (11)  where A is the m u l t i p l i e r on the fair-bond-pricing equation (8), a n d v' , v' , and v[ represent m a r g i n a l effects of the firm's decisions on the fair-bondp r i c i n g equation (8) characterized i n the appendix. K  B  E q u a t i o n (9) states that the firm invests up to the point where the cost of one unit of asset today equals tomorrow's expected discounted m a r g i n a l c o n t r i b u t i o n to dividends plus the benefits associated w i t h better financing conditions. T h e m a r g i n a l c o n t r i b u t i o n to dividends consists of the asset resale price a n d the m a r g i n a l after-tax income. T h e firm acts o n behalf of current equity claimants by valuing tomorrow's c o n t r i b u t i o n to dividends only i n the no-default state. E q u a t i o n (10) states that the firm issues debt up to the point where one unit of debt c o n t r i b u t i n g to today's dividends net of the costs of deteriorated financing conditions equals the expected discounted face value and after-tax interest b u r d e n on tomorrow's d i v i d e n d s if the firm does not default. E q u a t i o n (11) is used to determine the shadow value of claimants' debt holdings A. The tax a n d default frictions insure a n interior solution for the debt level B' chosen by the firm. T h e tax benefit arises because the interest payments are deductible to the firm at a higher rate t h a n the interest income is taxable to the debt claimant Tj > r . O n e unit of debt today is expected to generate (TJ — T )L' funds i f the firm does not default tomorrow. T h a t unit of debt today is also expected to cost X funds i f the firm defaults tomorrow. t  L  11  2.2  D e s c r i p t i o n o f S i m u l a t e d Series  T h e a p p e n d i x details how the m o d e l is calibrated and solved. T h e resulting p o l i c y series K', B', p, and t' are simulated from r a n d o m outcomes of technology shocks e. 1603 different series of 100 technology shocks are used to m a t c h the C o m p u s t a t sample described i n the appendix. E a c h series represents a s i m u l a t e d firm to m a t c h the C o m p u s t a t sample size of 1603 firms. O n l y the last 20 shocks are kept to m a t c h the C o m p u s t a t sample length of 20 years. F r o m these p o l i c y series, investment I, new debt issues AB , revenues 9K , d i v i d e n d D (where the indicates that the d i v i d e n d series does not include rights issues), and equity rate of r e t u r n r are c o m p u t e d . 1  a  +  +  T h i s section examines the a b i l i t y of the m o d e l to describe the investment a n d debt choices observed i n the data. Statistics describing the C o m p u s t a t sample are compared to simulated statistics generated from the m o d e l . T h e C o m p u s t a t d a t a definitions for the investment, new debt issues, revenues, d i v i d e n d , equity rate of return, a n d interest rate are p r o v i d e d i n the appendix. D e s c r i p t i v e statistics on these C o m p u s t a t series are presented i n T a b l e 2. F i r s t a n d second moments are c o m p u t e d for each of these 1603 firms and the resulting moments are averaged to represent the t y p i c a l m a n u f a c t u r i n g firm. T h e p r o m i s e d interest rate t' averages 0.1464, reflecting the riskiness of corporate claims. I n fact, the 1603 firms i n the sample survive for an average life of 13.9501 years. E q u i t y rates of r e t u r n r also reflect this riskiness w i t h a mean rate of 0.2229. T h e t y p i c a l C o m p u s t a t manufacturing firm invests nearly $60 m i l l i o n per year a n d generates $883 m i l l i o n i n revenues each year. N e w debt issues represent less t h a n $8 m i l l i o n per year, but issues are very volatile w i t h a s t a n d a r d d e v i a t i o n of $45 m i l l i o n . Investments are p o s i t i v e l y correlated w i t h b o t h sources of funds, internal revenues 6K and external new debt issues AB'i w i t h coefficients of 0.4320 and 0.2723 respectively. I n contrast to new debt issues, dividends D are not very volatile w i t h a s t a n d a r d d e v i a t i o n of $8 m i l l i o n from a mean of $18 m i l l i o n . Despite this evidence of smoothed dividends, dividends are highly positively correlated w i t h revenues, w i t h a coefficient of 0.4805. Because dividends and revenues move together t h r o u g h time, either of these variables may be used to p r o x y for economic conditions, i.e., the technology state. a  F i r s t and second moments of the simulated series are c o m p u t e d for each of these 1603 simulated firms. These moments are averaged to represent the t y p i c a l theoretical firm and reported i n T a b l e 3. T h e m a i n difference between Tables 2 a n d 3 is that the theoretical firm never defaults. T h e  12  promised c o u p o n rate is equal to the riskfree rate L' = p(iS ) = 0.0658. E q u i t y claimants are able to contract w i t h debt claimants at the riskfree rate, thereby o b t a i n i n g the lowest cost of debt financing a n d a v o i d i n g the default costs. I n t u r n , equity claims generate a lower mean rate of r e t u r n (0.1688) t h a n i n the C o m p u s t a t sample (0.2229). Ti  6  T h e possibility of default plays an i m p o r t a n t role i n the m o d e l . T h e threat of default defines the firm's o p t i m a l decisions. Decisions are made such that default is avoided i n a l l states. E x post, the possibility of default is always m i n i m i z e d . Note that default is avoided i n a l l of the discretized states 9. If the d o m a i n of the state space was not discretized (this alternative is not n u m e r i c a l l y feasible), default w o u l d occur i n the rare t a i l events a n d the interest rate w o u l d be slightly above the riskfree rate. O t h e r q u a l i t a t i v e results w o u l d r e m a i n unchanged. T h e t y p i c a l theoretical firm invests (4.0809) m u c h more t h a n it issues debt (0.0420), yet the standard d e v i a t i o n of debt issues 8.8701 is m u c h greater t h a n that of the investment 1.8952, as observed i n the data. Investments are highly correlated w i t h b o t h sources of funds, i n t e r n a l revenues 9K a n d external new debt issues AB', showing coefficients of 0.3245 a n d 0.9955. T h e t y p i c a l theoretical firm generates 15.5025 i n revenues each per i o d a n d pays out 1.1353 i n dividends. T h e two series are highly correlated, w i t h a coefficient of 0.7929. L i k e i n the data, dividends a n d revenues may be used to p r o x y for the technology state. D i v i d e n d s are more volatile t h a n i n the data, w i t h a standard d e v i a t i o n of 1.6249, because the risk n e u t r a l claimant does not care about s m o o t h payouts. a  Table 3 reveals that the operating income before depreciation is sometimes negative f(K;9) < 0. Revenues 9K become lower t h a n expenses F when revenues are more t h a n 1.5 standard deviations away from their mean. E c o n o m i c distress (1 - Tf)f(K;9) + Tf5K - I < 0 occurs i n the absence of any financial distress. a  T h e highest correlation coefficient i n Table 3 involves two variables chosen by the firm: investment and debt issues. A firm choosing a higher debt level today might not be able to repay debt claimants tomorrow, unless the firm also invests more today i n order to generate higher revenues tomorrow. Investments covary w i t h debt issues to avoid any possibility of default, leaving the interest rate required by debt claimants at a m i n i m u m . I n reality, Mauer and Triantis (1994) also obtain riskless debt at the optimum. In this chapter, the firm does not default even without a deadweight default cost X, because the firm would otherwise lose the tax benefit for one period due to the reorganization. 6  13  investment and debt issuing decisions may not perfectly adjust to eliminate any possibility of default. Nevertheless, the observed correlation between investment and debt issues is positive, like the correlation obtained from the model. Tables 2 and 3 also show that the correlation between the internal 9K and external AB' sources of funds is positive both in the data and in the model. This indicates that firms seek out financing on the external debt market when their internal funds are larger. In other words, variations in external funds exacerbate rather than offset variations in internal funds. In sum, descriptive statistics of the simulated series suggest that firms fully adjust their asset and debt levels to eliminate any possibility of default. The resulting theoretical moments compare well with those from the Compustat sample. Figure 1 graphs the policy functions K', B', and p. Because of the persistence p, firms experiencing low technology states 6 today expect low states tomorrow and thus a low marginal productivity of their asset base. Firms invest only small amounts K' and carry very little debt B'. As the technology state increases, the marginal productivity of the asset base also improves. Firms invest greater amounts and this investment is financed by higher debt levels. Technology state improvements generate larger dividends, as valued into the equity price p. The only source of dynamics in the model is through the technology state 6. W i t h no technology persistence p = 0, logc? ~ iid N(0, cr ). The dynamic model reduces to a sequence of static decisions. In this case, the investment decision is constant through time and consists of replacing the depreciated asset base each period I/K = 5. Debt levels B', equity prices p, and interest rates t' are also constant. In contrast to the data, the model with no persistence does not generate any correlation between investment I and debt issuing AB' decisions. a  7  2  Given policy functions K\ B\ and p, Figure 2 characterizes the minimum beginning-of-the-period funds CF + K — B that the firm must have to avoid default today. No default occurs if V =p+D > 0 u  p + CF + K-  B-K'  +  B'>0  CF + K - B > K' - B' - p, 7  .  This fact was first noted by Fazzari, Hubbard, and Petersen (1988).  14  where cash flows CF = (1 - Tf)(f(K;  9)-6K  - LB). F i r m s w i t h sufficiently-  h i g h cash flows CF, h i g h asset levels K, or low debt levels B do not default today.  F i g u r e 2 indicates that firms do not require as m u c h beginning-of-  the-period funds as the technology state improves. F i g u r e 3 shows the robustness of the benchmark results to different calibrations. Because the literature offers no guidance regarding the c a l i b r a t i o n of the revenues a and technology state A, p, a parameters, the effect of different values t h a n those estimated i n this study is investigated. T h e i m pact of different values for financing frictions r / , r , X is also e x a m i n e d . A s t  s u m m a r i z e d i n F i g u r e 3, the qualitative results of the b e n c h m a r k c a l i b r a t i o n are robust to the various calibrations. A larger sensitivity of revenues to asset variations a increases the marg i n a l p r o d u c t i v i t y of the asset base, irrespective of the technology state. A s the m a r g i n a l p r o d u c t i v i t y increases, the firm invests more a n d finances this greater investment w i t h a larger debt capacity. S i m i l a r l y , a larger technology state level A also increases the m a r g i n a l p r o d u c t i v i t y of the asset base, a n d thus the asset base and the debt level. A larger technological persistence p means that the technology state facing the firm today is more likely to persist tomorrow. Hence, a firm facing a low technology state today expects a low m a r g i n a l p r o d u c t i v i t y of its asset base tomorrow. It invests less and decreases its debt level. Conversely, a firm facing a h i g h technology state today expects a h i g h m a r g i n a l p r o d u c t i v i t y tomorrow, invests more, a n d increases its debt level. W i t h o u t technological persistence p = 0, the firm's p o l i c y functions are flat.  A s the  persistence  increases, the slopes of the investment and debt issuing p o l i c y functions become steeper. T h e technological v o l a t i l i t y a has the opposite effect.  A  larger v o l a t i l i t y means that the technology state facing the f i r m today is less likely to predict tomorrow's technology state. A firm facing a low technology state today is less likely to face a low m a r g i n a l p r o d u c t i v i t y of its asset base tomorrow. It invests more and increases its debt level. Conversely, a  firm  facing a h i g h technology state today is less likely to face a h i g h m a r g i n a l p r o d u c t i v i t y of its asset base tomorrow. It invests a n d borrows less. A n increase i n the interest income tax rate r tax benefit of debt (TJ — T )L'. L  t  decreases the m a r g i n a l  T h e firm chooses a lower debt level.  This  decrease i n funds leads to a lower investment. A n increase i n the corporate tax rate ry has two conflicting effects. O n one hand, it decreases the m a r g i n a l p r o d u c t i v i t y of the asset base, i m p l y i n g a lower asset (and debt) level. O n the other h a n d , it increases the m a r g i n a l tax benefit, i m p l y i n g a higher debt (and asset) level.  T h e net effect is to increase the debt level, leaving the 15  asset base v i r t u a l l y unchanged. F i n a l l y , a n increase i n the deadweight cost of defaulting X reduces the debt level a n d thus the asset base. 2.3  2.3.1  Investment Distortion  Distortion Caused by Financing Frictions  M o d i g l i a n i a n d M i l l e r (1958) show that a firm's investment decision is i n dependent of its financing policy w i t h frictionless markets. I n other words, the presence of debt i n a firm's c a p i t a l structure does not distort the investment decision away from its first-best level. I n reality, the U . S . t a x code favors the use of debt financing by allowing firms to deduct their interest payments at a higher rate t h a n the t a x rate faced b y debt claimants o n the interest income they receive. There is also evidence of legal a n d other costs p a i d b y distressed firms. T h e t a x benefit a n d default cost not only define a firm's o p t i m a l debt policy, but they also distort its investment decision. Indeed, it is the presence of debt financing frictions, such as the t a x benefit (jf — T )iB a n d the default cost XB, that links the investment decision to the debt financing decision. T h e impact of these financing frictions is examined by contrasting a firm's investment decisions i n a w o r l d w i t h a n d w i t h o u t financing frictions. b  W i t h no debt financing frictions, Ty = T = r — 0.4 a n d X = 0, the firm's i n t e r t e m p o r a l p r o b l e m simplifies to l  V (K,B,L;0)=  max  U  {D,K',B',L'}  D + BE \v (K', U  1  B', t'; 0')l^>o) J  subject to £> = (!-  T  ){$K  -  A  F)  +  (1 -  (1 -  T)S)K  -  K'  and  BE  (1 + (1 - T)L') 1, ,> v  0)  +  V^K',0,0-e') B'  (1 - Hv:>o))  A s expected, the debt financing decision is indeterminate. T h e fair-bondp r i c i n g equation above is obtained as a result of the firm's debt a n d c o u p o n decisions. T h u s , there is only one equation to identify two debt financing variables. A n y c o m b i n a t i o n of B' a n d t' that satisfies the f a i r - b o n d - p r i c i n g equation represents a possible solution.  16  T h e investment chosen is now the first-best level BE[(1 - T)Q'aK' a  x  (12)  + (1 - . ( 1 - T)5)] = 1  or  K' =  8(1 - T)aE[6']  l-a  1 - 0(1 - (1 - T)«J) }  Table 4 a n d F i g u r e 4 document the amount I — I a n d value V V of the investment distortion caused by the presence of a tax benefit a n d a default cost of debt, mm denotes the M o d i g l i a n i and M i l l e r (1958) framework w i t h o u t financing frictions described above, while variables w i t h o u t subscripts refer to the benchmark m o d e l w i t h financing frictions as described i n Section 2.1. Table 4 (up to Table 7) reports the investment d i s t o r t i o n amount a n d value, computed as the average over the 1603 s i m u l a t e d firms and the 20 periods, while F i g u r e 4 (up to F i g u r e 7) displays the investment d i s t o r t i o n amount and value, computed as the average over firms and periods a r o u n d each discretized technology state. mm  mm  T a b l e 4 shows that the mean of I - I is equal to 0.7966, representing a large 13.61 percent of the first-best firm value V . T h e tax benefit provides a d d i t i o n a l funds to the firm to over invest on average. Because of the presence of a tax benefit, firms are induced to borrow more. T h i s higher debt level today necessitates more investment today to avoid any p o s s i b i l i t y of default tomorrow. F i g u r e 4 shows that, i n low technology states, the firm actually underinvests to avoid the possibility of default. I n such low states, the firm avoids defaulting tomorrow by c a r r y i n g very little debt. A s a result, the firm does not invest much. A s the technology state improves, the firm levers up a n d increases its investment beyond the first-best level. mm  mm  A c c o r d i n g to Table 4, the a d d i t i o n a l value p r o v i d e d by the tax benefit is outweighed by the cost of the s u b o p t i m a l investment by a n average of V-V — - 8 . 4 7 0 1 or 14.88 percent of the first-best firm value V T h a t is to say, equity claimants do not benefit from financing frictions. A s displayed i n F i g u r e 4, the discrepancy of equity values worsens as the technology state improves. T h e firm takes on more debt, that finances more investment over a n d above the first-best level, resulting i n a lower value accruing to equity claimants. mm  mm  Table 4 a n d F i g u r e 4 indicate that the amount a n d cost d i s t o r t i o n caused by financing frictions are i m p o r t a n t . O n overinvests as a result of the tax benefit of debt financing their equity value. However, the firm actually underinvests 17  of the investment average, the firm thereby reducing i n low technology  states to avoid default despite the t a x benefit of debt. E q u i t y claimants lose value from the existence of financing frictions because the investment d i s t o r t i o n cost outweighs the t a x benefit of debt. 2.3.2  Debt Overhang  W i t h debt, conflicts between equity a n d debt claimants m a y arise w h e n a levered firm acts i n the interest of equity claimants only. M y e r s (1977) discusses the debt overhang p r o b l e m according to w h i c h a levered firm chooses a n investment policy that maximizes the value of its equity claims rather t h a n the t o t a l firm value. M y e r s shows that the firm underinvests due to the presence of debt i n its c a p i t a l structure. T h e impact of the debt overhang p r o b l e m is examined by extending M y e r s static framework to include d y n a m i c investment decisions when debt is already i n place. T h e debt overhang p r o b l e m is measured by contrasting the resulting investment decision I w i t h the firm's first-best investment level I . m  mm  T h e firm's p r o b l e m is to choose its d i v i d e n d D a n d investment K' policies to m a x i m i z e the value of its equity, given a n a r b i t r a r y a n d constant debt structure i n place (B,i). T h e B e l l m a n equation describing the i n t e r t e m p o r a l investment p r o b l e m is V (K;6) U  = max D + {D,K'}  BE[V (K';0')l(v,[>o)] U  v u  subject to D = (1 - Tf){6K  a  - F) + (1 - (1 - )S)K Tf  - K' - (1 -  T )tB. f  G i v e n the a r b i t r a r y c a p i t a l structure i n place, the firm invests to m a x i m i z e the equity value w i t h o u t considering the fair-bond-pricing equation. T h a t is precisely the nature of the conflict between equity a n d debt claimants: equity claimants ignore the effect of their investment decision o n the debt p r i c i n g equation. T h e investment decision is characterized by BE[{{\ - T )6'aK' a  f  1  + (1 - (1 - T )5)}l, ,> ] f  v  0)  = 1.  M y e r s (1977) takes the debt financing decisions as given. S i m i l a r l y , i n terest payments are now considered a fixed cost, aggregating w i t h the fixed cost of labor a n d other expenses F. Following the debt-to-asset c a l i b r a t i o n of the next m o d e l where the investment is chosen after the debt, F + LB is set to 9.2, where t = 0.0658 a n d B = 17.9083 are the mean simulated interest rate a n d debt level from Section 2.1. A fixed labor cost of F = 8.0216 is 18  applied to b o t h the M o d i g l i a n i and M i l l e r (1958) framework a n d the M y e r s framework. Table 5 a n d F i gure 5 document the amount I ~~Imm m  a n d value V V of the investment d i s t o r t i o n caused by debt overhang, mm denotes the firstbest M o d i g l i a n i and M i l l e r (1958) framework, while m denotes the M y e r s (1977) framework of no debt financing flexibility. Table 5 shows that the mean of I — I is equal to -2.8055, representing 8.23 percent of the firstbest firm value V . T h e debt overhang p r o b l e m is i m p o r t a n t o n average. D e b t i n place induces equity claimants to underinvest compared to the firstbest level. F i g u r e 5 shows that no overhang occurs i n low technology states. In low technology states, equity claimants who do not manage the debt p o l i c y must invest more t h a n the first-best level i n order to generate higher revenues tomorrow a n d decrease the p r o b a b i l i t y of defaulting tomorrow. Default happens i n the M y e r s framework because the firm does not bear any cost of defaulting. I n fact, the firm ignores the f a i r - b o n d - p r i c i n g equation. A s the technology state improves, equity claimants invest less t h a n the first-best level because the m a r g i n a l p r o d u c t i v i t y of the asset base is m i t i gated by the p o s s i b i l i t y of default. Table 5 shows that this agency conflict is very costly to equity claimants, w i t h an average of V — V = —34.9806 representing a very large 92.23 percent of the first-best firm value V . F i g u r e 5 indicates that the agency cost increases w i t h the technology state. Table 5 a n d F i g u r e 5 show that the amount and cost of the debt overhang p r o b l e m is very i m p o r t a n t . W i t h an a r b i t r a r y a n d constant debt p o l i c y of B and L, the debt overhang p r o b l e m occurs. T h e firm underinvests o n average. However, i n low technology states, the firm overinvests to decrease its p r o b a b i l i t y of defaulting tomorrow. m  m  mm  mm  mm  m  mm  mm  2.3.3  Debt Overhang with Optimal Debt  D e b t overhang presumes that there is debt already i n place a n d that the debt p o l i c y does not anticipate future investment decisions of equity claimants. T h e firm's investment p o l i c y is now e x a m i n e d w h e n the debt p o l i c y is opt i m a l l y chosen each p e r i o d before the investment decision is made. investment level w h e n debt is already, a n d o p t i m a l l y , p u t i n place I  The s  compared to the first-best level  is  I . mm  T h e firm's p r o b l e m is now sequential: each p e r i o d the firm chooses its debt p o l i c y B' a n d t' i n the first stage a n d it chooses its investment p o l i c y K' i n the second stage. S o l v i n g backwards, the B e l l m a n equation describing  19  the firm's intertemporal investment problem is V (K,Bf,i\0)  = mac D +  U  8E[V {K',B',t';0')l(v->o)] U  subject to D = (1 - r / ) ( ^  a  - F ) + (1 - (1 - TJ)5)K - K' + B' - (1 + (1 -  TJ)L)BJ.  The investment decision is not only a function of the state variables K, Bf, L, 6 but also a function of the first stage debt level B' and interest t' chosen. The investment decision is characterized by BE{{{\ - Tf^'aK'*-  + (1 - (1 - T )5)}l ,> ]  1  f  {v  0)  = 1.  (13)  The benchmark investment equation (9) differs from the sequential investment policy by its effect on the fair-bond-pricing equation XVK • W i t h sequential decisions, equity claimants ignore the effect of their investment on debt financing conditions. Working back to the first stage of the firm's problem, the intertemporal debt problem is represented by 1  V {K,Bf,L;6) u  = m xD  +  a  8E[V (K',B',L';0')l , } u  {v >0)  {B',i'}  subject to D = (1 - T )(6K  a  f  - F) + (1 - (1 - T )S)K - K' + B' - (1 + (1 f  T )t)B f  f  and the fair-bond-pricing equation BE  (1 + (1 - r j t ) l(v^>o) + I  A 1 (1 - 1( > ))  -g,  W  - 1-  0  The debt level and coupon equations (10) and (11) remain unchanged BE[(l + (l-T )i')l , > ] f  {v m  0)  = l-\v  B I  and E[(l-T )B'l , > ] f  {v m  = -\v ,.  Q)  l  Table 6 and Figure 6 document the amount I — I and value V — V of debt overhang when the debt is optimally put in place, s refers to the sequential model where the asset level is chosen after the debt policy, while s  20  mm  s  mm  mm refers to the first-best framework of M o d i g l i a n i and M i l l e r (1958). B o t h models are c a l i b r a t e d at F = 9.2 such that the sequential m o d e l replicates the mean debt-to-asset ratio observed i n the data. T a b l e 6 shows that h — Imm- T h e r e is no overhang on investment caused by debt w h e n the debt is o p t i m a l l y put i n place. To understand this result, note that the only difference between investment equations (12) a n d (13) is the no-default indicator function lr.y I n the sequential m o d e l , the firm is always able to fully adjust its debt p o l i c y to avoid default. Hence, the r e s u l t i n g investment p o l i c y is first-best. T h e f a i r - b o n d - p r i c i n g constraint reduces the equity value V w h e n compared to the equity value V w i t h o u t debt financing frictions. T h e cost of this a d d i t i o n a l constraint is V — V = —11.5729, representing 47.54 percent of the first-best firm value V . s  mm  s  mm  mm  Table 6 a n d F i g u r e 6 show that there is no overhang o n investment a n d the cost of o p t i m a l l y p u t t i n g debt i n place is m u c h smaller t h a n w h e n debt is taken as given.  2.3.4  Distortion Caused by Sequential Decisions  T h e cost of choosing its investment p o l i c y after the firm o p t i m a l l y chooses its debt p o l i c y is now quantified. T h e firm's sequential investment decision I is compared to the investment I simultaneously chosen w i t h the debt p o l i c y as described by the benchmark m o d e l of Section 2.1. s  Table 7 a n d F i g u r e 7 document the amount I — I a n d value V — V of the investment d i s t o r t i o n caused by choosing investment after debt. T a b l e 7 shows that the mean of I — I is equal to -0.7787, representing a mere 1.68 percent of the firm value w i t h simultaneous decisions V. T h i s investment d i s t o r t i o n I — I is the opposite measure of the investment d i s t o r t i o n caused by financing frictions I - I , because the investment choice w i t h debt o p t i m a l l y put i n place I„ is equal to the first-best I . T h e discrepancy between the means oi I — I = 0.7966 and I — I = - 0 . 7 7 8 7 results from a different c a l i b r a t i o n of fixed costs. / — I is o b t a i n e d from F = 9.5 that replicates the debt-to-asset ratio observed i n the d a t a for the b e n c h m a r k simultaneous m o d e l , while I — I is obtained from F = 9.2 that replicates the observed debt-to-asset ratio for the sequential m o d e l . I n this section, b o t h the sequential investment I and the simultaneous investment I are obtained w i t h F — 9.2. s  s  s  s  mm  mm  mm  s  mm  s  s  W h e n debt is chosen p r i o r to the investment decision, the firm invests less o n average. W i t h sequential decisions, debt claimants are not w i l l i n g  21  to lend as much funds to the firm. Although there is no debt overhang, the firm suffers from a reduced borrowing capacity. The debt is still riskless i' = 0.0658 but the firm does not borrow as much on average B = 13.9503 < 17.7360 = B. Without these funds, the firm does not invest as much. As discussed above, it actually invests at the first-best level rather than overinvest due to the debt financing frictions. W i t h sequential decisions, the investment decision is separated from the debt financing conditions and therefore it is not influenced by tax benefit of debt. Figure 7 shows that, in low technology states, investment with debt already put in place is actually higher than investment chosen simultaneously with the debt level. The firm does not sell as much of its asset base because these asset proceeds do not change the interest rate required by debt claimants when default is more likely to occur. The investment policy is decided after the debt is put in place. Thus, selling more assets does not make debt financing less expensive. For the same reason, as the technology state improves, the firm maximizing the equity value with debt in place does not have any incentive to invest beyond the first-best level. It thus invests less than the firm whose investment decision is influenced by the tax benefit of debt. The value of the investment distortion caused by debt in place averages V — V = —0.6039 or 9.04 percent of the firm value with simultaneous decisions V. The cost of making the investment decision after the debt is in place increases as the technology state improves. Table 7 and Figure 7 show that the cost of choosing the investment policy once debt is optimally put in place is non negligible, despite the small amount of investment distortion. The firm with sequential decisions invests at the first-best level, thereby investing more than a firm who makes simultaneous investment and debt decisions in low technology states and investing less than that firm in high technology states. The firm who makes sequential decisions does not take into account the tax benefit of debt when making its investment decision. It will therefore lose value compared to the firm who decides simultaneously on its investment and debt policies. s  s  2.4  Concluding Comments  on Investment Distortions  In this chapter, the interaction between investment and debt issuing decisions of a firm in the presence of the traditional tax benefit and default cost frictions is examined. The model generates investment and new debt issuing decisions that are positively correlated to avoid default through time, as observed in the data. Given that the model performs well compared to  22  the data, the chapter proceeds to measure various investment distortions caused by debt financing. F i r s t , the d i s t o r t i o n caused by debt financing frictions is measured. T h e tax benefit of debt induces the firm to increase its debt capacity a n d invest beyond the first-best level o n average. T h e cost of the overinvestment outweighs the tax benefit of debt thereby reducing the equity value below the first-best level. I n low technology states, the firm a c t u a l l y underinvests to avoid default despite the tax benefit of debt. Second, M y e r s ' s (1977) debt overhang p r o b l e m is measured. T h e debt overhang p r o b l e m obtains on average and becomes more i m p o r t a n t at higher technology states. T h i r d , the debt overhang p r o b l e m w i t h o p t i m a l debt is measured. W h e n debt is o p t i m a l l y put is place, there is no debt overhang: the resulting investment level is first-best. F i n a l l y , the cost of choosing i n vestment after the debt p o l i c y is measured. E q u i t y claimants lose value by choosing to invest after their debt is o p t i m a l l y put i n place because they do not consider the effect on their investment decision on the debt financing conditions. U n l i k e previous papers, the m o d e l characterizes the o p t i m a l investment scales chosen by the firm at each point i n time. I n line w i t h M e l l o and Parsons (1992), this chapter finds that the debt overhang cost V — V is very i m p o r t a n t . M a u e r and T r i a n t i s ' s (1994) conclusion that the operating p o l i c y is not affected by the c a p i t a l structure is due to their real o p t i o n p r i c i n g framework where there is value of w a i t i n g to invest. W i t h o u t such a feature, this chapter shows that the investment d i s t o r t i o n due to debt financing frictions I — I is i m p o r t a n t . m  mm  mm  3  Why is Investment Sensitive to Cash Flow?  In order to understand how financing constraints influence the sensitivity of investment to cash flow fluctuations, the cash flow s e n s i t i v i t y derived from a m o d e l of a firm w i t h o u t any constraint is compared to the cash flow sensitivity derived from a m o d e l of a firm w i t h o u t access to equity and debt markets. I n the spirit of F H P , firms who cannot raise any funds from external markets are called constrained firms, w h i l e firms w h o face no financing constraint are called unconstrained firms. T h e unconstrained firm m o d e l is identical to the benchmark m o d e l of Section 2.1, but repeated here for c o m p a r a b i l i t y w i t h the constrained firm m o d e l .  23  3.1  Unconstrained Firms  The Consumer T h e risk n e u t r a l consumer "c" maximizes its expected lifetime u t i l i t y oo  I  t=0  T h e B e l l m a n equation describing its i n t e r t e m p o r a l p r o b l e m is  U{S ,B ) C  C  =  max  C +BE  [U(S' ,B' )] C  C  {C,S ,B \ C  C  subject to the budget constraint C + S' P  C  + B' = c  {(p + d)S  c  + (1 +. (1 - T )i)B } 0  +  l  c  ( K i  >  0 )  (g-X)B (l-l > ). c  {Vu  0)  T h e consumer maximizes its u t i l i t y by choosing how m a n y goods C to consume, how many equity claims S' to buy, a n d how m u c h debt B' to hold, c  c  t a k i n g as given the e x - d i v i d e n d share price p, the dividend-per-share ratio d, the interest rate L, the firm residual g that accrues to debt claimants u p o n default as a p r o p o r t i o n of the debt face value, a n d the no-default state 1(.) (to be defined below), where B is the discount factor, T is the interest i n U  come tax rate, X is the deadweight default cost as a p r o p o r t i o n of the debt face value, a n d p r i m e d variables refer to tomorrow's beginning-of-the-period values. • T h e risk n e u t r a l consumer prices equity a n d debt c l a i m s a c c o r d i n g to the following two equations:  p = BE[(p' + d')l ,> ] (v  (14)  0)  and 1 = BE [(1 + (1 - T )0 1 ,> 4  {V  0)  + (g' - X)(l  -  1 >>0))\ {V  •  (15)  E q u a t i o n (14) shows that the consumer prices the equity c l a i m such that today's price equals tomorrow's expected discounted payoff.  T h e equity  payoff consists of the price a n d d i v i d e n d i f the firm does not default. S i m i larly, equation (15) shows that the consumer requires a n interest rate such that one u n i t of debt lent to the firm today equals tomorrow's expected discounted payoff. T h e payoff o n the debt c l a i m consists of the face value  24  and the after-tax interest payment if the firm does not default, or the net residual value if the firm defaults. The Firm The firm " / " maximizes the value to its equity claimants. The model assumes that there is no dilution. The firm cannot change its number of shares outstanding: S'f = Sf = 1. Then, the ex-dividend share price p becomes the ex-dividend equity value. The unlimited liability equity value is defined as V =p u  +d  (16)  and the dividend payment as D = d.  (17)  The equity value equation (14) is rewritten as V = D + BE u  where the indicator function is defined by V(Vu>o)  |f l Q  [  i  V  ^°  (18) ^I  o t h e r w i s e  If no default occurs tomorrow, equity claims are valued at V^. Otherwise, equity claimants are protected from debt claimants by limited liability. Thus, default is defined to occur tomorrow when the equity value l^l(v^>o) is nil, i.e., when the equity value with unlimited liability is less than zero. Clearly, by maximizing the unlimited liability equity value V , the firm also maximizes the limited liability equity value V l(y >0)The firm chooses how much dividend D to pay, how much to invest I, and how much debt to issue AB'f = B'j - Bf at which interest rate i', given its after-tax operating income before depreciation (1 — Tf)f(K;9), its capital cost allowance Tf5K, and its debt face value and tax-deductible interest payments (1 + (1 — Tf)i)Bf, where Tf is the firm's tax rate and <5 is the capital cost allowance rate. The firm makes its decisions after observing the beginning-of-the-period value for the technology state 6 and last period's choices of asset base K, debt B, and interest rate i. The following summarizes the timing of these decisions: u  u  u  8  For simplicity, the capital cost allowance rate is assumed equal to the true economic depreciation rate of the asset base. 8  25  the firm observes 9' given K',B',b' it chooses D',K",B", L"  the firm observes 6 given K , B , L it chooses D,K',B',  i'  Although the debt Bf is modeled with a one-period maturity, the firm can decide at each time period to roll it over AB'j = 0, to make a new issue AB'j > 0, or to retire a portion of its debt outstanding AB'^ < 0. The one-period maturity debt can thus be viewed as an infinite maturity debt with a floating rate. The dividend is defined by the firm's sources and uses of funds equation D = (l-Tf)f{K;0)-I  + TfSK + B' -(l f  + {l-T )L)Bf.  (19)  F  The firm's operating income before depreciation is the difference between its revenues and expenses 6) = 6K  a  f(K;  -  (20)  F,  where the Cobb-Douglas parameter a € (0,1) specifies decreasing returns to scale and F is a fixed cost representing labor and other expenses. The asset base is subject to depreciation and takes time to build. It evolves according to the accumulation equation 9  K'  =  (1 - 5)K  (21)  + L  The technology state is represented by the following first-order autoregressive process: ln0' = lnA + plnO + ae',  (22)  where A is a constant and e ~ iid N(0,1). The persistence p of the technology shock provides an exogenous source of dynamics. When making its dividend D, asset K', and debt financing (BJ,L') decisions, the firm must also take into account the pricing schedule at which the debt can be financed. Debt claimants require an interest rate i! such that the debt is fairly priced according to equation (15), restated here for convenience, BE [(1 + (1 -  T ) ') t  t  1(^> ) + (g - X)(l - \v>> ))] = 1. 1  0  Q  The firm's labor demand decision and the consumer's labor supply decision are not' modeled. 9  26  T h e firm knows that the residual gBf  accruing to debt claimants u p o n  default is the reorganized value of the firm gB  f  =  V (K,0A0), u  the equity value w i t h assets K, no debt, no interest, a n d a technology state 9.  D e b t claimants may then recapitalize the firm i n a n o p t i m a l manner.  10  I n fact, V (K,0,0;9)  takes into account the o p t i m a l r e c a p i t a l i z a t i o n from  U  that unlevered state. T h e consumer's debt p r i c i n g equation (15) becomes  BE  (1 + (1 - T j t ) 1 ( ^ > 0 ) +  ^  ^7  Ji -  X  1.  (V>>0))  1  l  (23) T h e firm does not choose whether to default or not. A l t h o u g h the firm positions itself to m i n i m i z e the p o s s i b i l i t y of default t o m o r r o w , default c o u l d nevertheless h a p p e n as a result of today's decisions D,K',B'f,  a n d i! w h e n  tomorrow's technology state 9' turns out to be m u c h lower t h a n expected. Default triggers an i m m e d i a t e reorganization process. E q u a t i o n s (19), (20), (21), a n d (23) are the only constraints facing the firm. T h e l o g a r i t h m i c technology process restricts revenues 9K  to be pos-  a  itive given that A > 0.  T h e firm experiences operating losses before de-  p r e c i a t i o n w h e n expenses F exceed revenues 9K .  W h e n net losses occur,  a  the d i v i d e n d is increased by a t a x subsidy, —Tf(f(K;  9) — 6K - iBf)  > 0.  u  D i v i d e n d s D are not restricted to be non-negative. Negative d i v i d e n d s are interpreted as rights offers. E q u i t y claimants find it w o r t h w h i l e to exercise these rights, otherwise default is triggered. I n fact, the firm optimizes w i t h respect to the d i v i d e n d policy. T h e firm decides o n the amount of d i v i d e n d s or rights issues that is o p t i m a l . I n a d d i t i o n to dividends, investments / a n d debt issues A B ' are not restricted to be non-negative. T h e firm is allowed to sell its assets a n d to retire its debt. B y definition, the residual g accruing to debt claimants upon default (when V < 0) is always less than the principal and after-tax interest income (1 + (1 — r )i) 1 0  u  L  V (K,B,i;8)= u  g  =  V (K,0,0;6)U  YAK^Ml  <(i + ( l -  (l + ( l - r ) i ) B < 0 /  T /  /  )0<(l + (l-r )0 t  because the corporate tax rate 77 is higher than the income income tax rate T . Tax asymmetries such as limited carryback and carryforward provisions are not addressed. L  1 1  27  T h e B e l l m a n equation describing the firm's i n t e r t e m p o r a l p r o b l e m is  V {K,B ,t;9) u  f  =  max  D+  BE\V {K',B' ,L';0')l , u  {D,K',B'f,t.'}  '  {v >0)  f  L  v  u  ~  '  subject to equations (19), (20), (21), a n d (23). T h e asset, debt, a n d c o u p o n decisions of the firm are characterized by the following equations: BE [{(1 - Tf^'aK"*-  1  + (1 - (1 - )5)} Tf  BE [(1 + (1 - T )L')l ,> ] f  {v  0)  l ^ > o ) ] + \v , (  K  = 1,  = 1 - \v ,,  (24) (25)  B  and  E (l-T )B l ,> ]=-\v ,, f  f (v  Q)  (26)  L  where A is the m u l t i p l i e r o n the consumer's fair-bond-pricing equation (23), and v' , v' , a n d v[ represent m a r g i n a l effects of the firm's decisions o n the fair-bond-pricing equation (23) characterized i n the appendix. E q u a t i o n (24) states that the firm invests up to the point where the cost of one unit of asset today equals tomorrow's expected discounted m a r g i n a l c o n t r i b u t i o n to dividends plus the benefits associated w i t h better financing conditions. T h e m a r g i n a l c o n t r i b u t i o n to dividends consists of the asset resale price a n d the m a r g i n a l after-tax income. T h e firm acts o n behalf of current equity claimants b y valuing tomorrow's c o n t r i b u t i o n to dividends only i n the no-default state. E q u a t i o n (25) states that the firm issues debt up to the point where one unit of debt c o n t r i b u t i n g to today's dividends net of the cost of deteriorated financing conditions equals the expected discounted face value a n d after-tax interest b u r d e n o n tomorrow's dividends i f the firm does not default. E q u a t i o n (26) is used to determine the shadow value of the consumer's debt holdings A. K  B  T h e t a x a n d default frictions insure a n interior solution for the debt level B'j. T h e t a x benefit arises because the interest payments are deductible to the firm at a higher rate t h a n the interest income is taxable to the consumer Tf > T . O n e unit of debt today is expected to generate ( r j — T )L' funds i f the firm does not default tomorrow. T h a t unit of debt today is also expected to cost X funds i f the firm defaults tomorrow. L  L  Equilibrium F i n a l l y , the e q u i l i b r i u m requires that a l l markets clear. T h e r e are two financial markets a n d one goods market. C l e a r i n g i n the equity market requires  28  that the number of shares purchased by the consumer be equal to the number of shares outstanding S' = S'f = 1. Similarly, clearing in the debt market requires B' = B'j = B'. Given that the budget constraint of the consumer and the sources and uses of funds equation of the firm are satisfied, the goods market also clears by Walras's law. c  c  3.2  Constrained  Firms  Without access to external markets, the model is somewhat simplified. The consumer's equity pricing equation (14) remains unchanged p = BE [(p + d')l ,> ]  .  1  (v  0)  The firm's problem is to choose its dividend D and investment K' policies to maximize the value of equity claims. The firm is constrained from financing itself with a debt issue B' = B = 0 or with a rights issue D > 0. The Bellman equation describing the intertemporal investment problem is V (K;6) = max D +  f3E[V (K';e')l , ]  U  u  {D,K'}  {v >0)  ~  u  subject to D = (1 - T )(6K  a  f  - F) + (1 - (1 - T )5)K - K' > 0. f  The investment decision is characterized by BE[{(\ - r )6'aK ,a  }  1  + (1 - (1 - r )5)}(l f  + r/)l £>o)] = 1 + V, (Vi  where rj is the Kuhn-Tucker multiplier disallowing rights issues. Clearing in the equity market is insured by S' = S' = 1. Because the budget constraint of the consumer and the sources and uses of funds equation of the firm are satisfied, the goods market clears by Walras's law. c  3.3  f  Results  The appendix details how the two models are calibrated, solved, and simulated. Figure 8 graphs the policy functions K', B', and p of the unconstrained firm. Because of the persistence p, firms experiencing low technology states 9 today expect low states tomorrow and thus a low marginal productivity of their asset base. Firms invest only small amounts K' and carry very little debt B'. As the technology state increases, the marginal  29  productivity of the asset base also improves. Firms invest greater amounts and this investment is financed by higher debt levels. The firm is able to fully adjust the asset and debt levels to avoid the possibility of default, as reflected by the constant interest rate L' = 0.0658. Technology state improvements generate larger future dividends, as valued into the equity price PFigure 9 shows that the policy functions K' and p of the constrained firm behave similarly to those of the unconstrained firm. Constrained firms have no access to debt or equity markets. Hence, firms with a low revenuesgenerating asset base lack funds to invest as much as desired. In those states, the Kuhn-Tucker multiplier restricting rights issues is binding r\ > 0. The only source of dynamics in the model is through the technology state 6. W i t h no technology persistence p = 0, log# ~ iid N(0, cr ). The dynamic model reduces to a sequence of static decisions. In this case, the investment decision is constant through time and there is no cash flow sensitivity. Information contained in Table 8 is taken from F H P . F H P classify Value Line firms during the 1970 to 1984 period into three classes, from mostfinancially-constrained to least-financially-constrained. Class 1 firms represent the most-constrained firms as identified by dividend-to-income ratios lower than 0.1, Class 2 firms have ratios between 0.1 and 0.2, and Class 3 firms represent the least-constrained firms as identified by ratios greater than 0.2. Table 8 summarizes F H P ' s descriptive statistics on the investment and cash flow ^ variables. Most-constrained Class 1 firms invest more than Class 2 firms, who in turn invest more than least-constrained Class 3 firms. Tables 9 and 10 indicate that unconstrained firms simulated from the model invest slightly more than theoretical constrained firms, with medians of 0.1000 and 0.0862 respectively. Table 8 also shows that most-constrained Class 1 firms have more cash flows than Class 2 firms, who in turn have more cash flows than least-constrained Class 3 firms. This is similar to simulated statistics of Tables 9 and 10. Theoretical unconstrained firms have less cash flows than theoretical constrained firms, with medians of 0.0027 and 0.0139 respectively. Table 8 also summarizes F H P ' s cash flow sensitivity results. Cash flow ^ sensitivities decrease monotonically from the most-constrained class to the least-constrained class. Tables 9 and 10 report the regression results of the simulated investment series on the simulated Tobin's Q and cash flow ^ series. Table 9 indicates that the theoretical unconstrained firm has a cash flow sensitivity of 4.5348, while Table 10 indicates that the theoretical constrained firm has a cash flow sensitivity of 0.5715. The cash flow 2  30  sensitivity results obtained from the models are not consistent w i t h F H P . F o l l o w i n g K Z ' s classification of constrained firms w h e n firms are restricted from investing more, constrained firms are further classified into two sub-groups: investment-constrained i f the K u h n - T u c k e r m u l t i p l i e r res t r i c t i n g rights issues is b i n d i n g and investment-unconstrained otherwise. In accordance w i t h Gross and P r a t a p and R e n d o n , investment-constrained firms have investment policies that are more sensitive to cash flow fluctuations t h a n investment-unconstrained firms, w i t h sensitivities of 1.3514 a n d 0.5444 respectively. These results are not consistent w i t h K Z . T h e cash flow variable is highly correlated w i t h the technology state 9, w i t h coefficients of 0.9867 for unconstrained firms and 0.3840 for constrained firms. T h i s suggests that investment may be sensitive to cash flow fluctuations only because cash flows p r o x y well for investment o p p o r t u n i t i e s . In this chapter, b o t h T o b i n ' s Q a n d cash flow ^ are endogenously constructed from realizations of the technology state 9. Hence b o t h variables are allowed to contain information about investment o p p o r t u n i t i e s . M o r e over, the technology state 8 represents the only source of uncertainty. W i t h only one source of uncertainty, there is a close l i n k between cash flow and investment. F o r example, i f some noise were to be added to cash flow the sensitivity of investment to cash flow fluctuations m a y be reduced. T h e unconstrained firm m o d e l yields the highest investment correlation w i t h the dividend-to-income ratio j^, while the constrained firm m o d e l yields the highest investment correlation w i t h the technology state 8. T h e r e is no single measure of investment opportunities that fits for a l l firms irrespective of their degree of financial constraint. T h e m a r g i n a l p r o d u c t i v i t y of the asset base is different across different degrees of financial constraint a n d cannot be captured by a single measure. T h e m e d i a n dividend-to-income ratio ^ is equal to 0 for unconstrained firms and to 0.9324 for constrained firms. Because unconstrained firms never default, they are able to contract w i t h debt claimants at the riskfree rate, thereby o b t a i n i n g the lowest cost of debt financing a n d a v o i d i n g the default cost. I n t u r n , unconstrained firms pay out a lower risk compensation, i.e., a lower d i v i d e n d , to its equity claimants t h a n constrained firms. C o n s t r a i n e d firms must promise larger dividends to compensate equity claimants for the default risk they face. C o n s t r a i n e d firms cannot raise debt or issue equity to better manage their solvency t h r o u g h various technology shocks. A s a result, firms w i t h no financial flexibility show more volatile d i v i d e n d s . T h e m o d e l of constrained firms, compared to the m o d e l of unconstrained firms, suggests that large and volatile dividend-to-income ratios p r o x y for greater 31  financial constraints. L o w dividend-to-income ratios are associated w i t h unconstrained (as opposed to F H P ' s most-constrained) firms and the h i g h dividend-to-income ratios are associated w i t h constrained (as opposed to F H P ' s least-constrained) firms. N o t e that, dismissing the m o d e l identification of financial constraint to follow F H P ' s a p r i o r i dividend-to-income identification, F H P ' s results obtain. L o w - d i v i d e n d firms, a p r i o r i identified by F H P as constrained firms but modeled here as unconstrained firms, have larger cash flow sensitivities t h a n h i g h - d i v i d e n d firms, a p r i o r i identified as unconstrained firms but modeled here as constrained firms. 3.4  C o n c l u d i n g C o m m e n t s on C a s h F l o w Sensitivities  M a n y questions have been addressed. C a n this chapter determine why i n vestment is sensitive to cash flow? Yes: because cash flows p r o x y for investment opportunities 9. T h i s chapter cannot replicate F H P ' s e m p i r i c a l result that cash flow sensitivities are larger for more constrained firms. T h i s chapter also cannot replicate K Z ' s e m p i r i c a l result that cash flow sensitivities are lower for more investment-constrained firms. T a b l e 11 summarizes the m a i n results of the cash flow sensitivity literature. A star * indicates that this chapter provides evidence i n support of the result. 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P a r k (1998) F i n a n c i n g Constraints a n d Internal C a p i t a l M a r k e t : E v i d e n c e from K o r e a n Chaebols, C a l i f o r n i a P o l y t e c h n i c State U n i v e r s i t y mimeo. [49] S h i n , H . a n d R . M . Stulz (1998) A r e Internal C a p i t a l M a r k e t s Efficient? Quarterly Journal of Economics 1 1 3 , 531-552. [50] Warner, J . (1977) B a n k r u p t c y Costs: Some E v i d e n c e , Journal of Finance 3 2 , 337-348. [51] W h i t e d , T . M . (1992) Debt, L i q u i d i t y Constraints, a n d C o r p o r a t e Investment: E v i d e n c e from P a n e l D a t a , Journal of Finance 47, 1425-1460.  [52] W i g g i n s , J . B . (1990) T h e R e l a t i o n between R i s k a n d O p t i m a l D e b t M a t u r i t y a n d the V a l u e of Leverage, Journal of Financial and Analysis 2 5 , 377-386.  37  Quantitative  4  Appendix  4.1  Effects of the Firm's Decisions o n the F a i r - B o n d - P r i c i n g Equation  The marginal effects of the firm's decisions on the fair-bond-pricing equation (8) are VK'  = -^[( -^^7 " ( 1  ( 1  M  + B{(T -T )L'+X}^, f  v > = -BE B  v (K',o,o-,e') u  B'  2  (27)  l  -S{{Tf-T,)i  -(1 - 1(^>0))  +X}  - ^  r  ,  (28)  and V > = # [ ( ! - T )l(vv>0)] - {{TfL  T )t + X}  t  t  d$(9)  (29)  dt' '  where <i> is the standard normal cumulative density function and 6 is the technology state at the default point. More specifically, 9 is defined by V (K',B',L';9)  = 0.  U  Substituting for equations (2), (4), (5), and (6), the default point is expressed as -  (1 - r )F - p' - (1 - (1 - T )5)K' F  + K" - B" + (! + ( ! -  f  (1 -  r )t')B' f  Tf)K'  A  The marginal effects of the firm's decisions on the probability of default are d^(0)  .,  m  (il-{l-r )5)  a0\  f  (l + a - r y K )  d§{8) dB  Tf)K'<  >o,  (30)  (31)  and du'  T  v  "'  K'  (32)  where (f) is the standard normal probability density function. Equations (30), (31), and (32) indicate that more investment decreases the probability 38  of default, while more debt or a higher coupon rate increases it. Equations (27) to (29) show how the firm's decisions affect the pricing schedule of debt claimants. Equation (27) shows that one unit of asset affects the expected discounted residual claim obtained by debt claimants upon default and the costs at the default point (both the deadweight cost X and the forgone tax benefit due to the reorganization {TJ — T )L'). Equation (28) shows that one unit of debt today affects tomorrow's expected discounted residual obtained by debt claimants upon default and the costs at the default point. Equation (29) shows that the interest rate affects the payoff of debt claimants when no default occurs and the costs at the default point. L  4.2  Data and Calibration  In order to obtain a solution, parameter values for 6, 6, Tf, T , X, a, A, p, a, and F are required. The discount factor 6 is set to 0.95 and the depreciation rate S is set to 0.1, in accordance with most dynamic investment studies since Kydland and Prescott (1982). According to the U.S. tax code, it is reasonable to assume that a representative firm faces a 0.35 federal flat rate and a 0.05 state flat rate. Hence the corporate tax rate ry is set to 0.4. Using individual income tax return data from the U.S. Internal Revenue Service, the personal interest income tax rate is proxied by the ratio of federal, state, and local income taxes to adjusted gross income r = 0.2. Warner (1977) estimates direct bankruptcy costs using data from eleven bankrupt U.S. railroad firms. These costs include the legal, accounting, and administrative costs directly related to the bankruptcy process. He shows that direct costs amount to one percent of a railroad's market value seven years prior to the petition date, and 5.3 percent at the petition date. Altman (1984) includes the indirect costs of lost profits. He estimates the total bankruptcy costs with a sample of eighteen industrial firms who went bankrupt during the 1970-1978 period. On average, total bankruptcy costs represent 12.4 percent of the firm value three years prior to the petition date, and 16.7 percent at the petition date. Andrade and Kaplan (1998) obtain results that are consistent with Altman's results. They estimate both direct and indirect financial distress costs and find that these represent between ten and twenty percent of firm value. I follow previous dynamic u  t  12  Andrade and Kaplan further show that the subsample of financially but not economically distressed firms have little financial costs. However, in this thesis, default is triggered by low technology shocks. Hence firms who are financially distressed are also economically distressed. 12  39  recapitalization models in representing the default cost as a proportion of the debt face value, rather than as a proportion of the firm value as estimated by the empirical literature. In their calibration, Fischer, Heinkel, and Zechner (1989) set their bankruptcy cost to five percent of the debt face value. Kane, Marcus, and McDonald's (1984) calibration assumes a higher value, fifteen percent of the debt face value. As a compromise, I set the deadweight default cost X at ten percent of the face value. Unlike the parameters just discussed, the literature does not offer guidance on calibrating a, A, p, a, and F. The Cobb-Douglas parameter a, the level A of the technology state, its persistence p, and its volatility a are set such that the firm's income equation (5) and its technology process equation (7) represent U.S. manufacturing firms. Equation (5) is log-linearized ln(f(K ; it  e ) + F) = it  a i  lnK  it  + ln9 ,  (33)  it  where f(Kit\0it) + F represents revenues, % denotes the firm and t the year. Equations (33) and (7) are then simultaneously estimated for each manufacturing firm using the Cochrane and Orcutt (1949) procedure. Annual Compustat data from the 1977-1996 period are used, where manufacturing firms are defined as those with SIC codes from 2000 to 3999. Estimating equations (33) and (7) requires data on firms' revenues f{Ku; 6i ) + F and assets K^. Revenues are captured by Compustat's Net Sales variable (data item number 12). The asset base is constructed from the Gross Property, Plant, and Equipment variable (data item number 7), the Capital Expenditures variable (data item number 128), and the Sale of Property, Plant, and Equipment variable (data item number 107). Asset book values, represented by the Gross Property, Plant, and Equipment variable, are converted into market values. First, the market value is set equal to the book value for the first year a firm appears in the sample. Then, the subsequent market values are generated with the restated accumulation equation (6) t  Kit+i =  (l-5)Kit+Iit,  where the investment is measured as the Capital Expenditures net of the Sale of Property, Plant, and Equipment. Book values of the asset base also serve to filter out firms with large discontinuities. These discontinuities are assumed to result from mergers, acquisitions, or divestitures. Firms are included in the sample if they satisfy the M & A filter that variations in book values net of investment do not exceed fifty percent. Finally, the annual data, expressed in millions of U.S. dollars, are deflated at the firms' fiscal 40  year-ends using the U.S. Bureau of Labor Statistics' m o n t h l y producer price index for a l l commodities. T h e C o b b - D o u g l a s parameter ai a n d the autoregressive parameters Ai, Pi, a n d Oi are estimated for each firm. M o r e t h a n four years of d a t a is needed to estimate these four parameters. O u t of the p o p u l a t i o n of 7196 manufacturing firms, 1603 firms have at least ten years of d a t a (on a l l Compustat series used i n this thesis) a n d survive the M & A filter, while 2218 firms show a m i n i m u m of eight years of d a t a a n d survive the filter. T h e parameter values used for the benchmark c a l i b r a t i o n are the means of the ten-year sample estimates. Table 1 documents the parameter values a n d the dispersion of the estimates. F i r m s that have been present for at least ten years d u r i n g the 19771996 w i n d o w are characterized by a sensitivity of their revenues to asset base variations of a = 0.4365, a technology state level of A = 2.9679, a persistence of p = 0.5866, a n d a volatility of a = 0.1836. F i r m s that have been present for a m i n i m u m of eight years show a s i m i l a r sensitivity to asset variations o f a = 0.4295, a s i m i l a r technology state level A = 2.9164, a n d a similar v o l a t i l i t y of a = 0.1885, but differ by a lower persistence of p = 0.5048. A l t h o u g h the labor d e m a n d a n d labor s u p p l y decisions are not modeled, the presence of expenses is acknowledged. L a b o r a n d other expenses F are represented by a fixed cost. T h e calibrated value varies across the different models presented i n this thesis such that the mean of the debt-to-asset ratio B/K series generated from the m o d e l approximates the mean i n the d a t a (0.4031). T h e debt-to-asset ratio is used for the c a l i b r a t i o n of F because the interaction between investment a n d debt issuing decisions is the m a i n focus of the thesis. A s such, the c a l i b r a t i o n of the thesis s h o u l d be based o n the observed mean ratio of these two variables. In a d d i t i o n to the asset base K, investment I, a n d revenues 9K series, other series are constructed from Compustat. T h e debt level B is measured by the L o n g T e r m D e b t variable (data i t e m number 9). T h e price p is represented by the Close P r i c e at the F i s c a l Y e a r - E n d (data i t e m number 199) m u l t i p l i e d by the number of C o m m o n Shares O u t s t a n d i n g (data i t e m n u m ber 25) because the number of shares is standardized to one i n the m o d e l . A s for the interest rate L, the Interest E x p e n s e o n L o n g T e r m D e b t (data i t e m number 101) is not available for most firms i n C o m p u s t a t . Instead, the interest rate t is proxied by today's Interest Expense (data i t e m n u m ber 15) d i v i d e d by the s u m of yesterday's L o n g T e r m D e b t a n d yesterday's D e b t i n C u r r e n t L i a b i l i t i e s (data item number 34). F i n a l l y , d i v i d e n d s D are a  41  measured as Common Dividends (data item number 21). These series are deflated by U.S. Bureau of Labor Statistics' producer price index. 4.3  Numerical Method  The model's equilibrium cannot be solved analytically, but can be approximated using numerical methods. Because the default indicator defined by equation (3) introduces so much curvature in the policy functions, the solution is approximated with finite element methods following Coleman's (1990) algorithm. Accordingly, the policy functions K', B', p, and t' are approximated by piecewise linear interpolants of the state variables K, B, i, and 8. Because the consumer is risk neutral, the endogenous state variables K, B, and t do not appear in the pricing and decision equations. Thus, the four-dimensional interpolant effectively simplifies to a unidimensional one. The state variable 6 is discretized using a uniform grid. This grid consists of ten uniformly-spaced points between the unconditionally lowest outcome i  of the technology state 6i = [A exp(-cr)] ^-f') and its unconditionally highest i  outcome 9^ = [A exp(cr)] -->''>. The approximation coefficients of the piecewise linear interpolants are chosen by collocation, i.e., to satisfy the Euler equations at all grid points. The approximated policy interpolants are substituted in the Euler equations (1), (8), (9), (10) and the coefficients are chosen such that the Euler residuals are set to zero at all grid points. The time-stepping algorithm is used to find these root coefficients. Given initial coefficient values for all grid points, the time-stepping algorithm finds the optimal coefficients that minimize the Euler residuals at one grid point, taking coefficients at other grid points as given. In turn, optimal coefficients for all grid points are determined. The iteration over coefficients stops when the maximum deviation of optimal coefficients from their previous values is lower than a specified tolerance level, e.g., 0.0001. The numerical integration involved in computing the Euler residuals is approximated with a Gauss-Hermite quadrature rule. Only two quadrature nodes are used, reducing the stochastic process to a binary process in which an up move of a occurs with probability 1/2 and a down move of —a occurs with probability 1/2. Following the homotopy principle, according to which policy functions of a well-behaved problem are approximated, the indicator function (3) is < 1  42  transformed to  * l + exp(- V )a  u  T h e policy approximations are first solved using a s m a l l slope, e.g., s = 1. S t a r t i n g values of the policy a p p r o x i m a t i o n coefficients are set to the deterministic steady state. T h e n , the slope is iteratively increased to a large value s = 1000, using coefficients from the previous iteration as s t a r t i n g values. Increasing the slope beyond s = 1000 does not affect the solution. 4.4  Simulation  T h e policy series K', B', p, a n d i' are simulated from r a n d o m outcomes of technology shocks e. P o l i c y series are generated for 1603 firms of 100 periods, keeping the last 20 periods to replicate the C o m p u s t a t sample length of 20 years. F r o m these policy series, investment / , cash flows CF = (1 — T )(f(K;6) -6K - iB), T o b i n ' s Q = ^ , d i v i d e n d D+ (where the + indicates that the d i v i d e n d series does not include rights issues), a n d income Inc — f(K;6) — 8K are computed. f  (  43  1  J  C  Table 1: Calibration of the Revenues Function 10-year sample  8-year sample  a  0.4365 (0.7081)  0.4295 (0.9320)  A  2.9679 (3.2524)  (3.7617)  P  0.5866 (0.3322)  0.5048 (0.3875)  a  0.1836  0.1885 (0.1639)  2.9164  (0.1611)  Note: a is the sensitivity of revenues to asset base variations. A, p, a n d a are the level, persistence, and volatility parameters of the technology process. S t a n d a r d deviations appear i n parenthesis.  44  Table 2: Descriptive Statistics from the Compustat Sample  mean standard d e v i a t i o n  I  AB'  59.9474 22.9612  7.7573 45.0239  1.0000 0.2723  1.0000  6K  a  883.1633 219.2099  D  r  17.9536 7.9950  0.2229 0.6300  t'  0.1464 0.1732  correlation  I AB' 6K D  0.4320  1.0000  r  0.3666 -0.0710  0.0609 0.1056 -0.0266  0.4805 0.0355  1.0000 -0.1066  1.0000  L'  -0.0371  -0.0879  -0.1392  -0.0713  0.0290  a  1.0000  Note: I is investment, AB' is the new debt issue, 6K is revenues, D is the d i v i d e n d p a i d to equity claimants, r is the equity rate of r e t u r n , a n d L' is the promised interest rate. A l l level variables are reported i n m i l l i o n s of dollars. a  45  T a b l e 3: D e s c r i p t i v e S t a t i s t i c s S i m u l a t e d f r o m t h e M o d e l  mean standard deviation  6K  I  AB'  4.0809 1.8952  0.0420  a  8.8701  15.5025 3.9525  D+  r  i'  1.1353 1.6249  0.1688 0.4182  0.0658 0.0000  1.0000 0.7049 NaN  1.0000 NaN  NaN  correlation  I AB' 0K D r i' a  +  1.0000 0.9955  1.0000  0.3245 0.6292 0.9514  0.2420 0.5811 0.9304  1.0000 0.7929 0.4507  NaN  NaN  NaN  Note: r is the equity rate of return, i! is the promised interest rate, I is investment, AB' is the new debt issue, 0K is revenues, D is the d i v i d e n d p a i d to equity claimants and does not include rights issues, r is the equity rate o f r e t u r n , a n d t' is the p r o m i s e d interest rate. T h e above statistics are based on the benchmark c a l i b r a t i o n , where B = 0.95, 8 = 0.1, Tf = 0.4, = 0.2, X = 0.1, a = 0.4365, A = 2.9679, p = 0.5866, a = 0.1836, and F = 9.5. N a N means N o t a N u m b e r . a  +  T t  46  Table 4: Investment Distortion Caused by Financing Frictions  I mean % of  V  mm  Imm 0.7966 (13.61)  V  -Vmm  -8.4701 (14.88)  Note: I — I is the amount and V — V is the value of the investment d i s t o r t i o n caused by the presence of a tax benefit and a default cost of debt. mm denotes the M o d i g l i a n i and M i l l e r framework of no financing friction described i n Section 2.3.1, while variables w i t h o u t subscripts refer to the benchmark m o d e l w i t h financing frictions of Section 2.1. F is c a l i b r a t e d at 9.5 such that the benchmark m o d e l replicates the m e a n debt-to-asset r a t i o observed i n the data. mm  mm  47  Table 5: Debt Overhang  lm mean % of V  mm  Imm  V  m  Vmm  -34.9806 (92.23)  -2.8055 (8.23)  Note: Im—Imm is the amount and V — V is the value of debt overhang, m denotes the Myers framework of investment decisions with arbitrary debt-inplace described in Section 2.3.2, while mm refers to the first-best Modigliani and Miller framework described in Section 2.3.1. F is calibrated at 8.0216. m  mm  48  Table 6: Debt Overhang with Optimal Debt  Is mean % of V  mm  Imm  Vmm -11.5729 (47.54)  0 (0)  Note: I — Imm is the amount and V — V is the value of debt overhang with debt optimally put in place, s denotes the sequential framework of investment decisions following optimal debt financing decisions described in Section 2.3.3, while mm refers to first-best Modigliani and Miller framework described in Section 2.3.1. F is calibrated at 9.2 such that the sequential model replicates the mean debt-to-asset ratio observed in the data. s  s  49  mm  Table 7: Investment Distortion Caused by Sequential Decisions  Is - I mean  -0.7787 (1.68)  % oiV  Vs  V  -0.6039 (9.04)  Note: I — I is the amount and V — V is the value of d i s t o r t i o n caused by debt i n place, s denotes the sequential framework of investment decisions following o p t i m a l debt financing decisions described i n Section 2.3.3, while variables w i t h o u t subscript refer to the benchmark m o d e l o f simultaneous investment and debt decisions of Section 2.1. F is calibrated at 9.2 such that the sequential m o d e l replicates the mean debt-to-asset ratio observed in the data. s  s  50  Table 8: Cash Flow Sensitivity Results of Fazzari, Hubbard, and Petersen (1988)  •jf-. mean standard deviation  CF mean standard deviation  regress CF K  Q  Class 1 Most Constrained  Class 2  Class 3 Least C o n s t r a i n e d  0.26 0.17  0.18  0.12  0.09  0.06  0.30 0.20  0.26 0.09  0.21  0.461  0.230  (0.027)  0.363 (0.039)  (0.010)  0.0008 (0.0004)  0.0046 (0.0009)  0.0020 (0.0003)  0.06  on:  Note: K denotes the c a p i t a l stock, I the investment, CF the cash flow, a n d Q is T o b i n ' s average q. S t a n d a r d errors are i n parenthesis.  51  Table 9: Cash Flow Sensitivities of Unconstrained F i r m s  CF K  Q  9  0.1000  0.0027  1.0351  1.0029  0.0000  1.0300  0.2055  0.2336  0.2446  /  median mean  0.1235  0.0049  1.0030  standard deviation  0.2140  0.0511  0.2569  correlation  1.0000  regress  D+ Inc  K  Intercept  0.4726 -0.4576  1.0000 0.5546  1.0000  0.4427  0.9867  0.5505  1.0000  0.6770  0.8388  0.2168  0.8173  4.5348  -0.8754  0.9843  (0.0027)  (0.0005)  (0.0006)  on:  1.0000  Note: K denotes the c a p i t a l stock, I the investment, CF — (l—Tf)(f(K;  6K -  LB)  state, D  +  the cash flow,  Q  =  (yX^)  T o b i n ' s average  K  q,  6 the technology  the d i v i d e n d p a i d to the equity claimants, a n d Inc = f(K;  the income. S t a n d a r d errors are i n parenthesis.  52  9) —  9) — 5K  Table 1 0 : Cash Flow Sensitivities of Constrained Firms  K  CF K  Q  e  D+  median  0.0862  0.0139  0.7607  1.0268  0.9324  mean  0.0914  0.0121  0.7481  1.0540  2.4248  standard deviation  0.0804  0.0787  0.2737  0.2348  160.0979  correlation  1.0000  regress  0.4535 0.0967  1.0000 0.5259  1.0000  0.7539  0.3840  0.2979  1.0000  0.0030  0.0004  -0.0011  0.0003  0.5715  -0.0881  (0.0119)  (0.0031)  on:  investment-unconstrained:  investment-constrained:  0.5444  -0.0860  (0.0117)  (0.0030)  1.3514  -0.4257  (0.0504)  (0.0350)  Inc  f  1.0000  0.1500 (0.0022) 0.1491 (0.0021) 0.1491 (0.0021)  Note: K denotes the c a p i t a l stock, I the investment, CF = (l—Tf)(f(K; 8K) the cash flow, Q = (i_r )i<  9) —  T o b i n ' s average q, 9 the technology state,  D+ the d i v i d e n d p a i d to the equity claimants, a n d Inc = f(K; income. S t a n d a r d errors are i n parenthesis.  53  Intercept  9) — 5K  the  Table 1 1 : Main Results of the Cash Flow Sensitivity Literature  Result  Literature  Empirical Lower ^  FHP  identifies more constrained firms. CF •• • •  M o r e constrained firms have larger Lower j^, firms have larger ^ KZ  Lower  sensitivities. sensitivities.*  does not identify more / - c o n s t r a i n e d firms.  M o r e / - c o n s t r a i n e d firms have lower ^ M o r e constrained firms have larger ^  HKS GH CHO  ^  sensitivities. sensitivities.  sensitivities not because T o b i n ' s Q mismeasures 0. ^  sensitivities because T o b i n ' s Q mismeasures 0*  Theoretical Gr, P R Go  M o r e / - c o n s t r a i n e d firms have larger ^ ^  sensitivities.*  sensitivities because T o b i n ' s Q mismeasures 8.*  Note: F H P refers to F a z z a r i , H u b b a r d , and Petersen (1988), K Z to K a p l a n and Zingales (1997), H K S to H o s h i , K a s h y a p , a n d Scharfstein (1991), G H to G i l c h r i s t and H i m m e l b e r g (1995), C H O to C u m m i n s , Hasset, a n d O l i n e r (1997), G r to Gross (1995), P R to P r a t a p a n d R e n d o n (1998), a n d G o to Gomes (1998).  / denotes investment, ^  the cash flow-to-asset ratio, Q  T o b i n ' s average q, 9 the u n d e r l y i n g investment opportunities, a n d  the.  dividend-to-income ratio. A star * indicates that the second chapter provides evidence i n support of the result.  54  Figure 1: P o l i c y F u n c t i o n s  0.8  1.0  Technology State  55  1.2  1.6  Figure 2: M i n i m u m Beginning — of — t h e - P e r i o d CF+K-B  Technology State  56  Funds  Figure 3a: S e n s i t i v i t y Analysis  a = 0.435  Figure 3b: S e n s i t i v i t y Analysis  a = 0.440  58  Figure 3i: Sensitivity Analysis  r = 0.15 c  Figure 3j: Sensitivity Analysis  r, = 0 . 2 5  Figure 4 : Investment D i s t o r t i o n Caused byFinancing Frictions 10  10  20  30  - 0  40  — •— 50 0.4  •J  0.6  0.8  1.0  1.2  Technology State  60  L_  1.4  1.6  '• ^~ I-mm • v-v " * mm  Figure 5: Debt  1.0  Overhang  1.2  Technology  61  State  1.4  1.6  Figure 6: Debt Overhang with O p t i m a l Debt  or  10 h  20 h  30  h  0  40  mm mm  50 0.4  0.6  0.8  1.2  1.0  Technology State  62  1.4  1.6  1.8  Figure 7: Investment D i s t o r t i o n Caused bySequential Decisions  i -r  v -v s  s  I  A  1  1  0.6  >  1  0.8  1  1  1  1.0  ;—i 1.2  Technology  63  State  1  1  1.4  i  i  1.6  i  l 1.8  Figure 8: P o l i c y F u n c t i o n s of U n c o n s t r a i n e d F i r m s  0  64  Figure 9: Policy Functions of Constrained F i r m s  65  

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