Appendix R: Technical notes for Footnote 3 (for referee s reference only)

Transcription

1 W &Yao, Main ank ent extaction, 011 endix R: Technica notes fo Footnote 3 fo efeee s efeence ony et e the emim imosed in oth good and ad states. We anayze the thee scenaios in the new setting, esectivey sticking to the same nmeing of eations in the ae. Scenaio : The investment decision with ank det ony Case 1: The manage on ehaf of shaehodes wod ike the fim to ndetake a oject with a non-negative etn on eity nde isk netaity, NPV [ ] 1 Max{,0} 0. eity ee the oigina ent extaction m disaeas t contains a emim. Note that the meaning of hee is dfeent fom what is oiginay sed in the ae. Main anks wi imose sch that 1 1 Min{ 1, 1 } instead of zeo as in the oigina setting whee ent extaction efected as m exicity in. ee ent extaction is modeed as main anks ehavio in setting inteest ates, and ent extaction shows in imicity thogh. Poosition 1: With ank financing ony, the manage, on ehaf of the shaehodes, chooses the investment oicy [ e ], in which e 1 = 1, 7 1 e = Poof: Pey ased on 1 1 Min{ 1, 1 }, main anks set the inteest ate as foows: Note that this has nothing to do with who makes cooate investment decisions. 1

2 W &Yao, Main ank ent extaction, 011 =, 3 1 = 1, 4 = Manages, acting in the inteests of the shaehodes, wi choose ojects accoding to condition. f, accoding to and 3, we have NPV [ ] 1 [ ] 0. eity NPV 0 ony eity 1. Ths, e = 1, i.e. 7 f, accoding to, we have NPVeity [ ] 0. 1 ccoding to 4, we have NPVeity 1 0 ony. Ths, again, e = 1, i.e. 7 f 1, accoding to and 5, we have 1 NPV eity [ ] NPVeity 0 ony. Ths, e =, i.e. 8. Case : f the main ank can make cooate investment decisions, the ayoff to anks is: NPV [[ ] 1 ] 1 Bank [ Max {,0} Min{ 1, 1 }] 0. 9 n 9, m disaeas t ent extaction is imicit in which contains.

3 W &Yao, Main ank ent extaction, 011 Poosition : With ank financing ony, the manage, on ehaf of the ank, wi choose the investment oicy [ ], in which 1 1 =, = Poof: f, accoding to 3 and 9, we have NPV Bank [ [ 1 { [ ] 1 ] 1 ] } 0. NPVBank ony. Ths, 1 =, i.e. f 1, accoding to 9, we have NPV Bank ccoding to 4, we have NPV Bank0 ony [ [ ] 1 ] 1 [ 1 ] gain, 1 =, i.e., 11 f 1, accoding to 5 and 9, we have 1 NPV Bank [ [ ] 1 ] 1 [ 1 ] 0. NPVBank 0ony Ths, 3

4 W &Yao, Main ank ent extaction, =, i.e., 1 Fig. 1. Rests of Poositions 1 and Undeinvest.d Oveinvest. [ e ] 1 [ ] [ ].a Undeinvest.c Oveinvest t tns ot that the ests in Fig. 1 ae simia to the oigina ones in the ae, excet nde- and oveinvestment get sevee fo safe ojects, i.e., when, is cose to the oigin. The eason is that, in the case of oveinvestment, anks have moe incentive to anch ojects with wose to get an nconditiona than to get m that is ootiona ony on. n the case of ndeinvestment, manages have moe incentive to ski ojects with owe to avoid aying a constant than to avoid aying m which is ony ootiona on. 4

5 W &Yao, Main ank ent extaction, 011 Scenaio : nvestment and det-eity financing decisions nde main ank conto The ank s tota ayoff incding eity hodings in the fim: NPV [ 1 D1 D1 ] 1 [ Max{ 1 D1, 0} Min{ D1, 1 }] ed 13 The main ank wi set an inteest ate that contains sch that D 1 1 Min{ 1, D1 } D. gain, ent extaction is imicity modeed in 13 thogh. Poosition 3: n the case of financing with new eity and det, the manage, on ehaf of the ank, wi choose the otima financing oicy, D, and the investment oicy [ ], sch that D =, o 1 and D = 1 and 1 0, 0 1 Cooay 3: n the case of financing with new eity and det, when the ank eies a highe ctoff eve, X, on its ayoff, i.e., NPV X, the manage, woking on ehaf of the ank, wi choose the investment oicy [ X ], in which X x = 1 1, 3 1 x = X and 1 0 4a 1 x = 1 X

6 W &Yao, Main ank ent extaction, 011 Notice that and Poof: Fom D 1 1 Min{ 1, D1 } D, anks set the inteest ate as foows. D 1 { D [ 1 ]} D D1, 16 1 D D D D1, D D 1 D. 18 Beow we ook at financing and investment decisions nde conditions 16, 17 and 18, esectivey. f D1 16, accoding to 13, we have NPV [ 1 1 [ 1 D1 D1 D1 ] D1 ] [ 1 D], 44 and dnpv dd Ths, D =, ecase NPV hee is an inceasing fnction of D. f the ank eies a highe ctoff eve, X, on its ayoff, i.e., NPV [ 1 D 1 D 1 ] 1 [ 1 D 1 D 1 ] [ 1 D ] X 6

7 W &Yao, Main ank ent extaction, 011 then, we have NPV [ ] 1 [ ] [ 1 ] X Ths, X 1 1 x, i.e., X 1 1 f 1 D D D D1 1 17, accoding to 13, we have D 1 [ D 1 ] NPV [ { 1 D1 } D D 1 [ D 1 ] D1 ] 1 [ 1 ] [ 1 D] D 46 and dnpv dd Ths, D =, ecase NPV hee is an inceasing fnction of D. f the ank eies a highe ctoff eve, X, on its ayoff, i.e., D 1 [ D 1 ] NPV D D [ { 1 1 } D 1 [ D 1 ] D 1 ] 1 [ 1 ] [ 1 ] D X D Since D =, we have f 1 D D 1 X 1 1 D x, i.e., X , accoding to 13, we have NPV [ 1 D1 D1 ] 1 [ 1 ] [ 1 D] 48 and dnpv dd

8 W &Yao, Main ank ent extaction, 011 Now we have to conside two cases. dnpv Case 1: f 1 0, then 1 1 >0. Ths, D =, ecase NPV dd hee is an inceasing fnction of D. f the ank eies a highe ctoff eve, X, on its ayoff, i.e., NPV [ 1 D 1 D 1 ] 1 [ 1 ] [ 1 D ] X Since D =, we have X , X i.e., x 1 = dnpv Case : f 1 0, then 1 1 <0. dd NPV is a deceasing fnction of D. Given 1 D = 1 1 D D 1 f the ank eies a highe ctoff eve, X, on its ayoff, i.e., D 18, NPV D D D X [ ] 1 [ 1 ] [ 1 ]. 1 Since D =, 1 we have 1 X , i.e. 1 x = X

9 W &Yao, Main ank ent extaction, 011 Fig.. Rests fo Poosition 3 B y B x O B [ y ] [ x ] [ ] [ ] 1 t tns ot that whie the oigina, stong cvate cased y the asymmetic ent extaction, m is gone in Fige, the main ests on ove- and ndeinvestment emain. so note that the ests nde conditions 1 0 4a and ae simia. The dfeence is tivia; fo, those staight ines ae steee than 1 0 not shown in Fige. 9

10 W &Yao, Main ank ent extaction, 011 Scenaio : Fim contoed financing decisions nde fnding cometition eithe det o eity fim s cost of sing ank oan ecomes: C Bank =. The fim wi choose eity financing C ity <C Bank, namey { 1 1 } 9, 30 Reca is the shae eied y the new eity hodes see 8 in the ae, and the maket exectation fo is = 1 + /. Given 1, we have , 3 Poosition 6: When sing eithe det o new eity to finance a oject, the manage, acting on ehaf of the existing shaehodes, efes new eity ove det as ong as C Bank >C ity, namey, whee 1 1 [ ] , 35 1 [ ] } 36,

11 W &Yao, Main ank ent extaction, Fom Poosition 6, the decision e to choose new eity instead of det is: 0 R1 0 R Poof: The fim wi choose eity financing } 1 1 { i.e., 1 Since ] 1 1 [ , 3 Given that is nomy distited in [, ], the otside eity investos exected ayoffs wi e:. ] ] [ 1 ] [ [ ]} 1 [ { 1 ]} 1 [ { 1 d d

12 W &Yao, Main ank ent extaction, fai maket ice nde isk netaity makes the investos exected eanings exacty ea to thei initia investment. Ths, =. Soving it, we have ] [. Consideing 31, 3, we have 1 36, 37 The fim wi choose eity financing } 1 1 { whie ] 1 1 [ and 1 Ths the fim wi choose eity financing when ] [, i.e. 0 R1 0 R To ndestand the decision e in R1-R, we need to conside thee cases: Case 1: 0 This condition is moe ikey when is owe. ee, the soe fo in R1, 1, is ositive; and the intecet, 1 /, is aso ositive. See Fige 4a. Note that the soe inceases with.

13 W &Yao, Main ank ent extaction, 011 Fige 4a: when is ow. Bank Financing ity Financing Ths, in genea, det is sed to finance ojects with high downside isk and new eity is sed to finance ojects with high gowth otentia t imited downside isk. f advese shocks occ, anks sffe moe, consistent with the est in the ae. Thee is, howeve, a sitation that may aow det to finance ojects with vey high and vey ow at the same time. This is ecase ank costs hee ae fixed font = instead of changing with as in the ae a ootion, m, of. This fthe demonstates why the oigina setting of the ae moe cates the te meaning of ex ost ent extaction. f ex ost fnding cometition is keen, is ikey to e ow and hence the ank hod ehavio tends to e contained fo high gowth fims which can ta into new eity see W, Sec and Yao, 009 fo some emiica sot in Jaan fo this view. 13

14 W &Yao, Main ank ent extaction, 011 Case : 0 This ecomes moe ikey when ecomes highe. The condition in case means that the soe fo in R, 1, is negative, and the intecet, / 1, is negative. Note that the soe inceases in, o ecomes moe fat with an incease in. Case has two sitations: Case a: 1 1 This means that the soe is steee than the soe fo nde the fist est e, -/1-, as shown in Fig. 4. Fige 4: when is high Bank Financing ity Financing This is the sitation vey simia to the est in the ae. 14

15 W &Yao, Main ank ent extaction, 011 Case : 1 1 This means that the soe in R is ess steee than the soe fo nde the fist est e, -/1-. Given its negative intecet, this means a cone sotion of a eity financing. n a cases, the message is eseved that an incease in aggavates the ias ank oan fo downside isk and eity fo wad otentia as shown in the ae. nd 15