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The dynamics of capital structure choice Yu, Albert Chun-ming 1985

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THE D Y N A M I C S OF  C A P I T A L STRUCTURE  CHOICE  By A L B E R T CHUN-MING B.Comm.(Hon.),  The U n i v e r s i t y  A T H E S I S SUBMITTED  of Windsor,  1983  I N P A R T I A L F U L F I L L M E N T OF  THE R E Q U I R E M E N T S FOR MASTER OF  YU  SCIENCE  THE D E G R E E OF  (BUSINESS ADMINISTRATION)  in THE F A C U L T Y OF GRADUATE S T U D I E S THE  F A C U L T Y OF COMMERCE AND  We  accept to  this  BUSINESS  thesis  the required  as  ©Albert  conforming  standard  THE U N I V E R S I T Y OF B R I T I S H May  ADMINISTRATION  COLUMBIA  1985  Chun-ming Yu, 1985.  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I  further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may  be granted by the head o f  department or by h i s o r her r e p r e s e n t a t i v e s .  my  It is  understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be allowed without my  permission.  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  DE-6  (.3/81)  written  i i  ABSTRACT  This  thesis  upon  the  the  dynamic  employs two-period  "tax  shield  capital  recapitalization d y n a m i c s of  the  effect  call  of  a  Simulated end  of  flotation  of  on  structure  bonds can  show t h a t  There  which  the  at  the  empirically  the  acme o f  studies  result  reducing; by  from  flotation  the  Also,  the  recapitalize  at  the  firm  value,  or  ex-  exceeds  not  observed firm  analyse  examined.  tolerable  will  the  can  allowing  with-  the  after-tax  recapitalization  recapitalize.  capital  value  This  structure  function,  is  not  as  most  on  bonds  assume.  important  if  firm  examine  By we  based  will  in  a  to  choice.  be  firm  gain  exists  the  the  inducing  there  which c o u l d  resulting extra  provision  approach  one,  recapitalization  shareholders  costs  capital  period  from  wealth  suboptimal  of  resulting  that  be  end  i f the  implies  Another  the  model  decision.  only  within  empirical  costs"  structure  firm's  costs.  necessarily  bankruptcy  one  boundary  may  at  results  period  dividend,  plus  state-contingent  i s no  i s that  call  call  provision,  thus  may  The be  reduces  provision  may  recapitalization  recapitalization and  call  provision  have been a v o i d e d .  costs  a  reduce in  and  the  wealth  states  which  incurs  flotation  gain too  the  in  small overall  firm  to  value  justify  firm  is  the  value.  i ii  T A B L E OF  CONTENTS Page  T i t l e Page Abstract T a b l e of C o n t e n t s L i s t of F i g u r e s Acknowledgement  i i i i i i v vi  1.  INTRODUCTION  2.  R E C E N T T H E O R I E S AND  3.  A MODEL FOR 3.1  FIRM  DEVELOPMENTS  4  RECAPITALIZATION  Background of the Model 3.1.1 N a t u r e o f R e c a p i t a l i z a t i o n B e h a v i o u r 3.1.2 R e a s o n s f o r R e c a p i t a l i z a t i o n 3.1.3 C r i t e r i a f o r R e c a p i t a l i z a t i o n  8 9 10  3.2  Functions  13  3.3  Model 3.3.1 3.3.2  3.4  3.5 4.  1  and  Objectives  of the Model  Structure Tax and B a n k r u p t c y C o s t A p p r o a c h The S t a t e - P r e f e r e n c e A p p r o a c h  E n v i r o n m e n t and A s s u m p t i o n s of t h e 3.4.1 T h e B a s i c F r a m e w o r k 3.4.2 C a p i t a l M a r k e t E n v i r o n m e n t 3.4.3 O b j e c t i v e o f t h e F i r m 3.4.4 C h a r a c t e r i s t i c s o f t h e F i r m 3.4.5 O t h e r A s s u m p t i o n s Four  15 17  Model  Cases  20 22 24 24 28 30  MODEL L A Y O U T 4.1 D e b t L e v e l D e t e r m i n a t i o n 4.2 D e f i n i t i o n o f V a r i a b l e s 4.3 C a s e I 4.4 C a s e I I 4.5 C a s e I I I 4.6 C a s e I V  35 37 39 44 48 54  5.  COMPUTER S I M U L A T I O N OF  57  6.  I N T E R P R E T A T I O N OF 6.1 6.2  THE  MODEL  RESULTS  59  Optimal Capital Structure Cashflow States Basic P r o p e r t i e s of R e s u l t s (Case I )  in Discrete 60  the Simulated 66  iv  6.3 C o m p a r i s o n o f C a s e s 6.4  I and I I  Interpretation of the E f f e c t s of R e c a p i t a l i z a t i o n 6.4.1 R e c a p i t a l i z a t i o n a s a C a l l O p t i o n ' 6.4.2 C h a n g e s i n F i n a n c i a l P o s i t i o n a f t e r Recapitalization 6.4.3 E f f e c t o f F o n t h e R e c a p i t a l i z a t i o n Boundary 6.4.4 I m p l i c a t i o n s o f t h e R e c a p i t a l i z a t i o n Boundary *  6.5 E f f e c t s o f a C a l l P r o v i s i o n o n F i r m V a l u e 6.5.1 T h e V a l u e o f t h e C a l l P r o v i s i o n 6.5.2 I m p l i c a t i o n s o f C a s e I V R e s u l t s 7. S E N S I T I V I T Y A N A L Y S I S 7.1 B a n k r u p t c y C o s t s 7.2 C o r p o r a t e T a x R a t e 7.3 D i s c o u n t R a t e 7.4 C a l l P r i c e 7.5 F l o t a t i o n C o s t s 8. SUMMARY AND C O N C L U S I O N S 8.1 S u m m a r y 8.2 Two I m p o r t a n t I m p l i c a t i o n s BIBLIOGRAPHY APPENDICES Appendix Appendix Appendix Appendix Appendix Appendix  1A 1B 1C 1D 1E 1F  70 71 75 82 85 88 91 93 97 99 99 104  of t h e Model  Case I S i m u l a t i o n Program Case I I S i m u l a t i o n Program Case I I I S i m u l a t i o n Program Case I V S i m u l a t i o n Program S i m u l a t i o n Input Data and Format .Simulation Results  108 110 111 114 116 119 122 125 126  V  L I S T OF  FIGURES Page  Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure  1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13a. 13b. 13c.  Figure  13d.  Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure  13e. 14a. 14b. 14c. 15. 16. 17a. 17b. 17c. 18a. 18b. 18c.  Criterion forRecapitalization S t r u c t u r e o f t h e Two P e r i o d M o d e l Case I Case I I Case I I I Case IV Numerical Example f o r S i m u l a t i o n Programs .... C a p i t a l Structure i n Discrete Cashflow States Case I R e s u l t Comparison of VLo C o m p a r i s o n o f VDo Comaprison o f VEo R e c a p i t a l i z a t i o n Boundary Capital Structure after Recapitalization Capital Structure after Recapitalization: Continuous Cashflow E f f e c t o f F l o t a t i o n C o s t s on VL a f t e r Recapitalization I m p l i c a t i o n s o f Case IV R e s u l t s E f f e c t o f B a n k r u p t c y C o s t s o n VLo/Wo E f f e c t o f B a n k r u p t c y C o s t s on VDo E f f e c t o f B a n k r u p t c y C o s t s on VEo E f f e c t o f T a x R a t e o n VLo/Wo .. E f f e c t o f D i s c o u n t R a t e o n VLo/Wo E f f e c t o f C a l l P r i c e on V L o E f f e c t o f C a l l P r i c e on VDo E f f e c t o f C a l l P r i c e on VEo S e n s i t i v i t y oh F l o t a t i o n C o s t s ( V L o ) S e n s i t i v i t y on F l o t a t i o n C o s t s (VDo) S e n s i t i v i t y on F l o t a t i o n C o s t s (VEo)  12 21 40 45 49 55 58 62 67 72 73 74 77 81 83 84 86 94 95 96 98 100 101 102 103 105 106 107  vi  ACKNOWLEDGEMENT  I  am i n d e b t e d  advice  with  t o a number  this  thesis,  A c k n o w l e d g e m e n t s must of  the  advices am  Thesis  deeply  Brander  Kevin  Chin  begin  Finally,  to  I  must  a r e mine  Rob H e i n k e l ,  C o m m i t t e e , who p r o v i d e d throughout  Dr.  grateful  for assistance  i t sf a u l t s  with Dr.  guidance  indebted  f o rtheir  thesis.  though  Supervisory  and constant  of people  Rex  advices  Thompson  alone. Chairman valuable Also,  I  and Dr.  James  and a s s i s t a n c e with  this  a l s o express  f o rh i sa s s i s t a n c e w i t h  my w o r k .  and  my a p p r e c i a t i o n t o  the graphics.  Albert  C. Y u  May 1 9 8 5  1  1.  The  firm  capital  controversial finance.  The  MM  structure  issue  Starting  Modigliani  complete  in  from  [1958],  theory  INTRODUCTION  has  academic  world  the pioneering  there  proposes  and  the  decision  [1973],  Baxter  suggest  a  between  the  financing  and t h e expected  gives ah  rise  optimal  t o a concave capital  costs.  in  [1978]  from  This  by  debt  tradeoff  function  and thus  structure.  There have been numerous e m p i r i c a l structure  area.  studies  shield  firm value  and  i n this  [1967] and Kim  bankruptcy  levered  Miller  Later  tax  a  irrelevance  markets.  Kraus and Litzenberger  been  of corporate  of  structure  capital  tradeoff  work  h a s b e e n much work  capital  perfect  long  decision;  however,  studies  of the c a p i t a l  recapitalization  ignored.  One  typical  financial  c h a r a c t e r i s t i c s of a sample of companies  attempts  structure, is  to  to  firm value examine  characteristics that  explain  these  through  ignores  the fact  Especially of  that, bound  in light  capital  time.  are  relationship variables.  structure  cross-sectional  structures  tolerable  and other  capital  capital  a  the  methodology  Heinkel tests  optimal;  flotation  for  suboptimal  of the c o n f l i c t i n g behavior,  capital  Another  approach  [1984]  assume  points  that  evidence  out  observed assumption  there  capital  the  financial  this  costs,  some  among  other  however  with  structure  and  measures  are  usually  and  common  costs  i s always structure.  on t h e  incorporation  role of  2  recapitalization may  lead  between and  to  costs  a  better  observed  firm The  into the capital  provision  treated  this  i s not necessarily as  without  The a n a l y s i s  thesis  two-period four  the  base case i t s only  situation  i n Case  when  with  structure  this  low  traditionally  thus  a reduced  i n the presence  example of  complexity.  other  than  stock.  one-period  bonds  fixed  flotation  i s  a  decision  Then  we a n a l y s e  are issued.  Now,  the  decision  beginning  o f t h e same p e r i o d .  Finally,  a call  introduced  i n Case  made  shows t h e e f f e c t  on t h e c a p i t a l s t r u c t u r e two-period  one  the  i s  capital  because  i s  debt  I n Case  i s made a t t h e e n d o f p e r i o d  IV and t h i s  in a  subdivided  one t w o - p e r i o d  decision  this  approach  choice  i s  structure  With  capital  of  S t a r t i n g .out f r o m  costs.  recursive  firm  this.  costs"  The model  issues  may  incurring  r e c a p i t a l i z a t i o n a t t h e end of period  recapitalization  provision  price  t o r e c a p i t a l i z e more  a " t a xand bankruptcy  model.  However,  call  implies  provision  I , the firm  two  choice  the  has  prevision,  a clear  of progressive  security  optional  while  characteristics,  the dynamics of c a p i t a l s t r u c t u r e  cases  allowed  provide  state-contingent  in  call  of a c a l l  will  since  the firm  costs;  follows  analyzes  III,  firm  f o rthe shareholders.  for a  flotation  recapitalization  as  of the r e l a t i o n s h i p  indentures  the case  incentive  than  unnecessary  and  i n bond  as a protection  an  frequently  This  structure,  decision  value. call  value.  understanding  capital  been  serve  structure  at  the one the  provision i s of  a  call  choice.  m o d e l , we c a n a n a l y s e  the effects of  3  recapitalization thus  on t h e f i r m ' s  hypothesize  firm  i s  function within  not  that  which  there  the  flotation  costs.  tax  flotation  rate,  the  capital  sensitivity Section and  Then-  the  and  functions  rates, and VIII.  IV  reasons  acme  not  of  of t h e f i r m  a  value levels  r e c a p i t a l i z e because of  discount  rate  decision  will  an o v e r v i e w  a  costs,  corporate  and c a l l  price  be a n a l y s e d  on  through  With  the  choice  be  A l l four  model.  cases  with  with  an  costs,  to  corporate  Finally,  and concluded  the  example  VI.  respect  of  computer  programs,  i n -Section  prices.  summarized  background,  of t h e model and t h e  i s simulated  flotation  and c a l l  choice.  i n t h e WATFIV  performed  costs,  the  simulation  interpreted i s  theories  of the two-period  are simulated  are  rates will  of  mechanisms.  i n bankruptcy  findings  description  f o r these  V.  recent  of c a p i t a l structure  the layout  analysis  discount  the  describes  model  results  of  and assumptions  capital stucture  sensitivity changes  costs,  of the issue  i n Section  the  structure  and  analysis.  two-period  programs  will  structure  Section  firm's  firm  II provides  underlying  the  choice  i s a t o l e r a b l e bound o f debt  I I I provides  approach,  at  capital  The e f f e c t s o f b a n k r u p t c y  development  Section  the observed  necessarily  and that  capital structure  Then the tax  the results i n Section  4  2.  RECENT THEORIES  The p i o n e e r i n g suggests  that  capital firm.  work  This  point  and  of view  i s  Hirshleifer  on t h e c a p i t a l  models  by  adding  analysis.  and  various  market  tax  bankruptcy  are  increases  the  payment  trustee  of the firm  advantages  advantages capital  suggest  than that  that  i s  which  there  maximize are  a  the  positive  i n c e n t i v e of  payments t o t h e  in  firm  default  and  this  cannot  meet  and  The e x p e c t e d value  of  [1973],  incurs value  the  t h e market v a l u e  there  of  future  of the firm  Baxter  [1967] and  i s a t r a d e o f f between t a x costs  as a r e s u l t  of t h i s t r a d e o f f .  capital  Management  the  fees.  t h e above approach, optimal  to  bankruptcy  and bankruptcy  costs.  projects  the interest  present  and hence  and expected  shields  agency  the  structure exists  Other  as  the  approach.  Kraus and L i t z e n b e r g e r suggest  imperfections  When t h e f i r m  legal  has been  modifying  of e q u i t y . i t  of t h e Stiglitz  there  to  other  reduces  [1978]  where  and  costs  decreases. Kim  value  then,  deductible  t o bondholders,  fees  cashflows  tax  markets, the  by  costs as a negative  taxes,  [1958]  on t h e v a l u e  structure controversy  In a market corporate bondholders  Modigliani  supported  Since  f i n a n c i n g has been a p o p u l a r  these  and  later  [1966].  Hypothesizing  incentive  tax  Miller  i n complete and p e r f e c t c a p i t a l  research  the  DEVELOPMENTS  s t r u c t u r e d e c i s i o n has no e f f e c t  [1969]  debt  of  AND  Jensen  and  an  optimal  and M e c k l i n g  structure exists  even  [1976] without  c o s t s because of t h e e x i s t e n c e of of the f i r m  will  shareholders'  conflicts  of i n t e r e s t  choose  wealth. between  investment In  cases  bondholders  5  and  shareholders,  chosen  and  result,  this  reduces the  bondholders w i l l  their  interests.  costs  incurred  represents  a  there  are  have  given  transfer  by  certain  up  depend  on  firm.  Jensen  and  minimize  costs the  These  and  point  and  optimal  this  agency rise  liability,  controlling  and  due  costs. the  Ch.  13]  empirical future  controversy. suggest tests  costs  large  firms.  chosen  i n an  risk.  as  to  These the  there  exists  an  tax  shields  and  There  mix  are  will  also  problems.  other  Barnea,  numerous agency  problems.  to  asymmetry,  to  information partial  ownership  with  interests.  growth  flotation  may  by  T h e r e h a v e b e e n n u m e r o u s e m p i r i c a l s t u d i e s on structure  Also,  firm  debt-equity  to agency  and  covenants  p r o j e c t s so  that  a  protect  shareholders.  costs.  i n c l u d e a g e n c y p r o b e l m s due  limited  agency  without  [1981] suggest  As  financing issued  out  even  Senbet  these  value  debt  to  be  convenants  keep  to  structure  which give  these  present  amount of  expected  circumstances  bond c o v e n a n t s  expected  will  bondholders.  i n c u r r e d because  net  Meckling  shareholders  the  to  bondholders  the  capital  bankruptcy  firm  costs  from  on  of  writing  amount of  positive  wealth  optimal  of the  opportunity  favour  wealth  insist  Costs  costs  Haugen  p r o j e c t s which  that  on of  However, Copeland there  this a  firm  third  is  First, hard  do  not  Weston  [1983,  the  usually is  have  that the  with  anticipated  to estimate.  firms are  difficulty  empirical test  capital  several d i f f i c u l t i e s  topic.  for smaller A  are  and  the  Second,  higher  than  a l l companies same  business  6  Miller that  the  fixed  and firm  g r o w s more  period  regressions show t h a t positive that  Modigliani  on  the  time  63  shield  on  the  weighted  leverage  studies  firm  structure  have  specific choice.  Ferri  found  between  debt  l e v e l of  the  of  a  firm  has  relationship the  structure  firm  Bradley, to  for  Their  have  and  a  multiple results  significant  this  implies  c a p i t a l decreases  a  as  positive  they  capital  a  value  that  firm  industry  however,  Also,  business  the  capital  on  relationship  structure  a  single-period  choice  the  model.  Their  leverage  is  inversely  distress the  model  of  a  corporate agency  on  class.  level;  shields,  financial test  relationship  leverage.  tax in  and  operating  negative  financial distress,  firm  Empirical  impact  the  choice  and  linear.  [1984] present  non-debt  of  i t s debt  and  operating  the  costs  on  found  simulate  show  its  capital  examine  indirect  and  between  the  structure risk  and  firm  Kim  of  capital  weak a  with [1979]  business  and  of  relationship  Jones  insignificant  and  costs  the  and  Jarrell  taxes,  variability  shields.  has  l e v e l and  include  expected  of  on  some e f f e c t s  i s not  choice  between debt  results  debt  value  cost  size,  They  personal  firm  firm's  leverage.  They  of  assumes  economy  cross-section  characteristics  class,  industry  model  the  companies.  advantages  focused  its  of  run  they  average  between a  risk  and  overall  relationships  the  than  which  increases.  Other  Size  a model  rapidly  electric utility  tax  impact  the  some  of  [ 1 9 6 6 ] use  and  firm. taxes,  costs  and  simulated related  non-debt  shows t h a t  to tax  there  7  exists  strong  leverage.  industry  These  earnings,  the  advertising inversely level shield. the to  that  simulated the  agency  costs.  incorporate equity Martin  and  They  firms ratio  latter  has that  structure  that  firms  is a  choose data  i s used omitted  industry choice.  there  of  are  are  determinant  industries9 rather the  than  existence  class  is a  key  the for  of  and is  tax in  directly  model does value  ratio  does  classes  of  not on not debt  measuring. i n an of  empirical  capital  period the  debt  model  firm  of  debt  non-debt  relate  leverage multiple  they  covering  of  the  the  the  variability  [1975] demonstrate  class  12  the  model and  measurement  i n the  Scott  in  equity  found  fact  amount of  t e s t does not  the  leverage  Also,  [1984] c r i t i c i z e s  r e s u l t s of  claims  industry  choice. from  the  volatility  financial  the  financial  development,  factors.  to  empirical  Also,  the  and  firm  above  e f f e c t of  firm  include  The  related  the  on  research  However, Mikkelson  for  that  of  the  directly  account  and  amount expenses.  sense the  influences  r e l a t e d to  is  influences  test  structure  1967-1972  analysis.  ratio  Common  because  preferred  shares.  determinant  of  and  the They  capital  8  3.  3.1  A MODEL FOR F I R M  RECAPITALIZATION  BACKGROUND OF THE MODEL  3.1.1  Nature  The  main  maximize  of R e c a p i t a l i z a t i o n  o b j e c t i v e of a corporate  the  equity value  applies  to firm  should  arrange  wealth  the  financial  of the firm.  structure  The c a p i t a l things,  expected  value  future  of the f i r m  earnings,  agency  possible  firm  variables.  specific  which  this,  now m a x i m i z e s  the  debt-equity bond equity  equity shares  financial  mixes.  shareholders'  recapitalization,  the market.  debt-equity  proportion  want  On  tax  rate,  of  of  numerous these  other  variables  m i x may n o t b e  the  In cases  to shift  to  like  another  subject  to  debt-  recapitalization.  can  increase  bonds o r by b u y i n g  the other  the  bankruptcy,  among a l l t h e d i f f e r e n t  a firm  would  the t o t a l  value  wealth,  i s called  p r o p o r t i o n by i s s u i n g  manager  shareholders,  wealth.  shareholders'  process  from  As  debt-equity  i s a maximum  This  c o s t s and  manager might  mix so t h a t  covenants,  During  optimal  and of  probability  c o s t s , expected  one  corporate  as the present  bankruptcy  change, t h e p r e v i o u s  The  also  structure decision i s a  the  the  i sto  T h e same r u l e  decisions.  r a t e of r e t u r n of bondholders  unlevered  manager  e q u i t y mix so as t o maximize  o f , among o t h e r  required the  capital  of shareholders.  function  Behaviour  hand,  involve  i t s back  debtequity  decreasing  issuing  new  the  common  9  shares,  buying  back/retiring  capital  market  or  provision Of  and t h e bond p r i c e  course,  these  the  costs.  they  fees,  Most  small  costs  price.  costless  whenever  and  the  costs  firm  include  and other t r a n s a c t i o n  fixed  costs  with  i t seems r e a s o n a b l e  only  a  t o assume  for Recapitalization  Numerous c i r c u m s t a n c e s  lead to recapitalization.  the variables determining  cause mix  call  are fixed.  3.1.2 R e a s o n s  in  so  be  the  i s a  the c a l l  Flotation  costs are  variable,  not  fees,  from  i f there  than  incurred  brokerage  of these  portion  will  mix.  bonds  bonds  i s higher  are  debt-equity  underwriting  their  transactions  recapitalization changes  calling  corporate  a. r e c a p i t a l i z a t i o n  and a higher Traditional  function  that  overall capital  of levered  the  value  Baxter  value  Litzengerger  [1973],  Kim [1978]  rise  unique  maximum  optimal  debt-equity  debt  level  there  i s no r e a s o n  firstly,  as long  against Stiglitz ).  firm  The f i r m  as i tmaximizes the  the debt-equity  some s t o c h a s t i c e v e n t s , equity  [1967],  mix.  for  m i x i s no l o n g e r  i n debt-equity  s t r u c t u r e t h e o r i e s propose  firm  firm  value  concave  i t s debt  equity  [1969],  and a  &  gives  corresponding  stay  shareholders' to  Kraus  concavity  should  secondly,  optimal.  a  This  with  this  wealth  recapitalize  mix of t h e f i r m or  mix  o f bonds and s t o c k s .  (  a  debt-equity  implies a shift  proportion  to  original  Changes  and  unless,  h a s c h a n g e d due t o  the  original  debt-  10  In  the  funds  first  or supply  cashflows  management  and  the firm  of  credit  In  of  of may  debt  settle  second  and  give  of the firm mix.  thus  rise  structure  i s  position  their  with  i n the  control  of  instantaneous  short  term  line  the firm  will  a long  term  debt  where  change  value  Other costs  the  financial  the optimal  an i n c r e a s e  capital  of  benefits  structure requires a  f a c t o r s such as and expected  i n the optimal to  level  i n tax rate  of the future tax  adjust  probability  future  capital  earnings  structure.  the  suboptimal  level.  there  interest  a r e no t r a n s a c t i o n c o s t s , i t of the  firm  i s any d e v i a t i o n , even v e r y  debt-equity  mix.  debt-equity  However,  may  in  for recapitalization  market  there  changes  necessary  to the optimal  be i n t h e b e s t  observed  with  A f t e r the change,  an o p t i m a l  t o a change  3.1.3 C r i t e r i a  optimal  this  change  i s  extra  stochastic  the  f o r funds  For example,  bankruptcy  Recapitalization  whenever  by a t e m p o r a r y  i s not under  case,  the present  bankruptcy,  would  with  t h e demand  debt-equity; ratio.  a  of funds.  require  issue.  increase  In  These  t h e bank.  debt-equity  higher  source  to the optimal  the  would  may  change  because  characteristics the  This  from  s t o c h a s t i c events  dealt  can only  recapitalize stock  be  mix.  the  or  an e x t r a  may  debt-equity  case,  when  In  this  are flotation  recapitalize  slight,  theoretical  mix would always  there  to  from t h e  world,  the  be a t t h e o p t i m u m . costs  associated  with  11.  recapitalization, time  the  serve  firm  as  budgeting net  mix  firm  value  criterion  in Figure  value  from  so  a  costs.  a  debt  suboptimal  takeover. successful,  mix The  Inside  recapitalization [1984]).  than  takes  a  In  is  concave  not mix  than  the  bounds  bidding  party  in  a  and  realize  between and  the  the  increment  corresponding  when  words,  in  firm  exceeds  the  function  of  debt,  flotation The  will  as  of  firm costs  firm  w i t h i n these  these  firm  only  increment  outside  the  capital  recapitalization  desirable. only  costs  other  suboptimal  bound, the  i s less  a  increment  this  b o u n d on  this  every  to adjust i t s  place  zero.  i f the  ratio,  debt-equity  recapitalize  difference  firm  evaluating  Given  tolerable  recapitalization a  the  in  For  i n c u r r e d ; these  recapitalization  recapitalization  debt-equity  the  1.  As  only  from  against  shown  allow  i s optimal  provides  are  for  i s greater  flotation  value  different.  recapitalization  resulting  corresponding  F,  incentives  project,  recapitalization  is  costs  continuously.  present  value  situation  recapitalizes,  negative  debt-equity  its  the  will  bounds;  encourage  takeover  will,  a profit  in firm costs  value  a i f  from from  (Heinkel  12  Figure 1 Criterion  for Recapitalization  PEBT- saurry REVITALIZE  Source:  V  •TOLERABLE 60UND  adapted from H e i n k e l , "A Simple Test of Relevance", University of B r i t i s h  R., Perceived Columbia,  RECAPITALIZE  Capital  Structure  u n p u b l i s h e d , P.15.  13  3.2 F U N C T I O N S AND O B J E C T I V E S OF THE MODEL A  two  period  model  recapitalization  behaviour  assumptions.  The  relationship  between  overall  level.  of equity Also,  flotation and  model  analyze  costs,  the  bankruptcy  sets  equity,  value  of  the debt,  under t h e  and the optimal  influence  costs,  of  way o f a n a l y s i n g  of  debt  changes  the corporate  on t h e r e c a p i t a l i z a t i o n  model assumes a f i r m w i t h  sequence o f two s t o c h a s t i c , the  ability  to  finance  financing.  T h e d e b t may  The  focuses  model  after The  one p e r i o d  equity  this  in  tax rate,  decision  The  objective  the  Also,  and  the.  want  to  determine  allows costs,  us  to  debt  discount  rate  and  decision. examine  bankruptcy  some  debt  maturity.  flotation  t o maximize  costs. the value  costs,  i s t o understand  how debt  the  capital  level,  equity, Finally, impact  the  corporate  change  of changes tax  impact value.  structure  firm value, after  sensitivity  the  on t h e f i r m .  the  r e c a p i t a l i z a t i o n on f i r m  such as optimal  recapitalization  of  i s made  thesis  costly  of  with  time.  of  value  a  t o r e c a p i t a l i z e the firm  the existence  of t h i s  characteristics,  with  cashflows and  have a one o r two p e r i o d  option  we  to a project  dependent  project  on t h e d e c i s i o n  given  at that  access  serially  recapitalization decision  of  a  value maximization,  we  simulate  different  presents of  to  value.  The  of  presented  the r e c a p i t a l i z a t i o n decision  the interest rate  firm  be under  the value  firm value,  objective  will  and the  analysis  in flotation  rate  and  the  1 4  We  hope  this  optimal  capital  capital  structure  study  structure decision  provides and for  insights  possibly a  firm.  a  i n the  strategy  theory for  of the  15  3.3  MODEL S T R U C T U R E  3.3.1  Tax  and  The  Bankruptcy  model  bankruptcy  cost  because  the  of  Cost  employs  a  point  view.  of  resulting  offsetting  the  as  a d i s i n c e n t i v e to debt most  associated tax  the  f a c t o r of  the  and  overall value  considering  leverage  increases  equal  the  to  resulting tax  approach  Hirshleifer  [1966],  reach  Later  firm  o p e n up  However,  the  and  favourable  however,  there  bankruptcy  costs  i s the  cost  tax  of  A  of  the  reduced  mean-variance  of  borrowing,  by  an  tax  amount  deductions  structure  Litzenberger approach  and  payment  models employing  capital  is  increased.  firm  future  and  tax  has  the  Various  Kraus  shield  borrowing  advantage  value  of  tax  payments to debtholders  shareholders  of  by  the  (state[1973]  and  Rubinstein  conclusions.  research debt  by  this  Stiglitz  [ 1 9 7 4 ] shows  f i n a n c i n g i s the  portfolio  and  portfolio since  market  by  leverage  capital.  the  value  of  new  i s s u i n g debt  desirable  for  the  theoretical advantage  from  left  similiar  another can  of  issue  preference  shield;  expected  the  borrowing.  deductibility  [1973])  cost  the  the  of  reduces  only  present  from  Part  so  tax  financing.  with  i t .  corporate  financing is  tax  higher  of  means t h a t ' t h e Thus,  Debt  obvious advantage  deductible  hence  traditional  interest  is  The  Approach  opportunities  allows  positions  for  that  this  they  could  advantage  the  investors  investors to achieve  than  v a l u a t i o n of  fact  that  more  before. i s not  the  16  objective  of the model,  A firm into  entering  an  certain  any debt  obligation period  that  future  chance  that  the firm  this  to  would  Thereafter, they  value  of  firm  the  fees and other costs of  the  costs  firm  chance  that  and  incorporate into  theoretical  cannot  this  chance  the expected  world of p e r f e c t the  stockholders  to bondholders  3.3.2 [1959],  meet of  [1966])  default. the  i f t h e market below i t s  case,  legal  i s a  they  fees,  trustee  The  value  because  other  can  these  than  the  assume t h e r e i s a l w a y s  a  i t s payments.  Investors  bankruptcy  they  transfer  will  and  perceived  of  In a  are  ownership  have  decision  there  i s  no i m p a c t  (Arrow  no from  costless  (Stiglitz  will  bankruptcy  securities.  where  default  The S t a t e - P r e f e r e n c e A p p r o a c h Hirshleifer  the  a  the  over  falls  be r e d u c e d  markets  structure  take  the firm  of the firm's  under  in  and t h e r e  are incurred.  We  of bankruptcy  the firm's capital  to  case,  value of the  valuation  the possibility  i s involved  to parties  stockholders.  the  not  enter  payments over  concern  will  be p a i d  costs,  on  i s  bankruptcy  bankruptcy  the  going  of bankruptcy  the firm  perceive  costs  can l i q u i d a t e a  will  t h e agreement and  In either  o f b a n k r u p t c y must  bondholders  will  in  fixed  have t h e r i g h t  as  firm.  agreement  are uncertain  breach  value, or i f t h i s  reorganize  some  cashflows  firm.  dismantled  financing  of insolvency  case, bondholders  the  be i g n o r e d .  make  and a r i s k  sense  In  i twill  and  a ta l l  [1974]).  [1964],  Debreu  17  In  evaluating  recapitalization  the  value  behaviour  assume u n c e r t a i n streams two  periods.  different  cashflows  obtain at  There  are  different  the  are  represent  etc.  Once t h e of  product equal  firm  the  of  earnings  to the  variables  i n the  state  and  of  model a r e  The  causes  to  the  the Each  and  the  state  of  of  economic  various  states  recession, depression,  the  world  i s revealed,  the  exactly.  earnings state  equals  level of  A l l the on  this  is  nature  just and  the  the  sum  of  the  probabilities  is  e v a l u a t i o n s of  the  one.  corresponding  based  due  earnings  exclusive.  an  periods.  nature  of  of  nature  conditions.  level  of  of  second  to  state-  what  business  earnings.  the  knowing  determined  expected  lead  uncertainty  normalcy,  the  would  we  next  the  are  and  the  later,  f o r example,  probabilities  i t s  model,  over  In  s t a t e s of  corresponding  and  period  firm  fundamental  uncertain state  state  the  mutually  economy;  probability of  and  two  first  and  prosperity,  the  probability  not  the  the  in" t h e  can  the  of  firm  states.  potential  exhaustive  uncertainty  in  to a p a r t i c u l a r  captures  The  of  f u t u r e economic  states  of  end  a  future cashflows  different  form  numerous  corresponds  earnings  of  the  presented  the  state  nature  in  model takes  in  investment  payoffs  preference  will  An  of  The  sum  state-preference  principle. There approach First,  are and we  outcome from  several they  are  assume the  key  assumptions  discussed  the  frirm  and  associated with  this  below. each  firm's probability  i n v e s t o r can  distribution  of  relate its  an end  18  of  period  possibly  occur.  investor the  earnings  will  shareholders'  both  portfolios is with  their  utility Let state  can of  s represent may  utility  firm  expected  is  total just  state  and  occurrence  the  overall  The  and  finally, are  the  functions by  Myers  choose  their  future return  utility  linear  about  associated  function  of  the  that  the  state. the  i n v e s t o r ' s judgement  contingent received in  utility  time  of  the  ( s , t ) and (s,t),  U(s,t)  then  contingent  of  we  returns  risk  t we  assume  neutral,  that  i.e.  shareholders they  have a  and  linear  function. model  cashflows decision  of over  recapitalization the  involves a  model w i l l  be  which  two  series  s o l v e d by  state-preference within  of  out  of  and  as:  bondholders utility  h i s wealth  will  represent  of  an  pointed  i s an  r e t u r n s t o be  S Fourth  t  o b j e c t i v e of  utility  expected  f o r each  can  of  utility  a  that  only concerned  bondholders  I f P<s,t)  of of  formulate the  a  occur.  probability the  and  as  nature  value  shareholders' Third,  function defined  value  are  A l s o , the  portfolios  present  Investors  that their  maximized.  t h a t the  present  shareholders  such  of  the  state-independent.  [1968],  is  maximize wealth.  state  assume  the  of p e r i o d p a y o f f s and  are  the  each  S e c o n d , we  i s to maximize  firm  end  with  a  approach  to apply  assumes  periods. of  The  recursive  dynamic  firm  recapitalization and  the  programming approach.  The  provides a  a dynamic  uncertain  decisions  simple  programming  analytic  solution.  model This  19  approach  allows  decision  of  us  to observe  the  firm  the  advantages of  clearly  under d i f f e r e n t  the  capital  economic  structure  and  business  conditions. Despite there  are  disadvantages  situation,  i t  exhaustive  and  Incompleteness are  some  should  not  firm  defined  of  be  and  a  in  always  the  difficult  problems.  analysing  to c l a r i f y  states the  i t .  to  exclusive  s t a t e s and  concern  the  state-preference  associated with  mutually  obvious  interested the  is  the  In a  their  this  analysis  the  recapitalization  recapitalization  of  nature. nature  disadvantage  our  are  world  set  overlapping  However,  nature  a of  in  of  real  define states  approach,  since  just  process.  we  behaviour  are of  arbitrarily  20  3.4  Environment  3.4.1 In  Basic  the  two  period  at  the  uncertainties number  of  periods,  Figure  at nature  point  So,  the  levels  i n the  top.  Xi  period  one.  end  period  and  various  f i g u r e are the  arranged  exhaustive  and  we  the  that  leads  the  the  of  each of Each  to  a  are a the  state  number  two  out  of  of  already  at  model  at  the  cashflows  smallest  cashflow  are  period  A l l the  the  jth level  X i has  There  two.  with of  future  form  of  firm starts  in a period have  end  state.  i t h level  the  earnings.  one  The and  periods.  the  s t a t e s of  time  Y i j represents given  at  f i r m having  takes  period  diagram.  cashflows  this  period of  a  two  particular  end  current  two  and  of  the  tree  of  nature,  end  represents  of  Model  consider  each  their  2 shows the a  of  of  at  we  earnings  the  by  States  end  i n the  represented  of  model,  each having  of  the  Framework  states  nature  states  Assumptions of  The  earnings  of  and  at  the  cashflow  the  end  of  at  the  occurred.  mutually  exclusive  following properties: (2)  I  P(Yij)  Also, Where  3  P(Xi)  i s the  = P(Yij|Xi).P(Xi) p r o b a b i l i t y of  (3) Xi.  Figure Structure  of  the  2 Two P e r i o d  Model  22  3.4.2  C a p i t a l Market We  Environment  E f f i c i e n c y of the C a p i t a l have assumed t h a t  their  utility  objective future  to  payoffs.  efficient  In  terms  assumed can  that  gain  of  prices  the basis  information of  that  the  across  state  determine  the  market and  first  we  expected  assume  that  an  i t achieves  efficiency  (  firm  of  will  of the  a n d no  one  information.  For  assume  exist.  can  so  that we  that  the statecan  readily  recapitalization decision  and the  with  the  i s t o maximize  fundamental  p r i c e s of the unlevered signals  they  no  assume  a l l when  estimate  firm,  at  homogeneous  Also,  by  has  of the firm  manager  i s observed  investors  values  bonds a r e c o r r e c t  We  can  i t i s  individual investor  and the f i r m  state  optimal  efficiency,  the earnings  period.  earnings  of the firm  terms  sense  o f p u b l i c l y known  concerning  Once  future  In  the  a r e a t S o , no  earnings  contingent  objective  objective,  that Their  of  a random w a l k p a t t e r n  inefficiencies  obtains.  corresponding  we  investors  informational the true  in  value  e f f i c i e n c y ,fundamental  follow  superior  that  present  information-arbitrage  given  beliefs  and  ) and a l l o c a t i o n a l e f f i c i e n c y .  on  end  neutral  state-independent.  the  market  example,  the  are risk  In a t t a i n i n g this  information-arbitrage [1982]  are  maximize  capital  Tobin  investors  functions  i s  Market  assumption  that  shareholders'  the  wealth.  e f f i c i e n c y , we a s s u m e t h a t firm,  levered  for investors,  firm, i . e , they  the  stocks fully  23  and  instantaneously  information market value  price of  utility  of  are  each  security  assumed  to  have  of  allocational  the  firm  investors  and  maximize  their  net  recapitalization,  present  the  firm  to  net  the  payoffs.  the  present  Since  a l l  state-independent  present  value  we  their  values.  If there  will  a call  proceed  firm  should  call  the  bonds  back  in  the  market  i f  the  call  is  at  funds  p r o v i s i o n on  so  is a  with the  that  as  from  In  the  bonds of buying  i s lower  to  gain  i t .  i n s t e a d of price  assume  the them  than  the  value. M a r k e t of  the  effect  We are  sufficient securities.  the  model  recapitalization so  included made.  Imperfections f u n c t i o n s of  of  conditions;  markets  words,  allocate  the  be  other  efficiency,  firm,  are  relevant  utilities.  where  One  is  of  net  case  economic  there  will  In  linear  this  their  available  i s equal  future streams  maximizing  terms  a l l  known.  functions, maximizing  same t i m e In  is publicly  a l l expected  investors  the  which  reflect  taxes,  flotation  i n the  model.  assume t h a t a l l price market  takers. power  to  is  under  participants  change  of  the the  costs  assumption in  the  the  market  bankruptcy  additional  None  analyse  imperfect  c o s t s and  One  to  will  capital  i n v e s t o r s have price  of  the  24  3.4.3  O b j e c t i v e of  The  objective  value of  of  the  the  accrue from in  to  the  the  of  the firm  undertaken  the  i s to maximize  plus  the  residual  the  equal  one, of  wealth.  the  debt  Thus,  the  shareholders,  at  debt  the  plus  firm;  present i . e . , the  is  firm  value  of  the  market  value  of  the  financing  to  existing  of  At  at of  time debt)  equity).  the  total  end  of  market  shareholders'  value  net  the  and  on  the  who  to  i s to maximize  impact  instead,  will  debt  value  So  the  proceeds  (market v a l u e  possible  overall  that  decision-maker  equity value.  directly  maximizing the  at  for  profit  of  (market  firm  beginning  the  accrue  the  present  shareholders  future  proceeds  equity value  does not  A l l  existing  So of  the  cashflows  periods. the  the  i n v e s t o r s pay  proceeds  firm  to debt  At  the  their  recapitalization  o b j e c t i v e of  maximize  to  of  o b j e c t i v e of  value,  price  later  the  the  2,  share  objective  zero  period  to  part  the  shareholders,  firm  in Figure  i n the  Since by  i s to maximize  i t s shareholders.  firm  turn, sacrifice  Thus,  firm  f i n a n c i n g accrue  bondholders.  the  of  p e r i o d , So  of  debt  Firm  wealth  current  securities  the  i s no  objective proceeds  equity.  longer is  to  to  the  25  3.4.4 C h a r a c t e r i s t i c s o f t h e F i r m Since  our  decision  entity  decision which,  opportunity the by  next  i s  to  and the r e l a t e d  production an  aim  focus  financial  i s ignored.  by  means  to realize  two p e r i o d s .  of  These  position  of the firm, the  The f i r m  i s considered  earnings  as  possesses  an  patterns  a t t h e end of  patterns  are described  t h e s t a t e - c o n t i n g e n t approach p r e v i o u s l y o u t l i n e d and a r e  the  of the firm  value  stocks  and bonds  payoffs  to  since  This the  implies balance  The  assume  of  concentrate  only  lower  only  of  pure  discount  future  are merely  providing  next  periods.  period  expected  two  hand  side of  debt  and  of  This  of the changes  bonds,  without  amount a t a c e r t a i n  that  of  the present  will on t h e period  period.  a r e assumed  to  allows  to  i n debt making the  us  and equity adjustments  firm  i s ,the firm  date  in  i n the next  equity.  I n a d d i t i o n , bonds  i s just  earnings  the firm  depend  We  two a r e dependent  earnings  position  two p e r i o d s  conditions.  Lower  securities  discount  bond  the next  period.  financial  claims.  pay a f i x e d  of the  expected  the right  business  in  on t h e e f f e c t s  the firm's other  the  only  over  and  of the previous  outstanding  consist  in  of the firm  earnings  one i w o u l d mean The  in  by t h e v a l u e  the  The a s s e t s  we c o n s i d e r  economic  that  earnings  represent  Thus,  sheet.  earnings  exogenous  these  the earnings  that  structure choices.  i s affected only  the investors.  means t o g e n e r a t e  the  recapitalization  some e a r n i n g s  of the firm's c a p i t a l  to  the  i t s nature,  independent  on  on  consist  promises to  and the market value value  of  the  of  future  26  amount by  that  the  bondholders  r e q u i r e d r a t e of  market  value  of  the  expect  the  discount  bond  r e q u i r e d r a t e of  ability  the  earnings rate  of  would  decrease the  the  On  have  probability are  other  there  fact,  the  stock  to  the  reduction i n expected  policy.  Earnings  earnings after  before bond  costs  flotation thus  interest  taxes. EBIT of  are  is the  period  one  earnings  i n p e r i o d two,  future  of  the  taxes  given  the  of  the  In t h i s  case,  the  bankruptcy  the  bonds the  the  state  is  value  same,  residual  due  dividend  periods .  The  are a l l  net  and  amount  taxes  dividends.  the  of  cost.  is  Bankruptcy  t o be e x t r a o r d i n a r y  the  serially  incorporate  value  that  costs  the  a  chance  remain  assumed  of  and  firm  two  included in  securities  market  bonds and  (EBIT)  as  interest  bonds  of  the  least  positively  values  will  of  bankruptcy  costs are  market  the  expected  value  flotation  not  the  the  period.  at  shareholders  expenses and  bonds and  earnings  better  the the  the  f o l l o w s a pure  and  payments,  and  next  each  interest  to the  Because  firm  in  distributed and  is a  i n c r e a s e , or  assume t h a t the  of  i f the  value  the  So  o n l y on  i.e.,  i n c r e a s e the  market  of  We  will  both  debt,  i s reduced,  the  discounted  depends similiar  value  hand,  bankruptcy and  pay  i n c r e a s e i n the market  good e a r n i n g s  of  In  An  r a t e would  the  lower,  higher.  o f f the  can  debtholders.  r e t u r n on  market  i n p e r i o d one,  will  costs  the  in interest  high  firm  t o pay firm.  reduce  debt.  are  firm  firm  r e t u r n of  prevailing of  the  firm  earnings  correlated, at  the  conditional of  before  nature  end  the of  expected in  period  27  one,  and  Residual  from  earnings  dividends. the not  market due  the  to  information  Thus  the  values the  relevant in  period  effect of  the  amount of  content  of  financial  decisions  one  be  the  earnings  securities  earnings  i n the  will  earnings  in period  in that  in that  paid  out  as  one  on  same p e r i o d  is  period,  in period  made.  one.  but  to  the  28  3.4.5  Other  Besides and  Assumptions  the assumptions  the c h a r a c t e r i s t i c s  still  is  assumed  constant. effect  This of  that  required  a of  a change of  neutrality  and  stockholders  cash  flows  having  will  environment  conditions  are  apply  same d i s c o u n t  First,  one  are this  the  payments.  the s e c u r i t i e s .  i t s securities  two.  allows  the of  rates  to  expected  instead  to  for  of  a l l the be  tax  making  this arising  importantly,  amplifies  Changes  us  assumption  between p r i n c i p a l  more  deductible  be  bondholders  in  to observe  and  making  the e f f e c t the  have a more p r o f o u n d e f f e c t This  to  complication  repayment  the  both  assumed  the  debt  the assumption  Also,  reasons  avoids  of  assumed  tax deductible,  are  decisions.  more need  that  expense  two  debt  tax  financial now  and  S e c o n d l y and  payment  further  with  implies  the  the  simplifies  investors  There  recapitalization  is  and  along  of  Similiarly,  analysis  of  will  structure.  the  bondholders  structure  the value  in  the  on  on  Again, this  to  whole  rate  bonds i s  confusion  periods.  interest  interest  avoid  for  two  assumption  allocating  rate  to shareholders  the  assumption.  sell  several  discount  in capital  i n both periods  deductible.  We  the  only  proceeds  of  market  the  This  risk  taxes  firm,  in interest  return  confusion  situation.  the  the  assumption  within  avoids  that  change  rate  constant  from  of  the c a p i t a l  required.  It  with  on  on  of  capital the  value  the e f f e c t  of  dramatically. the assumption in  the  that  capital  the  market  firm  can  buy  whenever  or the  29  manager  desires.  bankruptcy we  have  model  costs  In  are both  ignored  not  the  at  the  add  to the a n a l y s i s  arising present problems  investment  in  of  other  and  by  flotation  l u m p sum  financial  any  agency  p r o d u c t i o n problems.  i f we areas  include such  to exploit  co-ownership,  on  the  potential as  giving the  etc.  costs  amounts.  decisions  recapitalization  value projects caused  fixed  the e x i s t e n c e of  only c o n s i d e r s the  effect  addition,  of  Finally,  problem. the  We  The  firm  and  are  aiming  so  i t does  firm, agency up  and  problems  positive  bondholders,  net  agency  30  3.5 F o u r  Cases  There  are  different some  cases  scenarios  and  c o n d i t i o n s common  is  assumed  if  the firm  the  c a n n o t meet  costs  a  fixed  arising  from  simplicity,  states  in  states  a  shareholders  corresponding  However,  cost  of earnings.  an  assumed  that  are irrelevant  chance  of  the  i . e , a l lthe  of  the personal  of  amount.  occurrence  t o be e q u a l ,  equal  Also,  Flotation  are a fixed  of  are  maturity  i s incurred.  probabilities a r e assumed  there  to  The t a x r a t e  i t s obligations at the  the recapitalization  the  i s  model  fora l l levels  bankruptcy  period  i t  the  t o a l l the four cases.  i n a p e r i o d have  Finally,  i n  assumptions.  t o be c o n s t a n t  debt,  For  four  occurrence.  tax rates of the  t o the financial  policy  of  the  firm. In time  case  one,  period  zero,  of  maturity  its  optimal  this  periods.  the  those end  under  earnings of  case,  Earnings  shareholders  will  period  determination determined  issue only  bonds w i t h  Once t h e f i r m  mix  the  based  the pure  i s allowed  firm only  i n period  will upon  make the  the  a  length  has determined i t will  residual  Thus,  i t s capital second  period  optimal  by t h e s e c o n d p e r i o d  debt  level  earnings.  to the so that  repaymentat of  No  w i t h i n t h e two  dividend policy  valuation  keep  period.  one a r e a l l d i s t r i b u t e d  not c o n t r i b u t e t o debt  two. of  t o i s s u e any debt a t  t h e end of t h e second  debt-equity  decision  earnings.  decides  structure i n period zero,  mix u n t i l  In this  structure  will  two p e r i o d s .  capital  in  the firm  they  of  debt-equity  change  i f  debt  and  will  only  the the be  31  In  case  two,  we  discount  bonds w i t h  firm  the  has  twice,  first one  of  debt  is  the  issue  by  of  one  bonds are  bonds  of  the  period  can  only  firm  by  and  before  debt  i n the  the  of in  the  period  the  second  second  issue  earnings.  i t seems t h a t  the  at  size  off  The bonds  again  earnings  is inferior  over  discount  by  the  pure  period.  the  paid  two,  bonds  u s e d , we  structure  and  one  case,  amount of  second  two-period  one-period  the  of  p e r i o d one  this  t o be  issues only  one-period  of  In  which  maturity  issue  two.  Similiarly,  of  firm  i s a f f e c t e d only  Comparing case issue  to  bonds have  affected only  a  l e n g t h of  beginning  period  s i n c e the  period.  a  option  once at  beginning  consider  two  having  to having  looking at  the  single  two  periods.  determine  a  If  issues  two-period  optimal  a l l the  capital  earnings  states  0  at  the  level two So  end  the  second  i n p e r i o d one earnings  using  changes  earnings. longer  the  (due  optimal.  case,  one  the  overall  and  optimal  firm  harmful  Since  value  effects  equity  ratio  higher  than  bankrupt.  the  The  higher  two-period  the  below  becomes  the  in  probability expected  is  i s not  that  bankruptcy  period  in  period peribd  possibly not  allowed  no  matured in  this  suboptimal  maximum.  period  of  second  bonds have  shareholders. high  of  mix  earnings  correlation).  level  distribution  possibly be  becomes t o o  serial  earnings  recapitalization  will  optimal  distribution  debt-equity  mix  to  the  expected  original  H o w e v e r , when t h e  to p o s i t i v e  conditional  The  period  period.  i s revealed  i n v e s t o r s r e v i s e the  two  at  of  First, one, the costs  and  There are  two  i f the  debt-  there  is  firm will  will  a go  reduce  32  both  the  market  objective  of  values  maximizing  undesirable.  Second,  the  i f the  probability  of  bankruptcy.  advantage  tax  b e n e f i t s from  of  the  costs  since  firm  reduces  the  amount  Once  the  firm  so  as  Despite disadvantage bonds  issuing of  bonds  once.  bonds o n l y extra In first  flotation case  earnings  at  level i t s  flotation  of  of  the  expected decrease thus  advantage  of  case  the  can  be  Each  have  the  i s s u e of  the  costs,  preferred to  the  flexibility  so the  issuing  bonds a r e added  the  value.  incur twice of  is  to  firm  bonds  costs.  will  p e r i o d one  b o n d s up  flotation  bonds t w i c e  that amount  two-period two-period exceeds  the  incurred. consider  issues two-period  recapitalize  adjust  we  one-period  the  the  and  in  maximum e q u i t y  amount o f  value  costs  three,  level  s t r u c t u r e of  in  Thus  will  the  capital  One-period  i f the  has  The  c o s t s as  the  distributed.  one-period  fixed  one  some o f  earnings  i s s u e new  one-period  flotation  of  is  optimal  lower  stock  can  higher  requires a  lose  financing.  out  earnings  the  result  than  because of  the  in period  lower  the  bonds  advantages,  of  of  dividends  to a t t a i n  the  debt  Given  this  ratio  i t will  more t a x e s  the  wealth,  a  Also,  value  must pay  desired.  adjusted  the  have  increase  one-period  flexibility. revealed,  but  amount of  Issuing  will  bonds w i l l  bankruptcy the  firm  stocks.  debt-equity  low,  value  bonds and  shareholders'  becomes t o o  of  the  of  debt, end  of  the  case  but  the  the  in firm  first  which has  the  the  option  period.  period  one  is  revealed,  debt-equity  mix  so  as  the  to a t t a i n  firm  Once firm  the  to the can  maximum  33  equity  value.  Cases allow in  two a n d t h r e e  recapitalization  case  with  t w o , a new  the  likely  of  debt  that  exceed  of f l o t a t i o n  i s issued  level  a t the end p e r i o d in  n o t be a b l e  the  will  call  market  1  resources  of  the  case  of  three,  part  The  firm  three,  call  i f the  p r i c e of t h e bonds.  from a zero some  the  We  to  the  two-period debt  cases,  the  recapitalization  flexibility  costs  and  debt  with  firm  and to  avoids perform  period. model,  one price. call  we  examine a  provision  allowed  period  predetermined  the bonds only  i s  due  two-period  however, a c a l l  a t t h e end of a  more  final  bonds.  at  allows  every  to  bonds  As a r e s u l t ,  flotation  Thus  recapitalization  t o case  outstanding  option  of the  similiar the  debt  in  extra  start  i s s u i n g new  r e s u l t i n g from  the  i t  be l o s t  Thus,  necessary  very  In case  i s not optimal.  recapitalization  In  value  to justify  recapitalization  unnecessary  one.  However,  i s  and t h e f i r m does not s t a r t  equity  mis-allocation  and  incurred.  costs.  one.  both  The f i r m w i l l  1  from  will  that  always  one  value  of the shareholders  debt  a  costs  i s  costs.  i n equity  the flotation  expense  may  t=2  a t t h e end of p e r i o d  extra  increment  issue at  flotation  the gain  the wealth  i n the sense  a t t h e end of p e r i o d  debt  attendant  from a zero  will  are similiar  to and  i s  call  added  t h e bonds  repurchase  Of c o u r s e , price  add a c a l l a b l e  i s  case  the  the firm  below  clause  the  to the  Except i n the case o f an unlevered capital structure; however, t h i s i s suboptimal since the tax advantage i s very large.  34  analysis on  the  to allow  recapitalization  callable can  clause  Case  four  as  cases  includes  case  three,  equity  value  one-period  debt  feature  flexibility  now  involves  maximizing  is  added  the  four  cases  so  that  we c a n o b s e r v e  the  financial  firm's  case  i n case  of  allows  decision  securities.  option  the  and i t  an  This  in  almost one.  the e f f e c t of each  case  two  compulsory  i n the sense feature  Finally,  each  debt  A s we p r o c e e d t o  option  progressive  us t o i s o l a t e  complexity.  two-period  i s allowed  decision.  four.  with  feature  a t t h e end of p e r i o d  more  recapitalization  a call  having  of progressive  the simplest  added  recapitalization  t o having  show a p a t t e r n  The  an  Actually,  provision  such.  one r e p r e s e n t s  outstanding.  t h e e f f e c t of t h i s  decision.  i s analogous  be e v a l u a t e d All  us t o o b s e r v e  a call  in  the  provision  complexity factor  that  across  separately  o f t h e f a c t o r s on  of the f i r m and the v a l u a t i o n  of  the  35  4.  4.1  Debt L e v e l  Determination  Theoretically, which  the  number that  only  capital All that  the  the  Xb  for  <  represent Yia  of  the  debt  < Do  bankrupt. paid  out  the  stockholders Yib for is  any  hand, By  1  the  l e s s than  expected  If Yia  meet  the  cashflows Yia  costs  keeping  of  cashflow Yib,  both  bankruptcy  the  any  of  the  will  the  larger  Yia  < Yib,  we  the  arranged  such  < b.  of  incurred the As  the  long  two  0  and and  such t,  goes  this  Yia  this  is  bounds.  On shield  achieve  a  <  true When  and  the 1  and  < Do  is  bankruptcy  tax  Assuming a constant tax r a t e of t c f o r whole i s s u e of D is tax deductible, g o v e r n m e n t w i l l be r e d u c e d b y t c . D o .  =  Do  period  as  and  change. the  Let  bondholders  incurred  can  end  t  bondholders  B are  not  i s , the  in  for a  p r o b a b i l i t y of  larger D < Do  to  l e v e l s between  costs  at  before  be  indicates  firm pursues at  payments.  B will  finite  studied  2 are  < Yib  obtains  payments  a  period  be  levels  firm.  Yia  the  costs  receive  bankruptcy  that  to  in Figure  < b and  level  Bankruptcy of  the  cashflows  < Yib.  f i r m cannot  of  debt  assuming  l e v e l s i n any  l e v e l s need  a  number of  However,  earnings  decision  states  infinite  on.  these  structure  are  take  possible some o f  Xa  that  there  f i r m can  of  MODEL L A Y O U T  will  larger  the f i r m , since tax paid to  D  the other be. tax  the the  36  shield  with  a higher  expected  bankruptcy  realize  the  costs Yib  is  range Y i a and Now of  without  = Yib Yib  the  levels  cashflow decision  above f o r the  the  firm  debt  levels.  range  of  cashflow  after  a  certain  we  consider only  levels.  = Yib,  a l l the  other  cashflow  is still  expected  outcomes. of  So  shield  since i t  increasing  From debt  to  that the  Do  range Y i a and  other  hand  the  keeping  only  while  keeping  i.e.  the  debt  way  to  bankruptcy  debt  levels  the  level  at  between  the  Yib.  suppose  Yia.  tax  i s t o h a v e Do  superior  the  costs constant.  largest  constant  D w h i l e on  The  level  the  best  gives  the  bankruptcy  a r g u m e n t s , we firm This  are  those  can  Yib  obtains  debt  level  largest  see  which  involves examining  levels  and  cashflows those  debt  then level levels  within tax  the  shield  costs. that  equal  i m p l i e s t h a t the  amount of d e b t  instead  a  the  relevant  the  possible  capital  structure  finite  number  remains constant jumps  to  i s attained. which  equal  within  another As the  a  of a  level result, cashflow  1  *h similiar treatment can be found in Kraus, Alan & L i t z e n b e r g e r R o b e r t H., "A S t a t e - P r e f e r e n c e M o d e l o f O p t i m a l F i n a n c i a l Leverage", Journal of Finance, September 1973, 911-922.  37  4.2  Definition Before  the  the  model  earlier. =  Xi  different  needs In  and  obtained  of V a r i a b l e s  the the  and  Do,D1  PDi,PDij  be  are  discussed,  defined.  following,  the  X i and  the  notation  Y i j were  s u b s c r i p t i i s used  s u b s c r i p t s i , j are  D1 =  to  cases  used  together  of  defined when  Do  when X i  has  =Y i j . the  face  t  1 and  t =  2.  payoff  to  the  =  = the  periods  value  1 and  PEi,PEij  =  similiar  VDo,VDi  =  the  as  market  periods  of  2  debt  bondholders  value 1  but  of  to  the  at  end  of  shareholders.  debt at  the  end  of  respectively.  VEo,VEi  = as  above, but  for value  VLo,VLi  = as  above,  the  but  at  due  respectively.  above,  0 and  outstanding,  sum  of  of  equity.  debt  and  equity  values. VU DIV1  = unlevered = the end  Wo  = the  amount o f of  period  total  objective W1  = the  wealth  period RECAPCF  = the  firm  value  at  dividends  S  .  distributed  the  one.  wealth  of  shareholders  i s to maximize of  at  at  S  .  Our  Wo.  shareholders  at  the  end  of  1.  extra cash  equityholders  i n f l o w or as  a  outflow  result  to  of  recapitalization. CP m  = call  price  = number o f  f o r the  bonds  states at  the  i n case end  of  IV.  period  one.  38  n  =  number of  states  dependent  of  each  P(Xi),P(Yij)  =  the  probability  F  =  floatation costs selling  in period  of  of  debts. costs.  B  =  bankruptcy  R  =  l/(1+discount  T  = corporate  tax  state  occurrence  rate).  serially  in period  applying  rate.  two  to  of any  one. Xi,Yij. buying  or  39  4.3  Case  In  I  this  bonds  case,  which  the  mature  recapitalization the  at  is  1  Figure  cashflow firm  3,  Do  less  full  payment.  than  D,  the  firm  residual  than  are  the  For  firm does  the  amount a f t e r  PDij  to  shareholders  1  f o r each  On  the  and  debt  maximizes  and  0.  If  than  D  B are  bankruptcy  ,  the  costs i f  i f cashflows  other  hand,  receive  less  receive nothing.  shareholders  i f  their  are  receive  If the  tax payments, i . e . Do  otherwise i f Yij >  give  the  incurred.  i f cashflows  i f Yij > 0]  =  the  they  debt  state  no  determine  relevant  bondholders  the  (5)  to  receive nothing  bankrupt,  (Yij-Do).(1-T)  (4) and  p e r i o d and  is less  after  go  =0 Equations  discount  that  t  c o s t s of  B.  Do,  at  period 2  B and  = Do  =  the one  shareholders,  = MAX[Yi j-B, PEij  of  goes bankrupt not  of  level  residual  than  second In order  the  debt  equal  larger  the  each  bankruptcy  larger or  of  pure  optimum.  end  the  than  cashflows  the  receive  are  end  and  i s the  and  two-period  1 i s allowed.  i s the  at  goes bankrupt  Bondholders  are  the  structure,  wealth  level  cashflows  issues  evaluated  shareholders' In  at t =  optimal capital  levels  firm  (4) Do  otherwise  (5)  the  and  payoffs to bondholders  i n p e r i o d two.  As d i s c u s s e d above, the r e l e v a n t debt equal the cashflow l e v e l s .  levels  In  order  are  to  those  find  which  Figure 3 Case I t=2  Y11  P(Yi j ) = 1/(m.n)  Y 12 YIJ Yin Y21 Y22 Y2j Y2n Yi 1 Y 12 YTJ  Yin Yml Ym2 YmJ All cashflows here accrued to shareholders, none to bondholders.  Ymn  s  41  the  values  of t h e bonds and stock a t time  determine  the  corresponding adjustments incurred The  expected  present on  a t time  values t  z e r o , we  of =  payoffs  values  at  0  ,  the  value  of e q u i t y .  zero  when t h e t w o - p e r i o d  written  the value  of equity.  but  any  cashflows  tax  shield  a t t = 0.  period i s paid  value  of equity value m  the  with  some  costs are  and  this  These c o s t s a r e assumed  t o be  from  these  wealth  firm  since  Also, the cashflow  first  to  bonds a r e i s s u e d .  o f f as t h e bonds a r e i s s u e d and t h e  receive  and  Flotation  costs are paid out of the shareholders'  reduces  need  there  at the  not  a r e no  end  out as a d i v i d e n d and thus increases accordingly.  does  of  the  the present  So,  n PDij.P(Yij).R  i=1  2  (6)  j=1  m  n PEij.P(Yij).R  i=1  (7)  2  j=1  m - F +  i=l  We the  can calculate stock  possesses  for  the value  a given  debt  of the bonds and t h e v a l u e level.  At time  zero,  an o p p o r t u n i t y f o r i n v e s t o r s t o share  of  the firm  the  future  42  cashflows firm  are  will  be  of  the  the  the  assumed  firm  they  have  this  reason, to W  In need  time  sum  all  The  value  of  two  periods.  debt  financing  In  the t = 2,  we  level  the  assets cashflows  firm.  market  A l l  value  shareholders  their  of  because  future cashflows.  at  time and  wealth  each  D which  value  zero  debt  of  of  the  the  gives  For  should  value,  be  i.e.  shareholders, appropriate  the  of  the  as  c o s t s and  is  after-tax value by  the  maximum VL  i s i t s market  the  firm  and  we  debt  is  the  value  i f  be  the  I n an firm  of  thus  are  value  of  are  no  and  l e v e l s are p o s s i b l e a n d j = 1,n .  should  the  of be  unaltered.  levered  same,  the  amount  bankruptcy  the  the  within  the VU  imperfect  value  reflects  cashflows  cashflows  there  the  should  unlevered  this  i s independent  where  irrelevant.  a p p r o p r i a t e debt i . e . Y i j , i = 1,m  firm  expected  expected  taxes,  firm  the  the  Theoretically,  pursued  long  have,  the  for  This  unlevered  structure  the  the  VE  a p e r f e c t market  flotation  the  wealth  future  bonds of  equity value  financed.  as  to  of  in real  the  i.e.  assets  level.  equity  one  +  unlevered  constant  the  share  the  of  and  investment  bonds,  part  VL  debt  new  belong  to maximize  debt  present  selling  of  = VD  production  purchase  zero,  to determine  The  no  shareholders'  = VL  optimal  so  sacrificed  the  1  The  Bondholders  from  order  levels.  the  fixed,  when t h e y  bonds a t  equal  firm.  undertaken.  proceeds  the  1  of  i.e. market  costs, firm  capital like  levered  cashflow  and  the firm  levels  at  43  value  should  reduced  by  the  bankruptcy expected  be  tax  different.  present  costs  and  shields  The  value  of  increased  realized  unlevered  by  the by  the  firm  after-tax, the  firm.  present  value  is  expected value  of  44  4 .4 Case In  II  case  beginning optimal values  of  at  at  present  value  cashflow  level  cashflow  levels  face D1,  value  the  of  other  the  Shareholders the  residual  the  In  at  of  value  amount  of  level  of  that  the  after  are  left  amount,  t =  Xi, i =  issues at  .  Let t =  bond payments and  with  nothing  there  is  we  will  vary  If  the  D1  be  1.  the  I f Yaj  >  shareholders  Yaj  On  after  the  <  bondholders  any,  the  4,  taxes.  i f  and  should  only possible  payment and  bankrupt  period  VEo,  t =1  the  firm full  of  1 t o m.  1, 1,n  levels  In F i g u r e  j =  goes  i f  1.  =  the  equity  debt  0,  issued at  t  the  d i v i d e n d s and  Yaj,  receive their  firm  at  and  levels  t=  expected  at  debt  optimal  at  at  to determine  cashflow  cashflow  t = 2 are  the  the  debt  obtains  debt  order  equity value  value  bonds  corresponding  different  the  residual  hand,  two.  firm  Xa  bondholders  receive  the the  to  one-period  need t o determine 1 under  of  according  and  and  present  that  issues  one  i s because  the  see  we  t =  include  can  firm  level  t=0,  This  the  periods  debt  pursued one.  two,  D1. receive  bankruptcy  costs. Each  of  becomes t h e rise  to  relevant  optimal  the  expressions  1  the  maximum  f o r PD  In t h i s case, value because shareholders.  debt  and  debt  level  levels  given  shareholders' PE  are  the  are  evaluated  Xi obtains wealth.  same a s  in  i t i s t h e same a s m a x i m i z i n g the market value of debt  1  and  i f i t In  this  equations  D1  gives case, (4)  the o v e r a l l firm i s accrued to  fIgure Case I  Issue 1-period bonds. Issuing costs F. Debt level = Do  111  t=2  Issue t-period bonds, issuing costs F. Debt level = D »  Yi 1 Y 12  XI  YJJ Y"ln Y21 X2  Y22 Y2J Y2n Yi 1 Yi2 Y_ij Y?n Ymi Ym2 Ymj Ymn  P(Xi) = • 1/(m.n) ^U/Xi) = 1 / m  P  1 / n  46  and  (5).  And  f o r a debt  level  D1  =  Yaj,  n VDa  =  ^_ j  =  PDa j . P ( Y a j | X a ) .R  (8)  1  n VEa  =  ^  PEa j . P ( Y a j | X a ) . R  - F  (9)  j=1 Now firm  we  issues one-period  value t  =  move b a c k w a r d  of  1.  this  paid with  the  residual  bondholders entitled of  the  in  at  equity  the  expected at  t = On  the  1  full  amount and  firm  at  cashflow the  to  the at  of  t = 0,  value  1  other  firm.  1  the  t  =  is Xi and  of  amount  the of  are  issuing  Bankruptcy  would  costs  levels  payments  market  present  value  value  the  lead  to are  1 firm  to are  market  the  of  at  receive  shareholders  F.  The p r e s e n t v a l u e of the e x p e c t e d t = 0 i s g i v e n by: m & = H ( o p t i m a l V L i ) . P ( X i ) .R i=1 where V L i = VDi +  market  more c a s h f l o w s  B  The  bondholders  the  costs  of  the  the  expected  So  the  4.  shareholders  the  present  h a n d , X i < Do  > Do,  after  second p e r i o d . includes  and  cashflows  addition,  since there  and  0  the  dividends  present  VEo,  the  as  t = 0 in Figure  on  a m o u n t Do  In  dividends  the  at  obtained  taxes.  t =  end  1 less  b o n d s Do  to  i s s u e depends o n l y  I f the  are  i n time  value coming  value of  firm  of the  value  bankruptcy  of  incurred  and  value  as  of  t  =  » (10) VEi  47  bondholders  receive  after  bankruptcy  Xi  been p a i d  has  the  residual  costs. out  as  bankruptcy  firm  goes  receive  the  cashflows at  firm  inherit  criterion  bankrupt,  the  maximizing  to maximizing  the o v e r a l l  the  debt  levels  the  largest  analysis level  Do  and  =  there  and  shareholders  market are VL  any,  nothing  since  payments.  can  no  Bondholders  period  is  bond  cashflow.  v a l u e of  the  evaluated  longer  take over  shareholders! wealth  Again,  the  i s equivalent firm.  with  i s the optimum.  the  So  Each  the for a  of  above debt  = X i , m  VD  costs  t = 2.  second  of  relevant  i f  Shareholders receive  When t h e  and  amount,  m  n  ^PDi.P(Xi).R + i=1  I i ^ Y i j . P ( Y i j ) .R i=1  where  I i = 0 i f no  (11)  j=1  bankrupt  1 i f bankrupt  in state  in state  i  i  m VE  =  PEi.P(Xi).R  + J i . (optimal  V L i ) . P ( X i ) .R]-F  i=1  where J i =  1 i f no 0  bankrupt  i f bankrupt  in state  in state  i  i  (12)  48  4.5  Case I I I  In and  this i t  issue  case,  has  new  the  obtained  period  at at  t = 2.  In  t  1  of  because  problem  is  decision  based  of  relevant the is  one  Xa  the  cashflow  level,  possibly  occur  firm  and  equity  the  levels  the  total  faces  two  cashflow  best the  to  recapitalization,  the  of  level  t = 2.  choices and  cashflow  cashflow  this  low  may  at  cashflow  next  probability  be  necessary  we  need  =  0,  to  of  with  to  Figure 1,  the  decision  at  approach  this  the  present Each  expectation  shareholders'  firm t =  j  =  5,  we  1.  and  wealth  issues at  at  t =  0  Given  this  1,2,...,n,  can  can  see  that  the  or  no  recapitalization  to determine  yet  recapitalization  this  the  Yaj,  face  shareholders.  largest  debt  we  have not  maximizing  obtained  In  t =  expected  only  t  at  ways  wealth  know t h a t  at  i t to  large  i n p e r i o d one  o b j e c t i v e of  face value  we  allows  of  recapitalization  rise  be  a  and/or  wealth.  of  the  has  recapitalization  gives  the  low  0  more  probability  hand,  =  has  large  revised  which  be  A  firm  the  i s evaluated  Do  this  1,  level  Let  firm  of  debt  optimum.  and  t  issued  probability  knowing  expected  The  mean h i g h  anticipate on  bonds  needed.  other  cashflow  to  1.  bonds a t  higher  and  One  the  and  the  debt-  not  been o b s e r v e d .  value  On  t =  evaluating  =  would  shareholders'  uncertainty  t =  the  financing choice  1  imply  future cashflows  maximize  back  s t r u c t u r e as =  Thus a t  buy  bonds a t  its  t  would  period. of  in  issues two-period  option to  i t s capital  cashflow  firm  one-period  flexibility alter  the  the  present  value  Case I I I t=1  t=2 Recapitalization allowed. Option to buy back bonds issued at t=0 and issues new 1-period bonds at a cost F.  Cashflow net of tax and floatation costs Is accrued to shareholders.  50  of  the total If  there  remain  equity  i s  a t Do.  expected  of  wealth  of shareholders  no  recapitalization,  A t t = 1, s h a r e h o l d e r s '  after-tax  a t t = 1.  the wealth  previous  dividends  after-tax  cashflows.  the  cashflow  as  described  wealth  The  where  determined  that of  there  So,  period market  part  unlike  a t t = 1 were  given  the  issued at t  a t t = 0.  the after-tax  that  The period  Xa  by  t h e same  way  occurs,  the  We  c a n go b a c k  1 i n case  bonds. values  I f the firm  recapitalization t o Case  I I because  level  Xa h a s o b t a i n e d .  corresponding a s a new  costs  there  have This  are  of  F  are  D1.  I ti s  debt  levels  the gives  condition the values  t o t h e new o p t i m a l  D1.  i s s u e o f bonds w h i c h mature a t The f i r m  i n the capital Since  both  we  recapitalizes,  I I t o determine  they  with the  Again,  t h e same way a s t h e o p t i m a l  i s considered  Do  i s compared  recapitalization.  and  exactly  issue  (13)  shareholders  end of the second p e r i o d .  debt  i s no l o n g e r  of equity at t = 1 i s a f f e c t e d  of  i s  t o D1  e q u i t y and debt  the  I I .  the  1 and the value of  of debt  are just  Xa h a s o c c u r r e d .  cashflows  D1  =  includes  a t t = 2 and i s e v a l u a t e d  wealth  i s changed  t =  t  would  ( l - T ) . X a + VEa(Do)  that  incurred.  at  =  above  assuming Do  i n case  wealth  level  of the shareholders i s : W1  case  levels  choice.  the debt  to shareholders  dividends  The v a l u e  each  at t = 1 because,  bonds o u t s t a n d i n g  = 0 and the proceeds accrued  one  at  The m a r k e t v a l u e  of shareholders  cases,  expected  under  i s  market a  buys  back  a n d i s s u e s D1  difference  o f t h e o l d i s s u e a n d t h e new  the o l d of one-  between  the  issue, the firm  51  will  have a  and  this  the  positive accrues  shareholders  flotation-cost optimal  debt W1  or to  at  t  negative  shareholders. =  is  wealth  compared  decision see  are  at  maximum  t =  1,  at  t =- 1.  the  the  market  at.,  t....=.  firm  t =  value 1.,  of  and  are  given  that  Xa  (14)  above  two  only  decisions when  wealth.  the  we  that We  can  corresponding  need  a l l  the  to  similiarly  the  possible  optimal  f o r each  step  dicisions  cashflows  i s to determine  at  t  =  1,  bondholders; bond v a l u e  the  bonds.  at  market  to  t  t  =  at  t =  value  obtained  the  =  and  levels  the  wealth  0,  1, the  bonds w i l l  there  bondholders  the  value  of  is  So to  in the  o l d debt  i s just  the  the  bonds of  the  case,  value  issue at  present  no again  either market  be  is  i s independent  1.  of  the  if  Thus,  hence a l s o at  has  new  0.  entitled,  The  the  i=1,2,...,m.  give  wealth  next  recapitalization  bonds.  thus  for X i , will  the the  the  d e c i s i o n and  recapitalizes  from  bondholders  1  i.e.  after  VDa(Do)  wealth ' for  The  at  -  of  i.e.  shareholders'  Xa,  and  equity, given  recapitalize  on  analysis  recapitalization,  their  this  wealth  + VEa(Dl)  under  larger  shareholders'  repurchased  firm's  a  5 that  shareholders If  will  conditional  above  obtained of  firm  shareholders'  cashflows The  the  Figure  determine  the  and  cashflow  total  after-tax  of  = VDa(Dl)  shareholders  generates  from  wealth  of  the  cashflow,  + RECAPCF  w h e r e RECAPCF  The  value  recapitalization  (l-T).(Xa-F)  =  So  1 i n c l u d e s the  d i v i d e n d s , the  and  recapitalization  of  t  =  value  of  52  expected payoffs using, value  the  to  bondholders.  methodology  of debt  given  expected value  of  debt  This  Case  level  of the market  I I .  Do  is  value  can  be  evaluated  A t t = 0, just  the  the  market  discounted  of o l d debt at t =  1.  1  m VDo  = 21  VDi.P(Xi).R  i=1 The  value  of  e q u i t y a t t = 0 depends  payoff  that  i s accrued  first  and  second p e r i o d .  of  shareholders  decision.  So  expected optimal  to shareholders  at t =  1 under  the value  value  of  This  at  only  on  the  end  i s equivalent  the optimal  recapitalization  total  of  to the  the  wealth  recapitalization  of e q u i t y a t t = 0 i s the  shareholders'  the  wealth  at t =  at t =  1 under  discounted 1 under  the  decision.  m VEo  = ^  W*.P(Xi).R  i=1 W*  = shareholders' optimal  Now total  we  1  As  recapitalization  the values  shareholders'  values, value  have  i.e.  wealth  the  wealth  of debt and  firm  of bonds a t t = 0 accrues  i n Case  11, _n  VDi  =  ^_ j =1  decision. e q u i t y a t t = 0.  at t = 0 i s just  levered  PDij.P(Yij).R  to  the  value  t h e sum  because  shareholders.  of  the  The these market  53  So  f a r the analysis  pursued level, the  at each  second  analysis. wealth  t  =  0.  is  done  In order  of the r e l e v a n t debt period cahsflows The  one  at t = 0 i s the  which  for to find levels  should  be  maximizes  optimum.  a  given  debt  level  out the optimal with value  debt  equal  to  substituted into  the  total  shareholders'  54  4.6 C a s e  IV  Case  IV  i s  similiar  case  I I I except  that a  provision  i s i n t r o d u c e d i n t h e bonds.  We  approach  as  alteration.  above  but  shows t h e s i t u a t i o n in  case  With  a  recapitalizes, the  market  only  when  resulted the  call  there  increment  With  this  determining  same a s  in  different debt at  t  =  1  decision.  Case  will  and t h i s the  price  capital  will,  price  than  call  wealth  i s  I f the firm  as i t  i s  exercise the c a l l  below  provision  price  and the  higher  than  recapitalizes,  on r e c a p i t a l i z a t i o n  cashflow:  i n Case  the  receive  an should  call amount  of  of  value  price, less  should  of  dependent  bondholders  this  i s  debt  recapitalization  o f bonds a t t h a t  than  i s the debt  value  b e c a u s e when t h e f i r m  anticipate  of bonds a t t = 0  of the i s  process  I I I , the value of  o f t h e market  debt  the  decision  value  I n Case  i s independent  decision  cashflow,  the  I I I .  value  value  (15)  recapitalization  However,  and the market  than  Bondholders  I I I .  the present  recapitalization  higher  now, t h e f i r m  recapitalization  that  Now  recapitalize  in  i f the c a l l  will  the optimal  from  i s just  the  debt  = VD(D1) - MIN[CP,VD(Do)]  revised  6  old  i s higher  effect  Figure  the  i n shareholders'  i s a positive  same  recapitalizes  flotation costs.  RECAPCF  of  price  the  When t h e f i r m  provision  The f i r m  can use  call  IV.  the o l d debt  market  after-tax  back  call  price.  w i t h a minor  of Case  I I I , i t buys  market.  »  to  on  decides time  the to i s  of the o l d issue  the  market  value.  a t t = 0 and t h e market  reflect  this.  Thus,  the  Figure 6 Case  Xm  IV  56  value  of debt at t = 0 i s given m VDo  = ^  by:  . VDi.P(Xi).R  (16)  i =1 where VDi  = market if  decision  = market if  = call  value  market  recapitalize  of debt a t t = 1 = recapitalize  value  price  of debt at t = 1 = no  decision  market  and  value  and  of debt  < call  i f decision  =  value  of debt  price  recapitalize > call  price  57  5. In to  order  simulate  the  to the  different  this  COMPUTER S I M U L A T I O N OF  purpose,  interpret model w i t h  cashflow the  WATFIV p r o g r a m s .  with  ease the equity  firm  changes  Larger  numbers of  extensive can  be  manual  of  four  can  cases  readily  model,  one  and  and see as  the how  debt  be  Also,  without  need  two.  For  simulated  can  determine  corresponding the  the  we  represents  above are  p r o g r a m s , we  s t a t e s can  calculations.  the  numbers w h i c h  described  levels  cashflow  manual  of  these  A l s o , we  performed  value level  debt  of  the  changes.  simulated  without  sensitivity  analysis  performing  repetitive  work.  The  four  numerical run  debt  i n the  set  cases  With  optimal  values.  a  results  states in periods  four  with  and  the  MODEL  are  example w i t h  through  Appendix  cases  1f.  the  shown  cashflow  programs  and  in  Appendices  levels the  shown  1a  to  in Figure  results  are  Id. 7  shown  A is in  00  Figure 7 Numerical Example for Simulation Programs tc=0  K=10%  B=3500  F=1800 D =2376 VL=2227 VD=1440 VE=787 4091  D =8537 VL=6274 VD=5338 VE=936 7368  7368  4042 .8537 3684  0 =14375 VL=11651 VD=10453 VE=1197  -9246  59  6.  As  mentioned  earlier  Determination', superior  to  adjacent value will  inbetween  trend  continues  cashflow.  levels levels  and  the  should  two  present  Thus  our  analysis  graph show  discrete  tax  nature  of  the  model and  optimal  capital  structure.  analyse  the  section  simulated  ends  implications  of  with the  thus  results the  model.  to  debt  level shield This state debt  against  debt  in  betweeen structure  of c l a r i f i c a t i o n ,  under  The  tradeoff the  of  discrete  a condition for  later  sub-sections  detail.  discussion  the  connected. the  of  a  discrete  capital  resulting  in  on  points  Then t h e  two  next  Anything  firm's  of  For  tax  the  values  analyse  shield  are  costs constant.  reaches  purpose  will  levels  i s equal  expected  i s based  have a l l the  sub-section c o s t s and  the  points.  the  level  Level  i n c r e a s e i n debt  firm  f o r the  for  an  level  plotting  'Debt  levels.  debt  bankruptcy  debt  graphs h e r e a f t e r w i l l  bankruptcy  of  the  However,  following  value  on  to cashflow debt  i f the  until  points i s suboptimal  decision.  equal  states,  expected  RESULTS  section  possible  cashflow,  the  the  levels  the  i n c r e a s e the  in  other  s t a t e s of  keeping  the  debt  a l l  while  of  I N T E R P R E T A T I O N OF  Finally, two  an  will this  important  60  6.1  Optimal Capital  Without Db  = Yab  Structure  bankruptcy  states,  in Discrete  Cashflow  an  i n debt  increase  t o D(b+1) = Ya(b+1) would  lead  t o an  the p r e s e n t v a l u e of expected t a x s h i e l d Db].R .  However,  2  are  bankruptcy  increases  from  more  of  state  bankrupt. incurs  if  the  value Yab  the  tax  Yab  level  the p o r t i o n  For  each  state of  2  tax  to  shields to  or  shield  larger  D(b+1) 2  firm  the  the  firm  firm  be  in  i s not  2  m  of  large  So  as  the  tax  enough  t h e amount  firm  value  actually  of is  realize.  Ya(b+1),  only  realized  instead  of  states.  Only  realize Db  the debt  those  an  to  follows:  2  cannot states  increase D(b+1).  from  -tc.Da.R  in In  expected  level  tc.D(b+l).R  n  state  than  increasing  - t c . Y a b . R ) , but  the  Part  i n the p r e s e n t v a l u e of  = Ya(b+1)  present  i n face value of debt  increasing  go  avoided  in  smaller  can  will  have been  have  can  one  bankrupt  firm  not  than Ya(b+1) can  from  debt  goes  2  does  the  firm  tc.Db.R .  i n those  from  of  case, the t o t a l  increment  increase  increment  resulting  value  the  could  by  of  cashflow  resulted  the  tc.Ya(b+1).R  realized  tax shields  shields  general,  Yab  the  which  In t h i s  to the  Thus an  2  when t h e r e  face  B which  i t which  of  tax  tc.D(b+1).R .  equal  of  in  is different  a l l the tax b e n e f i t s .  contributed  increment  tc.[D(b+1)  obtains,  Db..  the  from  equal to  the  in  instead  2  because  just  increase  Yab  was  level  t o D(b+1) = Ya(b+1) t h e r e i s  actually  tc.Yab.R  to realize  shield  tc.Yij.R  Yab  tax shield  i s lost  cashflow  =  bankruptcy costs  i s just  shield  Db  situation When  cashflow,  debt  of  states.  If  and  the  States  Db 2  tax = (or  61 m  n  A P V [ E ( T S ) ] = t c . [ D ( b + 1 )-Db] . Y_  Y-  i=a  (  p  Y i  J)-  j=b+1 where P ( Y i j )  Using level  the  to  D(b+1)  bankruptcy, in  same e x a m p l e  Yab,  general,  after-tax debt  =  increment  from  Db  APV[E(B)]  Equations  =  from  debt  levered  firm  value  higher  relevant  equations increase  will or  Figure above.  with of  firm  at of  value  as  cashflow  level  whether  the  changes  from  and  an  example  one  including the  of  of  Thus  expected in  of  (18)  costs  level  net  effect  those  tax the  to the  next  of  the  level  of  two  would  cashflow.  described  the  irrelevant  show t h e  firm  at  debt  levels  The  values  w i t h the  dashed  line.  r a t e of  change  of  the  from  one  changes  This  dashed  i t s value line  i n c r e a s e d or  cashflow  of on  arguments  value  level  has  effect  debt  the  connected  line  1/m.n  value.  the  s t a t e s of  next.  value  state  of  represent  debt  to the  state  increase  i n c r e a s e i n debt  levered firm  dashed  firm  the  the  the  debt  2  bankruptcy  increase the  = Y i j are  the  an  show t h e  above  an  D  from  (18)  show w h e t h e r  levels  more  value  =  Thus  i n between  firm  slopes  we  lines  the  incurred.  where P ( Y i a )  level.  shows  debt  i n the present  financing  solid  values  the  The  8  costs B are  - tc).B.P(Yab).R  as  1/m.n  t o D(b+1) = Ya(b+1) i s  and  decrease  The  various  (1  (17)  benefit  mean o n e  costs resulting  = Yab  =  increasing  would  bankruptcy  bankruptcy  level  above,  Ya(b+1)  and  the  as  <17)  R 2  level  to  only  decreased the  shows as  debt  other.  If  CM M3  Figure 8 Capital Structure in Discrete Cashflow States VL OR W  * all vertical distances between the highest point of solid segment to the lowest point of adjacent segment are the same.  OPTIMAL \  J VII  y/2  L  .KtoM-CONCrWlT/  .maximum amount of cashflow possibly attained by the firm D  63  we  increase  Ya(b+1),  debt  the levered  depending AVL  the  level  firm  from  Db  value w i l l  =  Yab t o D(b+1) =  increase  or  decrease  on t h e n e t o f e q u a t i o n s (17) and (18) :  =  {APV[E(TS)]  - APV[E(B)]}/[Ya(b+1)  - Yab] =  m { t c . ( Y a b + 1 - Y a b ) . ^ i=a  The  t h e a b o v e v a l u e on t h e c a p i t a l  i s summarized as slope  of dashed  line  optimal  decision  AVL  zero  stay,optimal  negative  decrease  = 0  solid  segments  f o r a l l debt Only  observed  points  levels,  the  are  Suppose  begins  bankruptcy increasing. the  expected  i n Figure  to costs This debt  capital  the debt increase  as  starts  shown  exists  exceeds  bankruptcy costs  by  debt be  because  equal to cashflow  o u t a t Db  the  until  firm  segment w i l l  i n Figure  Ya(b+1),  increase  debt  decision  levels  t h e same w h i l e  situation level  structure  level  point  suboptimal  of each  (debt  debt  the value of the  those  point  optimal  remain  8 show  including  highest  i n the firm's  levels).  Once  follows:  increase  levels.  and  structure  positive  The  these  (19)  £»VL > 0  A.VL < 0  when  [Ya(b+1) - Yab]  2  of  2  j=b+1  (1-tc).B.P(Yab).R } /  effect  decision  Yij,P(Yij).R  =  8.  tax  1 +  Yab  Expected shield  i t reaches  i s  Ya(b+1).  the present v a l u e of an  amount  equal  to  64  that  of  levered this the  firm  drop  the  probability constant The  will  of  constant  of  be  occurrence  of tax  given  the  by  increases, the  slope  lines  of  can  the  term  the  never  The  the  drop  in firm  value.  bankruptcy in  a l l  i n the  inside  solid  increases  exceeds  the  highest  case  firm  will  equity  because  go  becomes  debt cannot  be  costs  states,  i n Figure are  By  Since  and  equal  drop  is  8.  just  modifying  and  larger  the  the  s e g m e n t s and  the  lines  have a negative  firm  of  costs  state.  marginal  these  should  equation  be  (17),  the  (20)  2  above e q u a t i o n  when t h e  the  (18),  j=b+1  from  the  bankruptcy  the  n  i=a see  equation  that  P(Yij),R  can  in  in  :  m  We  the  sudden d r o p  of  segments  segments.  is a  shown  segments  shield  f o r each  are  As  have constant  between a l l the  increment  there  d e p e n d s on  occurrence  larger  slopes  slopes  value  of  m o d e l we  So  at Ya(b+1).  in firm  are,  our  (18).  value  probability  they in  equation  i t s debt possible  bankrupt zero.  increased  bondholders  are  On with now  that  as  debt  level  summation  sign decreases  decreases.  However,  slope. level  The into  s t a t e of i n a l l the the  other  further entitled  minimum an  amount  states hand,  the  the  zero which  In  and  increases to  these is  cashflow.  and  this value  value in  of  debt  residual  65  cashflow  after  residual  amount c a n n o t be  Now, tax  f o r an shield  increase  i s zero  bankruptcy though  paying  always  a  shareholders'  i n debt  cannot  limit  wealth,  as long  in  8 as a h o r i z o n t a l  the  dashed  paying  the bankruptcy  i s  just  i n cases  goes bankrupt  Minimum V L ( o r  W)=  the costs  m  expected So  expected given  and  m H i=1  n Z  j=1  <  1  thus  VL  line both This  amount, (21)  an  i s shown  I , I I I and IV) and  i n equation  i s  obtain  amount  residual  even  there  value,  cannot  minimum  ,  after when  n MAX[0,Yij-B].P(Yij).R  2  (22)  j=1  Now t h e f i r m g o e s b a n k r u p t i n a l l s t a t e s value of the a f t e r - t a x expected bankruptcy  amount  the  i n a l l the states, i . e .  ^ i=1  This  increase in  further.  firm  this  levels.  l i n e and the s o l i d segments c o i n c i d e here.  value  firm  debt  indefinitely,  This  and  1  l i n e a t t h e end of t h e  wealth  floor  the  where  as the f i r m  of c a s h f l o w .  shareholders'  higher  increased  to the levered  amount  (or  i s a point  increase  infinite Figure  with  costs  l e v e l , t h e minimum  be  l e v e l may  floor  bankruptcy  increased  and t h e r e  costs  the debt  the certain  and the present c o s t s i s g i v e n by  ~ tc).P(Yij).R .MIN[B,Yij]  i s t h e maximum t h a t  2  the firm  i s expected  (21) t o pay.  66  6.2  Basic The  P r o p e r t i e s of  two  p e r i o d model  result  of  shown  using  a  concave the  simulated  cashflow  in  function This  as  that and  the  in  debt  low  a  given  hand,  low  large  debt  tax  firm  shield  (17)  decreased  the  same.  i n tax  value  an  shield  as  debt  the  line  level  concave p a t t e r n , there that are  quantity  are  i s not  an  in  Figure  On  levels.  the of Thus  leads  increment  to  a in  in  the  However, as  the  (18)  9 shows a  concave.  the  increment  in  in equation  segments,  strictly  see  increases,  increment  equation  and  small  increase  quantity  in  some  the  tax  increase  level  increases.  the  an  the  constant  debt.  are  smaller.  i n debt  larger,  VL  level  concave  can  equation from  this  of  we  of firm  in  traditional  that  thus  levered  (17),  9  states  value  f o r a l l debt  and  because  of  the  be  Figure  face  debt  a  I.  strictly,  becomes  but  best  not  resulting the  can  wealth  i n the  increase  costs  while  the  b  I)  traditional  the  that  the  shows  becomes l a r g e r and  has  the  remains constant  becomes s m a l l e r  asterisks,  a and  (17)  bankruptcy  Although  though  equation  debt,  using  see  with  the  Case  shareholders'  As  of  I  (Case  This  From e q u a t i o n  levels,  equation  level  level  value  can  is large. by  increment  levered  We  of  costs  expected  6.  roughly,  debt  level  bankruptcy  Case  approach.  provides  function.  of  consistent  increment  quantity other  is  Results  s i m u l a t i o n on  same a s  a  cost  at  value  i t i s plotted against  result  bankruptcy  at  i s the  produces  used here  result  Figure  (which  case)  firm  Simulated  computer  shows t h e  value  the  as  firm (17)  remains  roughly  marked  However,  by this  Figure 9  CASE I RESULT 10000 - i  8000 H 6000 H  >  o" 4000 >  Legend 2000 H  A  VLc_  x VI* • VEb  0  — I —  5000  10000  15000  Do  I  20000  25000  68  is  not a v i o l a t i o n  bankruptcy of  of the r e s u l t  c o s t s approach.  These p o i n t s a r e j u s t  the discreteness i n the  (17), Db  hand,  the  equation  increment  which  resulting  more t h a n  offset  Non-concavity level than  to  will  follow  D(b+1) - Db.  The  cannot  offset  costs.  S o f r o m Db decrease  non-concavity So  that  on t h e VL  exist  between  these  D(b+1)  could  be  cashflow valid  Db,  firm  an i n f i n i t e  states  become  probability  of  first  an  debt  smaller  tax  i n expected  has  costs.  increase the  shield  bankruptcy  increase  gives rise  of concavity  D(b+2)  such  levels  by  that  occurrence  that  and  to the  level.  The  With in  the  the  such  assumption  model,  difference  intervals  model  of cashflow  gaps  non-concavity  constant period  whenever  t h e two  the non-concavity w i l l  number o f s t a t e s continuous.  occurs  have a l a r g e  assuming  However, t h e two sense  tax  level  i s much  a  line.  i s not the o p t i m a l debt  the  large  the other  i n bankruptcy  v a l u e and t h i s  three cashflow  states.  i s  expected  incremental  increment  level  c o s t s g i v e n by  in  further  resulting  D(b+1),  eliminated  in  increment  t o D ( b + 2 ) we h a v e in  equation  T h u s we h a v e  D(b+2) - D(b+1)  in general, a violation  there  bankruptcy  On  i n c r e a s e i n debt  w h e n we  the constant  be l a r g e .  increase  large  the constant  such  a  a  In  o f D(b+1) - Db.  large  from  D(b+2)  then  i n expected  a sudden  the result  I f D ( b + 1 ) - Db  (17) w i l l  (18) i s independent  situation shield  i n equation  levels.  tax plus  t o i n c r e a s e t h e debt  = Yab t o D(b+1) = Y a ( b + 1 ) .  , the quantity  with  cashflow  s u p p o s e we a r e c o n s i d e r i n g  from  and  of the t r a d i t i o n a l  a  i s  of still  disappear that  the  of equal continuous  69  function states  i s analogous  with  the  of  as  equity  these  lines.  These  decreasing. the  the  two  firm's each  debt  see  of a  Figure  levels.  In  i f D  In  this  and  any  face the  are  upward  As  level  debt  of  general  trend  on  future claim  increases,  increment  the  fact,  the  line  i s increased case,  the  increase  of  beyond  firm in  the  will  D  will  go  cannot  lines  value  VD  and  are  as  due  highest  in  on  the for  (17)  has  We  can  l a r g e s t two  debt  to have  zero  this.  a  cashflow  bankrupt  to  VD  of  start  or  addition  Equation  the  VE  discussed  the  increment  off at  VD  the  bondholders  decreases.  levels  debt  increasing  because of  of  increases. the  levels  a q u a n t i t a t i v e treatment 9 t h a t VD  of  the  debt  and  debt  monotonically  troughs  cashflow  value  increases  sloping trend  the D  the  value  not  between  another.  that  ranges between  increase  provided  in  slope  lines  cashflow.  already  just  of  p e a k s and  has  will  the  one  see  value  as  intervals  close  can  face  The  VD  debt  we  are  irregularity  above. of  9,  decreases  Again,  regular  states very  From F i g u r e increases  to  $20961.  i n a l l the  increase  the  states  payoff  to  bondholders. The  same  decreases high At and  debt  as  arguments debt  levels  level and  this  debt  level,  the  full  amount of  either  bankruptcy  equity  consists  dividends  which  can  be  applied  increases,  finally  the  becomes  firm  or  only  of  i s $2587  two  the  levels  VE  cashflow  bond payment. the  expected  i n our  example.  line  which  at  very  off  2 5 8 7 w h e n Do  goes bankrupt  period  costs  but  to  =  i n a l l the  20961. states  is distributed Thus the  value  of  as  value  of  period  one  70  6.3  Comparison  Case  I  present  is a in  each case added  the  can  debt  see  level  cashflows. incurring  example,  Case  are  we  period  to  Since cashflow  structure  This than the  the  in other  levels.  other  the debt  Case I I .  I I has  the  analyse  higher  Case  II  former  are  cases  higher.  to bear the  i n mind  any levels  may why  are debt are  comparing produce  be  values  optimal  one  i n Case  Case  levels  period  In  other  while  firm's  II debt  cashflow  to the  II values  and  Case  two  equal  i n the  end  of  capital  with that  of  interpretations.  of  Case  i n Case  I.  At  I  in  2 of  I.  II with  levels  in  =  latter,  values  i n Case  t  disadvantage  misleading  some f i r m  corresponding l e v e l may  Case  Case  about  the  not  irrelevant  I and  Case  cashflow  levels  base  over  the  to the  the  flexibility  t h a t debt  equal  the  I  outweighs  one  of  Case  In comparing  period  cases  reason  effect  are  than  beliefs  has  to  Case  values  of  revised  effects  compared of  that  of c o n s i d e r i n g  the  values  advantage  adjust to  decision,  i s the  Instead  f l o t a t i o n c o s t s rather than  have  equal  levels  the  I I has  II values  cases,  should  levered firm  However, two  properties  l a t t e r t h r e e as  the  will  with  three cases.  t h a t Case  Case  II  base case  other  Comparing  we  this  typical  I and  i n d i v i d u a l l y , we  general. I:  Cases  f e a t u r e s i n the  case. II,  of  but  II are these  lower  points,  suboptimal  in  71  6.4 I n t e r p r e t a t i o n  6.4.1  Recapitalization  From for  Figure  Case  debt  Case  end  of  call  resulting  realize  the  of t h i s [RECAPCF  This  in  call option  + VLI(DI)  gain  atthe  when  potentials.  than  in  with  The  a  call costs  just  the  Thus  the  tool  to  increment  in  the debt  i s this  the  wealth.  at different  than  can exercise  wealth  the firm  the  i s larger  to the flotation  in  that  recapitalize  larger  - VL1(DO)  -  values  levels.  (1 -. t c ) . F ] . R  of r e c a p i t a l i z a t i o n  and not the bondholders. bondholders  the  p e r i o d one market the firm  to  the  of The  i s:  t  whether  wealth  shareholders'  option  for a l l  t o the fact  i n C a s e I III r e p r e s e n t s  at  to  =0,  i s  values  as necessary,  the firm  i s analogous  gain  added v a l u e  shareholders  wealth  and the  wealth  analogous  value  in  I  recapitalizes  The o p t i o n  feature provides  upside  shareholders'  firm  option which  increment  recapitalization  The  price  recapitalization  of Case  c a n be a t t r i b u t e d  outlay.  to a call  The  those  the levered firm  i n shareholders'  when t h e g a i n  price. of  one.  flotation costs  option  Option  can r e c a p i t a l i z e ,  increment  analogous  than  result  I I Ithe firm  resulting  Recapitalization  10, we c a n s e e t h a t  This  period  of  as a C a l l  III- are higher  levels.  in  the  of the Effects  are entitled value  will  benefits  only  the  As e x p l a i n e d  earlier,  t o the present  value of  o f bonds and t h i s  recapitalize  (23)  i s independent  o r n o t at t -  1.  On  Figure 10  COMPARISON OF VLo 8500 -i  8000 H  7500 H  Legend  7000 A  VLo I  x VLoJN • VLo IV 6500 5000  10000  15000  Do  20000  25000  Figure 11  COMPARISON OF VD  COMPARISON OF VE 8000^  6000 H o LxJ >  4000 Legend  VE I x VE III • VE IV A  2000  — I —  5000  10000  15000 Do  I  l  20000  25000  75  the  other  hand,  recapitalization the  cashflow,  dividends  after  recapitalization increase  I.  the  recapitalization  and  the  this  value  cannot an  shareholders' under  benefit under  In firm  order  firm  value  t = 0, g i v e n  those  in  firm  value  the firm  results  how  Case  We  i s as  and  that  1  Again, So  when  of e q u i t y and remain do  values  of  the not debt  a s shown i n F i g u r e s  11 a n d 1 2 .  after  the capital  Recapitalization structure  we n e e d  debt  evaluate this  i s  i s  made.  levels  levels  i f  the c a p i t a l the  of  the  t o compare t h e  i s no r e c a p i t a l i z a t i o n ,  should  no  These a r e  various  decision  I.  least  , a t t = 1, a t v a r i o u s d e b t there  will  t h e same.  Position  a t t = 1 because  recapitalization  there  Bondholders  remain  recapitalization,  at  If  values  values  levels.  levels  that  costs.  of equity at t =  increase or at  debt  t o determine  recapitalization. of  than  in Financial  changes a f t e r  levered  the value  by t h e o p t i o n t o r e c a p i t a l i z e  the simulated  and  t a x and f l o t a t i o n c o s t s .  will  debt  value  i s t h e same  to recapitalize,  different  Changes  levered at  wealth  different  exactly  6.4.2  option  the  o f e q u i t y a t t = 0 depends on  cashflow, after  If  wealth  on  firm  flotation  wealth.  be l e s s  depends  d e c i s i o n , these  Also, the value  dividends  i s  and  shareholders'  Case  same  tax  shareholders'  in  wealth  t h e new o p t i m a l  i s an o p t i m a l  recapitalization,  there  shareholders'  time  chosen with the  there  i s  structure when  the  A t t = 1, o n e o f t h e  76  cashflow  s t a t e s has obtained,  conditional structure are of  on t h e o b s e r v e d of the firm  analysed the  flotation For  a  RECAP" under  capital  given  different  debt  of  "VL a f t e r 2  In  , under 3  recapitalize  given  "N" m e a n s t h a t  at t =  0,  does at  levels  moment  means  that  face  value  does  chosen  after  the  t  =  levels  0.  after  "VL  before  firm  , the  decision.  The  values ex-  at t = 1 for  t = 1.  At  this  made. decides  chosen  recapitalize  not occur at the debt  and  between  1  firm  of debt  not  at  values  ex-dividend  chosen  d e c i s i o n has been  the firm  recapitalization  neither  values  the levered  debt  one  the  debt  and  firm  chosen  different  "Y"  capital  recapitalization.  and the r e c a p i t a l i z a t i o n  of  8537  value  ex-dividend  a t t = 1, t h e l i n e  levered  the recapitalization 13a,  face  level  just  The  13a shows t h e c o m p a r i s o n  and a f t e r  RECAP" r e p r e s e n t s  Figure  and  Figure  levels  Xi  recapitalization, time,  the  level.  values are  t h e w i t h - and e x - d i v i d e n d  structure,  cashflow  represents  dividends  using  costs are paid, before  observation line  cashflow  and compared.  firm's  so t h e l e v e r e d f i r m  We  optimal  to  at t = 0 at  that  can see t h a t debt  c l o s e t o 8537.  The  level firm  1  I n e v a l u a t i n g f i r m v a l u e s when t h e r e i s no r e c a p i t a l i z a t i o n , debt l e v e l s r e l e v a n t a t t = 0 a r e used because these a r e t h e debt level of the firm until t = 2 i f i t does not recapitalize.  2  F l o t a t i o n c o s t s have a l s o been p a i d because dividends the residual of p e r i o d one cashflow after paying flotation costs.  3  are the  When t h e f i r m r e c a p i t a l i z e s , i t buys back t h e o l d d e b t i s s u e a n d i s s u e s new o n e - p e r i o d b o n d s . A t t = 1, t h e f i r m faces the cashflow l e v e l s a t t = 2 as t h e i r r e l e v a n t debt l e v e l s .  A f t e r Div. VLi  78  recapitalizes dicussed capital  only  before  of  t  =  closely  to  not need  discussed and  (14)  the  decisions  The  firm  Figure  i t also  the  model  has  In  only  when  will wealth  than  resmebles bound to  the very  which  the  determine  this  recapitalization  layout  Case  III.  of  wealth  and  only  no if  larger  one  firm  the  of  recapitalize  period  the  of  criterion  recapitalization  for  a  As  suboptimal  larger  order  shareholders'  is  of  shareholders'  13a  Putting  (l-tc).Xa  in  curve.  because  Theoretically,  costs.  recapitalization.  recapitalize  tolerate  is  shows the  will  given  can  VL  bound  recapitalization  the  of  the  is a  increment  examine  recapitalization  a  firm  recapitalize.  in  (13)  the  1 because  to  of  1 , there  i f the from  Figure  will  extremes  costs.  flotation  b o u n d , we as  only  1 resulted  after-tax  firm  which  flotation  recapitalize at  the  in Figure  structure  presents  on  =  1  under  shareholders  (13)  level  t  recapitalization.  than  equations  cashflow  at  Equations  after  that and  before  (14)  Xa,  together,  the  firm  will  :  + VE1(DO) <  ( 1 - t c ) . ( X a - F ) + VE1(D1) +  RECAPCF  Rearranging, (l-tc).F  <  RECAPCF  or  (l-tc).F  <  VD1(D1) - VD1(DO) + VE1(D1)  or  (1-tc).F  <  VL1(D1)  Equation  (27)  recapitalize. if  the  from  increase  + VE1(D1) -  in  shows t h a t  a the  ex-dividend  recapitalization  -  VE1(Do)  - VL1(DO)  represents  It  VE1(Do)  exceeds  criterion firm  levered the  (27)  will firm  after-tax  for  the  firm  recapitalize value  to  only  resulting  flotation  costs.  79  Equations  (13)  shareholders' (27)  wealth  represents  value.  So  and  has  The  in  value,  thus  objectives In  under "VL  two  i s that  13a, line  different after  debt  RECAP"  line  VLold  Both  firm  value  cashflow  lines  Xa  i n Figure values  determining levels  the  firm  c r i t e r i o n of objective  ( 1 4 ) ,the term  i s  RECAPCF firm  recapitalization  both  chosen  the  under  of the  a n d VLnew  at t =  VL1(D1),  line firm  a t t = 0.  i s the ex-dividend  only  firm  that a This  are  those  levels  they  saying  that  between  the firm  in Figure  the  firm  value  1.  will at t =  value  it-  costs  the  same  are both  the  t h e two  a t some p o i n t s .  different  second  Equat i o n  i f  e x p l a i n s why  obtained  the  levels. levels  (27)  i s  in  cashflow  level  a l l  debt  recapitalize  because  period  c a n be e l i m i n a t e d i f t h e c a s h f l o w  a s shown  1  period  other  relevant  =  particular  But f o r VL1(Do), are  t  flotation  on t h e p e r i o d o n e c a s h l f o w levels.  at  before  V L 1 ( D 1 ) on t h e  after  I I because  1 given  levels  "VL  c a n be d e t e r m i n e d  occurred.  a t some d e b t  cashflow  discrepancy  on  13a c o i n c i d e w i t h e a c h  conditional  discrete  levered  which  i s also the value  has  r e l e v a n t debt  two  the  component o f t h e l e v e r e d  lies  as t h e o p t i m a l V L i i n Case  one  are  of  levels  are  Firm  t h e VD  shows t h e v a l u e  This  levered  i n equation  no m a t t e r  VL1(Do)  recapitalizes.  way  the result  a r e t h e same.  This  paid.  maximizing  model,  i n equation  the c r i t e r i o n  on  maximize  period  i s t h e same  captured  Figure  RECAP".  based  a t t = 1 a n d now  our  reason  already  are  a criterion to  recapitalization used.  (14)  period This are not  basically  i f the difference  1 a n d t h e maximum  firm  value  80  attainable flotation 13a  through costs.  recapitalization  S o we  exceeds  c a n draw a h o r i z o n t a l  t o c r e a t e a boundary  within  which  the  the  after-tax  line  i n Figure  firm  will  not  recapitalize. However,  in  order  structure  of the firm  look  at  the  that  this  Figure  structure  after  curve  criterion modifying  are for  actually shows  in capital we  The  affects  need  to  reason  is  the wealth  the changes i n the  recapitalization.  with-dividend  A l lthe  values.  recapitalization  Equation  change  VL o f t h e f i r m .  which 13b  the  recapitalization,  with-dividend  i s the value  13b  analyse  after  shareholders.  Figure  to  can  capital  values  in  case,  the  In t h i s be  of  determined  by  (27) :  From E q u a t i o n ( 2 7 ) , (l-tc).F  < ex-div VL1(D1)  or,  (l-tc).F  <  or,  (l-tc).F  < w i t h - d i v VL1(D1) - w i t h - d i v VL1(Do)  Note:  before  So  we  within of  the firm  "VL  dividends VL1(D1)  the firm drops  will  low  RECAP"  after  recapitalization  When  there are flotation  recapitalization amount after  not r e c a p i t a l i z e . to  equal RECAP"  will  to the a f t e r - t a x line  the  in Figure  of the  firm  costs.  of the f i r m  after  t h a t maximum p o i n t by  flotation  1 3 b , we  line  after-tax  flotation  c o s t s , the value than  RECAP"  The maximum p o i n t on t h e  t h e r e a r e no  lower  costs  Once t h e v a l u e  the with-dividend value  when  be  justify  (28)  flotation  o n t h e "VL b e f o r e  enough  is  VL1(Do)+div)  i s also before  costs, i t recapitalizes.  before  VL1(Do)  (ex-div VL1(D1)+div)-(ex-div  c a n draw a b o u n d a r y  which  flotation  - ex-div  costs.  can see t h a t  From  the  an "VL  the optimal  oo  Figure  13 b  CAPITAL STRUCTURE AFTER RECAP 11000-1  10000 H  > Q Q) d) CD  9000 H  8000 H  7000 H  Legend A  V L before RECAP  x V L of. RECAP of. F  6000  -r—i  5000  - i  5L  10000  15000  Do  —  r  20000  1  25000  82  debt  level  presents debt the  after of  level  flotation  that  period  determined  using  independent  of  essentially,  the  after in  level  we c a n s e e t h a t  13c  This  which  Case  the firm  assumes-  a  t h e new  i s based level  on i s  costs.  the  by an  i s  So amount  geometry  can never  implication  the  I I and t h i s i s  s h i f t s downward From  by  i s that  flotation  recapitalization.  recapitalization. Figure  of  of  line  reason  and the optimal  methodology  the  unaffected  to recapitalize  levels  t h e w h o l e VL  diagram,  i s  The  chooses  cashflow  (1-tc).F after  the  costs.  the firm  second  of  recapitalization  lose  value  plotted  continous  of  again  function  of  cashflow.  6.4.3  Effect  Case  o f F on t h e R e c a p i t a l i z a t i o n  III  Appendix results  1c  i s with  a r e shown  recapitalization costs  increases.  recapitalization of for  the firm  run  various in  This  costs  increases,  decreases. after-tax  The amount  since  We  now  firm  value  see of  the e x i s t i n g value  in  and t h e  that  the  flotation  probability  as the l e v e l  of decrease  of increase  program  of  debt  level  in  order  optimal. that  amount  the  low firm  shows  the  can  as the l e v e l that  t o a very  t o be  13d  13d.  implies  i s lower  simulation  of f l o t a t i o n costs  increases  has t o l e a d  Figure  the  levels  Figure  bound  recapitalization Also,  through  Boundary  after  flotation  recapitalization  i s exactly  in flotation  of  costs.  equal  to the  Figure Capital  Structure  after  13c  Recap.:  Continous  Cashflow  00  picture. 1 3 d  EFFECT OF F ON VL after RECAP 12000-1  10000 H  >  *  > Q  8000 H  Q)  O M—  Legend  m  A VL before RECAP  6000 H  x F=500 • F=1800 El F=2800 4000 0  5000  10000  •  Do  15000  20000  25000  85  6.4.4  I m p l i c a t i o n s of  With  the  tolerable not  above bound  the  debt  because  recapitalize  once the  i.e.,  the  flotation The the  on  the  one  VLo  new  is  low,  the  curve.  the  because  to  Without  is  firm  as  1,  the  level  value  the the  firm  will  amount of  the  I f the  the  firm  Recapitalization B.  The  is  at  Point  and  either  value  value  (before  C.  i m p l i e s the 13e.  position  B or  cashflow  optimal  level  can  cashflow shift  level  to  This  Point level  C at  turns  A  firm  and  i s smaller  than  are  serially  optimal  point the  C  1.  is  i f i t  debt  costs. B which  firm  is  value  costs.  down t o  observe  out  obtained  VL1(low)  lower  i s on  i f Point  t =  point  bankruptcy  shift  only  the  because  cashflows  the  0,  f u n c t i o n changes  recapitalizes,  of  t =  in  period  firm  only  change  At  the  choose a  function to  T h u s we  costs.  after-tax flotation  i s optimal  final  Point  i f the  amount o f  will  in firm  expected  the  firm  firm  bound;  D1*.  two  cannot  of  I f the  and  will  this  cashflow  i s at  one  The  a  hits  in Figure  function will  periods  reduce  by  also  the  firm  recapitalization,  causes  apply  the  debt  and  reduced  level  firm  value  after-tax flotation  boundary  t =  value  suboptimal.  Point  At and  optimal  correlated  now  the  information obtained.  new  level  debt  s t r u c t u r e d e c i s i o n i s at  i s -o b t a i n e d  of  Do*  exceeds  costs.  suggests  the  in firm  increase  s t r u c t u r e curve  capital  w i t h i n which  increment  present  Boundary  p e r i o d model  flotation  recapitalization  firm's  two  levels  potential  costs)  capital  the  the  after-tax  once  Recapitalization  findings, of  recapitalize  justify  the  This  VLI'(low). higher  than  recapitalizes  Point A  The  same  t o be  high  at  t =  0  arguments at  t =  1.  g6 Figure Implications  of  13e Case  IV  Results  87  In  Figure  13e,  Point  recapitalization The levered  above  values  capital  findings  observe  the optimal  values.  that  value  project.  costs  recapitalization usually misleading  treated  that  than  Point  Instead,  Empirical  decision of  usually  is  D  the  conclusions.  This  observed  optimal  may  not  a  ignore  and  and  observe  those  positive  net  on  the  presence  of  the  capital  and the  necessarily  conducted the  one and  level  not  we  studies  recapitalization  bound. as  the debt  e m p i r i c a l l y do  recapitalization  structure  flotation  lower  suggest  we  such  present  i s  i s suboptimal.  firm value  represent  E  resulting  structure  t h u s may  lead  is to  88  6.5  Effects  6.5.1  The  Case  10  I I I . the  the  firm t =  call  remain  lower  price  the  bonds.  call  or  the  at  call  the  provision.  the  than  than  only the  market  and debt  i s shown of  constant  t =  price  recapitalization  will  the  only  when t h e  firm  In  those  decision  value  shown firm  of  does not  s t a t e s i n which  i n Case  decision  because  cashflow  and  shareholders'  I I I , the i t will thus  wealth.  result  in can  equity.  the  of  only the The  increase  is  calls the  added  call  During  i f the  call  will  increase  remain  constant  call  increase the of  debt  increase  12.  It will  provision  value  of  firm  the  bonds  recapitalization call  that  bonds  0 will  cashflow  e x e r c i s e the  and  the  Figure  call  of firm  i n c r e a s e d by  equity at a  price  value  when t h e  11.  in  bonds  The  price  of  be  is  the c o n d i t i o n s  The  in Figure  as  the  price.  price  IV  wealth  market  market  cannot  the  so  to  under  decrease  recapitalization,  and  call  optimal decision.  of  i n Case  shareholders'  the  is  so  wealth  b o n d s when t h e  This  i s lower,  Value  provision  provision  hand, v a l u e remain  the  a call  price  value  This  other  least  of  to  same w h e n t h e  provision.  On  equal  i s lower  i s an  the So  call  Firm  Provision  1 i s higher the  the  than  or  on  shareholders'  to c a l l  recapitalization will  Call  addition  exercise  that  the  than  The  bonds a t  will  of  Provision  shows t h a t  lower  allows the  a Call  Value  Figure always  of  provision. is  cannot  an  optimal  change  this  recapitalization equity in  and payoff  total to  89  shareholders is  a l s o the decrease In  Case  those  this  - call  t o bondholders  recapitalization  possible  p r i c e ) and  that  the  i n that  call  i n c r e a s e d and, as a r e s u l t ,  recapitalization  shareholders, the value  between  value value  the value of debt  the market  bondholders In  recapitalization  cannot  equity  of debt  i n those price  share  general, value of  of e q u i t y  increases.  of debt  will  at t  =  will can  become  only,  the  decrease  the difference price  because  recapitalization.  0  will  i n c r e a s e a t t = 0.  a t t = 0 as a r e s u l t  may  The  and the c a l l  the b e n e f i t of  in  cashflow  benefits  states i s s t i l l  of debt  state.  provision  recapitalization  Since  this  i s suboptimal  d e c i s i o n because  optimal.  in  of debt  i n payoff  s t a t e s which  III , i t i s  change be  i s (market p r i c e  decrease The  of the c a l l  and  increase i n  provision  i s  •  n (VDi  - CP).PROB(Xi).R.I  (24)  i=1 w h e r e CP i s t h e c a l l 1 = 0  when  1 when call  price  recapitalization recapitalization  price  i s below  i s suboptimal i s optimal  the market  and  price  of  debt. However,  the increase  i n the value  more c o m p l i c a t e d .  In those  suboptimal  Cases  of  equity  is  optimal  i n both  i s zero. i n Case  of equity a t t = 0 i s  s t a t e s where  recapitalization  I I I and IV, the i n c r e a s e  In those  s t a t e s where  I I I , the increase  in  i s  value  recapitalization  i n the value  of  equity  90  at  t = 0 i s a l s o t h e amount  states  where  optimal is  i n Case  equal  incurred at  t  to  present  1  equation state  due  value  (24) above.  i s suboptimal  IV, the increase i n value  i n that  =  given  recapitalization  i n equation  to  (24) minus  i n Case  optimal  I I I but  of equity at t = 0  the extra flotation  plus the increase i n value the  In the  new d e b t  of  level.  of the increase i n e q u i t y value  costs equity  Thus t h e  at t  =  0  i s  by :  n y  [ ( V D i- CP).I - F ( l - t c ) . I . J  +  i=1 (VEnew - V E o l d ) . I . J ] . P ( X i ) . R  where  1 = 0  when  recapitalization  1 when r e c a p i t a l i z a t i o n call  price  (25)  i s suboptimal i s o p t i m a l and  i s below market p r i c e  of  debt. J  = 0 when r e c a p i t a l i z a t i o n is  optimal  The at in  above  t = 0 and t h i s expected  equation the  equation  i s  value  change  i s the increase i n the value  the value  the wealth  in total  i n that  shares  value  at t =  1.  of the c a l l at  t  =  state  i n Case I I I .  i s also the present  also  of  shareholders' the  suboptimal  shareholders' wealth  state  i n Case I I I .  1 when r e c a p i t a l i z a t i o n is  i n that  0.  of the increase So  the  provision However,  a t t = 0 i s t h e sum o f d e b t shareholders' wealth  of equity  above  added t o since  and e q u i t y ,  at t = 0 i s given  91  by  t h e d i f f e r e n c e between  equations  (24) and (25) :  n ^  [VEnew - V E o l d  - F(1-tc)].R.P(Xi).I.J  (26)  i=1 The  levered  firm  wealth,  at  =  expected  flotation  value  introduced. share  costs  between  and  decreases  above  anticipate  as defined  wealth  possible  because  there  optimal  as  that  result  incurs  flotation  there  i s no c a l l  costs  thus  a call  call  may  the total  decreases..  of  which the  which  the  not  Bondholders  will  bonds  this  and  expected  loss  wealth  In  will  be  recapitalization  call  could  n o t be a b l e  have  been  fact, reduced becomes  avoided  in firm  to offset  i s  in  p r o v i s i o n and the firm  The i n c r e a s e  value  does  p r i c e a t t = 0.  shareholders'  firm  level,  provision i s  provision  the  t h e bond  provision.  recapitalization and  will  a r e some c a s e s a  high  However,  i n our model,  incorporate into  simulation  IV Results  the firm  i n equity  increases  t h e bond p r i c e .  shareholders.  bondholders'  our  provision  benefits  will  increase  as the c a l l  that  when t h e  the increase i n  In  f i n d i n g s imply  anticipation  i s  a call  decreases  wealth,  shareholders'  are set at a relatively  I m p l i c a t i o n s of Case  necessarily  costs  total  and the expected  In conclusion,  price  The  to  thus  a tradeoff  of the f i r m  shareholders'  it  i s  costs  flotation  the value  6.5.2  0  and  a t t = 1 due t o r e c a p i t a l i z a t i o n .  example, so  t  value,  reduced  the and  value  i f due  flotation so  does  92  shareholders'  wealth.  93  7.  Sensitivity WATFIV 1e.  analysis  program  7.1  structure  Bankruptcy Figure  decision  costs.  Higher  We  value  of debt  i s also  level  of bankruptcy  lower  the  discount rate,  tax  t h e change i n  variables.  can see t h a t costs, costs  Figure  f o r higer  14a  firm  accrued  reduces firm  decreasing  the  value, as  the  i s increasing.  shows  bankruptcy  that  costs.  the optimal debt This i s  because  an  costs,  i n equation  ( 1 8 ) , i s higher than  the increment  tax  a s shown by e q u a t i o n  ( 1 7 ) . Thus  lower  bankrupcy  costs  debt and tax  level this  shield  would  reduce  reduction  the high  c a n more  than  i n expected  for  i n debt  expected  the increment  level i s  increase as  level  t h e amount  and hence  i s  level,  the levered  So t h e l e v e r e d  shareholders' wealth,  different  f o r a g i v e n debt  reduces  a t t = 0.  costs  under  the lower  during bankruptcy  which  Also,  using  s e t i n Appendix  so as t o a n a l y s i s  to these  bankrupcty  the bondholders  market  III  costs  higher the bankruptcy  value.  costs,  14a s h o w s t h e v a l u e s o f t h e f i r m  bankruptcy the  a r e used  on C a s e  1d a n d t h e d a t a  of bankruptcy  and f l o t a t i o n  capital  ANALYSIS  i s performed  i n Appendix  Various levels  rate  to  SENSITIVITY  expected offset  the loss  bankruptcy in  i n expected  shield. Figure  14b s h o w s t h a t  value of debt  i s d e c r e a s i n g as the  figure  14a  EFFECT OF BANKRUPTCY COST ON VL/W 9500 -i  Legend A B=1000 x B=3500 • B=6000  7500  "l 5000  10000  r  Do  15000  r  20000  1 25000  CTl  Figure  11 b  EFFECT OF BANKRUPTCY COST ON VD 8000  Legend A B=1000 x B=3500 • B=6000 —I  25000  Do  Figure 14 c  EFFECT OF BANKRUPTCY COST ON VE  97  level fact  of bankruptcy that  belongs costs, are  once to  the firm  the  the less  i s left  i s  that  considerably issue  expected  expected  and t h e value  rate  optimal  decision,  i s  i t  resulted  of  the  issue  the  The drops  of the  level  of  recapitalization bankruptcy  to  costs  recapitalize.  present 1  much  under  will  increase  costs  increase.  value the  of the optimal  or at  least  Figure  14c  result.  tax rate  tax  rate.  i s that  remains constant.  debt  effect  level  the increment  from an i n c r e a s e hand,  o f s e n s i t i v i t y a n a l y s i s on t h e  One o b v i o u s  the optimal  implies that  other  So  i s  at t =  so  decision.  thus  level  decision  15 s h o w s t h e r e s u l t  rate  higher  the  t h e same when b a n k r u p t c y  corporate  the  as  there  but the value  i s a minimum.  wealth  Figure  drops  debt  and  firm  In fact,  of debt  old  level  shareholders'  7.2 C o r p o r a t e  tax  debt  equity  shows e x a c t l y t h i s  tax  the  of  recapitalization remain  of  of the  the bankruptcy  now b e c o m e s a n o p t i m a l  costs  increases  the  and the higher  value  i s due t o t h e  cashflow  to i t s suboptimality  bankruptcy  increases Since  due  This  f o r the bondholders.  value  i s an o p t i m a l  cashflow  goes bankrupt,  the market  recapitalization  reason  i s increasing.  bondholders  some c a s e s w h i c h  that  new  costs  i n debt  the increment  increases.  i n expected  level  has  i n expected  Thus t h e o p t i m a l  d e b t , l e v e l s so as t o u t i l i z e  o f an i n c r e a s e i n  debt  Higher  tax shield  increased. bankruptcy  level  the higher  will  On costs  be  at  tax shield.  figure  15  EFFECT OF TAX RATE ON VL/W 11000 - i  10000^  o  >  9000H  A.  8000 -I  Legend A tc=0.20  7000 H  6000 $ —  f  5000  R  -  - -  10000  T—-  15000  Do  20000  —I  25000  x  tc=0.40  •  tc=0.70  99  With higher the  tax  7.3  Discount  r a t e , l a r g e r amount of  a u t h o r i t y and  The shown  tax  of  in Figure  rate.  Call  can  the  increases. face see call  Call of  the  examine the  of  debt  and  debt,  the  change  than  bonds  of  16  levered  firm  to  will  value  the  level  the  of  whole  optimal  debt  is  reduce  However, the  that  i n the  the  firm  p r i c e s are debt  that firm  set the  at  can  effect  of  a change  value  the  capital discount  line  shifts  level.  chance  call  debt price  Thus the  is  reduced.  As  =  i s so,  for a  of  earlier,  the  We  can  we  need  the  value  given  face  call  price  the  at  debt  probability  discussed  of  increasing  mean t h a t  value  17a price  0.  with  i n c r e a s e s as  price.  t  2/3  p r i c e on  shows t h a t  market  call  and  this  in call  would  Figure  I V when c a l l  issues at  f o r the  the  and  1/2  e x p l a i n why  17b  of  IV  increases  we  the  1/3,  firm  value  Figure  Case  i n Case  Before  Higher  is less  higher  decreases.  rate  a f f e c t e d by  any  equity.  increases. there  firm  values.  in Figure  levered  to  of  the  a n a l y s i s i s d o n e on  price.  value  the  discount  see  value  value that  payable  Price  Sensitivity shows  a l l  d e c i s i o n i s not  We  levered  r a t e on  Higher  of  downward w i t h o u t  7.4  discount  16.  value  structure  the  are  Rate  effect  present  thus  taxes  of  t to  =  1, be  calling  bondholders  Figure 16  EFFECT OF DISCOUNT RATE ON VL/W 9000 - i  8500  o  8000H  > 7500 H Legend A R=1+0.05  7000  X R=1+Q.1Q • R=1+0.20 6500  — I —  0  5000  :  10000  15000  Do  I  20000  — I  25000  Figure 17a  EFFECT OF CALL PRICE ON VLo 8300 -i  Figure 17 b  EFFECT OF CALL PRICE ON VD 6000 - i  Legend A CP=D/3 x CP=D/2 • CP=2D/3 1  25000  Cb  Figure  17c  EFFECT OF CALL PRICE ON VE 8000-a  7000  6000 H  5000 H 4000 H  Legend A CP=D/3  3000-H  x CP=D/2 • CP=2D/3  2000 5000  10000  15000  Do  20000  25000  104  will  l o s e the  bonds and of at  the  calling t =  0.  price  d i f f e r e n c e between call  the  price.  bonds w i l l  The  price  firm  has  increase equity  and  this  decreases,  value  larger the  at  7.5  t =  1 will  to  Flotation  higher  higher  These  costs  higher  flotation  so  The  18c  i s fewer  flotation value  of  decision  there  debt  as  call  17c.  bonds.  are  the  price  as  to  As  the the  This  will  Also,  value  of  higher  chance  of  net  effect  is  a  decreases.  will  costs debt i n Case  debt  out  reduce  value. to  costs,  the  before  because  resulted  offset  paid  firm  of  than  wealth  conform  value  the  cashflow.  flotation  are  levered and  increases  of  increases because  to c a l l  call  the  probability  value  in Figure  equity  example,  as  i n the  of  Costs  be  18a  our  value  shareholders'  the  of  i n c r e a s e as  In  recapitalization in  i s shown  price  market  equity  recapitalization  in firm  With  reduction  of  probability  recapitalizing. decrease  a  market  i n c r e a s e the  market value  decreases  call  So  the  of the The  these  will  the the  from  not  III.  of  costs.  the  of  equity  simulated  results  has  firm and  in  and thus  Figures  arguments.  not  change  affected This  increment  flotation  cashflow  value  the  of  recapitalization  high  i n c r e a s e s because, as is  frequency  result  by  when  the  discussed the  i s shown  level  of  before,  the  recapitalization in Figure  18b.  Figure  16 a.  SENSITIVITY ON F 10000 -i  9000 H  "A  8000  Legend  7000 H  A F=500 x F=1800  6000  • F=2800 —I  5000  10000  15000  Do  1  20000  25000  F/cjure  18 b  SENSITIVITY ON F 6OOO-1  does n « * cUuje  F  4000 H o Q > 2000 H  Legend A F=500 x F=1800 • F=2800 5000  10000  15000 Do  20000  25000  \-\cjure  1&  c  SENSITIVITY ON F 10000 - i  8000  o LU >  6000 H  4000 H Legend A F=500  2000 H  x F=1800 • F=2800 5000  10000  15000  Do  20000  25000  108  8.  8.1  SUMMARY AND  CONCLUSIONS  Summary  This which  thesis employs  bankruptcy  shield  model,  and  expected  the objective of  maximizing  under  I n Case  one  provision cases, call  bond,  on t h e b o n d s  the effect  p r o v i s i o n on t h e v a l u e s and the levered  The  simulated  the firm  has  i s added  value  firm  results  lacks  flexibility  the  the  other  IV.  equity  Issuing  hand,  but  two  but extra issuing  incurs  less  adds  the  However, o n l y  benefit  and not the bondholders.  beginning because  firm  value  call four  shareholders'  The v a l u e  resulting  the concavity  issuing  bonds  costs are  issuing  bond  costs.  o p t i o n and i t always  o f p e r i o d one i s n o t a f f e c t e d by  t h e new  of  and t h e  one t w o - p e r i o d  to a call  firm.  these  one-period  i s analogous  to  With  a  of r e c a p i t a l i z a t i o n  Recapitalization value  two-period  Then  are consistent with  the advantage of f l e x i b i l i t y On  First  a t t h e end  costs.  i n Case  firm  value.  function.  incurred.  of  i t i s s u e s two one-  i s s u e s one  of debt,  With  conditions.  i s allowed  flotation  one.  the dynamics  then  I I I , the firm  fixed  we c a n e x a m i n e  wealth  of  with  of period  various  bond and o p t i o n a l r e c a p i t a l i z a t i o n period  debt  we c a n a n a l y s e  i s s u e s one t w o - p e r i o d bonds.  of  at the beginning  structure choice  firm  period  "tax  wealth  two-period  capital the  the  a two p e r i o d s t a t e - c o n t i n g e n t model  c o s t s " approach with  shareholders' this  develops  from  the shareholders of debt  at  the  recapitalization recapitalization  109  consists  o f new d e b t a n d e q u i t y a n d t h e o r i g i n a l  receive  the  market  recapitalizes. gain the  in gain  the  the  there  firm  will  value  in  show  than value, to  recapitalization.  level  the  debt  As a  level  will  i s low and i n c r e a s e  presence  of  boundary  Outside  of e q u i t y ; t h i s the  lowered  possible  this  value,  flotation  within  which  boundary, the  expected of  flotation equity  as  addition  the value  loss  of debt  i n value  The  of  a  call  and i n c r e a s e s  bondholders  will  when t h e f i r m  at the beginning  this.  and hence  complicated  the  f o l l o w s because  bond p r i c e  to reflect  firm  that  decreases  bonds and thus  value  i s larger  by an amount e q u a l  a recapitalization  results  always  anticipate  more  the  i n amount t o  levered firm  optimal  not r e c a p i t a l i z e .  when  recapitalize.  provisi.on  is  the  of  i s equal  The  costs after  only  value)  be r e d u c e d  Because  exists  will  Simulated  levered  firm  costs.  will  flotation  i t i s high.  firm  is  (which  when p e r i o d one c a s h f l o w  the  the  flotation  o l d d e b t when t h e f i r m  recapitalize  wealth  of r e c a p i t a l i z a t i o n ,  decrease  costs,  the  i n with- or ex-dividend  after-tax  when  of  will  shareholders'  or ex-dividend,  result  the  The f i r m  after-tax  with-  value  bondholders  calls  o f p e r i o d one  overall  effect  shareholders'  wealth,  on  the  at t = 0  and i s a t r a d e o f f between  the increase  c o s t s and  increase  in  chance  of  a  the  result  expected  of  a  higher  recapitalizing. Sensitivity the  optimal  costs.  a n a l y s i s shows t h a t b o t h debt  A higher  level  corporate  decreases tax rate  the firm  with higher implies  a  value  and  bankruptcy lower  firm  110  value  and  discount the  a  higher  rate  optimal  the  firm  high  value  and  will  lower  debt  level.  because,  a  high  recapitalization Finally,  optimal the A  higher  i n our call  states  Implications  There are period  model.  the  observed  of  the  there  two  firm  the  level  important First,  value  of  firm  i s not  will  not  necessarily  are  number  of  costs.  imply  fewer  value.  Model  firm  often  be  r e c a p i t a l i z e and acme  of  the  two-  assume  that  indicates  T h i s may  the  increase  costs  the  recapitalization  at  affect  flotation  studies a  higher  will  a r i s i n g out  of  a  not  flotation  firm  empirical  tolerable  price  the  the  issues  function.  will  costs  lower  capital structure  exists a  which  thus a  Also,  reduces  flotation  8.2  Important  example,  hence  and  but  call  price  and  higher  level.  firm value  recapitalizations  Two  debt  the  acme  incorrect  since  boundary the  of  within  observed  the  firm  debt value  function. 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Management  R u b i n s t e i n , M., 'A Mean-Variance Synthesis of F i n a n c i a l T h e o r y ' , J o u r n a l o f F i n a n c e ( M a r c h 1973) 181.  ,  Corporate pp. 167-  Stiglitz, J., 'A Re-Examination of the M o d i g l i a n i - M i l l e r T h e o r e m ' , A m e r i c a n E c o n o m i c R e v i e w (December 1969) p p . 784793. Stiglitz, Policy', 866.  J . , 'On t h e Irrelevance American Economic Review  of Corporate (December, 1974)  Financial pp. 851-  T o b i n , J . , 'On t h e E f f i c i e n c y o f t h e F i n a n c i a l S y s t e m ' , F r e d Hirsch Memorial Lecture, Hirsch Memorial Trust, New York, May 1984.  11 3  A P P E N D I  C E S  11 4  A P P E N D I X 1A C A S E I S I M U L A T I O N PROGRAM  C  C C  I N T E G E R X , Y, Z, F L A G REAL B ( 1 0 ) , T ( 5 ) , R ( 5 ) , R E S , F ( 1 0 ) R E A L O V L , OVD, O V E , OVU, OD REAL P D ( 6 4 , 6 4 ) , P E ( 6 4 , 6 4 ) , B A ( 6 4 , 6 4 ) REAL D ( 6 4 ) , SUMD(64), S U M E ( 6 4 ) , SUMBA(64) R E A L PROB REAL V D ( 6 4 ) , V E ( 6 4 ) , V L ( 6 4 ) , V U ( 6 4 ) REAL V D D ( 6 4 ) , V E E ( 6 4 ) , V L L ( 6 4 ) , D D ( 6 4 ) REAL E 1 ( 1 0 ) , E 2 ( 6 4 ) REAL DIVPV INPUT R E A D ( 2 , * ) M,N READ(2,*) ( B ( I ) , I = 1 , 3 ) READ(2,*) ( F ( I ) , I = 1 , 3 ) READ(2,*) ( T ( I ) , 1 = 1 , 3 ) READ(2,*) (R(I),1=1,3) R E A D ( 2 , * ) (E1 ( I ) ,1 = 1 ,M) MN=M*N READ(2,*) (E2(I),1=1,MN) X=2 Y=2 Z= 2 G=2 PROB'=1 . 0 / ( M * N )  initializing variables DO 1 I=1,MN SUMD(I)=0 SUME(I)=0 SUMBA(I)=0 OVL=0 OVD=0 OVE=0 OVU=0 1 CONTINUE C c a l a c u l a t e expected d i v i d e n d from p e r i o d one DIVPV=0 DO 2 3 1=1,M DIVPV=DIVPV+E1(I)*(1.0/M)*(1-T(Y))*(l/(1+R(Z))) 23 CONTINUE DO 2 1=1,MN D(I)=E2(I) DO 3 J=1,MN I F ( D ( I ) . L E . E 2 ( J ) ) THEN DO PD(I,J)=D(I) PE(I,J)=(E2(J)-D(I))*(1-T(Y)) BA(I,J)=0 — E L S E DO RES=E2(J)-B(X) PD(I,J)=AMAX1(0.0,RES) PE(I,J)=0 I F ( R E S .GE. 0 ) T H E N DO BA(I,J)=E2(J)  115  ELSE  3  *  DO BA(I,J)=B(X) END I F END I F SUMBA(I)=SUMBA(I)+BA(I,J) SUMD(I)=SUMD(I)+PD(I,J) SUME(I)=SUME(I)+PE(I,J) CONTINUE VD(I)=SUMD(I)*PROB/((1+R(Z))**2) VE(I)=SUME(I)*PROB/((1+R(Z))**2)+DIVPV-F(G) V L ( I ) = V D ( I ) + V E (I ) VU(I)=VL(I)-T(Y)*D(l)+(1-T(Y))*SUMBA(I)*PROB/ ((1+R(Z))**2)  C IF  ( O V L .GE. V L ( I ) ) GO TO 2 OVL=VL(I) OVE=VE(I) OVD=VD(I) OVU=VU(I) OD=D(I) 2 CONTINUE C ARRANGE D E B T L E V E L S I N A S C E N D I N G ORDERS DO 741 J=1,MN AMIN=1.0+D(MN) DO 143 1=1,MN I F ( D ( I ) . L E . A M I N ) THEN DO AMIN=D(I) K=I END I F 143 CONTINUE DD(J)=D(K) VDD(J)=VD(K) VEE(J)=VE(K) VLL(J)=VL(K) D(K)=2.0+D(MN) 741 CONTINUE C PRINT DO 99 1=1,MN WRITE(9,234) D D ( l ) , V D D ( I ) , V E E ( I ) V L L ( l ) 234 FORMAT ( 4 ( F 1 2 . 4 , 1 X ) ) 99 CONTINUE W R I T E ( 9 , 1 5 4 ) OD,OVD,OVE,OVL 154 FORMAT ( 4 ( F 1 2 . 4 , 1 X ) ) STOP END $EXECUTE f  A P P E N D I X 1B C A S E I I S I M U L A T I O N PROGRAM $COMPILE INTEGER X,Y,Z,FLAG,P,INDEX,Q,W REAL B ( 3 ) , T ( 3 ) , R ( 3 ) , R E S , F ( 3 ) REAL E l ( 8 ) , E2(8,8) REAL E A R N ( 2 , 8 , 8 , 8 ) REAL O V L ( 8 ) , O V E ( 8 ) , O V D ( 8 ) , O V U ( 8 ) REAL O D ( 8 ) REAL OVL0,OVE0,OVD0,OVU0,OD0 REAL P D ( 2 , 8 , 8 , 8 ) , P E ( 2 , 8 , 8 , 8 ) , B A ( 2 , 8 , 8 , 8 ) REAL D ( 2 , 8 , 8 ) REAL S U M D ( 2 , 8 , 8 ) , S U M E ( 2 , 8 , 8 ) , S U M B A ( 2 , 8 , 8 ) REAL PROB(2) REAL V D ( 2 , 8 , 8 ) , V E ( 2 , 8 , 8 ) , V L ( 2 , 8 , 8 ) , V U ( 2 , 8 , 8 ) R E A D ( 2 , * ) M,N READ(2,*) ( B ( I ) , I = 1 , 3 ) READ(2,*) ( F ( I ) , I = 1 , 3 ) READ(2,*) ( T ( I ) , I = 1 , 3 ) READ(2,*) ( R ( I ) , I = 1 , 3 ) READ(2,*) (E1(I),1=1,M) MN=M*N READ(2,*) ((E2(I,J),J=1,N),1=1,M) X=2 Y=2 Z=2 G=3 PVOVL=0 PVF=0 PROB(1)=1.0/M PROB(2)=1.0/N C INITIALIZING VARIABLES DO 12 P=1,2 DO 4 1=1,M DO 5 J = 1 , N SUMD(P,I,J)=0 SUME(P,I,J)=0 ! SUMBA(P,I,J)=0 VL(P,I,J)=0 OVL(I)=0 OVL0=0 5 CONTINUE 4 CONTINUE 12 CONTINUE DO 13 I = 1 , M DO 14 J = 1 , N DO 15 K=1,N EARN(2,I,J,K)=E2(I,K) D(2,I,K)=E2(I,K) 15 CONTINUE 14 CONTINUE 13 CONTINUE • C DO 16 1=1,M DO 17 K=1,M  11  EARN(1,I,1,K)=E1(K) D(1,K,1)=E1(K) CONTINUE CONTINUE W=N P=2 DO 1 1 = 1 ,M IF (P .EQ. 1) THEN DO U=1 Q=1 L=M W=1 ELSE DO U=0 Q=2 L=N  *  END I F DO 2 J=1,W DO 3 K=1,L IF ( D ( P , I , J ) .LE. EARN(P,I,J,K)) THEN DO PD(P,I,J,K)=D(P,I,J) PE(P,I,J,K)=(EARN(P,I,J,K)-D(P,I,J)) * ( 1 -T (Y) ) +U*PVOVL+U*PVF BA(P,I,J,K)=0 ELSE DO RES=EARN(P,I,J K)-B(X) PD(P,I,J,K)=AMAX1(0.0,RES)+U*PVOVL PE(P,I,J,K)=0 IF (RES .LT. 0) THEN DO BA(P,I,J,K)=EARN(P,I,J,K) ELSE DO BA(P,I,J,K)=B(X) END I F END I F SUMBA(P,I,J)=SUMBA(P,I,J)+BA(P,I,J,K) SUMD(P,I,J)=SUMD(P,I,J)+PD(P,I,J,K) SUME(P,I,J)=SUME(P,I,J)+PE(P,I,J,K) CONTINUE VD(P,I,J)=SUMD(P,I,j)*PROB(Q)/(1+R(Z)) VE(P,I,J)=SUME(P,I,J)*PROB(Q)/(1+R(Z)) -U*F(G) PRINT, PVF,PVOVL,VE(P,I,J) VL(P,I,J)=VD(P,I,J)+VE(P,I,J) VU(P,I,J)=VL(P,I,J)-T(Y)*D(P,I,j)+(1-T(Y))* SUMBA(P,I,j)*PROB(Q)/(1+R(Z)) IF (OVL(I) .LT. V L ( P , I , J ) .AND. P .EQ. 2) THEN DO R  *  *  OVL(I)=VL(P,I,J) OVE(I)=VE(P,I,J) OVD(l)=VD(P,I,J) OVU(l)=VU(P,I,J) OD(l)=D(P,I,J)  118  END I F I F (OVLO . L T . V L ( P , I , J ) .AND. P .EQ. 1) THEN * DO OVL0=VL(P,I,J) OVE0=VE(P,I,J) OVD0=VD(P, I , J ) OVU0=VU(P,I,J) OD0=D(P,I,J) END I F 2 CONTINUE 1 CONTINUE I F ( P .EQ. 2 ) THEN DO DO 471 1=1,M PVOVL=PVOVL+OVL(I) 471 CONTINUE PVOVL=PVOVL*PROB(1)/(1+R(Z)) PVF=F(G)/(1+R(Z)) P=1 GO TO 11 END I F C OUTPUT DO 98 P=1,2 L=N DO 9 9 1=1,M I F ( P .EQ. 1) L=1 DO 9 9 9 J = 1 , L I F ( P .EQ* 2 ) THEN DO PRINT, D ( P , I , J ) , V L ( P , I , J ) END I F WRITE(9,543) D ( P , I , J ) , V D ( P , I , J ) , V E ( P , I , J ) , * VL(P,I,J) 543 FORMAT (4(F12.4,1X)) 999 CONTINUE 99 CONTINUE 98 CONTINUE C DO 9 6 1=1,M WRITE(9,246) O V D ( l ) , O V E ( l ) , O V L ( l ) , O D ( l ) 246 FORMAT (4(F12.4,1X)) WRITE(7,*) O V D ( l ) , O V E ( l ) , O V L ( l ) , O V U ( l ) , * OD(I) 96 CONTINUE WRITE(9,85) OD0,OVD0,OVE0,OVL0 85 FORMAT (4(F12.4,1X)) STOP END $EXECUTE  119  A P P E N D I X 1C C A S E I I I S I M U L A T I O N PROGRAM $COMPILE INTEGER X,Y,Z,FLAG,G REAL D(8,8),E1(8),E2(8,8) REAL P D ( 8 , 8 ) , P E ( 8 , 8 ) REAL T ( 3 ) , R ( 3 ) , B ( 3 ) , R E S , F ( 3 ) REAL SUMD(8,8,8),SUME(8,8,8) REAL VD(8,8,8),VE(8,8,8),VL(8,8,8) REAL DIV(8,8,8),W(8,8,8) REAL R E D I V ( 8 , 8 , 8 ) , C F ( 8 , 8 , 8 ) REAL REW(8,8,8) REAL OVD(8),OVE(8),OVL(8),OVU(8),OD(8) REAL DECVD(8,8,8),DECVE(8,8,8) REAL DSUMD(8,8),DSUME(8,8) REAL VD0(8,8),VE0(8,8),VL0(8,8) REAL VDD0(8,8),VEE0(8,8),VLL0(8,8),DD(8,8) R E A L OVL0,OVD0,OVE0,OD0 REAL E X D V L ( 8 , 8 , 8 ) , R E E X D V L ( 8 , 8 , 8 ) REAL PROB(2) CHARACTER D E C I D E ( 8 , 8 , 8 ) C R E A D ( 2 , * ) M,N READ(2,*)(B(I),I=1,3) READ(2,*)(F(I),I=1,3) READ(2,*) ( T ( I ) , I = 1 , 3 ) READ(2,*) ( R ( I ) , I = 1 , 3 ) READ(2,*) ( E 1 ( I ) , 1 = 1 , M ) READ(2,*) ((E2(I,J),J=1,N),1=1,M) DO 17 1=1,M READ(7,*) O V D ( I ) , O V E ( l ) , O V L ( I ) , O V U ( l ) , O D ( l ) 17 CONTINUE X=2 Y=2 Z= 2 G=2 PROB(1)=1.0/M PROB(2)=1.0/N C INITIALIZING VARIABLES DO 11 I = 1 , M DO 2 2 J = 1 , N DO 33 K=1 ,M SUMD(I,J,K)=0 SUME(I,J,K)=0 DSUMD(I,J)=0 DSUME(I,J)=0 OVL0'=0 33 CONTINUE 22 CONTINUE 11 CONTINUE C M A I N PROGRAM 10 DO 1 1 = 1 , M DO 2 J = 1 , N D(l ,J)=E2(I,J) DO 3 K=1,M  1 20  DO 4 L=1,N I F ( D ( I , J ) .LE. E 2 ( K , L ) ) THEN DO PD(K,L)=D(I,J) PE(K,L)=(E2(K,L)-D(I,J))*(1-T(Y)) ELSE DO RES=E2(K,L)-B(X) PD(K,L)=AMAX1(0.0,RES) PE(K,L)=0 END I F SUMD(I,J,K)=SUMD(I,J,K)+PD(K,L) SUME(I,J,K)=SUME(I,J,K)+PE(K,L) CONTINUE VD(I,J,K)=SUMD(I,J,K)*PROB(2)/(1+R(Z)) VE(I,J,K)=SUME(I,J,K)*PROB(2)/(1+R(Z)) VL(I,J,K)=VD(I,J,K)+VE(I,J,K) DIV(I,J,K)=E1(K)*(1-T(Y)) W(I,J,K)=DIV(I,J,K)+VE(I,J,K) EXDVL(I,J,K)=VL(I,J,K)+DIV(I,J,K)  4  C REDIV(I,J,K)=(E1(K)-F(G))*(1-T(Y)) CF(I,J,K)=OVD(K)-VD(l,J,K) REW(I,J,K)=REDIV(I,J,K)+OVE(K)+CF(I,J,K) REEXDVL(I,J,K)=VL(I,J,K)+REDIV(I,J,K) C IF  3  (W(I,J,K) .GE. REW(I,J,K)) THEN DO DECIDE(I,J,K)='N' DECVD(I,J,K)=VD(I,J,K) DECVE(I,J,K)=W(I,J,K) ELSE DO DECIDE(I,J,K)='Y' DECVD(I,J,K)=VD(I,J,K) DECVE(I,J,K)=REW(I,J,K) END I F DSUMD(I,J)=DSUMD(I,J)+DECVD(I,J,K) DSUME(I,J)=DSUME(I,J)+DECVE(I,J,K) CONTINUE VDO(I,J)=DSUMD(I,J)*PROB(1)/(1+R(Z)) VEO(I,J)=DSUME(I,J)*PROB(1)/(1+R(Z))-F(G) VLO(I,J)=VD0(I,J)+VE0(I,J)  C IF  2 1  C C 102 101  (OVL0 .LE. V L 0 ( I , J ) ) THEN DO OVL0=VL0(l,J) OVD0=VD0(I,J) OVE0=VE0(l,J) ODO=D(I,J) END I F CONTINUE CONTINUE DO 104 K=1,M DO 101 1=1,M DO 102 J=1 ,N PRINT, D ( I , J ) , V L ( I , J , K ) PRINT, D ( I , J ) , D E C I D E ( I , J , K ) , E X D V L ( I , J , K ) ,REDIV(I,J,K) CONTINUE CONTINUE  104 CONTINUE C ARRANGE DEBT L E V E L S I N A S C E N D I N G ORDERS DO 741 J = 1 , M DO 4 8 9 J J = 1 , N AMIN=1.0+D(M,N) DO 143 1=1,M DO 2 1 4 1 1 = 1 ,N I F ( D ( I , I I ) . L E . A M I N ) T H E N DO AMIN=D(I,11) K=I KK=I I END I F 214 CONTINUE 143 CONTINUE DD(J,JJ)=D(K,KK) VDDO(J,JJ)=VD0(K,KK) VEE0(J,JJ)=VE0(K,KK) VLL0(J,JJ)=VL0(K,KK) D(K,KK)=2.0+D(M,N) 489 CONTINUE 741 CONTINUE C OUTPUT DO 99 1=1,M DO 9 9 9 J = 1 , N WRITE(9,154) DD(I,J),VDD0(I,J),VEEO(I,J) * VLL0(I,J) 154 FORMAT ( 4 ( F 1 2 . 4 , 1 X ) ) 999 CONTINUE 99 CONTINUE C WRITE(9,742) OD0,OVD0,OVE0,OVL0 C742 FORMAT ( 4 ( F 1 2 . 4 , 1 X ) ) STOP END $EXECUTE  CASE  A P P E N D I X 1D I V S I M U L A T I O N PROGRAM  $COMPILE INTEGER X,Y,Z,FLAG,G REAL D(8,8),E1(8),E2(8,8) REAL  REAL REAL REAL REAL REAL REAL  PD(8,8),PE(8,8)  T(3),R(3),B(3),RES,F(3) SUMD(8,8,8),SUME(8,8,8) VD(8,8,8),VE(8,8,8),VL(8,8,8) DIV(8,8,8),W(8,8,8) REDIV(8,8,8),CF(8,8,8) REW(8,8,8)  REAL  OVD(8),OVE(8),OVL(8),OVU(8),OD(8)  REAL  DECVD(8,8,8),DECVE(8,8,8)  REAL  DSUMD(8,8),DSUME(8,8)  REAL  VD0(8,8),VE0(8,8),VL0(8,8)  REAL V D D 0 ( 8 , 8 ) , V E E 0 ( 8 , 8 ) , V L L 0 ( 8 , 8 ) , D D ( 8 , 8 ) REAL OVL0,OVD0,OVE0,OD0 REAL  CP(8,8)  REAL PROB(2) CHARACTER D E C I D E ( 8 , 8 , 8 ) C R E A D ( 2 , * ) M,N READ(2,*) ( B ( I ) , I = 1 , 3 ) READ(2,*) ( F ( I ) , I = 1 , 3 ) READ(2,*) ( T ( I ) , I = 1 , 3 ) READ(2,*) (R(I),1=1,3) READ(2,*) (E1(I),1=1,M) READ(2,*) ((E2(I,J),J=1,N),1=1,M) DO 17 I = 1 , M READ(7,*) O V D ( l ) , O V E ( l ) , O V L ( l ) , O V U ( l ) , O D ( l ) 17 CONTINUE X=2 Y=2 Z= 2 G=2 PROB(1)=1.0/M PROB(2)=1.0/N C INITIALIZING VARIABLES DO 11 1=1,M DO 22 J = 1 , N DO 33 K=1,M SUMD(I,J,K)=0 SUME(I,J,K)= 0 DSUMD(I,J)=0 DSUME(I,J)=0 OVL0=0 33 CONTINUE 22 CONTINUE 11 CONTINUE C M A I N PROGRAM 10 DO 1 1=1,M DO 2 J = 1 , N D( I , J ) = E 2 ( I , J ) C P U ,J)=D(I , j ) / 2 .  123  DO  3 K=1,M DO 4 L = 1 , N I F ( D ( I , J ) . L E . E 2 ( K , L ) ) THEN DO PD(K,L)=D(I,J) PE(K,L)=(E2(K,L)-D(I,J))*(1-T(Y)) E L S E DO RES=E2(K,L)-B(X) PD(K,L)=AMAX1(0.0,RES) PE(K,L)=0 END I F SUMD(I,J,K)=SUMD(I,J,K)+PD(K,L) SUME(I, J , K)=SUME(I,J,K)+PE(K,L) CONTINUE VD(I ,J,K)=SUMD(I,J,K)*PROB(2)/(1+R(Z)) VE(I,J,K)=SUME(I,J,K)*PROB(2)/(1+R(Z)) VL(I,J,K)=VD(I,J,K)+VE(I,J,K) DIV(I,J,K)=E1(K)*(1-T(Y)) W(I , J , K ) = D I V ( I , J , K ) + V E ( I , J , K ) REDIV(I,J,K)=(E1(K)-F(G))*(1-T(Y)) I F ( V D ( I , J , K ) . L T . C P ( I , J ) ) THEN DO CF(I,J,K)=OVD(K)-VD(l,J,K) E L S E DO CF(I,J,K)=OVD(K)-CP(I,J) END I F REW(I,J,K)=REDIV(I,J,K)+OVE(K)+CF(I,J,K) IF  ( W ( I , J , K ) .GE. R E W ( I , J , K ) ) THEN DO DECIDE(I,J,K)='N' DECVD ( I , J , K ) = VD ( I , J , K ) D E C V E ( I , J , K ) = W ( I , J , K) E L S E DO DECIDE(I,J,K)='Y' I F ( V D ( I , J , K ) .GE. C P ( I , J ) ) THEN DO DECVD(I,J,K)=CP(I,J) DECVE(I,J,K)=REW(I,J,K) E L S E DO DECVD(I,J,K)=VD(I,J,K) DECVE(I,J,K)=REW(I,J,K) P R I N T , 'YES','NO C A L L ' , DECVD(I,J,K),DECVE(I,J,K) END I F END I F DSUMD(I,J)=DSUMD(I,J)+DECVD(I,J,K) DSUME(I,J)=DSUME(I,J)+DECVE(I,J,K) CONTINUE VD0(I,J)=DSUMD(I,J)*PROB(1)/(1+R(Z)) VEO(I,J)=DSUME(I,J)*PR0B(1)/(1+R(Z))-F(G) VLO(I,J)=VD0(I,J)+VE0(I,J) IF  (OVL0 . L E . V L 0 ( I , J ) ) OVL0=VL0(I,J) OVD0=VD0(I,J) OVE0=VE0(l,J) OD0=D(l,J) END I F  THEN  DO  124  2 1  CONTINUE CONTINUE C ARRANGE DEBT L E V E L S I N A S C E N D I N G ORDERS DO 741 J = 1 , M DO 4 8 9 J J = 1 , N AMIN=1.0+D(M,N) DO 143 1=1,M DO 2 1 4 11 = 1 , N I F ( D ( I , I I ) . L E . A M I N ) T H E N DO AMIN=D(I,II) K=I KK=II END I F 214 CONTINUE 143 CONTINUE DD(J,JJ)=D(K,KK) VDDO(J,JJ)=VD0(K,KK) VEEO(J,JJ)=VE0(K,KK) VLLO(J,JJ)=VL 0(K,KK) D(K,KK)=2.0+D(M,N) 489 CONTINUE 741 CONTINUE C OUTPUT DO 9 9 1=1,M DO 9 9 9 J = 1 , N WRITE(9,851) D D ( I , J ) , V D D 0 ( I , J ) , V E E O ( I , J ) * VLL0(I,J) 851 FORMAT ( 4 ( F 1 2 . 4 , 1 X ) ) 999 CONTINUE 99 CONTINUE C WRITE(9,156) ODO,OVD0,OVE0,OVL0 C156 FORMAT ( 4 ( F 1 2 . 4 , 1 X ) ) STOP END $EXECUTE  125  APPENDIX  1E  I N P U T DATA AND FORMAT 3, 1000, 500, .20, .05, 4091 , o, 13684,  3, 3500, 1800, .40, .10, 7368, 2376, 9246,  6000, 2800, .60, .20, 12670, 6704, 14375,  4042, 20961,  8537,  DIMENSIONS B A N K R U P T C Y COST F L O T A T I O N COSTS TAX RATES DISCOUNT RATES PERIOD 1 CF PERIOD 2 CF PERIOD 2 CF  A P P E N D I X 1F CASE I SIMULATED D E B T :L E V E L 0 .0000 2376 .0000 4042 .0000 6704 .0000 8537 .0000 9246 .0000 13684 .0000 1 4375.0000 20961 .0000 8537 .0000  RESULTS VD 0 .0000 1 7 4 5. 4 5 7 0 2598 .1670 3743 .4390 4263 .6360 4202 .6640 51 03 . 8 5 9 0 4 9 0 9 .371 0 5192 .7500 4263 .6360  CASE I I SIMULATED DEBT L E V E L 4091 . 0 0 0 0 7368 .0000 1 2670.0000 0 .0000 2376 .0000 6704 .0000 4042 .0000 8537 .0000 1 3684.0000 9246 .0000 14375 .0000 20961 .0000 1 4 4 0. 0 0 0 0 5338 . 1 790 1 0453 .3300 4091 . 0 0 0 0  VE 6990. 6750 5943. 4020 5300. 8670 4420. 8630 391 5. 9 0 6 0 3759. 6520 3026. 0970 2949. 9530 2587. 0890 3915. 9060  VL 6 9 9 0 . 67 50 7688. 8590 7 8 9 9 . 031 0 81 6 4 . 3 0 0 0 81 7 9 .5 4 2 0 7 9 6 2 . 3160 81 2 9 .9 5 7 0 7859. 3240 7779. 8390 81 7 9 .5 4 2 0  RESULTS  VD 3719. 0920 6495. 0190 8891 . 5 5 8 0 0. 0 0 0 0 1 4 4 0 .0 0 0 0 2031 . 51 50 3674. 5470 5 3 3 8 . 1790 5837. 2690 8405. 4530 10453. 3300 11388. 4800 786. 9092 9 3 5 . 81 84 1 1 9 7 .4 5 5 0 3719. 0920  VE 7221 . 1090 3407. 6520 178. 1 736 1 6 5 0 .9 0 9 0 786. 9092 0. 0 0 0 0 2570. 3640 935. 8184 0. 0 0 0 0 3062. 5460 1 1 9 7 .4 5 5 0 0. 0 0 0 0 2226. 9090 6273. 9960 11650. 7800 7221 . 1 0 9 0  VL 1 0 9 4 0 . 1900 9902. 6710 9069. 7316 1650. 9090 2226. 9090 2031 . 5 1 5 0 6244. 9100 6273. 9960 5837. 2690 11467. 9900 11650. 7800 11388. 4800 2376. 0000 8537. 0000 14375. 0000 1 0 9 4 0 . 1900  CASE  I I I SIMULATED  DEBT L E V E L . 0.0000 2376.0000 4042.0000 6704.0000 8537.0000 9246.0000 13684.0000 14375.0000 20961.0000  CASE  VD 0.0000 1745.4550 2598.1650 3743.4320 4263.6320 4202.6600 5103.8550 4909.3630 5192.7420  I V SIMULATED  DEBT  LEVEL 0.0000 2376.0000 4042.0000 6704.0000 8537.0000 9246.0000 13684.0000 1 4375.000020961.0000  RESULTS VE 7864.5740 6428.5350 5602.4210 4429.0890 3969.2380 3812.9800 3079.4290 3129.7530 2766.8860  VL 7864.5740 8173.9880 8200.5850 8172.5190 8232.8710 8015.6400 8183.2850 8039.1170 7959.6280  VE 7864.5740 6882.7530 6286.1130 5332.7770 4833.7850 4687.2960 3770.3550 3792.1250 2794.2420  VL 7864.5740 8 0 3 9 . 1170 7882.1250 7979.9020 8039.t130 7743.7570 7906.7690 7711.8390 7711.8390  RESULTS  VD 0.0000 1156.3640 1596.0140 2647.1260 3205.3300 3056.4640 4136.4140 3919.7170 4917.5970  


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