Common Stock Financing Problems

 

COMMON STOCK FINANCING

 

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Chapter 4

115

Illustrative Problems

Mr. Mr. Amat Amatya, ya, a dissatisf dissatisfed ed stockhol stockholder der o the Dabu Daburr Company, Company, desire desires s representation on the board. The Dabur Company, which has 9 directors, has 1 million shares

ILLUSTRATION 1.

outstandin. a. !ow ma many ny sha share res s woul would d Mr. Mr. Amatya Amatya ha"e to cont contro roll to be assu assure red d o 1 dire direct ctors orship hip under a ma#ority$rule %non$cumulati"e& %non$cumulati"e& "otin system' b. (e (e$comp $compute ute )art %a&, %a&, as assumi sumin n a cumu cumulati" lati"e e "o "otin tin syst system. em. SOLUTION

*i"en, +umber o shares outstandin %+&  1,---,-- T  Total otal number o d directors irectors to be elected %& 9 a. Desired number number o d directors irectors to be elec elected ted %des.&  1 +umber o shares re/uired to elect desired number o directors %re/.&  ' Under non-cumulative voting: 0e ha"e, re re/. /.  m mor ore e tthan han - per percen centt shar shares es or  2 1  --,--1 shares !ence, --,--1 shares are re/uired to elect one director with certainty. b.

Unde Under r cum cumul ulat ativ ive e v vot otin ing: g: re/. re/.  2 1 2 1  1--, 1--,---1 1 shar shares es 3nder cumulati"e "otin system only 1--,--1 shares are re/uired to elect one director with certainty.

As one o the minority minority sha share rehol holde ders rs o the 4. Cor Corpor porati ation, on, Mr Mr.. 565 is dissatisf diss atisfed ed with the curre current nt oper operation ations s o the compan company y. !e eels that i he could ain membership on the company5s board o directors, he could persuade the company to make impro"ements. impro"e ments. The problem is that current manaement controls 7 percent o the stock. !e controls only 7 percent, and the balance is held by other minority shareholders. There are a total o --,--- "otin shares. Ten directors will be elected at the ne8t annual stockholder meetin. a.  "ot "otin in is is non non$cum $cumulat ulati"e, i"e, can M Mrr. 565 e elect lect hims himsel el as as a direc director' tor' b. :uppose :uppose he is able able to pe persua rsuade de all the m minori inority ty sharehol shareholder ders s that he should should b be e ele elected cted..  "otin is non$cumula non$cumulati"e, ti"e, can they elect him' c.  "o "otin tin  is c cumu umulat lati"e i"e,, can he e ele lect ct hi him m as a dire directo ctor' r' d. 0hat perc percent ent o the the minority minority s share hares s othe otherr than his his own will he he needs needs to h ha"e a"e "oted "oted or or him to be certain o election' e. 0hat is tthe he nu numbe mberr o director directors s the minority minority s shar harehol eholders ders c can an elect elect with c certa ertainty inty' ' [TU

ILLUSTRATION 2.

2058 (!"#$

SOLUTION

*i"en, +umber o shares outstandin %+&  --,--- shares +umber o shares held by c current urrent manaement  7; o o --,--- sha shares res  -,--1 shares are re/uired to elect Mr. 565 with certainty. 4ut Mr. 565 has only ,--- "otes, while ma#ority shareholder can cast ; 'alcul 'alculati ation on o% des desire ired d nu numbe mber r o% dir direct ectors ors (de (des# s# re/  1>,-- %1>,--- − 1& B 11  des B --,--des   >.7 directors  The minority shareholders can elect only > directors with certainty.

 The oom$Company oom$Company common stock is priced at (s 1- a share on the market. +otice is i"en that stockholders can purchase one new share at a price (s 1-- or e"ery our shares held. a. At app appro ro8ima 8imately tely wh what at mark market et price price will each each rih rihtt sell' 0h 0hy y will th this is be the appr appro8i o8imate mate price' b. 0hat eec eectt will the the iss issuanc uance e o ri rihts hts ha"e ha"e on on the o oriin riinal al mar marke kett price' price' ILLUSTRATION 3.

SOLUTION

*i"en, Current price o stock %)-&  (s 1:ubscription price %):&  (s 1-+umber o rihts re/uired to purchase one new share %&  ? a. ∴

b.

Appro8imate price o riht %E r&  ' Appro8imate Er     (s 1Ealue o each riht is (s 1 The calculated "alue o riht is appro8 appro8imate imate "alue because actual price is determined in the market. M): ater rihts oerin will decrease to the e8tent o "alue o each riht. )e  )- $ Er  1- $ 1-  (s 1?!ence, e8$riht price will be 1?-.

An#a An#ana na Fhan Fhanal al5s 5s to tota tall as asse sets ts cons consis istt o ?9?9- shar shares es o 4ri 4riht ht Gand Gand Corporation and (s >,--- in cash. 4riht Gand now oers stockholde stockholders rs one additional share at a price o (s >- or each f"e shares held. The current market price o the stock is (s ,--:ubscription price %)s&  (s >Current market price %)-&  (s .>.Pre)aration o% statement o% 3ealt* )osition i%  1. I% s*e e4ercises all *er rig*ts: 8istin number o shares  ?9- shares  T  Total otal number o rih rihts ts

 ?9- rihts

.. H .  1 share  1 rihtsI

+umber o new shar shares es that can be purchased    9= s shares hares Market price per share ater e8ercise o rihts %) e&  )- − Er   (s .-  (s .-

 

118

Chapter 4

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CAPITAL STRUCTURE MANAGEMENT

tatement o% 3ealt* )osition

Description Value Value of stocks [(490 + 98) shares @ Rs 332.50]............................ 2.50]............................................................................ ................................................ ash !ala"ce ....................................................... .......................................................................................... ................................................ ....................... .......... Rs 2,000 #ess$ ash %a&'e"t for "e share (98 shares @ Rs 20).....................................................1,90 Total wealth...................... wealth......................................................... ...................................................................... ......................................................................... ...................................... 2.

6.

Amount Rs 19,110

 

I% s*e sells all *er rig*ts tatement o% 3ealt* )osition

Description Value Value of stocks [490 shares @ Rs 32.5].................................................................................... 32.5]........................................................................................ .... ash !ala"ce ....................................................... .......................................................................................... ................................................ ....................... .......... Rs 2,000 *$ ash fro' sale of r-hts [490 r-hts @ Rs 2.50]............................................................ 2.50]............................................................ 1,225 Total wealth...................... wealth......................................................... ...................................................................... ......................................................................... ...................................... I% s*e sells 700 rig*ts and e4ercises 0 rig*ts +umber o new shares can be purchased   1= shares tatement o% ealt* Position

Amount Rs 15,925 3,225 Rs 19,150

Description Value Value of stocks [(490 + 18) shares @ Rs 332.50]............................ 2.50]............................................................................ ................................................ ash !ala"ce ................................ .................................................................. ..................................................................... .................................................... ................. 2,000 *$ ash fro' sale of r-hts (400 r-hts @ Rs 2.50)...........................................................1,000 #ess$ ash %a&'e"t for "e shares [18 @ Rs 20]..................................................................30 Total wealth...................... wealth......................................................... ...................................................................... ......................................................................... ...................................... 7.

40 Rs 19,150

Amount Rs 1,510

 

2,40 Rs 19,150

 

Amount Rs 15,925 2,000 Rs 17,925

I% s*e neit*er sells nor e4ercises t*e rig*ts: tatement o% ealt* )osition

Description Value Value of stocks [490 shares × Rs 32.50].......................................................... 32.50]....................................................................................... ............................. ash !ala"ce........................... !ala"ce............................................................. ..................................................................... ........................................................... ................................ ........ Total wealth...................... wealth......................................................... ...................................................................... ......................................................................... ......................................

ILLUSTRATION 5. :unrise :un rise Tea Tea Company Company plans to raise an addi addition tional al rupe rupee e o 1- million throuh rihts oerins. Current market price o the company is (s >-. t has >--,--shares outstandin. :tockholders are oered a new share at a price o (s 1-- each.

9euired: a. !ow many new shares shares w will ill ha ha"e "e tto o be sold to raise raise re/u re/uire ired d unds' unds' b. !ow many rih rihts ts w will ill be be rre/ui e/uired red to pu purch rchase ase a new new sh share are' ' c. 0ha 0hatt w will ill be theore theoretic tical al " "alu alue eo o riht rihts' s' d. Ca Calc lcul ulat ate e e8$ 8$ri rih hts ts pr pric ice. e. e. Mr. Mr. *opal Th Thapa5s apa5s total total assets assets consis consistt o 1-- shar shares es o :un :unrise rise Tea Company Company and c cash ash balance o .

(s 1,---. )repare statements o Mr. Thapa5s total assets beore rihts oerins. )rep )repar are e state statemen mentt showin showin Mr. Mr. Thap Thapa5s a5s tot total al assets assets ater ater rih rihts ts oerin oerins s or each each o  these courses o action i, i. he se sell lls s all hi his s ri rihts ts.. ii ii.. he e8er erci cise ses sa all ll his his rri iht hts. s. iii. he sells sells @- rih rihts ts a and nd e8erc e8ercises ises ?- riht rihts. s.

SOLUTION

a. b. c. d.

e.

+um +umber ber o ne new w sha share res s to be so sold ld to ra raise ise re re/ui /uire red d un unds ds    1--,--- shares +umber o rihts re/uired to purchase a new share    > rihts Th Theo eore retic tical al "alu "alue e o rih rihts ts %Er&     (s 8$rihts pr price %%) )e&  )- − Er  (s >- − (s -  (s >-tatem tatement ent o o%% o)a o)all T*a T*a)a, )a,s s asse assets ts (! (!e%o e%ore re ri rig*t g*ts s o;e o;erin rings# gs#

Description

Amount

 

COMMON STOCK FINANCING

%. i.

ii. ii.

• 

Value Value of stocks (100 shares @ Rs 250)........................................ 250)........................................................................... ................................................ ............... ash !ala"ce ................................ .................................................................. ..................................................................... ................................................. ......................... ............. Total assets............................ assets............................................................... ..................................................................... ................................................................... ................................. Pre)ar Pre)arati ation on o% t tate atemen mentt o% e ealt alt* * )os )ositi ition on a% a%ter ter r rig* ig*ts ts o;e o;erin rings gs I% *e s sel ellls a all ll *i *is s r rig ig* *ts tatement o% o)al T*a)a,s assets Description Value Value of stocks (100 shares @ Rs 200)........................................ 200)........................................................................... ................................................ ............... ash !ala"ce ........................................... .............................................................................. ............................................................ ................................. ........ Rs 15,000 *$ ash recee fro' sale of r-hts (100 r-hts @ Rs 50)................................................5,000 Total assets............................ assets............................................................... ..................................................................... ................................................................... ................................. I% *e e4er e4erci cises ses all all * *is is rig* rig*ts ts tatement o% o)al T*a)a,s assets

Chapter 4

 

iii iii..

 

20,000 Rs 40,000

Amount Rs 30,000

 

Description Value Value of stocks [(100 + 40/2) shares @ Rs 200]............................................................................

10,000 Rs 40,000

Amount Rs 24,000

ash !ala"ce.................................................. !ala"ce.................................................................................... .................................................... ............................ .......... Rs 15,000 *$ ash fro' sale of r-hts [0 r-hts @ Rs 50].......................................... 50]................................................................. .......................3,000 3,000 #ess$ ash %a&'e"t for "e shares [40/2 shares @ Rs , 100].............................................2,000 Total assets............................ assets............................................................... ..................................................................... ................................................................... .................................

Rs 25,000 15,000 Rs 40,000

Amount Rs 20,000

Description Value Value of stocks [(100 + 100/2) shares @ Rs 200].......................................................................... ash !ala"ce.................................................. !ala"ce.................................................................................... .................................................... ............................ .......... Rs 15,000 #ess$ ash %a&'e"t for "e shares [100/2 shares @ Rs 100].............................................5,000 Total assets............................ assets............................................................... ..................................................................... ................................................................... ................................. I% *e sells sells &0 ri rig*t g*ts s and e4e e4erci rcise se 70 rig rig*ts *ts tatement o% o)al T*a)a,s assets

11

 

1,000 Rs 40,000

ILLUSTRATION 6.  The stock o the +ational Corporation is sellin or (s - per share. The company then issues rihts to subscribe to one new share at (s ?- or each f"e rihts held. a. 0hat iis s the theo theoret retical ical "alue "alue o o a rih rihtt whe when n the stoc stock k is sellin sellin rih rihts$on' ts$on' b. 0hat is is the theo theoret retical ical "alue "alue o o one s share hare o sto stock ck when when it  oes oes e8$ri e8$rihts' hts' c. 0hat is is the theo theoret retical ical "alue "alue o o a rih rihtt whe when n the stoc stock k sells sells e8$rih e8$rihts ts at (s (s -' d. :hi"a :hi"a Mish Mishra ra has ( (s s 1,-1,--- at the time + +ation ational al stock stock oe oes s e8$rih e8$rihts ts at (s - per share share.. !e eels that the price o the stock will rise to (s @- by the time the rihts e8pire. Compute his return on his (s 1,--- i he %1& buys +ational stock at (s -, or %>& buys the rihts at the price computed in part c, assumin his price e8pectations are "alid. SOLUTION

*i"en, :ellin price o stock  :ubscription price %)s&%) &  (s (s ?+umber o rihts re/uired to purchase one new share %&   a. *en t*e stoc< is selling rig*ts on=  Theoretical "alue o ri riht ht %Er&    (s 1.@7 !ence, theoretical "alue o riht is (s 1.@7 when the stock is sellin rihts onJ b. *en it goes e4-rig*ts=  Theoretical "alue o a s share hare when it oes e8$riht %)e&    (s ?=.-  (s 1,>- T  Total otal retur return n in (s E Ealue alue o shares shares at the end o period − n"estment  (s 1,>-- − (s 1,---  (s >- T  Total otal retur return n in percent    -.>- or >-; I% %und is used to )urc*ase rig*ts= Ealue o riht %Er&  (s > Kunds a"ailable  (s 1,--+umber o rihts that can be purchase purchased d    -- rihts Ea Ealue lue o rihts when M): increases to (s @Er     (s ? Ealue o total rihts  (s ? × --  (s >,-- T  Total otal retur return n in (s  (s >,--- − (s 1,--1,---  (s 1,-- T  Total otal retur return n in percent   1 or 1--;

 The Miller Company has the balance sheet and income statement in table i"en below. The company plans to raise an additional (s  million throuh a rihts oerinJ the additional unds will continue to earn 1-. percent. The price$earnins ratio is assumed to remain at 1 times, the di"idend payout will continue to be @ percent, and the ?- percent ta8 rate will remain in eect. %Do not attempt to use the ormula i"en in the chapter. Addition Add itional al inormatio inormation n is i"en i"en her here e that "iolates the othe otherr thin thins s cons constant tantLL assumptio assumption n inherent in the ormula.& a. Assumin subscription subscriptio n price o (s - a shareJ ILLUSTRATION 7.

b.

1. !ow many additional shares o st stock ock will ha"e ha"e to be sold' >. !ow many rihts will be re/uired to purchase one new share' per share.

PROBLEM 6.

Value of a R-ht

 The 4ikash Ku Kurniture rniture Company has rown rapidly durin the past f"e years. yea rs. (e (ecen cently tly,, com compan pany y has disco" disco"er ered ed some ood in"e in"estm stment ent opportunity. t plans to raise an additional (s 1-,--,--- throuh rihts oerins. Current market price o the stock is (s 1-. 4ut subscription price is set at (s 1-- which is e/ual to its par "alue. Company has ?-,--shares outstandin.

9euired: a. +u +umb mber er o new new s sha harres to be be iss issue ued. d. b. +um +umber ber o o ri rihts hts rre/u e/uir ired ed to purc purchas hase e one new new shar share. e. c. Th Theo eore reti tica call " "al alue ue o ea each ch ri rih ht. t. d. e. PROBLEM 7.

Value of a R-ht

The Theor oreti etical cal "alu "alue e o a sha share re w when hen s stoc tock k oe oes s e8$ri e8$riht ht.. Th Theo eore reti tica call "alu "alue e o a rih rihtt when th the e st stoc ock k sells sells e8$ri e8$rih hts ts and the the actual market price oes to (s 1? per share.

 The :hikhar Company plans to raise an additional (s 1- million throuh a rihts oerin. Current market price is (s 11-. 4ut e8istin shareholders are oered one new share at (s -. Currently company has 1-,--,--shares outstandin. a. !ow many additional shares o stock will ha"e ha"e to be sold' sold' b. !ow many rihts will be re/uired to purchase purchase one new share' share' c. 0hat will be the "alue o each riht' d. 0ha 0hatt will be be the ma mark rket et pri price ce per per share share ater ater riht rihts s oer oerin in' ' e. :uppos :uppose e you hold hold 1-- shar shares es o :hikha :hikharr Company CompanyQs Qs sto stock ck and and ha"e (s ,--- cash balance beore the rihts oerin. oerin. :how your wealth position beore and ater rihts oerin assumin you e8ercise your rihts.

PROBLEM 8. R-hts =ffer"-s

*anesh Thapa5s total assets consist o -- shares o Delta Company and (s 1-,--- in cash. The company now oers stockholders one additional share at a price o (s 1- or each two shares held. The current market price o the stock is (s million shares o  common stock throuh a rihts oerin. The company currently has >million milli on shar shares es outst outstandin andin. . ach shareh shareholder older will recei"e recei"e one riht or each shares currently held. Thereore, each riht will enable shareholders to purchase -.1- shares. :e"en :prins common stock currently is sellin or (s > per share and the subscription subscription price o the rihts will be (s >> per share. a. Calcul Calculate ate the theo theore retic tical al "alue "alue o the rrih ihtt or both both the riht rihts$on s$on an and d e8$rihts cases. b. Det Deter ermin mine e the amount amount that that th the e mark market et price price o th the e company company5s 5s sto stock ck is e8pected to drop on the e8$ri e8$rihts hts date, assumin all other thins thins are e/ual. c.  the m mark arket et pr price ice o o :e"en :e"en :prin :prin  common common stoc stock k inc incre rease ases s to (s