Capital Structure without w ithout Taxes Taxes
15.1
Alpha Corporation Corporation and Beta Corporation Corporation are identical identical in in every every way except except their their capital capital structur structures. es. Alpha Alpha Corporation, an all-equity firm, has 5,000 shares shares of stoc outstandin!, currently currently worth "#0 per share. share. Beta Corporation uses levera!e in its capital structure. $he maret value of Beta%s Beta%s de&t de&t is "#5,000. $he cost of this de&t is 1#' per annum. (ach firm is expected to have earnin!s &efore interest of ")50,000 in perpetuity. *either firm pays pays taxes. Assume that every investor can &orrow &orrow at 1#' per annum. +hat is the value of Alpha Corporation +hat is the value of Beta Corporation +hat is the maret value of Beta Corporation%s equity ow much will i t cost to purchase #0' of each firm%s equity Assumin! each firm meets its earnin!s estimates, what will &e the dollar return to each position in part over the next year d over Alpha%s equity and replicates f. Construct an investment strate!y in whi ch an investor purchases #0' Alpha%s &oth the cost and dollar return of purchasin! #0' of Beta%s Beta%s equity. g. s Alpha%s Alpha%s equity more or less risy than Beta%s equity (xplain. a. b. c. d. e.
15.#
Acetate, Acetate, nc., nc., has has equity equity with a maret maret value value of of "#0 million and de&t de&t with with a maret maret value of "10 "10 million. million. $he cost of the de&t is 1/' per annum. $reasury $reasury &ills that mature in one year yield ' per annum, and the expected return on the maret maret portfolio over the next year year is 1'. $he &eta of Acetate%s Acetate%s equity is 0.. $he firm pays no taxes. a. b. c.
+hat is Acetate%s de&t-equity ratio +hat is the firm%s wei!hted avera!e cost of capital +hat is the cost of capital for an otherwise-identical all-equity firm
15.)
2evered, 2evered, nc., nc., and and 3nlever 3nlevered, ed, nc. nc. are are identic identical al in every way except except their capital capital structur structures. es. (ach company company expects to earn "4 million &efore interest per year in perpetuity, with each company distri&utin! all its earnin!s as dividends. 2evered%s perpetual de&t has a maret value of "#5 milli on and costs ' per annum. 2evered has /.5 million shares outstandin!, outstandin!, currently worth "100 per share. 3nlevered has no de&t and 10 million shares outstandin!, currently worth "0 per share. *either firm pays taxes. s 2evered%s stoc a &etter &uy than 3nlevered%s stoc stoc
15./
$he 6e 6e&len Company Company and the the 7ni!ht 7ni!ht Company Company are identical identical in every every respect respect except except that that 6e 6e&len is is not levered. $he maret value of 7ni!ht Company%s 4-percent &onds is "1 million. 8inancial information for the two firms appears &elow. &elow. All All earnin!s streams are perpetuities. perpetuities. *either firm pays taxes. Both firms distri&ute all earnin!s availa&le to common stoc holders immediately. Veblen
9ro:ected ;peratin! ncome t oc oc ?equired ?eturn on (quity @r s Baret 6alue of >toc Baret 6alue of =e&t 6alue of the 8irm +ei!hted +ei!hted Avera!e Cost of Capital @r wacc =e&t-(quity ?atio
" )00,000 " )00,000 0.1#5 " #,/00,000 " #,/00,000 0.1#5 0
K night
"
)00,000 40,000 " #/0,000 0.1/0 " 1,1/,000 1,000,000 " #,1/,000 0.110 0.5/
a.
b.
15.5
An investor who is a&le to &orrow at 4' per annum wishes to purchase 5' of 7ni!ht%s equity. Can he increase his dollar return &y purchasin! 5' of 6e&len%s equity if he &orrows so that the i nitial net cost of the two options are the same iven the two investment strate!ies in part a, which will investors choose +hen will this process cease
rimsley, nc., is an all-equity firm with 100,000 shares of common stoc outstandin!, worth "50 per share. *either the firm nor its shareholders pay any taxes. Consider three stocholders of rimsley, s. annon, s. 8inney, and s. race. All three individuals can &orrow and lend at #0' per annum, the same rate at which the firm lends and &orrows. $he value of their holdin!s in rimsley and of their personal &orrowin! and lendin! positions are listed &elowD
s. annon s. 8inney s. Crace
6alue of Crimsley > hares " 10,000 50,000 #0,000
$otal $otal Borrowin! 2endin! " #,000 " 4,000 -
rimsley%s mana!ement has recently decided to alter the firm%s capital structure so that the de&t-to-equity ratio of the firm is 0.#5. n order to do this, rimsley issued "1 million in de&t yieldin! #0' per annum and used the funds to repurchase #0,000 shares. *one of these shares were repurchased from s. annon, s. 8inney, or s. race. $he three stocholders wish to alter their positions so that their payoffs after the restructurin! equal their payoffs prior to the restructurin!. Assume that rimsley immediately distri&utes all earnin!s availa&le to stocholders at the end of the year and that the restructurin! will have no effect on the firm%s earnin!s &efore taxes. >how the values of each of the investor%s shares in rimsley, as well as their &orrowin!, and lendin! positions after they have ad:usted their portfolios. 15.4
?ay&urn anufacturin!, nc., is currently an all-equity firm that pays no taxes. $he maret value of the firm%s equity is "# million. $he cost of this unlevered equity is 1' per annum. ?ay&urn plans to issue "/00,000 in de&t and use the proceeds to repurchase stoc. $he cost of de&t is 10' per annum. a. b. c.
15.
After ?ay&urn repurchases the stoc, what will the firm%s wei!hted avera!e cost of capital &e After the repurchase, what will the cost of equity &e (xplain. 3se your answer to part b to compute ?ay&urn%s wei!hted avera!e cost of capital after the repurchase. s this answer consistent with part a
>trom, nc. is an all-equity firm with #50,000 shares of common stoc outstandin!. (ach share is worth "#0. $he firm pays no taxes. $he appropriate discount rate for the firm%s unlevered equity is 15'. >trom%s earnin!s last year were "50,000, and mana!ement expects that the firm%s earnin!s will remain at "50,000 per annum into perpetuity. >trom is plannin! to &uy a competitor%s &usiness for ")00,000. ;nce acquired, the competitor%s facilities are expected to increase >trom%s earnin!s &y "1#0,000 per year. $he competitor is also an all-equity firm with the same riss as >trom and a required return on its equity of 15'. a. b.
Construct the maret-value &alance sheet for >trom &efore the announcement of the &uyout is made. >uppose >trom decides to issue equity in order to fund the &uyout. i. Accordin! to the efficient-maret hypothesis, what wil l >trom%s stoc price &e immediately after the announcement. ii. Construct >trom%s maret-value &alance sheet immediately after the announcement. iii. ow many shares will >trom need to issue in order to fund the &uyout iv.Construct >trom%s maret-value &alance sheet after the equity issue &ut &efore the purchase is finaliEed. v. Construct >trom%s maret-value &alance sheet after the purchase is finaliEed.
c.
15.
vi. +hat is the expected return to >trom%s equity holders after the &uyout vii. +hat is >trom%s wei!hted avera!e cost of capital after the &uyout >uppose >trom decides to issue 10' de&t in order to fund the &uyout. i. Construct >trom%s maret-value &alance sheet immediately after the announcement. ii. Construct >trom%s maret-value &alance sheet after the de&t issue &ut &efore the purchase is finaliEed. iii. Construct >trom%s maret value &alance sheet after the purchase is finaliEed. iv. +hat is the expected return to >trom%s equity holders after the &uyout v. +hat is >trom%s wei!hted avera!e cost of capital after the &uyout
$he ulf 9ower Company, an all-equity firm, is plannin! to &uild a new power plant. 8inancial data pertainin! to the company and the new power plant are listed &elow. Assume all earnin!s are paid out as dividends. Company Data Annual (xpected (arnin!s @in perpetuityD *um&er of >hares ;utstandin!D
"# million 10 million
New Power Plant nitial ;utlayD Added Annual (xpected (arnin!s @in perpetuityD
"#0 million ") million
$he new power plant has the same ris as existin! assets. $he current required rate of return on the firm%s equity is 10 percent. Assume there are no taxes and no costs of &anruptcy. Construct ulf%s maret value &alance sheet &efore the firm announces that it will &uild the new power plant. +hat is the price per share of ulf%s equity b. >uppose ulf decides to issue equity to fund the initial outlay for the power plant. i. Construct ulf%s maret-value &alance sheet immediately after the announcement. +hat is the new price per share of the firm%s equity ii. ow many shares will ulf need to issue in order to fund the outlay iii. Construct ulf%s maret-value &alance sheet after the equity issue &ut &efore the outlay is made. iv.Construct ulf%s maret-value &alance sheet after the outlay has &een made. v. +hat will the value of ulf 9ower &e if common stoc is issued to finance the construction of the new power plant c. >uppose ulf decides to issue "#0 million of ' &onds in order to fund the initial outlay for the power plant. i. Construct ulf%s maret-value &alance sheet immediately after the announcement. +hat is the new price per share of the firm%s equity ii. Construct ulf%s maret-value &alance sheet after the de&t issue &ut &efore the outlay is made. iii. Construct ulf%s maret-value &alance sheet after the outlay has &een made. iv. +hat will the value of ulf 9ower &e if de&t is issued to finance the construction of the new power plant v. Calculate the rate of return required &y equity holders after &oth the de&t i ssue and the completion of the new plant. vi. Calculate the firm%s wei!hted avera!e cost of capital after &oth t he de&t issue and the completion of the new plant. a.
15.
n a world with no taxes, no transaction costs, and no costs of financial distress, are the followin! statements true, false, or uncertain (xplain your answers. f a firm issues equity to repurchase some of its de&t, the price per share of the firm%s stoc will rise &ecause the shares are less risy. b. oderate &orrowin! will not increase the required return on a firm%s equity. a.
15.10
2ist the three assumptions that lie &ehind the odi!liani-iller theory in a world without taxes. Are these assumptions reasona&le in the real world (xplain.
15.11
=i!ital >ound, nc., is an all-equity firm with 1 million shares of common stoc outstandin! at "10 per share. =i!ital is expected to !enerate "1,500,000 of annual earnin!s in perpetuity. ichael 2efton is interested in acquirin! a 1' stae in the firm%s equity. e will either &orrow #0', /0', or 40' of the purchase price at an interest rate of 10' per annum. Assume that =i!ital >ound does not pay any taxes and that the firm immediately distri&utes all of its earnin!s as dividends. a. b.
15.1#
ow much will it cost for ichael to purchase 1' of =i!ital%s equity, net of de&t, !iven each financin! choice +hat is the expected return on ichael%s investment !iven each financin! choice
2ocomotive Corporation is plannin! to repurchase part of its common stoc &y issuin! corporate de&t. As a result, the firm%s de&t-to-equity ratio is expected to rise from /0' to 50'. $he firm currently has ".5 million worth of de&t outstandin!. $he cost of this de&t is 10' per annum. 2ocomotive expects to earn ").5 million per annum in perpetuity. 2ocomotive pays no taxes. +hat is the maret value of 2ocomotive Corporation &efore and after the repurchase announcement +hat is the expected return on the firm%s equity @r > &efore the announcement of the stoc repurchase plan c. +hat is the expected return on the equity of an otherwise identical all-equity firm @r 0 d. +hat is the expected return on the firm%s equity @r > after the announcement of the stoc repurchase plan a. b.
Capital Structure with Corporate Taxes
15.1)
$he maret value of a firm with "500,000 of de&t is "1,00,000. $he pre-tax interest rate on de&t is 10' per annum, and the company is in the )/' tax &racet. $he company expects ")04,000 of earnin!s &efore interest and taxes every year in perpetuity. a. b.
+hat would the value of the firm &e if it were financed entirely with equity +hat amount of the firm%s annual earnin!s is availa&le to stocholders
15.1/
An all-equity firm has 15,000 shares of common stoc outstandin!, currently worth "#0 per share. ts equity holders require a #0' return. $he firm decides to issue "1 million of 10' de&t and use the proceeds to repurchase common stoc. Accordin! to odi!liani-iller, what is the maret value of the firm%s equity after the repurchase Assume a )0' corporate tax rate.
15.15
>trider 9u&lishin! Company, an all-equity firm, expects perpetual earnin!s &efore interest and taxes @(B$ of "#.5 million per year. >trider%s after-tax, all-equity discount rate is #0'. $he firm is su&:ect to a )/' corporate tax rate. a. b. c. d.
15.14
+hat is the value of >trider 9u&lishin! f >trider issues "400,000 of de&t and uses t he proceeds to repurchase stoc, what will the value of the firm &e (xplain any difference in your answers to parts a and b. +hat assumptions are you main! when valuin! >trider
i&son, nc., expects perpetual earnin!s &efore interest and taxes of "1.# million per year. $he firm%s pretax cost of de&t is ' per annum, and its annual interest expense is "#00,000. Company analysts estimate that the unlevered cost of i&son%s equity is 1#'. i&son is su&:ect to a )5' corporate tax rate. a. b.
+hat is the value of this firm f there are no costs of financial distress or &anruptcy, what percenta!e of the firm%s capital structure would &e financed &y de&t
c.
15.1
reen anufacturin!, nc., plans to announce that it will issue "#,000,000 of perpetual de&t and use the proceeds to repurchase common stoc. $he &onds will have a 4' annual coupon rate. reen is currently an all-equity firm worth "10,000,000 with 500,000 shares of common stoc outstandin!. After the sale of the &onds, reen will maintain the new capital structure indefinitely. reen currently !enerates annual pretax earnin!s of "1,500,000. $his level of earnin!s is expected to remain constant in perpetuity. reen is su&:ect to a corporate tax rate of /0'. a. b. c. d. e. f. g.
15.1
+hat is olland%s value +hat is olland%s cost of equity @r > +hat is olland%s wei!hted avera!e cost of capital @r wacc
+illiamson, nc., has a de&t-to-equity ratio of #.5. $he firm%s wei!hted avera!e cost of capital @r wacc is 15', and its pre-tax cost of de&t is 10'. +illiamson is su&:ect to a corporate tax rate of )5'. a. b. c.
15.#0
+hat is the expected return on reen%s equity &efore the announcement of the de&t issue Construct reen%s maret-value &alance sheet &efore the announcement of t he de&t issue. +hat is the price per share of the firm%s equity Construct reen%s maret-value &alance sheet immediately after the announcement of the de&t issue. +hat is reen%s stoc price per share immediately after the repurchase announcement ow many shares will reen repurchase as a result of the de&t issue ow many shares of common stoc will remain after the repurchase Construct the maret-value &alance sheet after the restructurin!. +hat is reen%s stoc price per share after the restructurin! +hat is the required return on reen%s equity after the restructurin!
$he olland Company expects perpetual earnin!s &efore interest and taxes @(B$ of "/ million per year. $he firm%s after-tax, all-equity discount rate @r 0 is 15'. olland is su&:ect to a corporate tax rate of )5'. $he pre-tax cost of the firm%s de&t capital is 10' per annum, and the firm has "10 million of de&t in its capital structure. a. b. c.
15.1
s the conclusion in part b applica&le to the real world
+hat is +illiamson%s cost of equity capital @r > +hat is +illiamson%s unlevered cost of equity capital @r 0 +hat would +illiamson%s wei!hted avera!e cost of capital @r wacc &e if the firm%s de&t-to-equity ratio were 0.5 +hat if it were 1.5
eneral $ools @$ expects earnin!s &efore interest and taxes @(B$ of "100,000 every year into perpetuity. $he firm currently has no de&t, &ut it can &orrow at 10' per annum. $%s cost of equity @r 0 is #5', and the firm is su&:ect to a corporate tax rate of /0'. a. b.
+hat is the value of the firm +hat will the value of $ &e if it &orrows "100,000 and uses the proceeds to repurchase equity
15.#1
>tephenson ?eal (state Company is an all-equity firm with 15 million shares of common stoc outstandin! worth ")#.50 per share. >tephenson is plannin! to purchase a hu!e trac of land in southeastern $exas for "100 million. $he land will su&sequently &e leased to tenant farmers, increasin! >tephenson%s annual expected pre-tax earnin!s &y "#5 million in perpetuity. $he firm%s unlevered cost of equity capital @r 0 is 1#.5'. >tephenson is su&:ect to a corporate tax rate of /0'. $he interest rate on >tephenson%s &onds is ' per annum. a. b. c.
d.
e.
f >tephenson wishes to maximiEe its total maret value, would you recommend that it issue de&t or equity in order to finance the purchase (xplain. Construct >tephenson%s maret-value &alance sheet &efore it announces the purchase. >uppose >tephenson decides to issue equity in order to finance the purchase. i. +hat is the net present value of the pro:ect ii. Construct >tephenson%s maret-value &alance sheet after it announces that the firm will finance the purchase usin! equity. +hat is the new price per share of the firm%s stoc ow many shares will >tephenson need to issue in order to finance the purchase iii. Construct >tephenson%s maret-value &alance sheet after the equity issue &ut &efore the purchase has &een made. ow many shares of common stoc does >tephenson have outstandin! +hat is the price per share of the firm%s stoc iv. Construct >tephenson%s maret-value &alance sheet after the purchase has &een made. >uppose >tephenson decides to issue de&t in order t o finance the purchase. i. +hat will the maret value of >tephenson &e if the purchase is financed with de&t ii. Construct >tephenson%s maret-value &alance sheet after &oth the de&t issue and the land purchase. +hat is the price per share of the firm%s stoc +hich method of financin! maximiEes the per share stoc price of >tephenson%s equity