Ch.14 (Problems and Solutions)
36.
Net operating income The Congress Company has identified two methods for producing playing cards. One method involves using a machine having a fixed cost of $10,000 and variable costs of $1.00 per dec of cards. The other method would use a less expensive machine !fixed cost " $#,000, but it would re%uire greater variable costs !$1.#0 per dec of cards. &f the selling price per dec of cards will be the same under each method, at what level of output will the two methods produce the same net operating income'
a. b. c. d. e.
#,000 decs 10,000 decs 1#,000 de decs (0,000 de decs (#,000 de decs
36.
Answer: b
Total cost Method 1 = $1.00(Q) + $10,000. Total cost Method 2 = $1.50(Q) + $5,000. Set equal and Q + $10,000 = $5,000 = 10,000 =
solve for Q $1.50(Q) + $5,000 $0.5(Q) Q.
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Diff: M
41.
Capital structure and stock price
Anser! c "i##! $
The following information applies to *ott +nterprises Operating income !+-&T $00,000 ebt $100,000 &nterest expense $ 10,000 Tax rate 204
/hares outstanding +/ /toc price
1(0,000 $1.2# $13.20
The company is considering a recapitali5ation where it would issue $26,000 worth of new debt and use the proceeds to buy bac $26,000 worth of common stoc. The buybac will be undertaen at the pre7recapitali5ation share price !$13.20. The recapitali5ation is not expected to have an effect on operating income or the tax rate. 8fter the recapitali5ation, the company9s interest expense will be $#0,000. 8ssume that the recapitali5ation has no effect on the company9s price earnings !:+ ratio. ;hat is the expected price of the company9s stoc following the recapitali5ation' a. b. c. d. e.
$1#.0 $13.3# $16.00 $1<.0 $(0.26
41.
Answer: c
!e can do th"s #role% & us"n' the * efore and after the reca#"tal"at"on. ecall that * = r"ce*S.
*-/T /nterest *-T Ta3 (40) 7/ Shares *S $1.50. *
-efore the reca#. fter reca#. $00,000 $00,000 10,000 50,000 $20,000 $250,000 116,000 100,000 $184,000 $150,000 120,000 100,0009 $184,000120,000 = $1.45. $150,000100,000 = $18.401.45 = 12 .
9120,000 ($4:,000$18.40) s * = 12 after the reca#"tal"at"on (recall the quest"on states that "t does not chan'e), ;e
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Diff: M
44.
%ptimal capital structure and &amada e'uation
Anser! d "i##! N
8aron 8thletics is trying to determine its optimal capital structure. The company9s capital structure consists of debt and common stoc. &n order to estimate the cost of debt, the company has produced the following table ebt7to7total7
+%uity7to7total7 -efore7tax assets ratio !wc
assets ratio !wd of debt 0.10
ebt7to7e%uity ratio !:+
0.<0 3.04 0.60 3.( 0.30 6.0 0.=0 6.6 0.#0 <.=
0.(0 0.0 0.20 0.#0
-ond rating
0.10:0.<0 " 0.11
88
0.(0:0.60 " 0.(#
8
0.0:0.30 " 0.2
8
0.20:0.=0 " 0.=3
--
0.#0:0.#0 " 1.00
-
cost
The company9s tax rate, T, is 20 percent. The company uses the C8> to estimate its cost of common e%uity, s. The ris7free rate is # percent and the maret ris premium is = percent. 8aron estimates that if it had no debt its beta would be 1.0. !&ts ?unlevered beta,@ bA, e%uals 1.0. On the basis of this information, what is the company9s optimal capital structure, and what is the firm9s cost of capital at this optimal capital structure' a. . c. d. e.
44.
;c = ;c = ;c = ;c = ;c =
0. 0.: 0.8 0.6 0.5
; d = ; d = ;d = ; d = ; d =
0.1 0.2 0. 0.4 0.5
!>> !>> !>> !>> !>>
= = = = =
14.6 10.6 8.: 10.15 10.1:
%ptimal capital structure and &amada e'uation
Anser! d "i##! N
B " #4D > 7 B " =4. s " B E ! > 7 Bb. ;8CC " d wd !1 7 T E s wc. Fou need to use the :+ ratio given for each capital structure to find the levered beta using the Gamada e%uation. Then, use each of these betas with the C8> to find the s for that capital structure. Ase this s and d for each capital structure to find the ;8CC. The optimal capital structure is the one that minimi5es the ;8CC. !:+
0.11 10.=64
b " bAH1 E !17T!:+I ;8CC
1.0==3
s " B E ! > 7 Bb
11.200#4
wc
0.<
d
3.04
wd
0.1
0.(#
1.1#00
11.<000
0.6
3.(
0.(
0.2
1.(#31
1(.#2(<
0.3
6.0
0.
0.=3
1.2000
1.2000
0.=
6.6
0.2
1.00
1.=000
12.=000
0.#
<.=
0.#
10.6 10.(( 10.1# 10.16
or example, if the :+ is 0.11 b " 1.0H1 E !1 7 T!:+I " 1.0H1 E !1 7 0.2!0.1111I " 1.0==3. s " B E ! > 7 Bb " #4 E =4!1.0==3 " 11.204. The weights are given at 0.< and 0.1 for e%uity and debt, respectively, and the d for that capital structure is given as 3 percent. ;8CC " d wd !1 7 T E s wc " 34 0.1 !1 7 0.2 E 11.204 0.< " 10.=64. o the same calculation for each of the capital structures and find each ;8CC. The optimal capital structure is the one that minimi5es the ;8CC, which is 10.1#4. Therefore, the optimal capital structure is 204 debt and =04 e%uity.
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
4. Capital structure and stock price
Anser! d "i##!
Jippy asta Corporation !JC has a constant growth rate of 3 percent. The company retains 0 percent of its earnings to fund future growth. JC9s expected +/ !+/ 1 and s for various capital structures are given below. ;hat is the optimal capital structure for JC' ebt:Total 8ssets (04 0 20 #0 30 a. b. c. d. e.
45.
+xpected +/
s $(.#0 .00 .(# .3# 2.00
1#.04 1#.# 1=.0 13.0 16.0
ebt:Total 8ssets " (04 ebt:Total 8ssets " 04 ebt:Total 8ssets " 204 ebt:Total 8ssets " #04 ebt:Total 8ssets " 304
Capital structure and stock price
Answer: d
The o#t"%al ca#"tal structure %a3"%"es the f"r%?s stoc< #r"ce. !hen the det rat"o "s 20, e3#ected *S "s $2.50. @"ven the f"r%?s #ol"c& of reta"n"n' 0 of earn"n's, the e3#ected d"v"dend #er share A 1 "s $2.50 0.80 = $1.85. The stoc< #r"ce 0 "s $1.85(15 8) or $21.::. !hen the det rat"o "s 0, e3#ected *S "s $.00 and e3#ected A 1 "s $.00 0.80 = $2.10. The stoc< #r"ce 0 "s $2.10(15.5 8) = $24.81. S"%"larl&, ;hen the det rat"o "s 40, A 1 = $2.285 and 0 = $25.2:. !hen the det rat"o "s 50, A 1 = $2.625 and 0 = $26.25. !hen the det rat"o "s 80, A 1 = $2.:0 and 0 = $25.45. The stoc< #r"ce "s h"'hest ;hen the det rat"o "s 50.
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Diff: T
46.
Capital structure and stock price
Anser! b "i##!
Kiven the following choices, what is the optimal capital structure for Chip Co.' !8ssume that the company9s growth rate is ( percent. ividends er /hare $#.#0 =.00 =.#0 3.00 3.#0
ebt Batio 04 (# 20 #0 3# a. b. c. d. e.
46.
Cost of +%uity !s 11.#4 1(.0 1.0 12.0 1#.0
04 debtD 1004 e%uity (#4 debtD 3#4 e%uity 204 debtD =04 e%uity #04 debtD #04 e%uity 3#4 debtD (#4 e%uity
Capital structure and stock price
Answer: b
B"rst, calculate the stoc< #r"ce for each det level us"n' the d"v"dend 'ro;th %odel, 0 = A1(
A"vshare $5.50 6.00 6.50 8.00 8.50
0 $5.50(0.115 0.02) $6.00(0.12 0.02) $6.50(0.1 0.02) $8.00(0.14 0.02) $8.50(0.15 0.02)
>learl&, $60.00 "s the h"'hest #r"ce, equ"t& "s the o#t"%al ca#"tal structure.
so
25
= = = = =
$58.:. $60.00. $5.0. $5:.. $58.6.
det
and
85
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Diff: T
Capital structure and stock price
47.
Anser! a "i##!
lood >otors is an all7e%uity firm with (00,000 shares outstanding. The company9s +-&T is $(,000,000, and +-&T is expected to remain constant over time. The company pays out all of its earnings each year, so its earnings per share e%uals its dividends per share. The company9s tax rate is 20 percent. The company is considering issuing $( million worth of bonds !at par and using the proceeds for a stoc repurchase. &f issued, the bonds would have an estimated yield to maturity of 10 percent. The ris7free rate in the economy is =.= percent, and the maret ris premium is = percent. The company9s beta is currently 0.<, but its investment baners estimate that the company9s beta would rise to 1.1 if it proceeds with the recapitali5ation. 8ssume that the shares are repurchased at a price e%ual to the stoc maret price prior to the recapitali5ation. ;hat would be the company9s stoc price following the recapitali5ation' a. b. c. d. e.
47.
$#1.12 $#.6# $#=.0( $=6.<3 $3=.0
Capital structure and stock price
Answer: a
?s current cost of capital, dividends First, find the company per share, and stock price: < = 0.066 + (0.06)0. = 12. To f"nd the stoc< #r"ce, &ou st"ll need the d"v"dends #er share or AS = ($2,000,000(1 0.4))200,000 = $6.00. Thus, the stoc< #r"ce "s 0 = $6.000.12 = $50.00. Thus, & "ssu"n' $2,000,000 "n ne; det the co%#an& can re#urchase $2,000,000$50.00 = 40,000 shares. Now after recapitalization, the new cost of capital, DPS, and stock price can be found: < = 0.066 + (0.06)1.1 = 1.20. AS for the re%a"n"n' (200,000
40,000) = 160,000 shares are thus C($2,000,000 ($2,000,000 0.10))(1 0.4)D 160,000 = $6.85. nd, f"nall&, 0 = $6.850.12 = $51.14.
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Diff: T
4*.
Capital structure and stock price
Anser! d "i##!
*ascheid +nterprises is an all7e%uity firm with 13#,000 shares outstanding. The company9s stoc price is currently $60 a share. The company9s +-&T is $(,000,000, and +-&T is expected to remain constant over time. The company pays out all of its earnings each year, so its earnings per share e%uals its dividends per share. The firm9s tax rate is 0 percent. The company is considering issuing $600,000 worth of bonds and using the proceeds for a stoc repurchase. &f issued, the bonds would have an estimated yield to maturity of 6 percent. The ris7free rate is # percent and the maret ris premium is also # percent. The company9s beta is currently 1.0, but its investment baners estimate that the company9s beta would rise to 1.( if it proceeded with the recapitali5ation. ;hat would be the company9s stoc price following the repurchase transaction' a. b. c. d. e.
4.
$10=.=3 $10(.= $ 33.12 $ 32.=3 $ 30.20
Capital structure and stock price
Answer: d
The onds used "n the re#urchase ;"ll create a ne; "nterest e3#ense for the co%#an&. Th"s ;"ll chan'e net "nco%e. A"v"dends #er share ;"ll chan'e ecause net "nco%e chan'es and the nu%er of shares outstand"n' chan'es. 7e; "nterest e3#ense $:00,000 : = $64,000. 7e; net "nco%e ($2,000,000 $64,000)(1 0.) = $1,55,200. Shares re#urchased $:00,000:0 = 10,000 shares. 7e; shares outstand"n' 185,000 10,000 = 165,000 shares. 7e; d"v"dends #er share $1,55,200165,000 = $:.21. !e %ust also calculate a ne; cost of equ"t& 5 + (5)1.2 = 11. 7e; stoc< #r"ce $:.2111 = $84.68.
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Diff: T
4+.Capital structure and stoc price
Anser! a "i##! N
+tchabarren +lectronics has made the following forecast for the upcoming year based on the company9s current capitali5ation &nterest expense Operating income !+-&T +arnings per share
$(,000,000 $(0,000,000 $.=0
The company has $(0 million worth of debt outstanding and all of its debt yields 10 percent. The company9s tax rate is 20 percent. The company9s price earnings !:+ ratio has traditionally been 1(, so the company forecasts that under the current capitali5ation its stoc price will be $2.(0 at year end. The company9s investment baners have suggested that the company recapitali5e. Their suggestion is to issue enough new bonds at a yield of 10 percent to repurchase 1 million shares of common stoc. 8ssume that the stoc can be repurchased at today9s $20 stoc price. 8ssume that the repurchase will have no effect on the company9s operating incomeD however, the repurchase will increase the company9s dollar interest expense. 8lso, assume that as a result of the increased financial ris t he company9s price earnings !:+ ratio will be 11.# after the repurchase. Kiven these assumptions, what would be the expected year7end stoc price if the company proceeded with the recapitali5ation' a. b. c. d. e.
4!.
$26.0 $2(.#= $22.3= $20.2 $2=.<0
Capital structure and stock price
Answer: a
Diff: T
To ans;er th"s ;e need to deter%"ne the follo;"n' 1. Eo; %an& shares are currentl& outstand"n'F 2. !hat are the "nterest e3#ense and net "nco%e, efore and after the chan'eF -efore reca#"tal"at"on *-/T $20,000,000 /nterest 2,000,000 *-T $1:,000,000 Ta3es (40) 8,200,000 7/ $10,:00,000 *S = $.60. Shares outstand"n' = $10,:00,000$.60 = ,000,000 shares. fter reca#"tal"at"on 7e; shares = %"ll"on 1 %"ll"on = 2 %"ll"on shares. Total det = $20,000,000 + ($1,000,000)($40) = $60,000,000. /nterest #a&%ent = ($60,000,000)(0.1) = $6,000,000. 7et "nco%e *-/T /nterest
$20,000,000 6,000,000
"
*-T Ta3es (40) 7/
$14,000,000 5,600,000 $ :,400,000
*S = $:,400,0002,000,000 = $4.20. * = 11.5. 0 = ($4.20)(11.5) = $4:.0.
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
,.
Capital structure and -PS
Anser! d "i##!
-uchanan -rothers anticipates that its net income at the end of the year will be $.= million !before any recapitali5ation. The company currently has <00,000 shares of common stoc outstanding and has no debt. The company9s stoc trades at $20 a share. The company is considering a recapitali5ation, where it will issue $10 million worth of debt at a yield to maturity of 10 percent and use the proceeds to repurchase common stoc. 8ssume the stoc price remains unchanged by the transaction, and the company9s tax rate is 2 percent. ;hat will be the company9s earnings per share, if it proceeds with the recapitali5ation' a. b. c. d. e.
5#.
$(.( $(.2# $.(= $2.#( $#.#2
Capital structure and $%&
Answer: d
fter "ssu"n' the det, the co%#an& can re#urchase $10,000,000$40 = 250,000 shares leav"n' 650,000 shares outstand"n'. !e st"ll need to f"nd the e3#ected 7/ after "ssu"n' the det. !e?re '"ven the ant"c"#ated 7/ "s $.6 %"ll"on. Thus, the *-/T (efore the det "ssue) can e found as follo;s $,600,000 = *-/T(1 0.4) or *-/T = $5,454,545.45. The co%#an& ;"ll #a& $1,000,000 "n "nterest after "ssu"n' the det so the ne; *-T ;"ll e $5,454,545.45 $1,000,000 = $4,454,545.45. The ne; 7/ f"'ure ;"ll e $4,454,545.45(1 0.4) = $2,40,000. B"nall&, *S = $2,40,000650,000 = $4.52 after the reca#"tal"at"on.
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Diff: T
1. Capital structure and -PS
Anser! a "i##!
TCG Corporation is considering two alternative capital structures with the following characteristics.
ebt:8ssets ratio d
8 0. 104
0.3 124
The firm will have total assets of $#00,000, a tax rate of 20 percent, and boo value per share of $10, regardless of capital structure. +-&T is expected to be $(00,000 for the coming year. ;hat is the difference in earnings per share !+/ between the two alternatives' a. b. c. d. e.
51.
$(.63 $3.=( $2.36 $.0 $1.1<
Capital structure and $%&
Answer: a
The f"r% ;"ll have det of $500,000(0.) = Capital structure $150,000 and equ"t& of $50,000. !e?re told the shares have a oo< value of $10 so the nu%er of shares outstand"n' "s $50,000$10 = 5,000. /nterest e3#ense ;"ll e $150,000(10) = $15,000. !e can co%#ute *-T as *-/T / or $200,000 $15,000 = $1:5,000. lso, ;e can co%#ute 7/ as *-T(1 T) or $1:5,000(1 0.4) = $111,000. B"nall&, *S = $111,0005,000 = $.18. Capital structure !: The f"r% ;"ll have det of $500,000(0.8) = $50,000 and equ"t& of $150,000. The nu%er of shares outstand"n' "s $150,000$10 = 15,000. /nterest e3#ense ;"ll e $50,000(14) = $4,000. !e can co%#ute *-T as $200,000 $4,000 = $151,000. lso, ;e can co%#ute 7/ as $151,000(1 0.4) = $0,600. B"nall&, *S = $0,60015,000 = $6.04. The d"fference "n *S et;een ca#"tal structure and ca#"tal structure - "s $6.04 $.18 = $2.:8.
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Diff: T