FINC2011 Tutorial 5 BMA Chapter 4 Problems 5, 6, 7, , 16, 1, 20, 21, 24, 25, 27
5! Company Z's earnings and dividends per share are expected to grow indefinitely by 5% a year. If next year's dividend is $1 and the mar!et capitali"ation rate is #% what is the crrent stoc! price&
Answer P0 = 10/(.08 - .05) = $333.33.
6! Company Zprime is li!e Z in all respects save one( Its growth will stop after year ). In year 5 and afterward it will pay ot all earnings as dividends. *hat is Z prime's stoc! price& +ssme next year's ,- is $15.
Answer P4 = EPS5 / r P4 = [EPS1 × (1 + g1)3 × (1 + g2)] / r P4 = [$15 × (1 + .05)3 × (1 + 0)] / .08 P4 = $217.05 N!e !"#! $15 s !"e EPS %r &e#r 1. '"e 5 eren! grw!" r#!e s!s #%!er &e#r 4* s !"e enen! %r !"e %rs! grw!" r#!e ,s! e 3* (e#r 4 e#r 1). '"ere s n grw!" n &e#r 5. P0 = 1 / (1 + r) + [1 × (1 + g)] / (1 + r)2 + [1 × (1 + g)2] / (1 + r)3 + [1 × (1 + g)3] / (1 + r)4 + P4 / (1 + r)4 P0 = $10 / 1.08 + ($10 × 1.05) / 1.082 + ($10 × 1.052) / 1.083 + ($10 × 1.053) / 1.084 + $217.05 / 1.084 P0 = $15.0
7! If company Z /see -roblem 50 were to distribte all its earnings it cold maintain a level dividend stream of $15 a share. ow mch is the mar!et actally paying per share for growth opportnities&
Answer Pre = EPS1/r + P6 e#99 !"#! !"e re = 1/(r g). '"ere%re* re = $10/(.08 - .05) = $333.333. '"ere%re* 15/.08 + P6 = 333.33: !"ere%re P6 = $145.83.
! Consider three investors(
a.
2r. ingle invests for one year.
b.
2s. 3oble invests for two years.
c.
2rs. 4riple invests for three years.
+ssme each invests in company Z /see -roblem 50. how that each expects to earn a rate of retrn of #% per year.
Answer ;!" ne! &e#ren #! $10/s"#re #n ne! &e#rens #n res grw #s %99wsB
3I1 6 $1 3I7 6 3I1 8 /1 9 g0 6 $1 8 1.5 6 $1.5 3I: 6 3I7 8 /1 9 g0 6 $1.5 8 1.5 6 $11.: - 6 3I1 ; /r < g0 6 $1 ; /.# < .50 6 $:::.:: -1 6 - 8 /1 9 g0 6 $:::.:: 8 1.5 6 $:5. -7 6 -1 8 /1 9 g0 6 $:5. 8 1.5 6 $:=>.5 -: 6 -7 8 /1 9 g0 6 $:=>.5 8 1.5 6 $:#5.##
1 6 /3I /3I17 9 9-17 < <-100 ;; -1 6 6 /$1.5 /$1 9 :5. < :::.::0 ; $:::.:: 6 .# or #% rr7 6 9 :=>.5 < :5.0 ; $:5. 6 .# or #% r: 6 /3I: 9 -: < -70 ; -7 6 /$11.: 9 :#5.## < :=>.50 ; $:=>.5 6 .# or #%
Sne !"e r#!e % re!rn e#" &e#r s 8 eren!* e#" n>es!r s"9 ee! ! e#rn 8@.
16! ?oo! p -;, and -;@ ratios for ,ntergy /tic!er symbol ,4A0 sing Bahoo Dinance or another Internet sorce. Calclate the same ratios for the following
potential comparables( +merican ,lectric -ower /+,-0 Center-oint ,nergy /CE-0 and othern Company /F0. et ot the ratios in the same format as 4able ).1. +re the ratios for these electric companies tightly groped or scattered& If yo didnGt !now ,ntergyGs stoc! price wold the comparables give a good estimate& Answer
n!erne! eerse: #nswers w99 >#r&.
1! Consider the following three stoc!s(
a. toc! + is expected to provide a dividend of $1 a share forever.
b. toc! @ is expected to pay a dividend of $5 next year. 4hereafter dividend growth is expected to be )% a year forever.
c. toc! C is expected to pay a dividend of $5 next year. 4hereafter dividend growth is expected to be 7% a year for five years /i.e. ntil year =0 and "ero thereafter. If the mar!et capitali"ation rate for each stoc! is 1% which stoc! is the most valable& *hat if the capitali"ation rate is >%& Answer
10 eren! #!#9C#!n r#!eB
P toc! + 6 3I1 ; r 6 $1 ; .1 6 $1 P toc! @ 6 3I1 ; /r < g0 6 $5 ; /.1 < .)0 6 $#:.::
¿ [¿¿ 1 × ( 1 + g ) × ( 1 + g )]/ r (1 + r ) ¿ ¿ × ( 1 + g ) ¿ ×( 1 + g ) ¿ × ( 1 + g) ¿ × ( 1 + g ) ¿ × ( 1 + g ) P Stock C = + + + + + +¿ 1+r ( 1+ r ) (1 + r ) (1 + r ) (1 +r ) ( 1+ r ) 5
2
6
2
1
0
1
1
2
3
1
3
4
1
4
5
1
5
6
P toc! C 6 $5 ; 1.1 9 /$5 8 1.70 ; 1.1 7 9 /$5 8 1.770 ; 1.1: 9 /$5 8 1.7:0 ; 1.1 ) 9 /$5 8 1.7)0 ; 1.1 5 9 /$5 8 1.750 ; 1.1= 9 H$5 8 1.75 8 /1 9 0J ; .1K ;1.1= P toc! C 6 $1).51
A! # 10@ #!#9C#!n r#!e* S!? D "#s !"e 9#rges! resen! >#9e. sng !"e s#,e %r,9#s #s #>e w!" # 7@ #!#9C#!n r#!e* !"e >#9es #reB
P toc! + 6 $1 ; .> 6 $1)7.#= P toc! @ 6 $5 ; /.> .)0 6 $1==.=> P toc! C 6 $5 ; 1.> 9 /$5 8 1.70 ; 1.> 7 9 /$5 8 1.770 ; 1.>: 9 /$5 8 1.7:0 ; 1.>) 9 /$5 8 1.7)0 ; 1.>5 9 /$5 8 1.750 ; 1.>= 9 H$5 8 1.75 8 /1 9 0J ; .>K ; 1.>=
P toc! C 6 $15=.5
A! # 7@ #!#9C#!n r#!e* S!? F "#s !"e 9#rges! resen! >#9e.
20!
Company L's crrent retrn on eMity /AF,0 is 1)%. It pays ot onehalf of earnings as cash dividends /payot ratio 6 .50. Crrent boo! vale per share is $5. @oo! vale per share will grow as L reinvests earnings. +ssme that the AF, and payot ratio stay constant for the next for years. +fter that competition forces AF, down to 11.5% and the payot ratio increases to .#. 4he cost of capital is 11.5%.
a. *hat are L's ,- and dividends next year& ow will ,- and dividends grow in years 7 : ) 5 and sbseMent years&
b. *hat is L's stoc! worth per share& ow does that vale depend on the payot ratio and growth rate after year )&
Answer #. P9w#? r#! = 1 #&! r#! = 1.0 0.5 = 0.5 >en grw!" r#!e = g= P9w#? r#! × E = 0.5 × 0.14 = 0.07 Ne!* ,!e EPS0 #s %99wsB E = EPS0 /F? eG!& er s"#re 0.14 = EPS0 /$50 ⇒ EPS0 = $7.00 '"ere%reB 0 = #&! r#! × EPS0 = 0.5 × $7.00 = $3.50 e#r 0 1 2 3 4 5
EPS #n >ens %r sseGen! &e#rs #reB EPS $7.00 $7.00×0.5=$3.50 $7.00 × 1.07 = $7.4 $7.4 × 0.5 = $3.50 × 1.07 = $3.75 $7.00 × 1.07 2= $8.01 $8.01×0.5=$3.50×1.07 2 = $4.01 $7.00 × 1.07 3= $8.58 $8.58×0.5=$3.50×1.07 3 = $4.2 4 $7.00 × 1.07 = $.18 $.18×0.5=$3.50×1.07 4 = $4.5 $7.00 × 1.07 4 × 1.023 = $.3 $.3 × 0.8 = $7.51
EPS #n >ens %r &e#r 5 #n sseGen! &e#rs grw #! 2.3@ er &e#r* #s n#!e & !"e %99wng #99#!nB >en grw!" r#!e = g = P9w#? r#! × E = (1 0.08) × 0.115 = 0.023
P0 =
DIV1 1.115 1
+
DIV 2 1.115 2
+
DIV 3 1.115 3
+
DIV4 1.115 4
DIV5 + × 1 4 0.115 0.023 1.115
.
= 3.7451 + 4.0072 + 4.2883 + 4.5884 + 7.5093 × 1 4 = $65.453 1.115 1.115 1.115 1.115 0.115 - 0.023 1.115 '"e 9#s! !er, n !"e #>e #99#!n s eenen! n !"e #&! r#! #n !"e grw!" r#!e #%!er &e#r 4. 21! ,ach of the following formlas for determining shareholders' reMired rate of retrn can be right or wrong depending on the circmstances(
Dor each formla constrct a s,9e nmerical example showing that the formla can give wrong answers and explain why the error occrs. 4hen constrct another simple nmerical example for which the formla gives the right answer.
Answer #. An nrre! A9#!n. H!s"! Se,n!rens "#>e grwn & 30@ er &e#r sne !"e %r,en s rIe!e #! $1.25. '"sB r
=
DIV1 P0
+g=
1.25 100
+ 0 .30 = 0 .3125 = 31.25%
'"s s wrng e#se !"e %r,9# #ss,es ere!#9 grw!": ! s n! ss9e %r H!s"! ! grw #! 30@ er &e#r %re>er. A Drre! A9#!n. '"e %r,9# ,g"! e rre!9& #9e ! !"e 9 J#!"%9 #9r#* w"" "#s een grwng #! # s!e#& 5@ r#!e %r e#es. !s EPS1 = $10* 1 = $5* #n P0 = $100. '"sB
r
=
DIV1 P0
+g=
5 100
+ 0 .05 = 0 .10 = 10.0%
E>en "ere* & s"9 e #re%9 n! ! 9n9& rIe! #s! grw!" n! !"e %!re. % 9 J#!"%9 "#9s #9* #n energ& rss 9 !rn ! n! # grw!" s!?. . An nrre! A9#!n. H!s"! "#s rren! e#rnngs % $5.00 er s"#re. '"sB r
=
EPS1 P0
=
5 100
= 0 .05 = 5.0%
'"s s ! 9w ! e re#9s!. '"e re#sn P0 s s "g" re9#!>e ! e#rnngs s n! !"#! r s 9w* ! r#!"er !"#! H!s"! s enwe w!" >#9#9e grw!" r!n!es. Sse P6 = $0B P0 =
EPS1
100 =
r
+ PVGO
5 + 60 r
'"ere%re* r = 12.5@.
A Drre! A9#!n. n%r!n#!e9&* 9 J#!"%9 "#s rn ! % >#9#9e grw!" r!n!es. Sne P6 = 0B P0 = EPS1 + PVGO r
100 =
10 +0 r
'"ere%re* r = 10.0@.
24! Compost cience Inc. /CI0 is in the bsiness of converting @oston's sewage sldge into fertili"er. 4he bsiness is not in itself very profitable. owever to indce CI to remain in bsiness the 2etropolitan 3istrict Commission /23C0 has agreed to pay whatever amont is necessary to yield CI a 1% boo! retrn on eMity. +t the end of the year CI is expected to pay a $) dividend. It has been reinvesting )% of earnings and growing at )% a year.
a. ppose CI contines on this growth trend. *hat is the expected longrn rate of retrn from prchasing the stoc! at $1& *hat part of the $1 price is attribtable to the present vale of growth opportnities&
b. Eow the 23C annonces a plan for CI to treat Cambridge sewage. CI's
plant will therefore be expanded gradally over five years. 4his means that CI will have to reinvest #% of its earnings for five years. tarting in year = however it will again be able to pay ot =% of earnings. *hat will be CI's stoc! price once this annoncement is made and its conseMences for CI are !nown&
Answer a. r = 3I1 ; P0 9 g
r 6 $) ; $1 9 .) r 6 .# or #%
,-1 6 3iv1 ; /1 < reinvestment rate0 ,-1 6 $) ; /1 < .)0 ,-1 6 $=.=>
P 6 ,-1 ; r + -NF -NF 6 P < ,-1 ; r -NF 6 $1 < $=.=> ; .# -NF 6 $1=.=> b. 3I1 will decrease to( .7 × $=.=> 6 $1.::. @y plowing bac! #% of earnings CI will grow by #% per year for five years before retrning to its longrn growth rate of )%. 4he dividend will be 7% of earnings for years 15 and =% of earnings in year = and beyond.
Bear
1
7
:
)
5
=
,-!
$=.=>
$>.7
$>.>#
$#.)1
$O.>
$O.#
3I!
1.::
1.))
1.5=
1.=#
1.#1
5.##
P5 6 3I= ; /r < g) P5 6 $5.## ; /.# < .)0 P5 6 $1)=.O:
P 6 3I1 ; /1 9 r0 9 3I7 ; /1 9 r07 9 3I: ; /1 9 r0: 9 3I) ; /1 9 r0)9 3I 5 ; /1 9 r05 9 P5 ; /1 9 r)5 P 6 $1.:: ; 1.# 9 $1.)) ; 1.# 7 9 $1.5= ; 1.#: 9 $1.=# ; 1.#) 9 $1.#1 ; 1.#5 9 $1)=.O: ; 1.#5
P 6 $1=.1>
25! -ermian -artners /--0 prodces from aging oil fields in west 4exas. -rodction is 1.# million barrels per year in 71= bt prodction is declining at >% per year for the foreseeable ftre. Costs of prodction transportation and administration add p to $75 per barrel. 4he average oil price was $=5 per barrel in 71=.
-- has > million shares otstanding. 4he cost of capital is O%. +ll of --'s net income is distribted as dividends. Dor simplicity assme that the company will stay in bsiness forever and that costs per barrel are constant at $75. +lso ignore taxes.
a. *hat is the ending 71= vale of one -- share& +ssme that oil prices are expected to fall to $= per barrel in 71> $55 per barrel in 71# and $5 per barrel at in5% 71O. increases per+fter year.71O assme a longterm trend of oilprice
b. *hat is --'s ,-;- ratio and why is it not eMal to the O% cost of capital&
Answer #.Jrs!* ,!e !"e >ens* w"" eG#9 ne! n,e* %r 201 !"rg" 2020B
-rodction /million barrels0 -rice of oil;barrel /$0 Costs per barrel /$0
Aevene ,xpenses Eet Income /6 3ividends0 ori"on growth rates(
2016
2017
201
201"
2020
1.# =5 75
1.=>) = 75
1.55=# 55 75
1.))># 5 75
1.:)=5 57.5 75
11> )5
1)) )1#5
#5=751 :#O75
>7:O71: :=1O==5
>=OO15 ::==7:)
>7
5#5O
)=>)=
:=1O==5
:>7#5>)
ge>ene 6 /19 sales price growth rate0 8 /1 9 prodction growth rate0 < 1 ge>ene 6 /1 9 .50 8 1 9 /<.>0J < 1 ge>ene 6 <.7:5 or <7.:5% gDs!s 6 /19 costs growth rate0 8 /1 9 prodction growth rate0 < 1 gDs!s 6 /1 9 0 8 1 9 /<.>0J < 1 gDs!s 6 <.> or <>% -71O Aevenes 6 revene77 ; /r < g0 -71O Aevenes 6 $>=OO15 ; .O < /<.7:50J -71O Aevenes 6 $=77#7>)))
-71O Costs 6 costs 77 ; /r g) -71O Costs 6 $::==7:) ; .O < /<.>0J -71O Costs 6 $71:#O=7#
-71O 6 -71O revenes< -71O costs -71O 6 $=77#7>))) < 71:#O=7# -71O 6 $)17):>#1> -71= 6 3I71> ; /1 9 r0 9 3I71# ; /1 9 r07 9 /3I71O 9 P2010 ; /1 9 r)3 -71= 6 $5#5O ; 1.O 9 $)=>)= ; 1.O7 9 /$:=1O==5 9)17):>#1>0 1.O: -71= 6 $):O)O7O: -rice per share71= 6 -71= ; nmber of shares -rice per share71= 6 $):O)O7O: ; > -rice per share71= 6 $=7.>#
b. ,-71= 6 net income71= ; nmber of shares ,-71= 6 $>7 ; > ,-71= 6 $1.7O
,-;- 6 $1.7O ; $=7.># ,-;- 6 .1=) or 1=.)%
;
'"e EPS/P s gre#!er !"#n !"e s! % #!#9 e#se r!n #n e#rnngs #re e9nng.
27! 2exican 2otorsG mar!et cap is 7 billion pesos. Eext year's free cash flow is #.5 billion pesos. ecrity analysts are forecasting that free cash flow will grow by >.5% per year for the next five years.
a. +ssme that the >.5% growth rate is expected to contine forever. *hat rate of retrn are investors expecting&
b. 2exican 2otors has generally earned abot 17% on boo! eMity /AF, 6 . 170 and paid ot 5% of earnings as dividends. 4he remaining 5% of earnings has gone to free cash flow. ppose the company maintains the same AF, and investment rate in the longrn ftre. *hat is the implication for the growth rate of earnings and free cash flow& Dor the cost of eMity& hold yo revise yor answer to part /a0 of this Mestion&
Answer #. '"e ns!#n! grw!" %r,9# P= /(r K g) #n e se "ereB $200 = $8.5/(r-.075) S9>ng %r r* r = 0.1175. '"#! s* n>es!rs ee! #n 11.75@ r#!e % re!rn.
. 6>en !"e Le#n L!rs s 9wng #? 50@ % e#rnngs #%!er e#rnng 12@ n eG!&* !"e %r, #n ee! ! grw #! #n #nn#9 r#!e % n9& @ (E 9w#? = 0.12 0.50 = 0.0). A9&ng !"e ns!#n! grw!" %r,9# #g#n #n s9>ng %r r we ge!B $200 = $8.5/(r-.0) r = 0.1025. '"#! s* n>es!rs s"9 ee! n9& # 10.25@ r#!e % re!rn.
