FINC2011 Tutorial 5

FINC2011 Tu FINC2011 Tutorial torial 55

BMA Chapter 4 Problems 5, 6, 7, , 16, 1, 20, 21, 24, 25, 27 BMA Chapter 4 Problems 5, 6, 7, , 16, 1, 20, 21, 24, 25, 27

5!

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 crrent stoc! price& Answer

P 0 = 10/(.08 - .05) = $333.33.

6!

6! Company Zprime is li!e Z in all respects save one( Its growth will stop after year ). In year 5 and afterward it will pay ot all earnings as dividends. *hat is Z prime's stoc! price& +ssme next year's ,- is $15.

Answer

P 4 = EPS 5 / r

P 4 = [EPS 1 × (1 + g 1 )3× (1 + g 2 )] / r

P 4 = [$15 × (1 + .05)3 × (1 + 0)] / .08

P 4 _{= $217.05}

N!e !"#! $15 s !"e EPS %r &e#r 1. '"e 5 eren! grw!" r#!e s!s #%!er &e#r 4* s !"e enen! %r !"e %rs! grw!" r#!e ,s! e 3* (e#r 4  e#r 1). '"ere s n grw!" n &e#r 5. P 0 =  1 / (1 + r) + [ 1 × (1 + g)] / (1 + r)2 + [ 1 × (1 + g)2 ] / (1 + r)3 + [ 1 × (1 + g)3 ] / (1 + r)4 + P 4 / (1 + r)4 P 0 = $10 / 1.08 + ($10 × 1.05) / 1.082 + ($10 × 1.052 ) / 1.083 + ($10 × 1.053 ) / 1.084 + $217.05 / 1.084 P 0 = $15.0 7!

7! If company Z /see -roblem 50 were to distribte all its earnings it cold maintain

a level dividend stream of $15 a share. ow mch is the mar!et actally paying per share for growth opportnities&

Answer

Pre = EPS1/r + P6

e#99 !"#! !"e re = 1/(r  g). '"ere%re* re = $10/(.08 - .05) = $333.333. '"ere%re* 15/.08 + P6 = 333.33: !"ere%re P6 = $145.83.

!

! Consider three investors(

a. 2r. ingle invests for one year.

b. 2s. 3oble invests for two years.

c. 2rs. 4riple invests for three years.

+ssme each invests in company Z /see -roblem 50. how that each expects to earn a rate of retrn of #% per year.

Answer

;!" ne! &e#r<s >en #! $10/s"#re #n ne! &e#r<s re #! $350/s"#re (#99#!e & !#?ng !"e rren! &e#r<s re % $333.33  # 5@ grw!" r#!e)* <s %re#s!e >ens #n res grw #s %99wsB 3I16 $1 3I76 3I18 /1 9 g0 6 $1 8 1.5 6 $1.5 3I:6 3I78 /1 9 g0 6 $1.5 8 1.5 6 $11.: - 6 3I1 ; /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.## r 1 _{6 /3I}1 _{9 -}1 _{< -}_{0 ; -}_{6 /$1 9 :5. < :::.::0 ; $:::.:: 6 .# or #%} r 7 6 /3I7 9 -7 < -10 ; -16 /$1.5 9 :=>.5 < :5.0 ; $:5. 6 .# or #% r : 6 /3I: 9 -: < -70 ; -76 /$11.: 9 :#5.## < :=>.50 ; $:=>.5 6 .# or #%

Sne !"e r#!e % re!rn e#" &e#r s 8 eren!* e#" n>es!r s"9 ee! ! e#rn 8@.

16!

16! ?oo! p -;, and -;@ ratios for ,ntergy /tic!er symbol ,4A0 sing Bahoo Dinance or another Internet sorce. Calclate the same ratios for the following

potential comparables( +merican ,lectric -ower /+,-0 Center-oint ,nergy /CE-0 and othern Company /F0. et ot the ratios in the same format as 4able ).1. +re the ratios for these electric companies tightly groped or scattered& If yo didnGt !now ,ntergyGs stoc! price wold the comparables give a good estimate&

Answer

n!erne! eerse: #nswers w99 >#r&.

1!

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 valable& *hat if the capitali"ation rate is >%&

Answer 10 eren! #!#9C#!n r#!eB P  toc! + 6 3I1 ;r 6 $1 ; .1 6 $1 P  toc! @ 6 3I1 ; /r < g 0 6 $5 ; /.1 < .)0 6 $#:.::

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P toc! C _{6 $5 ; 1.1 9 /$5 8 1.70 ; 1.1}7 _{9 /$5 8 1.7}7_{0 ; 1.1}:_{9 /$5 8 1.7}:_{0 ; 1.1})₉ /$5 8 1.7)_{0 ; 1.1}5_{9 /$5 8 1.7}5_{0 ; 1.1}=_{9 H$5 8 1.7}5 _{8 /1 9 0J ; .1K ;1.1}= P toc! C 6 $1).51

A! # 10@ #!#9C#!n r#!e* S!? D "#s !"e 9#rges! resen! >#9e.

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 1.75 0 ; 1.>= 9 H$5 8 1.75 8 /1 9 0J ; .>K ; 1.>= P toc! C6 $15=.5

A! # 7@ #!#9C#!n r#!e* S!? F "#s !"e 9#rges! resen! >#9e.

20!

20! Company L's crrent retrn on eMity /AF,0 is 1)%. It pays ot onehalf of

earnings as cash dividends /payot ratio 6 .50. Crrent boo! vale per share is $5. @oo! vale per share will grow as L reinvests earnings.

+ssme that the AF, and payot ratio stay constant for the next for years. +fter that competition forces AF, down to 11.5% and the payot 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 sbseMent years&

b. *hat is L's stoc! worth per share& ow does that vale depend on the payot ratio and growth rate after year )&

Answer

#. P9w#? r#! = 1  #&! r#! = 1.0  0.5 = 0.5

>en grw!" r#!e = g= P9w#? r#! × E = 0.5 × 0.14 = 0.07 Ne!* ,!e EPS 0 #s %99wsB

E = EPS 0 /F? eG!& er s"#re

0.14 = EPS 0 /$50⇒ EPS 0 = $7.00

'"ere%reB  0 = #&! r#! × EPS 0 = 0.5 × $7.00 = $3.50

EPS #n >ens %r sseGen! &e#rs #reB

e#r EPS  0 $7.00 $7.00 × 0.5 = $3.50 1 $7.00 × 1.07 = $7.4 $7.4 × 0.5 = $3.50 × 1.07 = $3.75 2 $7.00 × 1.07 2 _{= $8.01 $8.01 × 0.5 = $3.50 × 1.07} 2 _{= $4.01} 3 $7.00 × 1.07 3 _{= $8.58 $8.58 × 0.5 = $3.50 × 1.07} 3 _{= $4.2} 4 $7.00 × 1.07 4 _{= $.18 $.18 × 0.5 = $3.50 × 1.07} 4 _{= $4.5} 5 $7.00 × 1.07 4 _{× 1.023 = $.3 $.3 × 0.8 = $7.51}

EPS #n >ens %r &e#r 5 #n sseGen! &e#rs grw #! 2.3@ er &e#r* #s n#!e & !"e %99wng #99#!nB

>en grw!" r#!e = g = P9w#? r#! × E = (1  0.08) × 0.115 = 0.023

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4 5 4 4 3 3 2 2 1 1 0 1.115 1 0.023 -0.115 DIV 1.115 DIV 1.115 DIV 1.115 DIV 1.115 DIV P $65.453 1.115 1 0.023 -0.115 7.5093 1.115 4.588 1.115 4.288 1.115 4.007 1.115 3.745 4 4 3 2 1

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'"e 9#s! !er, n !"e #>e #99#!n s eenen! n !"e #&! r#! #n !"e grw!" r#!e #%!er &e#r 4.

21!

21! ,ach of the following formlas for determining shareholders' reMired rate of retrn can be right or wrong depending on the circmstances(

Dor each formla constrct a s,9e nmerical example showing that the formla can give wrong answers and explain why the error occrs. 4hen constrct another simple nmerical example for which the formla gives the right answer.

Answer

#. An nrre! A9#!n. H!s"! Se,n!r<s e#rnngs #n >ens "#>e grwn & 30@ er &e#r sne !"e %r,<s %nng 10 &e#rs #g. Drren! s!? re s $100* #n ne! &e#r<s >en s rIe!e #! $1.25. '"sB

31.25% .3125 0 .30 0 100 1.25 g P DIV r 0 1

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'"s s wrng e#se !"e %r,9# #ss,es ere!#9 grw!": ! s n! ss9e %r H!s"! ! grw #! 30@ er &e#r %re>er.

A Drre! A9#!n. '"e %r,9# ,g"! e rre!9& #9e ! !"e 9 J#!"%9 #9r#* w"" "#s een grwng #! # s!e#& 5@ r#!e %r e#es. !s EPS 1 = $10*  1 = $5* #n P 0 = $100. '"sB 10.0% .10 0 .05 0 100 5 g P DIV r 0 1

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E>en "ere* & s"9 e #re%9 n! ! 9n9& rIe! #s! grw!" n! !"e %!re. % 9 J#!"%9 "#9s #9* #n energ& rss 9 !rn ! n! # grw!" s!?.

. An nrre! A9#!n. H!s"! "#s rren! e#rnngs % $5.00 er s"#re. '"sB 5.0% .05 0 100 5 P EPS r 0 1

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'"s s ! 9w ! e re#9s!. '"e re#sn P 0 s s "g" re9#!>e ! e#rnngs s

n! !"#! r s 9w* ! r#!"er !"#! H!s"! s enwe w!" >#9#9e grw!" r!n!es. Sse P6 = $0B PVGO r EPS P 1 0

=

+

60 r 5 100

=

+

'"ere%re* r = 12.5@.

A Drre! A9#!n. n%r!n#!e9&* 9 J#!"%9 "#s rn ! % >#9#9e grw!" r!n!es. Sne P6 = 0B PVGO r EPS P 1 0

=

+

0 r 10 100

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+

'"ere%re* r = 10.0@. 24!

24! Compost cience Inc. /CI0 is in the bsiness of converting @oston's sewage sldge into fertili"er. 4he bsiness is not in itself very profitable. owever to indce CI to remain in bsiness the 2etropolitan 3istrict Commission /23C0 has agreed to pay whatever amont is necessary to yield CI a 1% boo! retrn on eMity. +t the end of the year CI is expected to pay a $) dividend. It has been reinvesting )% of earnings and growing at )% a year.

a. ppose CI contines on this growth trend. *hat is the expected longrn rate of retrn from prchasing the stoc! at $1& *hat part of the $1 price is attribtable to the present vale of growth opportnities&

plant will therefore be expanded gradally over five years. 4his means that CI will have to reinvest #% of its earnings for five years. tarting in year = however it will again be able to pay ot =% of earnings. *hat will be CI's stoc! price once this annoncement is made and its conseMences for CI are !nown&

Answer

a.

r = 3I1; P 0 9 g

r 6 $) ; $1 9 .) r 6 .# or #%

,-16 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.

3I1 will decrease to( .7× $=.=> 6 $1.::.

@y plowing bac! #% of earnings CI will grow by #% per year for five years before retrning to its longrn growth rate of )%. 4he dividend will be 7% of earnings for years 15 and =% of earnings in year = and beyond.

Bear 1 7 : ) 5 = ,-! $=.=> $>.7 $>.># $#.)1 $O.> $O.# 3I! 1.:: 1.)) 1.5= 1.=# 1.#1 5.## P 5 6 3I= ; /r < g) P 5 6 $5.## ; /.# < .)0 P 5 6 $1)=.O:

P  6 3I1 ; /1 9r 0 9 3I7 ; /1 9r 07 9 3I: ; /1 9r 0: 9 3I) ; /1 9r 0) 9 3I5 ; /1 9 r 05 _{9 P} 5; /1 9r)5 P  6 $1.:: ; 1.# 9 $1.)) ; 1.#7 9 $1.5= ; 1.#: 9 $1.=# ; 1.#) 9 $1.#1 ; 1.#59 $1)=.O: ; 1.#5 P  6 $1=.1> 25!

25! -ermian -artners /--0 prodces from aging oil fields in west 4exas. -rodction is 1.# million barrels per year in 71= bt prodction is declining at >% per year for the foreseeable ftre. Costs of prodction transportation and

administration add p to $75 per barrel. 4he average oil price was $=5 per barrel in 71=.

-- has > million shares otstanding. 4he cost of capital is O%. +ll of --'s net income is distribted as dividends. Dor simplicity assme that the company will stay in bsiness forever and that costs per barrel are constant at $75. +lso ignore taxes.

a. *hat is the ending 71= vale of one -- share& +ssme that oil prices are expected to fall to $= per barrel in 71> $55 per barrel in 71# and $5 per barrel in 71O. +fter 71O assme a longterm trend of oilprice_{increases at 5% per year.}

b. *hat is --'s ,-;- ratio and why is it not eMal to the O% cost of capital& Answer

#.Jrs!* ,!e !"e >ens* w"" eG#9 ne! n,e* %r 201 !"rg" 2020B

2

2001166 22001177 220011 220011"" 22002200

-rodction /million

barrels0 1.# 1.=>) 1.55=# 1.))># 1.:)=5

-rice of oil;barrel /$0 =5 = 55 5 57.5

Costs per barrel /$0 75 75 75 75 75

Aevene

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1))

 #5=751 >7:O71: >=OO15

,xpenses )5 )1#5 :#O75 :=1O==5 ::==7:)

Eet Income /6

3ividends0 >7 5#5O )=>)= :=1O==5 :>7#5>)

g e>ene 6 /19 sales price growth rate0 8 /1 9 prodction growth rate0 < 1

g e>ene6 /1 9 .50 8 1 9 /<.>0J < 1

g e>ene 6 <.7:5 or <7.:5%

g Ds!s 6 /19 costs growth rate0 8 /1 9 prodction growth rate0 < 1

g Ds!s6 /1 9 0 8 1 9 /<.>0J < 1

g Ds!s 6 <.> or <>%

-71O Aevenes 6 revene77 ; /r < g 0

-71O Aevenes 6 $>=OO15 ; .O < /<.7:50J

-71O Aevenes 6 $=77#7>)))

-71O Costs 6 costs77 ; /r  g)

-71O Costs6 $::==7:) ; .O < /<.>0J

-71O Costs6 $71:#O=7#

-71O6-71O revenes < -71O costs

-71O 6 $=77#7>))) < 71:#O=7#

-71O 6 $)17):>#1>

-71= 6 3I71> ; /1 9 r0 9 3I71# ; /1 9r 07 9 /3I71O 9 P 2010 ; /1 9r)3

-71=6 $5#5O ; 1.O 9 $)=>)= ; 1.O7 9 /$:=1O==5 9)17):>#1>0 ;

1.O:

-71= 6 $):O)O7O:

-rice per share71= 6 -71= ; nmber of shares

-rice per share71= 6 $):O)O7O: ; >

-rice per share71= 6 $=7.>#

b.

,-71= 6 net income71=; nmber of shares

,-71= 6 $>7 ; >

,-71= 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#rnngs #re e9nng.

27!

27! 2exican 2otorsG mar!et cap is 7 billion pesos. Eext year's free cash flow is #.5 billion pesos. ecrity analysts are forecasting that free cash flow will grow by >.5% per year for the next five years.

a. +ssme that the >.5% growth rate is expected to contine forever. *hat rate of retrn are investors expecting&

b. 2exican 2otors has generally earned abot 17% on boo! eMity /AF, 6 .

170 and paid ot 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 longrn ftre. *hat is the

implication for the growth rate of earnings and free cash flow& Dor the cost of eMity& hold yo revise yor answer to part /a0 of this Mestion& Answer

#. '"e ns!#n! grw!" %r,9# P= /(r K g) #n e se "ereB $200 = $8.5/(r-.075)

S9>ng %r r* r = 0.1175. '"#! s* n>es!rs ee! #n 11.75@ r#!e % re!rn.

. 6>en !"e Le#n L!rs s 9wng #? 50@ % e#rnngs #%!er e#rnng 12@ n eG!&* !"e %r, #n ee! ! grw #! #n #nn#9 r#!e % n9& @ (E  9w#? = 0.12  0.50 = 0.0). A9&ng !"e ns!#n! grw!" %r,9# #g#n #n s9>ng %r r we ge!B

$200 = $8.5/(r-.0)