FINC2011 Tutorial 5

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 crrent stoc! price&

Answer P0 = 10/(.08 - .05) = $333.33.

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 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 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. 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 = $15.0

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en #! $10/s"#re #n ne! &e#res!r s"9 ee! ! e#rn 8@.

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! 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 < 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@ #!#9C#!n r#!e* S!? D "#s !"e 9#rges! resen! >#9e. sng !"e s#,e %r,9#s #s #>e w!" # 7@ #!#9C#!n r#!e* !"e >#9es #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@ #!#9C#!n r#!e* S!? F "#s !"e 9#rges! resen! >#9e.

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 EPS0 #s %99wsB 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 >ens %r sseGen! &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 >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

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 #99#!n s eenen! n !"e #&! r#! #n !"e grw!" r#!e #%!er &e#r 4. 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ens "#>e grwn & 30@ er &e#r sne !"e %r,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 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! ! 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 r

=

EPS1 P0

=

5 100

= 0 .05 = 5.0%

'"s s ! 9w ! e re#9s!. '"e re#sn P0 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 P0 =

EPS1

100 =

r

+ PVGO

5 + 60 r

'"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 P0 = EPS1 + PVGO r

100 =

10 +0 r

'"ere%re* r = 10.0@.

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&

b. Eow the 23C annonces a plan for CI to treat Cambridge sewage. CI's

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 ; 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. 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.##

P5 6 3I= ; /r < g) P5 6 $5.## ; /.# < .)0 P5 6 $1)=.O:

P 6 3I1 ; /1 9 r0 9 3I7 ; /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 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 at in5% 71O. increases per+fter year.71O assme a longterm trend of oilprice

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

-rodction /million barrels0 -rice of oil;barrel /$0 Costs per barrel /$0

Aevene ,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=751 :#O75

>7:O71: :=1O==5

>=OO15 ::==7:)

>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e 6 /1 9 .50 8 1 9 /0J < 1 ge>ene 6 ))) < 71:#O=7# -71O 6 $)17):>#1> -71= 6 3I71> ; /1 9 r0 9 3I71# ; /1 9 r07 9 /3I71O 9 P2010 ; /1 9 r)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! 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) r = 0.1025. '"#! s* n>es!rs s"9 ee! n9& # 10.25@ r#!e % re!rn.