Approaches to Valuation - Problem Set Solutions

7/23/2019 Approaches to Valuation - Problem Set Solutions

http://slidepdf.com/reader/full/approaches-to-valuation-problem-set-solutions 1/39

SOLUTIONS

APPROACHES TO VALUATION

Question 1

A. False. The reverse is generally true.

B. True. The value of an asset is an increasing function of its cash flows.

C. True. The value of an asset is an increasing function of its life.

D. False. Generally, the greater the uncertainty, the lower is the value of an asset.

E. False. The present value effect will translate the value of an asset from infinite tofinite terms.

Question 2

When euity is value!, the cash flows to euity investors are !iscounte! at their cost"the cost of euity# to arrive at a present value, which is the value of the euity sta$ein the %usiness.

When the firm is value!, the cash flows to all investors in the firm "inclu!ing euityinvestors, len!ers an! preferre! stoc$hol!ers# are !iscounte! at the weighte! averagecost of capital to arrive at a present value, which euals the value of the entire firm"generally much higher than the value of &ust the euity sta$e.#

The !istinction matters for two reasons'

"(# )ismatching cash flows an! !iscount rates can cause significant errors invaluation.

"*# +ot recogniing what the present value of the cash flows measures can also lea! tomisinterpretations. For instance, if the present value of cash flows to the firm istreate! as the value of euity, there is an o%vious pro%lem.

Question 3



A. - of CF to Euity / *012(.(* 3 *4*.012(.(*5* 3 *60.472(.(*57 3 *89.:(2(.(*5:3 "717.88379:4.01#2(.(*50 / ;7**:

B. - of CF to Firm / 7:12(.199: 3 7062(.199:5* 3 76:.802(.199:57 3797.092(.199:5: 3 ":(7.*634111#2(.199:50 / ;0(:9

Question 4

A. <t might %e !ifficult to estimate how much of the success of the private firm is !ueto the owner=s special s$ills an! contacts.

B. >ince the firm has no history of earnings an! cash flow growth an!, in fact, no potential for either in the near future, estimating near term cash flows may %eimpossi%le.

C. The firm=s current earnings an! cash flows may %e !epresse! !ue to the recession.?ther measures, such as !e%t@euity ratios an! return on assets may also %e affecte!.

D. >ince !iscounte! cash flow valuation reuires positive cash flows some time in thenear term, valuing trou%le! firms, which are li$ely to have negative cash flows in theforeseea%le future, is li$ely to %e !ifficult.

E. estructuring alters the asset an! lia%ility mi of the firm, ma$ing it !ifficult to usehistorical !ata on earnings growth an! cash flows on the firm.

F. nutilie! assets !o not pro!uce cash flows an! hence !o not show up in!iscounte! cash flow valuation, unless they are consi!ere! separately.

Question 5

+o. Any time a multiple is use!, there is implicit, in that multiple, assumptions a%outgrowth, ris$ an! payout. <n fact, any multiple can %e state! as an eplicit function ofthese varia%les.

Question 6

A. Average -2E atio / 7(.98

B. +o. Eliminate the outliers, %ecause they are li$ely to s$ew the average. Theaverage -2E ratio without GET an! ing Worl! is *0.(4.

C. ou are assuming that



"(# -aramount is similar to the average firm in the in!ustry in terms of growth an!ris$.

"*# The mar$er is valuing communications firms correctly, on average.

SOLUTIONS

ESTIMATION OF ISCOUNT RATES

Question 1

A. <t measures, on average, the premium earne! %y stoc$s over government securities.<t is use! as a measure of the epecte! ris$ premium in the future.

B. The geometric mean allows for compoun!ing, while the arithmetic mean !oes not.The compoun!ing effect, in con&unction with the varia%ility of returns, will lower thegeometric mean relative to the arithmetic mean.

C. The longer time perio! is most appropriate, %ecause it covers more of the possi%leoutcomes @ crashes, %ooms, %ull mar$ets, %ear mar$ets. <n contrast, a ten@year perio!can offer a slice of history that is not representative of all possi%le outcomes.

Question 2

ecent history is pro%a%ly not an appropriate %asis for estimating the premium, sincethis history can %e s$ewe! upwar! or !ownwar! %y a couple of goo! or %a! years.The premium shoul! %e %ase! on the fun!amentals !riving the )alaysian mar$et,relative to other emerging an! !evelope! mar$ets, an! estimate a premiumaccor!ingly. "se 6.0 to 8.0 as the premium over the long@term %on! rate.#

Question 3

CA-)' using T.Bill rate / 7.*0 3 (.(1 "8.:(# / (*.01

CA-)' using T.Bon! rate / 4.*0 3 (.(1 "0.01# / (*.71

The long@term %on! rate shoul! %e use! as the ris$@free rate, %ecause valuation is %ase! upon a long time horion.

8.:( is the arithmetic mean average premium earne! %y stoc$s over treasury %ills %etween (9*4 an! (991.



0.01 is the geometric mean average premium earne! %y stoc$s over treasury %on!s %etween (9*4 an! (991.

Question 4

An international portfolio manager woul! prefer a %eta estimate! relative to aninternational in!e. Daimler Ben returns woul! %e regresse! against returns on suchan in!e to estimate its %eta.

Question 5

A. Beta / (.41 (112011 3 *.11 (012011 3 (.*1 *012011 / (.0*

B. <f they pay the cash out as a !ivi!en!' Beta / (.41 (112701 3 (.*1 *012701 /(.7(

<f they $eep the cash in the firm' Beta / (.41(112011 3 1(012011 3 (.*1*012011 /1.9*

C. se *.11, the %eta for the software !ivision.

Question 6

A.

Beta D/E Unlevered

Beta

Weyerhauser (.(0 77.9( 1.90006818

Champion<nternational

(.(8 0:.(: 1.89146709

<ntenational -aper (.10 :0.01 1.8*:8*7*0

im%erly@Clar$ 1.9( ((.*9 1.80**46:(

The unlevere! %etas measure the %usiness an! operating leverage ris$ associate! witheach of these firms.

B. +ew %eta for im%erly Clar$ / 1.80 "( 3 "(@1.:# "1.71## / (.11

C. The average unlevere! %eta of these compara%le firms shoul! %e relevere! usingthe !e%t euity ratio of the initial pu%lic offering.

Average nlevere! Beta / 1.88

Beta of the <nitial -u%lic ?ffering / 1.88 "( 3 "(@1.:# "1.:1## / (.19



Question !

A. C-C shoul! have the highest %eta "%ecause of its high fie! costs# an! ellogg=sshoul! have the lowest %eta "%ecause of its low fie! costs#.

B. ?l! De%t2Euity atio / D2"D3E#2" ( @ D2"D3E## / 1.72 "(@1.7# / 1.:*84

nlevere! Beta "using D2E ratio of 71# / 1.882"( 3 "( @ 1.:# 1.:*84# / 1.61

+ew De%t2Euity atio / 1.60702"( @ 1.6070# / 7.14

+ew Hevere! Beta / 1.61 "( 3 "( @ 1.:# "7.14## / (.980

Question "

A.

Year Earnings _ Earnings Market Earnings Change

(988 ;(1.11 6.11

(989 ;(0.11 01.11 (1.11

(991 ;(8.11 *1.11 0.11

(99( ;(8.01 *.68 @(1.11

(99* ;(9.11 *.61 @8.11

(997 ;**.11 (0.69 4.11

Chg in Earnings / 1.(6(4 3 (.8*67 )ar$et Earnings Change

The accounting %eta is (.8*67.

B. The regression has only five o%servations, an! earnings figures can %e mislea!ing.

Question #

A. IC2-aramount Beta / (.10 401128011 3 (.61 *11128011 / (.*1

When leverage will not change after the acuisition, the euity %etas can %e weighte! %y euity mar$et values to get a approimate estimate of the %eta after the acuisition.

B. IC nlevere! Beta / (.612"( 3 "( @ 1.70#"(112*111## / (.40

-aramount nlevere! Beta / (.102"( 3 "( @ 1.70#"8(624011## / 1.96

IC2-aramount nlevere! Beta / (.40 *(112"*(11 3 67(6# 3 1.96 67(62"*(11 367(6# /(.(*



Jse values of the firm "!e%t 3 euity# as the weights for unlevere! %etasK

IC2-aramount Hevere! Beta / (.(* "(3 "( @ 1.70# "6:(62*111## / 7.8*

"+ew De%t / 8(6 3 (11 3 4011 / 6:(6L +ew Euity / *111#

C. iacom2-aramount Beta / (.10 40112(:111 3 (.(0 60112(:111 / (.(1

D. iacom nlevere! Beta / (.(02"( 3 "( @ 1.70#"*01126011## / 1.90

-aramount nlevere! Beta / (.102"( 3 "( @ 1.70#"8(624011## / 1.96

iacom2-aramount nlevere! Beta / 1.90 (11112"(1111 3 67(6# 3 1.96 67(62"(1111 3 67(6# / 1.908

se values of the firm "!e%t 3 euity# as the weights for unlevere! %etas.

iacom2-aramount Hevere! Beta / 1.908 "( 3 "( @ 1.70#"77(62(:111## / (.((

"+ew De%t / 8(6 3 *011 / 77(6#

Question 1$

A. <t measures the ris$less rate !uring the perio! of the analysis.

B. There were four common economic factors !riving stoc$ returns over theestimation perio!.

C. The factor coefficients measure the ris$ premium relative to each factor, an! the %etas measure sensitivity to the factor.

D. Epecte! eturn / 1.14* @ (.800 "@1.16# 3 (.::01 "1.1(# @ 1.(*: "1.1*# @ *.6::"1.1(# / 1.(6478 or (6.478

E. Epecte! eturn / 4.*0 3 (.10 0.01 / (*.1*0

The CA-) assumes that the mar$et factor captures all systematic ris$. The A-)allows for multiple sources of systematic ris$.

Question 11

A. >ee secon!@to@last column %elow.



B. >ee last column %elow.

Cost of Equity

Price DPS g Beta DDM CPM

)erc$ ;7*.11 ;(.14(0.11

(.(1(8.8(

(*.71

?g!en Co. ;*0.11 ;(.*0 :.11 (.71 9.*1 (7.:1

Mon!a"AD#

;*0.11 ;1.*6(1.11

1.60 ((.(9 (1.78

)icrosoft ;8:.11 ;1.11 +)F (.71 +)F (7.:1

C. se the CA-) estimate, %ecause

"(# the DD) cost of euity cannot %e calculate! for many firms, with no !ivi!en!san!2or no recor! of growth in the sameL an!

"*# the CA-) cost of euity has logical constraints. The DD) cost of euity !oesnot.

Question 12

A.

Market !alue

"eight s

Book !alue

"eights

De%t;*,111.11

m0.*: ;(9(8 *0.84

Euity ;74,(41.11m 9:.64 ;0011 6:.(:

B. Cost of Euity / 4.*0 3 (.(1 0.01 / (*.71

C. After@ta Cost of De%t / 4.:0 "( @ 1.70# / :.(9

D. Cost of Capital / (*.71 "74(41278(41# 3 :.(9 "*111278(41# / ((.86

Question 13

A. Cost of Euity / 4.*0 3 (.(1 0.01 / (*.71

B. After@ta Cost of De%t / 6.01 "( @ 1.:# / :.01

C. Cost of -referre! >toc$ / 7402:111 / 9.(*0



D. Cost of Capital / (*.71 "6(1 00#2J"6(1 00#3 40111 3 :111K 3 :.01 401112J"6(1 00# 3 40111 3 :111K 3 9.(*0 :1112J"6(1 00#3 40111 3 :111K /6.:9

SOLUTIONS

ESTIMATION OF CASH FLO%S

Question 1

C. <t is the cash that euity investors can ta$e out of the firm after financinginvestment nee!e! to sustain future growth.

Question 2

A. False. Capital epen!itures may %e greater than !epreciation.

B. False. The !ivi!en!s can ecee! the free cash flow to euity.

C. False. The FCFF is a pre@!e%t cash flow. <n the long term, it can %e eual to, %ut itcannot %e lower than the FCFE. <n any one year, however, the FCFE can ecee! theFCFF is there are su%stantial new !e%t issues.

D. False. The free cash flow to euity is after capital epen!itures.

Question 3

A. False. <t will result in too high a value.

B. True.

C. True.

D. False. There might %e loss of value !ue to loss of !epreciation ta %enefits.

E. False. The !iscount rate also goes up.

Question 4

A. FCFE in (99* / ;:(.(1 3 ;(*.01 @ ;(0 @ "(60 @ (81# / ;:7.41 million



FCFE in (997 / ;:8 3 ;(: @ ;(8 @ "*:1 @ (60# / @ ;*( million

B. Wor$ing Capital as -roportion of evenues' (99* / (6020:: / 7*.(6

Change in evenues in (997 / 4*1 @ 0:: / 64

FCFE in (997 / ;:8 3 ;(: @ ;(8 @ "(6020::# "4*1 @ 0::#

/ ;(9.00 million

Question 5

A. FCFE(99* / ;((6.9 3 ;067.0 @ ;811 @ ";9* @ ;7:.8# 3 "*111@(601#

/ ;8:.*1 million

FCFE(997 / ;(71 3 ;081 @ ;801 @ "@761 @ 9*# 3 "**11 @ *111#

/ ;0** million

B. FCFF(99* / ;((6.9 million 3 ;(61 "( @ "40*2661## 3 ;067.0 @ ;811 @ ";9* @ ;7:.8#

/ @ ;(79.60 million

"The ta rate is etraor!inarily high / 40*2661L the taa%le income is 661 million "9:1@ (61##

FCFF in (997 / ;(71 million 3 ;(6* "( @ "4612811## 3 ;081 @ ;801 @

"@761 @ 9*# / ;7:9.90 million

C. De%t atio / ;**11 million2";**11 million 3 66 ;*9# / :9.47

#$$% &ro'ection

+et <ncome / ;(76.81

@ "( @ 1.:947# "801 @ 081# (.14 / ;(::.(4

FCFE / @;4.74

D. "Also in millions#

+et <ncome / ;(76.81

@ "( @ 1.60# "801 @ 081# (.14 / ;6(.00

FCFE / ;44.*0



Question 6

#$$# #$$( #$$) #$$% #$$%

*no

de+t,

evenues ;8,:9: ;9,111 ;9,741 ;9,741@ ?perating Epenses ;4,:*: ;4,961 ;6,*:9 ;6,*:9

@ Depreciation ;86* ;841 ;89: ;89:

/ EB<T ;(,(98 ;(,(61 ;(,*(6 ;(,*(6

@ <nterest Epenses ;0(1 ;0(0 ;074 ;074

@ Taes ;74* ;:*1 ;:76 ;:76

/ +et <ncome ;7*4 ;*70 ;*:: ;*::

3 Depreciation ;86* ;841 ;89: ;89:

@ CapitalEpen!itures

;901 ;(,111 ;(,1:1 ;(,1:1

@ ∆Wor$ing Capital ";*70# ";0# ";1# ";1#

3 +et De%t <ssues ";701# ";:11# ;47 ;1

/FCFE ;(77 ";711# ;(4* ;98

3 <nterest Epenses"(@t#

;*:* ;(80 ;*1* ;*1*

@ +et De%t <ssues ";701# ";:11# ;47 ;1

/FCFF ;6*0 ;*80 ;71( ;711

Wor$ing Capital ;(91 ";:0# ";01# ";01# ";01#

Total De%t ;0,601 ;0,:11 ;0,111

De%t atio :7.8:

Ta ate 0*.4* 4:.(* 4:.(* 4:.(*

To get the new !e%t issues in (99:, ta$e :7.8: of the net capital epen!itures in that year "(1:1 @ 89:#

Question !

Year -C-E/shar

e

.erinal

!alue 0eal C-

( ;(.(* ;(.19

* ;(.*0 ;(.(8

7 ;(.:1 ;(.*9: ;(.06 ;(.:1

0 ;(.64 ;*7.7* ;*(.47

eal Cash Flow / +ominal Cash Flowt2"(.17#t



A. -resent alue / (.(*2(.(: 3 (.*02(.(:* 3 (.:12(.(:7 3 (.062(.(:: 3 "(.64 3*7.7*#2(.(:0 / ;(4.8:

B. eal Discount ate / (.(:2(.17 @ ( / (1.48

-resent alue /(.192(.(148 3 (.(82(.(148* 3 (.*92(.(1487 3 (.:12(.(148: 3"*(.47#2(.(1480 / ;(4.8:

"se real !iscount rates on real cash flows.#

Question "

A. Epecte! eturn / Epecte! Divi!en! iel! "( @ 1.74# 3 Epecte! -riceAppreciation "( @ 1.*0# / 1.1(8( 1.4: 3 1.(((9 1.60 / 9.00

B.

Before .a1es fter .a1es

Year E1&ected

DPS .erinal Price

E1&ected DPS

.erinal Price

( ;1.46 ;1.:7

* ;1.60 ;1.:8

7 ;1.8: ;1.0:

: ;1.9: ;1.41

0 ;(.14 ;4*.69 ;1.48 ;04.7:

Terminal price after taes / ;4*.69 @ "4*.69 @ 76.11# 1.*0 / ;04.7:.

C. -resent alue / ;1.:72(.1900 3 ;1.:82(.19005* 3 ;1.0:2(.190057 3;1.412(.19005: 3 ";1.48 3 ;04.7:#2(.190050 / ;76.64

D. -resent alue / ;1.462(.(7 3 ;1.602(.(75* 3 ;1.8:2(.(757 3 ;1.9:2(.(75:

3 ";(.14 3 ;4*.69#2(.(750 / ;74.99

Question #

A capital %u!geting pro&ect generally has a finite life. Conseuently it loses value over time. A stoc$ has an infinite life. <t generally increases in value over time, %oth as aconseuence of inflation an! real growth.

SOLUTIONS



ESTIMATION OF &RO%TH RATES

Question 1

Year EPS 2ro3th

rate(986 ;1.46

(988 ;1.66 (:.97

(989 ;1.91 (4.88

(991 ;(.(1 **.**

(99( ;(.7( (9.19

(99* ;(.0( (0.*6

A. Arithmetic Average/

(6.48

B. Geometric Average/

(6.40

C. The geometric average consi!ers the compoun!e! effects of growth. The arithmeticaverage !oes not.

Question 2

A. Hinear egression /E-> / 1.::(7 3 1.(6*"t#

Growth rate from this regressionmo!el euals

;1.(6* a year.

B. Hog@linear egression/

E-> / @1.08:( 31.(46: t

Growth rate from this regression mo!el euals (4.6: ayear.

C. Epecte! E-> net year using linear regression'

/ 1.::(7 3 1.(6* "6# / ;(.40

Epecte! E-> net year using log@linear regression'

/ Ep"@1.08:( 3 1.(46: "t## / ;(.81

Question 3



Year EPS Corrected g t

(986 6.*6 (

(988 6.9( 8.19 *

(989 @1.96 @((*.*4 7

(991 @*.4: (6*.(4 :

(99( 8.:* (7(.70 0

(99* @1.14 @(11.6( 4

(997 (1.60 (11.04 6

A. Geometric Average / "(1.6026.*6#"(24# @( / 4.6:

B. Arithmetic Average sing Correcte! Growth ates / 77.*1

C. Hinear egression / E-> / 7.8*6( 3 1.(789 "t#

Epecte! Growth ate / 1.(7892Average E-> / 7.(6

Question 4

A. etention atio / 4:

eturn on Euity / (4*020(6( / 7(.:

Epecte! Growth ate / 1.4: 7(.: / *1.(1

B. Growth ate in (997 / " ;0,(6( ".*0 @.7(:#2 ;(,4*0# 3 1.4: 1.*0 / @:.76

C. Growth ate After (997 / 1.4: 1.*0 / (4

Question 5

A. etention atio / ( @ ;4412;(181 / 1.7889

eturn on Assets / ";(181 3 ;001 "( @ 1.:##2";4111 3 ;4881# / (1.90

De%t2Euity atio / "488124111# / (.(:

Epecte! Growth ate' / 1.7889 "(1.90 3 (.(: "(1.90 @ "00124881# "( @ 1.:## /6.11

B. etention atio / 01

Total Assets / ;4111 3 ;4881 @ ;*011 / ;(1.781.

+ew eturn on Assets / "(1*1 3 001 "( @ 1.:##2(1781 / (7.1(



"The earnings %efore interest an! taes goes !own %y ;(11. The earnings after taeswill !rop %y ;41. +ote that interest epenses will %e lower after !e%t is pai! off, %utthe net income will go up %y an euivalent amount.#

+ew De%t Euity atio / ":78124111# / 1.67

+ew Epecte! Growth ate / 1.01 "(7.1( 3 1.67 "(7.1( @ 6"( @ 1.:### / 9.6*

"The growth rate net year will %e much higher as a result of the shift in the return oneuity, %ut the long term growth rate will now %e 9.6*#

C. Beta Before Change / (.(1

nlevere! Beta / (.(12"( 3 "48812"771 ;47## "( @ 1.:## / 1.9(68

"se mar$et value of euity for this calculation#

Beta After Change / 1.9(68 "( 3 ":7812"771 ;47## "( @ 1.:## / (.1:

Question 6

A. -re@<nterest, After@Ta -rofit )argin / EB<T "(@T#2>ales / (1 "( @ 1.74#2 41 /(1.46

Asset Turnover / >ales2Total Assets / 41271 / *

eturn ?n Assets / 1.(146 * / 1.*(7: 4r *(.7:

etention atio / 70

Epecte! Growth ate / 1.70 "1.*(7: 3 ( "1.*(7: @ 1.140 1.4:## / (7.:8

B. -re@<nterest, After@Ta -rofit )argin / 9.11

eturn on Assets / 1.19 * / (8

+ew Growth ate / 1.70 "1.(8 3 ( "1.(8 @ 1.140 1.4:##/ ((.(:

C. Brea$@Even Asset Turnover / 1.*(7:21.19 / *.76

Question !

A. Epecte! Growth ate / 1.97 "*0 3 1.(1 "*0 @ 8.01 "( @ 1.:## / *0.(1



B. The following woul! %e the epecte! changes '

"(# ?C will !ecline as the firm gets larger an! the marginal pro&ects are no longer aslucrative.

"*# Divi!en! payout ratio will increase.

"7# De%t2Euity ratio will increase as the firm gets larger an! safer.

":# The interest rate on !e%t will !ecline for the same reasons.

C. Epecte! Growth ate / 1.0 "1.(: 3 1.: "1.(: @ 1.16 "( @ 1.:## / 8.94

Question "

A. Weight analysts= forecasts the most, an! historical growth rates the least "or not atall#. <n estimating growth rates from fun!amentals, use pre!icte! values for thefun!amentals, rather than current values.

B. se growth rates from fun!amentals, an! reflect the epecte! changes from therestructuring in these fun!amentals.

C. Weight all three growth rates eually.

D. se fun!amentals on the remaining !ivisions to pre!ict growth.

SOLUTIONS

IVIEN ISCOUNT MOELS

Question 1

A. False. The !ivi!en! !iscount mo!el can still %e use! to value the !ivi!en!s that thecompany will pay after the high growth eases.

B. False. <t !epen!s upon the assumptions ma!e a%out epecte! future growth an!ris$.

C. False. This will %e true only if the stoc$ mar$et falls more than merite! %y changesin the fun!amentals "such as growth an! cash flows#.



D. True. -ortfolios of stoc$s that are un!ervalue! using the !ivi!en! !iscount mo!elseem to earn ecess returns over long time perio!s.

E. True. The mo!el is %iase! towar!s these stoc$s %ecause of its emphasis on!ivi!en!s.

Question 2

A. A stoc$ that pays no !ivi!en!s is not a sta%le stoc$. The Gor!on Growth mo!el isnot !esigne! to value such a stoc$. <f a company with sta%le growth insists on not

paying !ivi!en!s, %ut retains the FCFE, this FCFE can %e use! in the Gor!on Growthmo!el as the !ivi!en!.

B. A sta%le stoc$ cannot have a growth rate greater than the !iscount rate, %ecause nocompany can grow much faster than the economy in which it operates in the Gor!on

Growth )o!el. This upper limit on how high growth rates can go operates as aconstraint in the mo!el.

C. This shoul! not happen for a sta%le stoc$, for the same reasons state! a%ove.

D. <t is true that the mo!el smooths out growth rates in !ivi!en!s. <n present valueterms, though, this smoothing effect cannot have a large effect on the value estimateo%taine! from the mo!el.

E. The mo!el reuires that, in the long term, the growth rate for a firm is sta%le "close

to the growth rate in the economy#. Thus, cyclical firms, which maintain an averagegrowth rate close to a sta%le rate, cyclical ups an! !owns notwithstan!ing, can %evalue! using this mo!el.

Question 3

A. Cost of Euity / 4.*0 3 1.91 0.0 / ((.*1

alue -er >hare / ;7.04 (.1002".((*1 @ .100# / ;40.89

B. ;7.04 "( 3 g#2".((*1 @ g# / ;81

>olving for g,

g / "81 .((* @ 7.04#2"81 3 7.04# / 4.:4

Question 4



A. This shoul! increase %oth the cost of euity "%y raising interest rates# an! thenominal growth rate. Whether the increase will %e the same in %oth varia%les will!epen! in large part on whether an increase in inflation will a!versely impact realeconomic growth.

B. This shoul! affect the estimation of a sta%le growth rate. A much higher sta%legrowth rate can %e use! for firms in economies which are growing rapi!ly.

C. An analyst has very limite! flei%ility when it comes to using the Gor!on Growthmo!el in estimating growth. <f the growth potential of the in!ustry in which the firmoperates is very high, a growth rate slightly higher "( to *# than the growth rate inthe economy can %e use! as a sta%le growth rate. Alternatively, a two@stage or three@stage growth mo!el can %e use! to value the stoc$.

D. >ame as the answer to 7.

Question 5

A. Epecte! Earnings -er >hare in (999 / ;*.(1 (.(00 (.14 / ;:.:8

Epecte! Divi!en!s -er >hare in (999 / ;:.:8 1.40 / ;*.9(

Cost ?f Euity After (999 / 4.*0 3 (.( 0.0 / (*.71

Epecte! -rice at the En! of (998 / Epecte! D-> in (9992"$e, (999 @ g#

/ ;*.9(2".(*71 @ .14# / ;:4.(9

B.

Year EPS DPS

(99: ;*.:* ;1.69

(990 ;*.68 ;1.9(

(994 ;7.(9 ;(.10

(996 ;7.46 ;(.*(

(998 ;:.** ;(.79 ;:4.(9

Cost of Euity / 4.*0 3 (.:1 0.0 / (7.90

- of Divi!en!s an! Terminal -rice "N (7.90# / ;*6.09

Question 6

A. etention atio / ( @ -ayout atio / ( @ 1.:*2(.01 / 6*



eturn on Assets

/ "+et <ncome 3 <nt Ep "(@t##2"B of De%t 3 B of Euity#

/ "71 3 1.8 "( @ 1.780##2"6.4 3 (41# / (8.(9

De%t2Euity atio / 6.42(41 / .1:60

<nterest ate on De%t / 1.826.4 / (1.07

Epecte! Growth ate

/ 1.6* J.(8(9 3 .1:60 ".(8(9 @ .(107 "( @ 1.780##K / (7.0

lternatively5 and uch ore si&ly5

eturn on Euity / 712(41 / .(860

Epecte! Growth ate / 1.6* .(860 / (7.0

B. Epecte! payout ratio after (998'

/ ( @ g2J?C 3 D2E "?C @ i "(@t##K

/ ( @ .142".(*03.*0".(*0 @ .16"(@.780##

/ 1.0864

C. Beta in (997 / 1.80

nlevere! Beta / 1.802"( 3 "( @ 1.780# 1.10# / 1.8*:4

Beta After (998 / 1.8*:4 "( 3 "( @ 1.780# 1.*0# / 1.90

D. Cost of Euity in (999 / 6 3 1.90 0.0 / (*.*7

Epecte! Divi!en! in (999

/ " ;(.01 (.(700 (.14# 1.0864 / ;(.64

Epecte! -rice at En! of (998 / ;(.642".(**7 @ .14# / ;*8.*0

E.



Year EPS DPS

(99: ;(.61 ;1.:8

(990 ;(.97 ;1.0:

(994 ;*.(9 ;1.4(

(996 ;*.:9 ;1.61

(998 ;*.87 ;1.69 ;*8.*0

Cost of Euity / 6 3 1.80 0.0 / ((.48

- of Divi!en!s an! Terminal -rice "N ((.48# / ;(8.:6

F. Total alue per >hare / ;(8.:6

alue -er >hare sing Gor!on Growth )o!el

/ ;(.01 (.14 1.08642".(**7 @ .14# / ;(0.11

alue -er >hare With +o Growth / ;(.01 1.08642.(**7 / ;6.*(

alue of Etraor!inary Growth / ;(8.:6 @ ;(0.11 / ;7.:6

alue of >ta%le Growth / ;(0.11 @ ;6.*( / ;6.69

Question !

A. Cost of Euity / 4.*0 3 1.80 0.0 / (1.97

alue of >ta%le Growth / ;1.:8 (.162".(197 @ .16# / ;(7.16

B. alue of Etraor!inary Growth

/ ;1.:8 "42*# ".*0 @ .16#2".(197 @ .16# / ;4.41

C. The payout ratio is assume! to remain unchange! as the growth rate changes. The payout ratio in this case is assume! to remain at 41 "1.:821.81#.

Question "

A.

Period EPS DPS

( ;:.08 ;1.69

* ;0.7* ;1.9*

7 ;4.(6 ;(.16

: ;6.(0 ;(.*(

0 ;8.71 ;(.:7

4 ;9.:4 ;*.70



6 ;(1.09 ;7.04

8 ;((.40 ;:.9:

9 ;(*.08 ;4.::

(1 ;(7.7: ;8.11

B.Epecte! -rice at En! of *117

/ ";(7.7: (.14 1.41#2".((60 @ .14# / ;(:6.0:

"Cost of Euity / 4.*0 / 0.0 / ((.60#

C.

- of Divi!en!s @ Migh Growth / ;7.46

- of Divi!en!s @ Transition / ;9.(1

- of Terminal -rice / ;::.09

alue -er >hare / ;06.74

SOLUTIONS

FREE CASH FLO% TO EQUIT' ISCOUNT MOELS

Question 1

A. True. Divi!en!s are generally smoothe! out. Free cash flows to euity reflect the

varia%ility of the un!erlying earnings as well as the varia%ility in capital epen!itures.

B. False. Firms can have negative free cash flows to euity. Divi!en!s cannot %e lessthan ero.

C. False. Firms with high capital epen!itures, relative to !epreciation, may havelower FCFE than net income.

D. False. The free cash flow to euity can %e negative for companies, which eitherhave negative net income an!2or high capital epen!itures, relative to !epreciation.

This implies that new stoc$ has to %e issue!.

Question 2

A. alue -er >hare / ;(.61 (.162".(*17 @ .16# / ;74.*1

"Cost of Euity / 4.*0 3 (.10 0.01 / (*.17#



B.

Current Earnings per share / ;7.*1

@ "( @ Desire! De%t Fraction#

"Capital >pen!ing @ Depreciation# /87.4( ;(.11 / ;1.8:

@ "( @ Desire! De%t Fraction#

∆Wor$ing Capital/ 87.4(

;1.11 / ;1.11

Free Cash Flow to Euity / ;*.74

Cost of Euity / 4.*0 3 (.10 0.0 / (*.17

alue -er >hare / ;*.74 (.162".(*17 @ .16# / ;01.*1

This is %ase! upon the assumption that the current ratio of capital epen!itures to!epreciation is maintaine! in perpetuity.

C. The FCFE is greater than the !ivi!en!s pai!. The higher value from the mo!elreflects the a!!itional value from the cash accumulate! in the firm. The FCFE value ismore li$ely to reflect the true value.

Question 3

A.

Year EPS Ca& E1&

De&r ∆"C -C-E .er

Price

( ;*.6( ;*.41 ;(.71 ;1.10 ;(.4:

* ;7.(7 ;7.11 ;(.01 ;1.10 ;(.89

7 ;7.4* ;7.:6 ;(.67 ;1.10 ;*.(9

: ;:.(8 ;:.11 ;*.11 ;1.14 ;*.0:

0 ;:.87 ;:.4* ;*.7( ;1.14 ;*.97 ;8:.6:

4 ;0.(* ;:.91 ;:.91 ;1.1: ;0.18

The net capital epen!itures "Cap E @ Depreciation# an! wor$ing capital change isoffset partially %y !e%t "*1#. The %alance comes from euity. For instance, in year ('

FCFE / ;*.6( @ ";*.41 @ ;(.71# "( @ 1.*1# @ ;1.10 "( @ 1.*1# / ;(.4:#

Cost of Euity / 4.0 3 ( 0.0 / (*

Terminal alue -er >hare / ;0.182".(* @ .14# / ;8:.6:



-resent alue -er >hare / (.4:2(.(* 3 (.892(.(*5* 3 *.(92(.(*57 3 *.0:2(.(*5: 3"*.97 3 8:.6:#2(.(*50 / ;00.89

B.

Year EPS Ca& E1&

De&r ∆"C -C-E .er Price

( ;*.6( ;*.41 ;(.71 ;1.10 ;(.4:

* ;7.(7 ;7.11 ;(.01 ;1.10 ;(.89

7 ;7.4* ;7.:6 ;(.67 ;1.10 ;*.(9

: ;:.(8 ;:.11 ;*.11 ;1.14 ;*.0:

0 ;:.87 ;:.4* ;*.7( ;1.14 ;*.97 ;0*.19

4 ;0.(* ;:.91 ;*.:0 ;1.1: ;7.(7

Terminal alue -er >hare / ;7.(72".(* @ .14# / ;0*.19

-resent alue -er >hare / (.4:2(.(* 3 (.892(.(*5* 3 *.(92(.(*57 3 *.0:2(.(*5: 3"*.9730*.19#2(.(*50 / ;76.74

C.

Year EPS Ca&

E1& De&r ∆"C -C-E

.er

Price

( ;*.6( ;*.41 ;(.71 ;1.10 ;(.:7

* ;7.(7 ;7.11 ;(.01 ;1.10 ;(.44

7 ;7.4* ;7.:6 ;(.67 ;1.10 ;(.9*

: ;:.(8 ;:.11 ;*.11 ;1.14 ;*.*70 ;:.87 ;:.4* ;*.7( ;1.14 ;*.08 ;:0.80

4 ;0.(* ;:.91 ;*.:0 ;1.1: ;*.60

Terminal alue -er >hare / ;*.602".(* @ .14# / ;:0.80

-resent alue -er >hare / (.:72(.(* 3 (.442(.(*5* 3 (.9*2(.(*57 3 *.*72(.(*5: 3"*.08 3 :0.80#2(.(*50 / ;7*.86

The %eta will pro%a%ly %e lower %ecause of lower leverage.

Question 4

A.

Year EPS Ca& E1 De&rec ∆"C -C-E .er6

Price



( ;*.71 ;1.48 ;1.77 ;1.:0 ;(.06

* ;*.47 ;1.68 ;1.76 ;1.:8 ;(.8*

7 ;*.99 ;1.89 ;1.:* ;1.0( ;*.((

: ;7.:( ;(.1( ;1.:8 ;1.0: ;*.:00 ;7.89 ;(.(4 ;1.00 ;1.06 ;*.87 ;0*.49

4 ;:.(4 ;1.88 ;1.09 ;1.*1 ;7.6(

The net capital epen!itures "Cap E @ Depreciation# an! wor$ing capital change isoffset partially %y !e%t "(1#. The %alance comes from euity. For instance, in year (@

FCFE / ;*.71 @ ";1.48 @ ;1.77# "( @ 1.(1# @ ;1.:0 "( @ 1.(1# / ;(.06#

B. Terminal -rice / ;7.6(2 ".(710 @ .16# / ;0*.49

C. -resent alue -er >hare / (.062(.(74 3 (.8*2(.(745* 3 *.((2(.(7457 3*.:02(.(745: 3 "*.87 3 0*.49#2(.(7450 / ;70.10

Question 5

A.

Year # ( ) % 7

Earnings ;1.44 ;1.66 ;1.91 ;(.10 ;(.*7

"CapE@Deprec=n#

"(@O# ;1.10 ;1.14 ;1.16 ;1.18 ;1.(1

∆Wor$ing Capital

"(@O#;1.*6 ;1.7( ;1.76 ;1.:7 ;1.01

FCFE ;1.7: ;1.79 ;1.:4 ;1.0: ;1.47

-resent alue ;1.*9 ;1.71 ;1.71 ;1.7( ;1.7(

.ransition Period *u& to ten years,

Year 8 9 : $ #;

Growth ate (:.41 (*.*1 9.81 6.:1 0.11

Cumulate! Growth (:.41 *8.08 :(.(8 0(.47 09.*(

Earnings ;(.:( ;(.08 ;(.67 ;(.84 ;(.90

"CapE@Deprec=n# "(@O# ;1.(( ;1.(7 ;1.(: ;1.(0 ;1.(4

∆Wor$ing Capital "(@O# ;1.:0 ;1.79 ;1.71 ;1.** ;1.(7

FCFE ;1.8: ;(.16 ;(.*9 ;(.01 ;(.46

Beta (.78 (.7( (.*: (.(6 (.(1

Cost of Euity (:.09 (:.*( (7.8* (7.:: (7.10



-resent alue ;1.76 ;1.:( ;1.:7 ;1.:: ;1.:7

En!@of@Hife <n!e (

Sta+le 2ro3th Phase

Growth ate' >ta%le -hase / 0.11

FCFE in Terminal ear / ;(.9*

Cost of Euity in >ta%le -hase / (7.10

-rice at the En! of Growth -hase / ;*7.69

- of FCFE in Migh Growth -hase / ;(.0(

-resent alue of FCFE in Transition -hase / ;*.18

-resent alue of Terminal -rice / ;4.*1

alue of the >toc$ / ;9.69

B.

Year # ( ) % 7Earnings ;1.44 ;1.66 ;1.91 ;(.10 ;(.*7

"CapE@Deprec=n#"(@O#

;1.10 ;1.14 ;1.16 ;1.18 ;1.(1

∆Wor$ing Capital

"(@O#;1.*6 ;1.7( ;1.76 ;1.:7 ;1.01

FCFE ;1.7: ;1.79 ;1.:4 ;1.0: ;1.47

-resent alue ;1.*9 ;1.71 ;1.71 ;1.7( ;1.7(


Year 8 9 : $ #;Growth ate (:.41 (*.*1 9.81 6.:1 0.11

Cumulate! Growth (:.41*8.08 :(.(80(.47 09.*(

Earnings ;(.:( ;(.08 ;(.67 ;(.84 ;(.90

"CapE@Deprec=n#"(@ O#

;1.(( ;1.(7 ;1.(: ;1.(0 ;1.(4

∆Wor$ing Capital

"(@O#;1.01 ;1.:8 ;1.:7 ;1.74 ;1.*4

FCFE ;1.69 ;1.96 ;(.(4 ;(.70 ;(.0:

Beta (.78 (.7( (.*: (.(6 (.(1

Cost of Euity (:.09(:.*((7.8*(7.:: (7.10

-resent alue ;1.7: ;1.76 ;1.79 ;1.:1 ;1.:1

En!@of@Hife <n!e (

Sta+le 2ro3th Phase

Growth ate in >ta%le -hase / 0.11

FCFE in Terminal ear / ;(.68




-rice at the En! of Growth -hase / ;**.19

- of FCFE in Migh Growth -hase / ;(.0(

-resent alue of FCFE in Transition -hase / ;(.91

-resent alue of Terminal -rice / ;0.64

alue of the >toc$ / ;9.(6

C.

ear ( * 7 : 0

Earnings ;1.44 ;1.66 ;1.91 ;(.10 ;(.*7

"CapE@Deprec=n# "(@O#

;1.10 ;1.14 ;1.16 ;1.18 ;1.(1

∆Wor$ing Capital

"(@O#;1.*6 ;1.7( ;1.76 ;1.:7 ;1.01

FCFE ;1.7: ;1.79 ;1.:4 ;1.0: ;1.47

-resent alue ;1.*9 ;1.71 ;1.71 ;1.7( ;1.7(


ear 4 6 8 9 (1

Growth ate (:.41 (*.*1 9.81 6.:1 0.11

Cumulate! Growth (:.41*8.08 :(.(80(.47 09.*(

Earnings ;(.:( ;(.08 ;(.67 ;(.84 ;(.90

"CapE@Deprec=n# "(@O#

;1.(( ;1.(7 ;1.(: ;1.(0 ;1.(4

∆Wor$ing Capital

"(@O#

;1.:0 ;1.79 ;1.71 ;1.** ;1.(7

FCFE ;1.8: ;(.16 ;(.*9 ;(.01 ;(.46

Beta (.:0 (.:0 (.:0 (.:0 (.:0

Cost of Euity (:.98(:.98(:.98(:.98 (:.98

-resent alue ;1.74 ;1.:1 ;1.:* ;1.:7 ;1.:(

En!@of@Hife <n!e (

Sta+le 2ro3th Phase

Growth ate in >ta%le -hase / 0.11

FCFE in Terminal ear / ;(.9*

Cost ?f Euity in >ta%le -hase / (:.98-rice at En! of Growth -hase / ;(9.(9

- of FCFE <n Migh Growth -hase / ;(.0(

-resent alue of FCFE in Transition -hase / ;*.17

-resent alue of Terminal -rice / ;:.60

alue of the >toc$ / ;8.*9



Question 6

A.

Year # ( ) % 7

Earnings ;(.1* ;(.** ;(.:6 ;(.64 ;*.(*

"CapE@Deprec=n#"(@O#

;1.11 ;1.11 ;1.11 ;1.11 ;1.11

∆Wor$ing Capital

"(@O#;1.80 ;(.1* ;(.** ;(.:6 ;(.64

FCFE ;1.(6 ;1.*1 ;1.*: ;1.*9 ;1.70

-resent alue ;1.(0 ;1.(4 ;1.(6 ;1.(8 ;1.(9


Year 8 9 :

Growth ate (0.11 (1.11 0.11Cumulate! Growth (0.11 *4.01 7*.87

Earnings ;*.:7 ;*.48 ;*.8(

"CapE@Deprec=n#"(@O# ;1.11 ;1.11 ;1.11

∆€Wor$ing Capital "(@O# ;(.09 ;(.** ;1.46

FCFE ;1.80 ;(.:4 ;*.(:

Beta (.( (.( (.(

Cost of Euity (7.10 (7.10 (7.10

-resent alue ;1.:( ;1.4* ;1.81

En!@of@Hife <n!e (

Sta+le 2ro3th PhaseGrowth ate in >ta%le -hase / 0.11

FCFE in Terminal ear / ;*.*0


-rice at the En! of Growth -hase / ;*6.9*

- of FCFE in Migh Growth -hase / ;1.80

-resent alue of FCFE in Transition -hase / ;(.87

-resent alue of Terminal -rice / ;(1.:4

alue of the >toc$ / ;(7.(:

B. <t is impossi%le to say. Easier cre!it terms will increase wor$ing capital as a percentage of revenues, an! thus act as a !rain on cash flows. ?n the other han!, thehigher growth in revenues an! earnings will create a positive effect. The net effect can

%e either positive or negative.

C.



"orking Ca&ital as < of

0evenues!alue Per Share

41 ;8.4*

01 ;(1.88

:1 ;(7.(:

71 ;(0.:1

*1 ;(6.44

This assumes that there is no change in epecte! growth, as a conseuence.

Question !

A. Both mo!els shoul! have the same value, as long as a higher growth rate inearnings is use! in the !ivi!en! !iscount mo!el to reflect the growth create! %y theinterest earne!, an! a lower %eta to reflect the re!uction in ris$. The reality, however,is that most analysts will not ma$e this a!&ustment, an! the !ivi!en! !iscount mo!el

value will %e lower than the FCFE mo!el value.

B. The !ivi!en! !iscount mo!el will overstate the true value, %ecause it will notreflect the !ilution that is inherent in the issue of new stoc$.

C. Both mo!els shoul! provi!e the same value.

D. >ince acuisition, with the intent of !iversifying, implies that the firm is paying toomuch "i.e., negative net present value#, the !ivi!en! !iscount mo!el will provi!e alower value than the FCFE mo!el.

E. <f the firm is over@levere! to %egin with, an! %orrows more money, there will %e aloss of value from the over@leverage. The FCFE mo!el will reflect this lost value, an!will thus provi!e a lower estimate of value than the !ivi!en! !iscount mo!el.

SOLUTIONS

VALUIN& A FIRM ( THE FCFF APPROACH

Question 1

A. False. <t can %e eual to the FCFE if the firm has no !e%t.

B. True.

C. False. <t is pre@!e%t, %ut after@ta.



D. False. <t is after@ta, %ut pre@!e%t.

E. False. The free cash flow to firm can %e estimate! !irectly from the earnings %eforeinterest an! taes.

Question 2

A. FCFF / Net In)o*e 3 <nterest "(@t# 3 Depreciation @ Capital >pen!ing @ ∆Wor$ing

Capital

B. FCFF / "E+,nin-s .e/o,e t+0es 3 <nterest Epenses# "( @ ta rate# 3 Depreciation @

Capital >pen!ing @ ∆Wor$ing Capital

C. FCFF / EIT "(@ ta rate# 3 Depreciation @ Capital >pen!ing @ ∆Wor$ing Capital

D. FCFF / "EITA @ Depreciation# "(@ ta rate# 3 Depreciation @ Capital >pen!ing@ ∆Wor$ing Capital

E. FCFF / "NOI @ +on@operating Epenses# "(@ ta rate# 3 Depreciation @ Capital

>pen!ing @ ∆Wor$ing Capital

F. FCFF / FCFE 3 <nterest Epenses "( @ ta rate# @ +ew De%t <ssues 3 -rincipalepayments

Assume! no preferre! stoc$ is outstan!ing.

Question 3

A. FCFF in (997 / +et <ncome 3 Depreciation @ Capital Epen!itures @ ∆Wor$ing

Capital 3 <nterest Epenses "( @ ta rate#

/ ;661 3 ;941 @ ;(*11 @ 1 3 ;7*1 "( @ 1.74# / ;67:.81 million

B. EB<T / +et <ncome2"( @ ta rate# 3 <nterest Epenses / 66121.4: 3 7*1 /;(0*7.(*0 million

eturn on Assets / EB<T "(@t#2 "B of De%t 3 B of Euity# / 96:.8129111 / (1.87

Epecte! Growth ate in FCFF / etention atio ?C / 1.4 (1.87 / 4.01

Cost of Euity / 6 3 (.10 0.0 / (*.660



Cost of Capital / 8 "( @ 1.74# ":1112":111 3 (*111## 3 (*.660 / "(*1112":111 3(*111## / (1.84

alue of the Firm / 67:.812".(184 @ .140# / ;(4,807 millions

C. alue of Euity / alue of Firm @ )ar$et alue of De%t

/ ;(4,807 @ ;:,111 / ;(*,807 millions

alue -er >hare / ;(*,8072*11 / ;4:.*6

Question 4

A.

Yr EB=.D De&rec>n EB=. EB=. Ca& _ "C -C-- .er

*#?t, E1&6 !alue

1 ;(,*91 ;:11 ;891 ;07: ;:01 ;8* ;:1*

( ;(,:(7 ;:78 ;960 ;080 ;:97 ;91 ;::1

* ;(,0:6 ;:81 ;(,146 ;4:1 ;0:1 ;98 ;:8*

7 ;(,49: ;0*0 ;(,(49 ;61( ;09( ;(18 ;0*8

: ;(,800 ;060 ;(,*81 ;648 ;4:6 ;((8 ;068

0 ;*,17( ;471 ;(,:1( ;8:( ;618 ;(*9 ;477 ;(:,7*4

>$)?$9 fter #$$:

Cost of Euity / (7.10 (*.71

AT Cost of De%t / :.81 :.01

Cost of Capital / 9.76 9.49

Terminal alue

/ PEB<T "(@t#"(3g# @ "ev(998 @ ev(996# WC as of evQ2"WACC@g#

/ "8:( (.1:# @ "(7011 (.1900 (.1: @ (7011 (.1900#

1.16 2"[email protected]:# / ;(:,7*4

alue of the Firm

/ ::12(.1976 3 :8*2(.1976* 3 0*82(.19767 3 0682(.1976: 3 "477 3 (:9:(#2(.19760 /;((,(6*



B. alue of Euity in the Firm / ";((044 @ )ar$et alue of De%t# / (((6* @ 7*11 /;6,96*

alue -er >hare / ;6,96*24* / ;(*8.06

Question 5

A. Beta for the Mealth Division / (.(0

Cost of Euity / 6 3 (.(0 0.0 / (7.77

Cost of Capital / (7.77 1.81 3 "6.0 1.4# 1.* / ((.04

B.

Year De&rec>n EB=. EB=.*#?t, Ca& E1 -C-- .er !al

1 ;701 ;041 ;774 ;:*1 ;*44

( ;74: ;09: ;704 ;:76 ;*87

* ;769 ;4*9 ;768 ;:0: ;71*

7 ;79: ;446 ;:11 ;:6* ;7*(

: ;:19 ;616 ;:*: ;:9( ;7:*

0 ;:*4 ;6:9 ;:01 ;0(( ;74: ;0,1(:

+ow After 0 years

Cost of Euity / (7.77 (7.77

Cost of De%t / :.01 :.01

Cost of Capital / ((.04 ((.04

alue of the Division / *872(.((04 3 71*2(.((04* 3 7*(2(.((047 3 7:*2(.((04: 3"74: 3 01(:#2(.((040 / ;:,14* millions

C. There might %e potential for synergy, with an acuirer with relate! %usinesses. Thehealth !ivision at o!a$ might also %e mismanage!, creating the potential fora!!itional value from %etter management.

Question 6

A. Cost of Euity / 6 3 (.*0 0.0 / (7.88

Current De%t atio / (7:12"(7:1 3 (8.*0 (87.(# / *8.47

After@ta Cost of De%t / 6.:7 "( @ 1.:# / :.:4

Cost of Capital / (7.88 "1.6(76# 3 :.:4 "1.*847# / ((.(8



B. R C. >ee ta%le %elow.

D/ *D@E,

Cost of Beta Cost of . Cost

of Cost of -ir

De+t Equity De+t Ca&ita

l !alue

1 4.*7 (.1((*.0:

7.6:

(*.0:

;*,41:

(1 4.*7 (.16(*.9(

7.6:

((.99

;*,647

*1 4.97 (.(4(7.76

:.(4

((.07

;*,9(*

71 6.:7 (.*6(7.96

:.:4 ((.(( ;7,147

:1 8.:7 (.:((:.64

0.14

(1.88

;7,(07

01 8.97 (.4((0.86

0.74

(1.4(

;7,*40

41 (1.97

(.9( (6.07

4.04 (1.90

;7,(*0

61((.97

*.:*

*1.71

6.(4((.(1

;7,146

81((.97

7.:7

*0.8:

6.(4(1.89

;7,(:9

91(7.:7

4.:0

:*.:6

8.14((.01

;*,9*7

nlevere! Beta / (.*02"( 3 1.4 "(7:12"(87.( (8.*0## / (.1(

Hevere! Beta at (1 D2"D3E# / (.1( "( 3 1.4 "(1291## / (.16

FCFF to Firm +et ear / "476 @ *70# "( @ 1.:# (.17 / ;*:8.:7 million

alue of the Firm / *00.46 (.172"[email protected]#

Question !

A. Cost of Euity / 6 3 *.* 0.0 / (9.(1

After@ta Cost of De%t / (1.7("( @ 1.:# / 4.(9

)ar$et alue of Euity / :0.99 9 / ;:(7.9( million

Cost of Capital / (9.(1 ":(7.9(2":(7.9( 3 ((81## 3 4.(9 "((812":(7.9( 3 ((81## /9.0:

B. nlevere! Beta / *.*2"( 3 1.4 "((812:(7.9(## / 1.8(



+ew Beta / 1.8( "( 3 1.4 (# / (.71

+ew Cost of Euity / (:.(:

After@ta Cost of De%t / 6.0("( @ 1.4# / :.0(

Cost of Capital / (:.(: "1.0# 3 :.0( "1.0# / 9.7*

C.

2ro3th 0ate4ld

!alue

Ae3

!alueChange

7 ;(,968 ;*,1:4 ;46

: ;*,708 ;*,:07 ;90

0 ;*,910 ;7,101 ;(:0

The value of the firm is calculate! as follows'

FCFF in Current ear / *74 "( @ 1.:# 3 (19 @ (*0 / ;(*0.4 million

alue of the Firm Before the Change / (*0.4 "(3g#2".190:@g#

alue of the Firm After the Change / (*0.4 "(3g#2".197*@g#

SOLUTIONS

SPECIAL CASES IN VALUATION

Question 1

A.

Year EPS

(98: ;1.49

(980 ;1.6(

(984 ;1.91

(986 ;(.11

(988 ;1.64

(989 ;1.48

(991 ;1.19

(99( ;1.(4

(99* ";1.16#



(997 ";1.(0#

Average Earnings -er >hare / ;1.:8

+ormalie! Earnings -er >hare in (99: / ;1.:8 (.14 / ;1.0(

B.

+ormalie! Earnings -er >hare / ;1.0(

@ "Cap E @ Deprec=n# "( @ De%tratio# /

;1.*0

@ ∆€Wor$ing Capital "(@ De%t ratio#

/;1.14

+ormalie! FCFE +et ear / ;1.(9

"Assume that capital epen!itures an! !epreciation will grow 4

in (99:.#

Question 2

A.

Total Assets in (997 / ;*0,111 "in millions#

+ormalie! eturn on Assets / (*

+ormalie! eturn on Assets "pre@ta# / *1

Aoralied =ncoe stateent *+ased u&on #(< 04C,

Earnings Before <nterest an! Taes / 0111

<nterest Epenses / (:11

Earnings Before Taes / 7411

Taes "at :1# / (::1

+et <ncome / *(41

@ "Cap E @ Deprec=n# "(@De%t ratio# / 011

FCFE / (441

Cost of Euity / 6 3 (.( 0.0 / (7.10

Epecte! Growth ate / 0

Earnings %efore interest an! taes is calculate! using the ?C'

?C / EB<T "(@ ta rate# 2 Total Assets / (* "given in the pro%lem#

alue of Euity / "(441 (.10#2".(710 @ .10# / ;*(,40*

B. alue of Euity / ;*(,40*2(.(7105* / ;(4,9:*



Question 3

A.

Earnings -er >hare +et ear / ;0.0*

@ "Cap E @ Deprec=n# "(@ De%t ratio# / ;1.47@ " O Wor$ing Capital# "( @ De%t ratio# / ;1.1:0

FCFE +et ear / ;:.8:0

Cost of Euity / 6 3 (.( 0.0 / (7.10

Epecte! Growth ate / 0.11

Capital Epen!itures @ Depreciation / ";0.01 (.10 @ ;:.01 (.10#

De%t atio / :1

alue -er >hare / ;:.802".(710 @ .10# / ;41.(9

B. The value is very sensitive to assumptions a%out growth in (997. <f the earnings !onot ua!ruple in (997, the free cash flow to euity will %e significantly %elow ;:.80,an! the value lower than ;41.(9.

Question 4

A.

Earnings Before <nterest an! Taes / ;0*.61

@ <nterest Epense / ;(6.11

Earnings Before Taes / ;70.61

@ Taes ":1# / ;(:.*8

Earnings After Taes / ;*(.:*

@ "Cap E @ Deprec=n# "(@De%t atio# / ;7.60

@ ∆Wor$ing Capital "(@ De%t atio# / ;:.64

FCFE / ;(*.9(

EB<T / <nterest Epense <nterest Coverage ate / ;(6 7.(1 / ; 0*.61

The change in wor$ing capital is %ase! upon revenues growing at :.

B. Cost of Euity / 6 3 (.( 0.0 / (7.10

Epecte! Growth ate / :

alue of Euity / (*.9( (.1:2".(710 @ .1:# / ;(:8.74 million



Question 5

A.

Year Aet =ncoe *in illions,

(986 ;1.71

(988 ;((.01

(989 ";*.:1#

(991 ;6.*1

(99( ";:.41#

(99* ";(.91#

Average / ;(.48

+et <ncome / ;(.48

@ "Cap E @ Deprec=n# "( @ De%t ratio# / (.71

/ FCFE / ;1.78

B. Cost of Euity "until (994# / 6 3(.* 0.0 / (7.4

Cost of Euity "after (994# / 6 3 0.0 / (*.0

Year Aet

=ncoe

*Ca&6 E1 ?

De&rec>n, -C-E

.erinal

!alue

*# ? De+t 0atio,

(997 ;(.68 ;(.76 ;1.:*

(99: ;(.89 ;(.:7 ;1.:0

(990 ;*.11 ;(.01 ;1.01

(994 ;*.(* ;(.08 ;1.0: ;*9.67

Term ear ;*.*7 ;1.11 ;*.*7

Capital epen!itures are offset %y !epreciation in the terminal year.

Terminal alue / ;*.*72".(*0 @ .10# / ;*9.67

alue of Euity

/ 1.:*2(.(74 3 1.:02(.(745* 3 1.012(.(7457 3 "1.0: 3 *9.67#2(.(745:

/ ;(9.*: million

Question 6

A.

EB<T "%ase! upon operating margin of(*# /

;(,::1

<nterest Epenses / ;7:1



Earnings Before Taes / ;(,(11

Taes "at :1# / ;::1

+et <ncome "also FCFE#/ ;441

Cost of Euity / 6 3 (.(0 0.0 / (7.77

Epecte! Growth ate in FCFE / 4.11

alue of Euity/ "441 (.14#2 ".(777 @ .14#/

;9,1(1

B. alue of Euity "assuming two year !elay in return to profita%ility#

/ 91(12(.(77*0* / ;6,1(4 million

Question !

A.

Equity De+t )ar$et alue Weight 4(.4( 78.79

Cost of Component (7.77 0.(1

Cost of Capital / (7.77 "1.4(4(# 3 0.( "1.7879# / (1.(6

B.

Year #$$) #$$% #$$7 #$$8 .erinal

Year

EB<T "(@t# ;8.*0 ;9.18 ;9.98 ;(1.98 ;((.:*

@ "Cap E @Deprec=n# ;1.11 ;1.11 ;1.11 ;1.11 ;1.11

@ ∆Wor$ing Capital ;1.11 ;1.11 ;1.11 ;1.11 ;1.11

/ FCFF ;8.*0 ;9.18 ;9.98 ;(1.98 ;((.:*

Terminal alue ;(80.(8

Terminal alue / ;((.:*2".(1(6 @ .1:# / ;(80.(8

-resent alue / ;8.*02(.(1(6 3 ;9.182(.(1(65* 3 ;9.982(.(1(657 3 ";(1.98 3;(80.(8#2(.(1(65: / ;(00.41 million

C. alue of Euity / alue of Firm @ )ar$et alue of De%t / ;(00.41 @ ;(19 / ;:4.41million

alue of Euity -er >hare / ;:4.412(0.9 / ;*.97

Question "



A. nlevere! Beta for -u%licly Tra!e! Firms in >ame Business

/ (.712"( 3 1.4 1.*# / (.(4

De%t2Euity atio for -rivate Firm

/ De%t2Estimate! )ar$et alue of Euity / (1271 / 77.77

+ew Hevere! Beta For -rivate Firm / (.(4 "( 3 1.4 .7777# / (.79

+ew Cost ?f Euity / 6 3 (.79 0.0 / (:.44

B. -re@Ta Cost of De%t / ;(2;(1 / (1

After@Ta Cost of De%t / (1 "( @ 1.:# / 4

Cost of Capital / 4 "1.*0# 3 (:.44 "1.60# / (*.:9

C. Using the -ir &&roach

# ( ) % 7 .erinal

year

EB<T ;*.:1 ;*.88 ;7.:4 ;:.(0 ;:.98 ;0.*7

EB<T "( @ ta rate# ;(.:: ;(.67 ;*.16 ;*.:9 ;*.99 ;7.(:

@ "Cap E @Deprec=n#

;1.41 ;1.6* ;1.84 ;(.1: ;(.*: ;1.11

/ FCFF ;1.8: ;(.1( ;(.*( ;(.:0 ;(.6: ;7.(:Terminal alue ;:(.80

Terminal alue / ;7.(:2".(*:9 @ .10# / ;:(.80

-resent alue "alue of Firm# "N (*.:9# / ;1.8:2(.(*:9 3 ;(.1(2(.(*:9* 3;(.*(2(.(*:97 3 ;(.:02(.(*:9: 3 ";(.6: 3 ;:(.80#2(.(*:90 / ;*6.01 million

alue of Euity / ;*6.01 million @ ;(1 million / ;(6.01 million

Using the Equity a&&roach

# ( ) % 7 .erinal

year

+et <ncome ;1.60 ;1.9: ;(.(6 ;(.:4 ;(.87 ;(.98

@ "Cap E @ Deprec=n# "(@ De%tratio# / ;1.:0 ;1.0: ;1.40 ;1.68 ;1.97 ;1.11

/ FCFE ;1.71 ;1.:1 ;1.0* ;1.49 ;1.91 ;(.98

Terminal alue of Euity ;*9.6(



Terminal alue of Euity / ;(.982".(:44 @ .10# / ;*9.6(

-resent alue "using Cost of Euity of (:.44# / ;1.712(.(:44 3 ;1.:12(.(:44* 3;1.0*2(.(:447 3 ;1.492(.(:44: 3 ";1.91 3 ;*9.6(#2(.(:440 / ;(4.64 million

Question #

A. nlevere! Beta for Compara%le Firms / (.(02"( 3 1.4 .*0# / (.11

Cost of Euity "until (996# / 6 3 0.0 / (*.01

Cost of Capital "until (996# / (*.01

Beta after (996 for Boston Chic$en / (.(0

Cost of Euity "after (996# / 6 3 (.(0 0.0 / (7.7*0

Cost of Capital "after (996#

/ (7.7*0 "1.8# 3 8 "( @ 1.:# "1.*# / ((.4*

B.

(997 (99: (990 (994 (996

EB<T "(@t# ;9.6* ;(7.(* ;(6.6( ;*7.9( ;7*.*9

Cap E @

Deprec=n

;4.11 ;6.*1 ;8.4: ;(1.76 ;(*.::

FCFF ;7.6* ;0.9* ;9.16 ;(7.00 ;(9.8:

#$$: #$$$ (;;;.erinal

year

EB<T "(@t# ;76.(7 ;:*.61 ;:9.(1 ;0(.04

Cap E @Deprec=n

;1.11 ;1.11 ;1.11 ;1.11

FCFF ;76.(7 ;:*.61 ;:9.(1 ;0(.04

Terminal alue ;668.81

Terminal alue / ;0(.04 2".((4* @ .10# / ;668.81 million

-resent alue "using (*.01 for the first five years, an! ((.4* after that#/;7.6*2(.(*0 3 ;0.9*2(.(*0* 3 ;9.162(.(*07 3 ;(7.002(.(*0: 3 ;(9.8:2(.(*00 3;76.(72"(.(*00 (.((4*# 3 ;:*.612"(.(*00 (.((4**# 3 ";:9.(1 3 668.81#2"(.(*00 (.((4*7# / ;:1(.46 million

This is %oth the value of the firm an! the value of euity.



Documents

Approaches to Valuation - Problem Set Solutions