Principles of Corporate Finance Questions and Answers In this document you will find some sample questions about the topics included in the final exam. Answers are provided. The questions are usually in order of topic but not necessarily in order of difficulty. difficulty. Ch 5: Techniques Techniques of project valuation: !"# I$$# etc Ch 5 8. Payback Cons i dert hef ol l owi ngpr oj ec t s :
a. I ft heoppor t uni t ycos tofc api t al i s10%,whi c hpr oj ec t sha v eapos i t i v eNPV? b . Cal c ul a t et hepa y ba ckpe r i o df o re a chp r oj e ct . c . Whi c hpr oj ec t ( s )woul dafi r m us i ngt hepa ybac kr ul eac c epti ft hecut offper i od wer et hr e ey e ar s ? d . Cal c ul a t et hedi s c ou nt e dp ay bac kp er i o df o re ac hp r oj e c t . e . Wh i c hp r o j e ct ( s )wo ul dafi r mu si n gt h ed i s c oun t e dp ay ba ckr u l ea cc ep ti ft h ec ut o ff per i odwer et hr eey ear s ?
!" A
= − $)((( +
&)((( +).)(*
= −&'(.')
A8)%. a.
!"0 = − $/((( +
&)((( &)((( + +).)(* +).)(* /
+
&,((( +).)(*
+
!"C = − $((( +
&)((( &)((( + +).)(* +).)(* /
+
&)((( +).)(* ,
+
!rojects 0 and C have positive !"s. b.
!aybac1 A 2 one year !aybac1 B 2 two years !aybac1 C 2 four years
c.
A and 0
) a.odabasi 3 4As 6/
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&)((( +).)(* , &)((( +).)(* 5
+
&)((( +).)(*5
= +&,#(
= +&'.,-
!" A
&)((( +).)(*)
=
= &'('.('
d. The present value of the cash inflows for f or !roject A never recovers the initial outlay for the project# which is always the case for a ne9ative !" project. The present values of the cash inflows for !roject 0 are shown in the third row of the table below# and the cumulative net present values are shown in the fourth row: C (
7/#(((.(( 7/#(((.((
C )
C /
)#(((.(( '('.(' 7)#('(.')
)#(((.(( %/8.,5 7/8,.,8
C
,#(((.(( #((5./8 /#-,(.%(
C ,
)#(((.(( 8%.() #,/.%)
) ,
;ince the cumulative !" turns positive between year / and year # the discounted paybac1 period is:
/+
/8,.,8 #((5./8
= /.(' years
The present values of the cash inflows for !roject C are shown in the third row of the table below# and the cumulative net present values are shown in the fourth row: C (
C )
C /
C
7#(((.(( 7#(((.((
)#(((.(( '('.(' 7/#('(.')
)#(((.(( %/8.,5 7)#/8,.,8
(.(( (.(( 7)#/8,.,8
C ,
)#(((.(( 8%.() 75%).,5
;ince the cumulative !" turns positive between year , and year 5# the discounted paybac1 period is:
,+
5%).,5 8/(.'/ e.
= ,.', years
Q12I RRr ul e Mr Mr .Cy r usCl ops ,t hepr es i dentofGi antEnt er pr i s es ,hast omak eac hoi c e b et wee nt wop os s i bl ei n v es t me nt s :
/ a.odabasi 3 4As 6/
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Theoppor t uni t yc os tofc api t al i s9%.Mr .Cl opsi st empt edt ot ak eB,whi c hhast hehi gher I RR. a.Ex pl ai nt oMr .Cl opswh yt hi si sno tt hec or r ec tpr oc edur e. b . Sh owh i mh owt oad ap tt h eI RRr u l et oc ho os et h eb es tp r o j e c t . c . Sh owh i mt h att h i spr o j e c ta l s oh ast h eh i g he rNPV .
)/. a. 0ecause !roject A requires a lar9er capital outlay# it is possible that !roject A has both a lower I$$ and a hi9her !" than !roject 0. +In fact# !" A is 9reater than !"B for all discount rates less than )(=.* 0ecause the 9oal is to maximi>e shareholder wealth# !" is the correct criterion. d.
To use the I$$ criterion for mutually exclusive projects# calculate the I$$ for the incremental cash flows: A 7 B
C(
C)
C/
I$$
?/((
))(
)/)
)(=
0ecause the I$$ for the incremental cash flows exceeds the cost of capital# the additional investment in A is worthwhile.
!" A
= − ,(( +
/5( (( + ).(' +).('* /
!"0
= − /(( +
),( ).('
= & %).%8
c.
+
)-' +).('* /
= &-'.)(
NPV/ I RR. 16. Co ns i d erp r o j e c t sAa ndB: Cash Flows (dollars) Project
C 0
C 1
C 2
NPV at 10%
A
!30,000
1,000
1,000
"$#,#
%
!&0,000
33,000
33,000
" ','3
Cal c ul a t eI RRsf o rAa ndB.Wh i c hp r oj ec td oe st h eI RRr u l es ug ge s ti sbe s t ?Wh i c h L O8 3 pr oj ec ti sr eal l ybes t ?( )
1.
Answer: IRRA = discount rate (r ), which is the solution to the following equation: 1 1 = $30,000 $1,000 × − × + (1 ) r r r ⇒ r 2 I$$ A 2 /5.8'=
a.odabasi 3 4As 6/
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I$$0 2 discount rate +r *# which is the solution to the followin9 equation:
1 1 + × (1 +
$33,000 ×
r
r
)
r
= $&0,000
⇒ r 2 I$$0 2 /(.8'=
The IRR of project A is 25.69%, and that of B is 20.69%. However, project B has the higher NPV and therefore is preferred. The incremental cash flows of B over A are −$20,000 at time 0 and +$12,000 at times 1 and 2. The NPV of the incremental cash flows (discounted at 10%) is $826.45, which is positive and equal to the difference in the respective project NPVs.
Q2 2:Pr ofit a bi l i t yI nde xve r s usNPV. Cons i derpr oj ec t sAandBwi t ht hef ol l o wi ngc as h L O8 3 fl o ws :( ) C 0
C 1
C 2
C 3
A
!$3#
"$0
"$0
"$0
%
! &0
" &
" &
" &
a . Whi c hpr o j ec th ast h eh i g herNPVi ft h edi s c ou ntr at ei s1 0%? b.Whi c hhast hehi gherpr ofi t abi l i t yi nde x? c . Whi c hpr oj ec ti smos tat t r ac t i v et oafi r mt hatc anr ai s ean unl i mi t edamountoff undst opa yf ori t si nv es t mentpr oj ec t s ? Whi c hpr oj ec ti smos tat t r ac t i v et oafi r mt hati sl i mi t edi nt he f undsi tc anr ai s e?
a.
*A = !$3# " +$0 × annuit factor (10-, 3 eriods)/
1 1 − = $13.' 3 0 . 10 × 0.10 (1.10)
$0 ×
2 3&8
!"0 2 3&5( @&/5 × annuity factor +)(=# periods*
1 1 − 0.10 0.10 × (1.10)
$& ×
2 3&5(
3
= $1.1'
Thus !roject A has the hi9her !" if the discount rate is )(=. b.
!roject A has the hi9her profitability index# as shown in the table below: !roject A 0
!" of Cash Blow &,'.-, &8/.)-
Investment
!"
&8 &5(
&).-, &)/.)-
, a.odabasi 3 4As 6/
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!rofitability Index (.% (./,
c.
A firm with a limited amount of funds available should choose !roject A since it has a hi9her profitability index of (.%# i.e.# a hi9her ban9 for the buc1.D ote that A also has a hi9her !" as well. Bor a firm with unlimited funds# the possibilities are: +i* If the projects are independent projects# then the firm should choose both projects. +ii* Eowever# if the projects are mutually exclusive# then !roject A should be selected. It has the hi9her !".
Ch 6
Q11. Real andnomi nalflows CSCi sev al uat i ngane w pr oj ec tt opr oduc eenc aps ul at or s . Thei ni t i al i nv es t menti npl antandequi pmenti s$500, 000.Sal esofenc aps ul at or si n y e ar1ar ef or e cas t e da t$ 20 0, 0 00a ndc os t sat$ 10 0, 0 00 .Bo t ha r ee x pe ct e dt o i nc r eas eby10% ay eari nl i newi t hi nfl at i on.Pr ofi t sar et ax edat35%.Wor k i ngc api t al i neac hy earc ons i s t sofi nv ent or i esofr awmat er i al sandi sf or ec as t edat20% ofs al es i nt hef ol l owi ngy ear .
Thepr oj ec twi l l l as tfi v ey ear sandt heequi pmentatt heendoft hi sper i odwi l l ha veno f ur t herv al ue.Fort axpur pos est heequi pmentc anbedepr ec i at eds t r ai ght l i neo ver t hes efi v ey ear s .I ft henomi nal di s c ountr at ei s15%,s howt hatt henetpr es entv al ueof t h ep r oj e c ti st h es amewh et he rc a l c ul a t edus i ngr e alc as hfl o wsorno mi na lfl o ws . Answer ))* Revenues
200,000
Costs
100,000
Depreciation Pretax Proft Taxes at 35 Proft a"ter Tax Depreciation Cas# $%o& "ro' (perations C#an)e in *or+in)
100,000 0 0 0 100,000
40,000
100,000 4,000
5 a.odabasi 3 4As 6/
/()57)8
220,00 242,00 266,20 292,82 0 0 0 0 110,00 121,00 133,10 146,41 0 0 0 0 100,00 100,00 100,00 100,00 0 0 0 0 10,000 21,000 33,100 46,410 3,500 !,350 11,585 16,244 6,500 13,650 21,515 30,16! 100,00 100,00 100,00 100,00 0 0 0 0 106,50 113,65 121,51 130,16 0 0 5 ! 4,400 4,840 5,324 58,564
Capita% Capita% -nvest'ent
500,000
.et Cas# $%o&s Discount $actor / 15 Present a%ue
540,000 1000 540,000
.P
14!,510
102,10 0 0!56 !!,202
96,000 08!0 83,4!8
108,81 0 0658 !1,544
116,19 1 05!2 66,433
188,!3 1 049! 93,832
;ince the nominal rate is )5= and the expected inflation rate is )(=# the real rate is 9iven by the followin9: +) r nominal* 2 +) r real* × +) inflation rate* ).)5 2 +) r real* × +).)(* r real 2
(.(,5,5 2 ,.5,5=
Adjustin9 the cash flows to real dollars and usin9 this real rate 9ives us the same result for !" +with a sli9ht roundin9 error*.
.et Cas# $%o&s no'ina% 7ust'ent $actor "or Rea% C$ .et Cas# $%o&s rea% Discount $actor / 4545 Present a%ue .P
R 0 1 2 3 4 5 540,000 96,000 102,100 108,810 116,191 188,!31 1 540,000
0909 8!,2!3
0826 84,380
0!51 81,!51
0683 !9,360
0621 11!,18!
1000 540,000
095! 83,4!9
0915 !!,203
08!5 !1,545
083! 66,434
0801 93,834
14!,505
15. t ers pendi ng$3mi l l i ononr es ear c h,Be t t erMous et r apshasdev e l oped Pr oj ectNPV Af
ane wt r ap.Thepr oj ec tr equi r esani ni t i al i nv es t menti npl antandequi pmentof$6 mi l l i on.Thi si nv es t mentwi l l bedepr eci at eds t r ai ght l i neov erfi vey ear st oav al ueofz er o, but ,whent hepr oj ec tc omest oanendi nfiv ey ear s ,t heequi pmentc ani nf ac tbes ol df or $ 500 , 000 .Th efi r mb el i e v est h atwor k i n gc ap i t a late ac hda t emus tb emai n t a i ne da t10 % ofne xty ear ' sf or ec as t eds al es .Pr oduc t i onc os t sar ees t i mat edat$1. 50pert r apandt he t r apswi l l bes ol df or$4eac h.( Ther ear enomar k et i nge xpens es . )Sal esf or ec as t sar e gi v eni nt hef ol l o wi ngt abl e.Thefi r m pa y st axat35% andt her equi r edr e t ur nont he p r o j e c ti s12 %.Wh ati st h eNPV?
4)5
8 a.odabasi 3 4As 6/
/()57)8
ote: This answer assumes that the & million initial research costs are sun1 and excludes this from the !" calculation. It also assumes that wor1in9 capital needs be9in to accrue in year (. nit :a%es 500 600 1,000 1,000 Revenues 2,000 2,400 4,000 4,000 Costs Depreciation Pretax Proft inc%u7es sa%va)e in ear 5 Taxes at 35 Proft a"ter Tax Depreciation Cas# $%o& "ro' (perations C#an)e in *or+in) Capita% Capita% -nvest'ent .et Cas# $%o&s Discount $actor / 12 Present a%ue .P
200 6,000 6,200 1000 6,200
!50 1,200
900 1,200
1,500 1,200
1,500 1,200
900 1,200
50 18 33 1200 1,233 40
300 105 195 1200 1,395 160
1,300 455 845 1200 2,045 0
1,300 455 845 1200 2,045 160
1,193 0893 1,065
1,235 0!9! 985
2,045 0!12 1,456
2,205 0636 1,401
300 105 195 1200 1395 240 325 1,960 056! 1111
181
Q18. Pr oj ectNPV Awi dgetmanuf ac t ur erc ur r ent l ypr oduc es200, 000uni t say ear .I tbuy s
wi dgetl i dsf r om anout s i des uppl i eratapr i c eof$2al i d.Thepl antmanagerbel i e ves t hati twoul dbec heapert omak et hes el i dsr at hert hanbuyt hem.Di r ec tpr oduc t i on c os t sar ees t i mat edt obeonl y$1. 50al i d.Thenec es s ar ymac hi ner ywoul dcos t $150, 000andwoul dl as t10y ear s .Thi si nv es t mentc oul dbewr i t t enofff ort axpur pos es us i ngt hes ev eny e art axdepr ec i at i ons c hedul e.Thepl antmanageres t i mat est hatt he oper at i onwoul dr equi r eaddi t i onal wor k i ngc api t al of$30, 000butar guest hatt hi ssum c anbei gnor eds i nc ei ti sr ec ov e r abl eatt heendoft he10y ear s .I ft hec ompan ypa y s t axatar at eof35% andt heoppor t uni t yc os tofc api t al i s15%,woul dy ous uppor tt he pl antmanager ' spr opos al ?St at ec l ear l yan yaddi t i onal as s umpt i onst haty ouneedt o mak e.
A)%. Assume the followin9: a. The firm will manufacture wid9ets for at least )( years. b. There will be no inflation or technolo9ical chan9e. c. The )5= cost of capital is appropriate for all cash flows and is a real# after7tax rate of return. d. All operatin9 cash flows occur at the end of the year. e.
Fe cannot i9nore incremental wor1in9 capital costs and recovery. ote: ;ince purchasin9 the lids can be considered a one7year Dproject#D the two projects have a common chain life of )( years. Compute !" for each project as follows:
a.odabasi 3 4As 6/
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600 2,400
+&/ × /((#(((* × +) − ( .5* = − &)#(,#%%( ).)5 t t =) )(
−∑ !"+purchase* 2
+&).5( × /((#(((* × +) − ( .5* ).)5 t
)(
− $)5(#((( − $(#((( − ∑ t
=)
!"+ma1e* 2
(.),/' (./,,' (.)-,' (.)/,' + [ (.5 × $)5(#(((] × + + + + ).)5 / ).)5 ).)5 , ).)5 ) (.(%' ).)5 5
+
(.(%' ).)5 8
+
(.(%' ).)5 -
+
(.(,,5 &(#((( + ).)5 % ).)5 )(
= −&)#))%#/%
Thus# the wid9et manufacturer should ma1e the lids.
Q20. Pr oj ectNPV Ma r s h aJ o ne sha sbo ug htaus e dMe r c e de sho r s et r a ns p or t e rf o rh er Connec t i c utes t at e.I tc os t$35, 000.Theobj ec ti st os av eonhor s et r ans por t err ent al s .
Ma r s hah adb eenr e nt i n gat r a ns po r t e re v er yo t h erwee kf or$ 20 0p erd aypl u s$ 1. 0 0 permi l e.Mos toft het r i psar e80or100mi l esi nt ot al .Mar s haus ual l ygi v est hedr i v era $40t i p.Wi t ht henewt r ans por t ers hewi l lonl yhav et opayf ordi es el f uel and mai nt enanc e,atabout$. 45permi l e.I ns ur anc ec os t sf orMar s ha' st r ans por t erar e $ 1, 2 00pe ry e ar . Thet r ans por t erwi l l pr obabl ybewor t h$15, 000( i nr eal t er ms )af t erei ghty ear s ,when Mar s ha' shor s eNi k ewi l l ber eadyt or et i r e.I st het r ans por t erapos i t i v eNPV i n v es t me nt ?As s umean omi n al di s c oun tr a t eo f9 %a nda3 %f or ec as t e di nfl a t i o nr a t e . Mar s ha' st r ans por t eri saper s onal out l a y ,no tabus i nes sorfi nanc i al i nv es t ment ,s o t a x esc anbei gn or ed .
A/(.
The table below shows the real cash flows. The !" is computed usin9 the real rate# which is computed as follows: +) r nominal* 2 +) r real* × +) inflation rate* ).(' 2 +) r real* × +).(* r real 2 (.(5% 2 5.%= t 2
( 75#(((.(
t 2
)
Investment ;avin9s %#5%(.( Insurance 7)#/((.( Buel )#(5.( et Cash Blow 75#(((.( 8#/-.( !" +at 5.%=* 2 &),#(%-.'
t 2
/
t 2
%#5%(.( 7)#/((.( )#(5.( 8#/-.(
%#5%(.( 7)#/((.( )#(5.( 8#/-.(
t 2
,
%#5%(.( 7)#/((.( )#(5.( 8#/-.(
t 2
5
%#5%(.( 7)#/((.( )#(5.( 8#/-.(
t 2
8
%#5%(.( 7)#/((.( )#(5.( 8#/-.(
t 2
-
% )5#(((.( %#5%(.( %#5%(.( 7)#/((.( 7)#/((.( )#(5.( )#(5.( 8#/-.( /)#/-.(
Q24. Equi val entannualcashflows Asar es ul tofi mpr o v ement si npr oduc tengi neer i ng,
% a.odabasi 3 4As 6/
/()57)8
t 2
Uni t edAut omat i oni sabl et os el l oneofi t st womi l l i ngmac hi nes .Bot hmac hi nes p er f o r mt hes amef u nc t i o nb utdi ff eri na ge .Th ene wermac hi n ec ou l db es ol dt o da yf o r $50, 000.I t soper at i ngc os t sar e$20, 000ay ear ,buti nfi v ey ear st hemac hi newi l l r equi r ea$20, 000ov er haul .Ther eaf t eroper at i ngc os t swi l l be$30, 000unt i l t he mac hi nei sfinal l ys ol di ny ear10f or$5, 000. Theol dermac hi nec oul dbes ol dt odayf or$25, 000.I fi ti skept ,i twi l l needan i mmedi at e$20, 000o ver haul .Ther eaf t eroper at i ngc os t swi l l be$30, 000ay earunt i l t he mac hi nei sfinal l ys ol di ny ear5f or$5, 000. Bo t hma ch i nesar ef u l l yde pr e ci at e df o rt a xp ur p os es .Th ec ompa nypa y st a xa t3 5%. Cas hfl owsha v ebeenf or ec as t edi nr ealt e r ms .Ther eal c os tofc api t al i s12%.Whi c h ma ch i nes ho ul dUn i t e dAut o ma t i o ns el l ?Ex pl a i nt heas s ump t i o nsun der l y i ngy o ur answer .
/,. In order to solve this problem# we calculate the equivalent annual cost for each of the two alternatives. +All cash flows are in thousands.* Alternative 1—Sell the new machine :
If we sell the new machine# we receive the cash flow from the sale# pay taxes on the 9ain# and pay the costs associated with 1eepin9 the old machine. The present value of this alternative is:
!") = 5( − @( .5+5(
+
5 ).)/ 5
−
− (* − /( −
(.5 +5 − (* ).)/5
( ).)/
−
( ).)//
−
( ).)/
−
( ).)/,
−
( ).)/5
= −&'.%(
The equivalent annual cost for the five7year period is computed as follows: !") 2 GAC) × @annuity factor# 5 time periods# )/= 3'.%( 2 GAC) × @.8(5 GAC) 2 3/8.(/# or an equivalent annual cost of &/8#(/( Alternative 2—Sell the old machine :
If we sell the old machine# we receive the cash flow from the sale# pay taxes on the 9ain# and pay the costs associated with 1eepin9 the new machine. The present value of this alternative is:
!"/
= /5 − @(.5+/5 − (* − −
/( ).)/5
+
5 ).)/)(
−
( ).)/8
−
−
/( ).)/
( ).)/-
( .5 +5 − (* ).)/)(
− −
/( ).)/ /
( ).)/%
− −
/( ).)/
( ).)/ '
−
/( ).)/ ,
−
( ).)/)(
−
/( ).)/5
= −&)/-.5)
The equivalent annual cost for the )(7year period is computed as follows:
' a.odabasi 3 4As 6/
/()57)8
!"/ 2 GAC/ × @annuity factor# )( time periods# )/= 3)/-.5) 2 GAC/ × @5.85(
ANor malPr oj ect :
Val ui nganewComput ersys t em Ob so l e t eT ec hn ol ogi e si sc ons i de r i n gt h ep ur c has eo fan ewc ompu t e rs y s t e mt ohe l ph and l e i t swar ehous ei n v ent or i es .Thes y s t em c os t s$50, 000,i sex pec t edt ol as t4y ear s ,ands houl d r educ et hec os tofmanagi ngi n vent or i esby$22, 000ay ear .Theoppor t uni t ycos tofc api t al i s 10%.Shoul dObsol et egoahead? Answer :
Thene tpr es entv al uei s Thepr oj ec thasapos i t i v eNPVof$19, 738.Under t ak i ngi twoul di nc r eas et hev al ueoft he fir m byt hatamount .
I nvest mentTi mi ngPr obl em
Ob so l e t eT ec hn ol ogi e si sc o nt e mpl a t i n gt hepu r c ha seofane wc ompu t e rs y s t e m.Th e pr opos edi n v es t menthasane tpr es entv al ueofal mos t$20, 000,s oi tappear st hatt hec os t s a vi ngswoul deas i l yj us t i f yt hee x pens eoft hes y s t em.Howev er ,t hefi nanc i al manageri sno t per s uaded.Sher eas onst hatt hepr i c eofc omput er si sc ont i nual l yf al l i ngandt her ef or e s ugges t spos t poni ngt hepur c has e,ar gui ngt hatt heNPVoft hes y s t em wi l l beev enhi gheri f t hefi r m wai t sunt i l t hef ol l o wi ngy ear .Unf or t unat el y , s hehasbeenmak i ngt hes ame ar gumentf or10y e ar s ,andt hec ompan yi ss t eadi l yl os i ngbus i nes st oc ompe t i t or swi t hmor e effic i ents y s t ems .I st her eafla wi nherr eas oni ng?
Answer :
Obsol et eTechnol ogi es:Thegai nf r om pur chaseofacomput eri s TABLE r i s i ng,butt heNPVt oda yi shi ghe sti ft hec omput e ri spur c ha se di ny e ar3 ( dol l arv al ue si nt hous ands ) . Yearof Purchase
Costof PV NPVatYearof NPV r Comput er Savi ngs Pur chase( =1 0%) Today
)( a.odabasi 3 4As 6/
/()57)8
0
$50
$70
$20
$20. 0
1
45
70
25
22. 7
2
40
70
30
24. 8
3
36
70
34
25. 5
4
33
70
37
25. 3
5
31
70
39
24. 2
←opt i mal p ur c h as ed at e
Long-andShor tLi vedEqui pment-Equi val entAnnualCostConcept
Lowener gyl i ght bul bst y pi c al l ycos t$3. 50,hav eal i f eof9y ear s ,andus eabout$1. 60of el ec t r i c i t yay ear .Conv ent i onal l i ght bul bsar ec heapert obuy ,f ort heyc os tonl y$. 50.Ont he o t herhand,t he yl as tonl yaboutay earandus eabout$6. 60ofener gy . I ft hedi s countr at ei s 5 %,wh i c hp r od uc ti sc he ape rt ous e? T oans wert hi sques t i on,y ouneedfi r s tt oc onv er tt hei ni t i al c os tofeac hbul bt oanannual fi gur eandt hent oaddi nt heannual ener gyc os t .Thef ol l owi ngt abl es et soutt hec al c ul at i ons :
Low-Energy !l"
Con#ent$onal !l"
1. Initial cost, $
3.&0
0.&0
. stiated life, ears
2
1
3. Annuit factor at &-
'.10'
.2&
.2
.&
&. Annual energ cost, $
1.#0
#.#0
#. 6otal annual cost, $, = () " (&)
.02
'.1
. qui4alent annual annuit, $, =(1)5(3)
Assumption: nerg costs are incurred at the end of each ear.
I ts eemst ha tal o we ner g ybu l bpr o v i de sa na nn ual s a v i n go fa bo ut$7 . 12–$ 2. 0 9=$ 5. 0 3.
Whent oRepl aceanOl dMachi ne
Ou rear l i erc ompar i s ono fmac hi nesIandJt ookt hel i f eofeac hmac hi neasfi x ed.I n pr ac t i c e,t hepoi ntatwhi c hequi pmenti sr epl ac edr efl ec t sec onomi c s ,notphy s i c al c ol l aps e.
)) a.odabasi 3 4As 6/
/()57)8
Weus ual l ydec i dewhent or epl ac e.Fore x ampl e,weus ual l yr epl ac eac arno twheni tfi nal l y br eaksdownbutwheni tbecomesmor eexpensi veandt r oubl esomet okeepupt hana r e pl a c eme nt . r epl acementpr obl em:
Youar eoper at i nganol dmac hi net hatwi l l l as t2mor ey ear sbef or ei tgi v esupt heghos t .I t c os t s$12 , 00 0p ery e art oo pe r a t e .Yo uc anr e pl a cei tno w wi t han ewma ch i n et h atc os t s $25, 000buti smuc hmor eeffic i ent( onl y$8, 000pery eari noper at i ngc os t s )andwi l l l as tf or5 y e ar s .Shoul dy our epl ac et hemac hi neno w ors t i c kwi t hi tf orawhi l el onger ?The oppor t uni t yc os tofc api t al i s6%. Costs (tho!sands o dollars) &ear'
0
ew achine
&
qui4alent annual annuit
1
2
3
13.23 13.23 13.2 3
13.23 13.23
PV at *%
$&.'0 &.'0
Th ec a s hfl o wso ft h en ewma c hi n ea r ee qu i v a l e ntt oa na nn ui t yof$ 13 , 9 30p ery e ar .Sowe c aneq ual l ywel l as kwhe t h ery o uwo ul dwa ntt or epl a cey o uro l dmac hi n e,whi c hc o s t s $ 12 , 0 00ay e art or u n,wi t hane wo nec os t i n g$ 13 , 93 0ay e ar .
)/ a.odabasi 3 4As 6/
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CAsh Blow Gstimation# Capital 0ud9etin9 Hecisions
I dea:Us et hei nc r ement al c as hfl owsonl y . Sel f Tes t Afir mi sc ons i de r i nga ni n ve st me nti nane w ma nuf a ct ur i ngpl a nt .Thesi t eal r e adyi s ownedbyt hecompany,butexi st i ngbui l di ngswoul dneedt obedemol i shed.Whi chof t hef ol l owi ngshoul dbet r eat edasi ncr ement alcashflows? a. +he ,aret #al!e o the s$te.
7. +he ,aret #al!e o the e/$st$ng "!$ld$ngs. c. e,ol$t$on costs and s$te clearance. d. +he cost o a new access road !t $n last year. e. Lost cash lows on other rojects d!e to e/ec!t$#e t$,e sent on the new ac$l$ty. f. F!t!re derec$at$on o the new lant.
Answer : a,7. 6he site and 7uildings could ha4e 7een sold or ut to another use. 6heir 4alues are oortunit costs, which should 7e treated as increental cash outflows. c.
8eolition costs are increental cash outflows.
d.
6he cost of the access road is sun9 and not increental.
e.
ost cash flows fro other ro;ects are increental cash outflows.
f.
8ereciation is not a cash e<ense and should not 7e included, e
Di scountNomi nalCashFl owsbyt heNomi nalCostofCapi t al I tshoul dgowi t houtsayi ngt hatyoucannotmi xandmat chr ealandnomi nal qua nt i t i e s.Re alc as hflowsmus tbedi s count e da tar e aldi s countr a t e ,nomi na lc as h flowsa tanomi na lr a t e .Di s count i ngr e alc as hflowsa tanomi na lr a t ei sabi gmi s t a k e.
Separ at eI nvest mentandFi nanci ngDeci si ons
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Su pp os ey o ufi na nc eap r oj e ctp ar t l ywi t hd eb t .Ho ws ho ul dy o ut r e att hepr o ce edsf r om t h e debti s s ueandt hei nt er es tandpr i nc i pal pa y ment sont hedebt ?Thepr obabl ysur pr i s i ng ans wer :Regar dl es soft heac t ual fi nanc i ng,y ous houl dv i e wt hepr oj ec tasi fi twer eal l equi t y fi nanc ed,t r eat i ngal l c as hout fl owsr equi r edf ort hepr oj ec tascomi ngf r om s t oc k hol der sandal l c as hi nfl owsasgoi ngt ot hem
Pr oj ectCashFl ows I ti shel pf ul t ot hi nkofapr oj ec t ' sc as hfl owasc ompos edoft hr eeel ement s :
Hiscussion points: Chan9e in wor1in9 capital# salva9e value# etc AnEx ampl e: Ast henewl yappoi nt edfinanc i al managerofBl ooperI ndus t r i es ,y ouar eaboutt oanal y s ea pr opos al f ormi ni ngands el l i ngas mal l depos i tofhi ghgr ademagnes i um or e. 6 Youar egi v e n t hef or ec as t ss ho wni nt hes pr eads hee t .
), a.odabasi 3 4As 6/
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Fi na nc i a lpr oj e ct i onsf orBl oope r ' sma gne si um mi ne( dol l a rv a l ue si nt hous ands )
)5 a.odabasi 3 4As 6/
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Wec annows eeho w Bl ooperar r i v esati t sf or ec as tofwor k i ngc api t al :
0
1
2
3
*
$0
$,&0 0
$,#&
$,'& #
$,2
$3,032
0
. In4entories (.1& following ear>s e<enses)
1,&00
1,&'&
1,#&
1,'3#
1,3
0
0
3. ?or9ing caital (1 " )
1,&00
,0'&
,'2
,23
,'1'
3,032
0
1. Recei4a7les (51 re4enues)
No t e : Col umnsmaynotsum duet or oundi ng.
Pr oj e ctEv al ua t i on.
PCSh op pi n gNe t wo r kma yu pg r a dei t smo de mp oo l .I tl a s tu pg r a de d2y e ar sa go ,wh eni t s p en t$ 11 5mi l l i o no ne qu i p me ntwi t ha na s s ume dl i f eo f5y ea r san da na s s ume ds a l v a ge v al ueof$15mi l l i onf ort axpur pos es .Thefi r m us ess t r ai ght l i nedepr ec i at i on.Theol d e qui pmen tc anb es ol dt o da yf o r$8 0mi l l i on .Ane w mod em po ol c anbei ns t a l l e dt o da yf o r $150mi l l i on.Thi swi l l hav ea3y earl i f eandwi l l bedepr ec i at edt oz er ous i ngs t r ai ght l i ne depr ec i at i on.Thene w equi pmentwi l l enabl et hefi r mt oi nc r eas es al esby$25mi l l i onper y e aranddec r eas eoper at i ngc os t sby$10mi l l i onpery ear .Att heendof3y ear s ,t hene w equi pmentwi l l bewor t hl es s .As s umet hefi r m' st axr at ei s35% andt hedi s c ountr at ef or L O9 2 pr oj ec t soft hi ss or ti s10%.( ) Page 294 a. Whati st hene tc as hfl owatt i me0i ft heol dequi pmenti sr epl ac ed?
b .Wh ata r et h ei n c r e me nt a lc a s hfl o wsi ny ea r s1 ,2 ,a nd3? c.Whatar et heNPVandI RRoft her epl acementpr oj ect ?
Answer: .
a.
Annual dereciation is ($11& − $1&)5& = $0 illion. 0oo1 value at the time of sale is &))5 − +/ × &/(* 2 &-5 million.
;ales price 2 &%( million# so net7of7tax proceeds from the sale are: &%( − +(.5 × &5* 2 &-%./5 million Therefore# the net cash outlay at time ( is &)5( − &-%./5 2 &-).-5 million. b.
The project saves &)( million in operatin9 costs and increases sales by &/5 million. Hepreciation expense for the new machine would be &5( million )8
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per year. Therefore# includin9 the depreciation tax shield# operatin9 cash flow increases by: +&/5 &)(* × +) − (.5* +&5( × (.5* 2 &,(./5 million per year c.
!" 2 −&-).-5 @&,(./5 × annuity factor +)(=# years*
1 1 − = $.3&, 3 × 0.10 0.10 (1.10)
$'1.'& + $0.& ×
23
or &/%.5 million
To find the internal rate of return# set the !" of the annuity to &-).-5 and solve for the discount rate +r *:
1 1 − × (1 +
$0.& ×
r
r
= $'1.'& ⇒ = IRR = 31.33)3 r
r
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Ch 10 Sensitivity Analysis Sensi t i vi t yAnal y si s. Emper or ' sCl ot hesFas hi onsc ani nv es t$5mi l l i oni nanewpl antf or pr oduc i ngi n vi s i bl emak e up.Thepl anthasane xpec t edl i f eof5y ear s ,ande xpec t eds al es ar e6mi l l i onj ar sofmak eupay ear .Fi x edc os t sar e$2mi l l i onay ear ,andv ar i abl ec os t sar e $1perj ar .Thepr oduc twi l l bepr i c edat$2perj ar .Thepl antwi l l bedepr ec i at eds t r ai ght l i ne o ver5y ear st oas al v agev al ueofz er o.Theoppor t uni t ycos tofc api t al i s10%,andt het ax L O1 0 2 r at ei s40%.( )
a. Whati spr oj ectNPVundert hesebasecaseassumpt i ons? b. Whati sNPVi fv ar i abl ec os t st ur noutt obe$1. 20perj ar ? c . Wh ati sNPVi ffi x e dc os t st u r no utt ob e$ 1. 5mi l l i o np ery e ar ? d . Atwh atp r i c ep erj a rwo ul dp r o j e c tNPVe qu al z e r o ?
3.
Re4enue = rice × quantit = $ × # illion = $1 illion Gxpense 2 variable cost fixed cost 2 +&) × 8 million* &/ million 2 &% million
Hepreciation expense 2 &5 million5 years 2 &) million per year Cash flow 2 +) − T * × +revenue 3 expenses* + T × depreciation* 2 @(.8( × +&)/ million 3 &% million* +(., × &) million* 2 &/.% million a. !" 2 3&5 million @&/.% million × annuity factor +)(=# 5 years*
1 1 × − = $&.#1 0.10 × 0.10 (1.10) &
2 3&5 million &/.% million b.
million
If variable cost 2 &)./(# then expenses increase to: +&)./( × 8 million* &/ million 2 &'./ million CB 2 @(.8( × +&)/ million 3 &'./ million* +(., × &) million* 2 &/.(% million !" 2 3&5 million @&/.(% million × annuity factor +)(=# 5 years*
2 3&5 million &/.(% million c.
1 1 × − = $. & 0.10 × 0.10 (1.10)
If fixed costs 2 &).5 million# expenses fall to: +&) × 8 million* &).5 million 2 &-.5 million )%
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million
Cash flow 2 @(.8( × +&)/ million 3 &-.5 million* +(., × &) million* 2 &.) million !" 2 3&5 million @&.) million × annuity factor +)(=# 5 years*
1 1 × − = $#.'& & × 0.10 0.10 (1.10)
2 3&5 million &.) million d.
million
Call P the price per jar. Then: $evenue 2 P × 8 million Gxpense 2 +&) × 8 million* &/ million 2 &% million Cash flow 2 @+) 3 (.,(* × +8P 3 %* +(.,( × )* 2 .8P 3 ,., !" 2 35 @+.8P 3 ,.,* × annuity factor +)(=# 5 years*
2 35 @+.8P 3 ,.,*
1 × 1 − & 0.10 0.10 × (1.10)
2 35 @+.8P 3 ,.,* × .-'(% 2 3/).8-'5 ).8,8'P 2 ( ⇒ P 2 &).5' per jar Sc ena r i oAna l y si s .
Themos tl i k el yout c omesf orapar t i c ul arpr oj ec tar ees t i mat edasf ol l ows : •
Uni tpr i c e:$50
•
Var i abl ec os t :$30
•
Fi x edc os t :$300, 000
•
Ex pec t eds al es :30, 000uni t spery ear
Ho wev e r ,y our ec ogni z et hats omeoft hes ees t i mat esar es ubj ec tt oer r or .Suppos et hateac h v ar i abl ema yt ur noutt obeei t her10% hi gheror10% l owert hant hei ni t i al es t i mat e.The pr oj ec twi l l l as tf or10y ear sandr equi r esani ni t i al i nv es t mentof$1mi l l i on,whi chwi l l be depr eci at eds t r ai ght l i neov ert hepr oj ec tl i f et oafi nal v al ueofz er o.Thefi r m' st axr at ei s L O1 0 2 35%,andt her equi r edr at eofr e t ur ni s12%.( ) a.Whati spr oj ec tNPVi nt hebes t c as es c enar i o,t hati s ,as sumi ngal l v ar i abl est ak eont he bes tpos si bl ev al ue? b .Wh ata bo utt h ewo r s t c a s es c e na r i o ?
!rice "ariable cost
Jost Ki1ely &5( &(
0est Case &55 &/)'
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Forst Case &,5 &
Bixed cost ;ales
&((#((( (#((( units
&/-(#((( #((( units
&(#((( /-#((( units
Cash flow 2 @+) 3 T * × +revenue 3 cash expenses* + T × depreciation* Hepreciation expense 2 &) million)( years 2 &)((#((( per year 0est7case CB 2 (.85 × @#((( × +&55 3 &/-* 3 &/-(#((( +(.5 × &)((#(((* 2 &,8(#)(( Forst7case CB 2 (.85 × @/-#((( × +&,5 3 &* 3 &(#((( +(.5 × &)((#(((* 2 &)#)((
)/=# )(7year annuity factor 2
1 1 − 0.1 0.1 × (1.1) 10 = &.#&0
0est7case !" 2 +5.85(// × &,8(#)((* 3 &)#(((#((( 2 &)#5''#888 Forst7case !" 2 +5.85(// × &)#)((* 3 &)#(((#((( 2 3&%/,#/-%
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CH 7 Introducton to is! and eturn
I nwhi c hoft hef ol l owi ngs i t uat i onswoul dy ougett hel ar ges tr educ t i oni nr i s k Q5Di v er s i fic at i on b ys pr e ad i n gy o uri n v es t me ntac r o sst wos t o ck s ? a. Thet wos har esar eper f ec t l yc or r el at ed. b. Ther ei snoc or r el at i on. c . Ther ei smodes tnegat i v ecor r el at i on. d. Ther ei sper f ec tnegat i v ec or r el at i on. 5. ( d) Thi ss t r at egydoest hemostt or educer i sk sbec auset hest ock smov ei nopposi t e d i r ec t i on s .Wh enon eg oe su p,t h eo t h erg oe sdo wn,a ndv i c ev e r s a.Thi sdoe st h emo s tt or e du cer i s k i napor t f ol i o. T oc al c ul at et hev ar i anc eofat hr ees t oc kpor t f ol i o,y ouneedt oaddni nebo xes : Q6Por t f ol i or i sk
Us et h es a mes y mb ol st h atweus e di nt h i sc ha pt e r ;f o re x amp l e , x1 =pr opor t i oni nv es t edi ns t oc k 1andσ12 =c o v ar i a nc ebe t we ens t o c k s1an d2 .No wc o mp l e t et h en i n eb ox e s .
Q7Por t f ol i or i sk Su pp os et h es t an da r dde v i a t i ono ft h emar k e tr e t u r ni s20%.
e. Whati st hes t andar ddev i at i onofr et ur nsonawel l di v er s i fi edpor t f ol i owi t habet aof 1 . 3 ? f .Whati st hes t andar ddev i at i onofr et ur nsonawel l di v er s i fi edpor t f ol i owi t habet aof 0? g. Awel l di v er s i fi edpor t f ol i ohasas t andar ddev i at i onof15%.Whati si t sbet a? h . Ap oo r l ydi v e r s i fi edpo r t f o l i oh asas t an da r dd ev i a t i o no f20 %.Wha tc a ny o us a ya bo ut i t sbet a?
-.
a.
/8= /)
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b. Lero c. .-5 d. Kess than ).( +the portfolioMs ris1 is the same as the mar1et# but some of this ris1 is unique ris1*
Q8Por t f ol i obe t a Apor t f ol i oc ont ai nsequal i nv es t ment si n10s t oc k s.Fi v ehav eabet a of1. 2;t her emai nderhav eabet aof1. 4.Whati st hepor t f ol i obe t a?
i .1. 3. j .Gr eat ert han1. 3bec aus et hepor t f ol i oi snotc ompl et el ydi v er si fi ed. k . Les st han1. 3bec aus edi v er s i fi c at i onr educ esbe t a.
%. a. ). +Hiversification does not affect mar1et ris1.* This can be found by findin9 the avera9e of all of the betas: +5 x ).,* +5 x )./* )( 2 ).. 4) $is1 and diversification Konesome Nulch Jines has a standard deviation of ,/= per year and a beta of .)(. Amal9amated Copper has a standard deviation of )= a year and a beta of .88. Gxplain why Konesome Nulch is the safer investment for a diversified investor. A). In the context of a well7diversified portfolio# the only ris1 characteristic of a sin9le security that matters is the securityMs contribution to the overall portfolio ris1. This contribution is measured by beta. Konesome Nulch is the safer investment for a diversified investor because its beta +(.)(* is lower than the beta of Amal9amated Copper +(.88*. Bor a diversified investor# the standard deviations are irrelevant.
CH" CAP#
9. Tr ue/ f al se T r ueorf al s e?Ex pl ai norqual i f yasnec es sar y .
a .I n v es t o r sde ma ndh i g he re x p ec t e dr a t e so fr e t u r nons t o ck swi t hmo r ev a r i a bl e r at esofr et ur n. b.TheCAPM pr edi c t st ha tasec ur i t ywi t habe t aof0wi l l off erazer oex pec t edr e t ur n. c . Ani n v es t orwhoput s$10, 000i nT r eas ur ybi l l sand$20, 000i nt hemar k e tpor t f ol i o wi l l hav eabet aof2. 0. d.I n v es t or sdemandhi ghere x pec t edr at esofr e t ur nf r om s t oc k swi t hr e t ur nst hatar e
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hi g hl ye x pos edt omac r o ec on omi cr i s k s . e.I n v es t or sdemandhi ghere x pec t edr at esofr e t ur nf r om s t oc k swi t hr e t ur nst hatar e v er ysens i t i v et ofl uc t uat i onsi nt hes t oc kmar k et . A$ '.
a. Balse. investors demand hi9her expected rates of return on stoc1s with more nondiversifiable ris1.
b.
Balse. a security with a beta of >ero will offer the ris17free rate of return.
c.
Balse. Treasury bills have a beta of ( and the mar1et has a beta of ). Therefore# with ) of the investorMs money in T bills and / of his or her money in the mar1et# the beta will be: +) × (* +/ × )* 2 (.8-.
d.
True
e.
True
)5. CA!J The Treasury bill rate is ,=# and the expected return on the mar1et portfolio is )/=.
)5.
a.
b.
Jar1et ris1 premium 2 r m 3 r f 2 (.)/ 3 (.(, 2 (.(% 2 %.(=.
c.
β+r m 3 r f *
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r 2
d.
(.(, @).5 × +(.)/ 3 (.(,* 2 (.)8 2 )8.(=
Bor any investment# we can find the opportunity cost of capital usin9 the security mar1et line. Fith β 2 (.%# the opportunity cost of capital is: r 2 r f r 2
β+r m 3 r f *
(.(, @(.% × +(.)/ 3 (.(,* 2 (.)(, 2 )(.,=
The opportunity cost of capital is )(.,= and the investment is expected to earn '.%=. Therefore# the investment has a ne9ative !".
17. Cos tofc api t a l Eps i l onCor p.i sev al uat i ngane x pans i onofi t sbus i nes s .Thec as hfl ow
f or ec as t sf ort hepr oj ec tar easf ol l ows :
Page 214
Thefi r m' sex i s t i ngas se t shav eabe t aof1. 4.Ther i s k f r eei nt er es tr at ei s4% andt he e xpec t edr et ur nont hemar k etpor t f ol i oi s12%.Whati st hepr oj ec t ' sNPV?
)-.
Birst calculate the required rate of return +assumin9 the expansion assets bear the same level of ris1 as historical assets*: r 2 r f r 2
β+r m 3 r f *
(.(, @)., × +(.)/ 3 (.(,* 2 (.)5/ 2 )5./=
The use this to discount future cash flowsO !" 2 7/5./'
ear 0 1 2 3 4 5 6 ! 8 9
Cas# $%o&
Discount $actor 100 15 15 15 15 15 15 15 15 15
1 0868 0!54 0654 0568 0493 0428 03!1 0322 0280
P 10000 1302 1130 981 852 !39 642 55! 484 420
/, a.odabasi 3 4As 6/
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10
15
.P
0243
364 2529
Ch $ C%S& %F CAPI&A' Thi nkf oramomentwhatt hec os tofc api t al f orapr oj ec tmeans .I ti st her at eofr et ur nt hat s har ehol der scoul dex pec tt oear ni ft heyi nv es t edi nequal l yr i s kys ec ur i t i es .Soonewayt o es t i mat et hec os tofc api t al i st ofi nds ec ur i t i est hathav et hes amer i s kast hepr oj ec tand t henes t i mat et heex pec t edr at eofr et ur nont hes es ec ur i t i es .
11. Cos tofc api t a l Th et o t a lma r k e tv a l u eo ft h ec o mmo ns t o c ko ft h eOk e f e no k eeRe al Es t at eCompanyi s$6mi l l i on,andt het ot al v al ueofi t sdebti s$4mi l l i on.Thet r eas ur er es t i mat est hatt hebet aoft hes t oc ki scur r ent l y1. 5andt hatt hee xpec t edr i s kpr emi um ont hemar k e ti s6%.TheT r eas ur ybi l l r at ei s4%.As s umef ors i mpl i c i t yt hatOk ef enok e e debti sr i s k f r eeandt hecompan ydoesno tpa yt ax .
a . Wh ati st h er e qu i r e dr e t u r no nOk e f e no k ees t o c k ? b . Es t i ma t et h ec o mp an yc o s to fc a pi t a l . c . Wh ati st h ed i s c ou ntr a t ef o ranex pan s i onoft heco mp an y ' spr e sen tb us i n es s ? d.Su ppo set h ec omp an ywa nt st od i v e r s i f yi nt ot h ema nuf a ct u r eo fr os ec ol o r ed s pec t ac l es .Thebet aofunl e ver agedopt i c almanuf ac t ur er si s1. 2.Es t i mat et he r equ i r edr e t ur nonOk e f e nok e e' sne wv e nt u r e.
)). a.
r equity 2 r f
r assets b. r assets 2
β × +r m 3 r f* 2 (.(, +).5 × (.(8* 2 (.) 2 )=.
H G &, million &8 million × (.) = r debt + r equity = × (.(, + " " &)( million &)( million
.
(.(', 2 '.,=.
c.
The cost of capital depends on the ris1 of the project bein9 evaluated. If the ris1 of the project is similar to the ris1 of the other assets of the company# then the appropriate rate of return is the company cost of capital. Eere# the appropriate discount rate is '.,=.
d.
r equity 2 r f
β × +r m 3 r f* 2 (.(, +)./ × (.(8* 2 (.))/ 2 ))./=.
/5 a.odabasi 3 4As 6/
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r assets
H G &, million &8 million × (.))/ = r debt + r equity = × (.(, + " " &)( million &)( million
.
r assets 2
(.(%/ 2 %./=.
14. Companycostofcapi t al Youar egi v ent hef ol l owi ngi nf or mat i onf orGol denFl eec e Fi nanc i al :
Cal c ul at eGol denFl eec e' scompan yc os tofc api t al .I gnor et ax e s.
),.
The total mar1et value of outstandin9 debt is &((#(((. The cost of debt capital is %=. Bor the common stoc1# the outstandin9 mar1et value is: &5( × )(#((( 2 &5((#(((. The cost of equity capital is )5=. Thus# Nolden BleeceMs company cost of capital is:
r assets r assets 2
((#((( 5((#((( = × + (.(% ((#((( + 5((#((( × (.)5 ((#((( 5((#((( +
(.)/, 2 )/.,=
/8 a.odabasi 3 4As 6/
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