CAPITAL BUDGETING – THEORIES
1. The account accountng ng area in in hich !he !he on"# on"# o$%ect&e o$%ect&e o' (e)recia (e)reciaton ton accountn accountng g re"a!e* re"a!e* !o !he !he e+ec! e+ec! o' (e)reciaton charge* u)on !a, )a#-en!* i* a. Ca)i Ca)i!!a" $u(g $u(get etng ng $. Co*! Co*! &o" &o"uu-e e )ro )ro!! ana"# ana"#*i *i** c. Inco Inco-e -e (e! (e!er er-i -ina nato ton n (. Re*) Re*)on on*i *i$i $i"i "i!# !# acco accoun untn tng g A /. The -e!ho( -e!ho( o' )ro%ec! )ro%ec! *e"ecton *e"ecton hich hich con*i(er* con*i(er* !he t-e t-e &a"ue o' -one# -one# in a ca)i!a" ca)i!a" $u(getn $u(getng g (eci*ion i* acco-)"i*he( $# co-)utng !he a. Accountng Accountng ra!e ra!e o' re!urn re!urn on a&erag a&erage e in&e* in&e*!-en! !-en! $. Accountng Accountng ra!e ra!e o' re!urn re!urn inita" inita" in&e*!-e in&e*!-en! n! c. Di*c Di*cou oun n!e( !e( ca* ca*h h 0o 0o (. Pa#$ac #$ac )eri )erio( o( C 2. 3or a )ro%ec! )ro%ec! *uch a* a )"an! )"an! in&e* in&e*!-en! !-en!44 !he re!urn !ha! !ha! *hou"( *hou"( "ea&e "ea&e !he -are! -are! )rice o' !he r-5* r-5* *!oc unchange( i* non a* !he a. Co* Co*! o' o' ca) ca)i! i!a" a" $. Ne! Ne! )r )re*en e*en!! &a" &a"ue ue c. Pa#$ac #$ac )eri erio( (. Di*c Di*cou oun! n!e( e( ra! ra!e e o' re! re!ur urn n A 6. 7hich o' !he 'o""oing 'o""oing ca)i!a" ca)i!a" e,)en(i!u e,)en(i!ure re )"anning )"anning an( con!ro" con!ro" !echni8ue* !echni8ue* ha* $een critci9e( critci9e( $ecau*e4 i! -igh! -i*!aen"# i-)"# !he earning* are rein&e*!e( a! !he ra!e o' re!urn earne( $# !he in&e*!-en!: a. Pa#$ac #$ac )er )eriio( $. Acco Accoun untn tng g ra! ra!e e o' re! re!ur urn n c. Ne! Ne! )re )re*e *en! n! &a"ue a"ue -e!h -e!ho( o( (. Ti-e Ti-e a(%u a(%u*! *!e( e( ra! ra!e e o' re!ur re!urn n D ;. 7hich o' !he 'o""oing 'o""oing ca)i!a" ca)i!a" e,)en(i!u e,)en(i!ure re )"anning )"anning an( con!ro" con!ro" !echni8ue* !echni8ue* ha* $een critci9e( critci9e( $ecau*e i! 'ai"* !o con*i(er in&e*!-en! )ro!a$i"i!#: )ro!a$i"i!#: a. Pa#$ac #$ac -e! -e!h ho( $. Acco Accoun untn tng g ra! ra!e e o' re! re!ur urn n c. Ne! Ne! )re )re*e *en! n! &a"ue a"ue -e!h -e!ho( o( (. Ti-e Ti-e a(%u a(%u*! *!e( e( ra! ra!e e o' re!ur re!urn n A
<. An a(&an!ag a(&an!age e o' u*ing )a#$ac )a#$ac -e!ho( -e!ho( o' e&a"uatng e&a"uatng ca)i!a" ca)i!a" $u(getn $u(getng g a"!ernat&e a"!ernat&e** i* !ha! )a#$ac i* a. Preci* Preci*e e in e*t-a e*t-a!e* !e* o' o' )ro! )ro!a$i a$i"i! "i!# # $. Ea*# a*# !o a))" a))"# # c. Ba*e Ba*e( ( on on non non=c =ca* a*h h 0o 0o (a!a (a!a
(. In*en*it&e !o !he "e o' !he )ro%ec!>*? con*i(ere( B @. The -ini-u- re!urn !ha! a )ro%ec! -u*! earn 'or a co-)an# in or(er "ea&e !he &a"ue o' !he
.
.
co-)an# unchange( i* !he a. Curren! $orroing ra!e $. Di*coun! ra!e c. Co*! o' ca)i!a" (. Ca)i!a"i9aton ra!e C The eigh!e( a&erage co*! o' ca)i!a" a))roach !o (eci*ion -aing i* no! (irec!"# a+ec!e( $# !he a. a"ue o' !he co--on *!oc $. Curren! $u(ge! !on e,)an*ion c. Co*! o' (e$! ou!*!an(ing (. Pro)o*e( -i, o' (e$!4 e8ui!#4 an( e,i*tng 'un(* u*e( B I' !he *u- o' !he )re*en! &a"ue* o' a"" 'u!ure ca*h 0o* re"a!e( !o )ro)o*e( ca)i!a" e,)en(i!ure
(i*coun!e( a! !he co-)an#5* co*! o' ca)i!a" i* )o*it&e4 i! in(ica!e* !ha! !he a. Re*u"!an! a-oun! i* !he -a,i-u- !ha! *hou"( $e )ai( 'or !he a**e! $. Re!urn on !he in&e*!-en! e,cee(* !he co-)an#5* co*! o' ca)i!a" c. In&e*!-en! i* !he ne*! a"!ernat&e (. Di*coun! ra!e u*e( i* !he )ro)er co*! o' ca)i!a" B 1. In or(er 'or a )ro%ec! !o $e acce)!a$"e !o a co-)an# u*ing !he co*! o' ca)i!a" -e!ho( o' ana"#*i*4 !he re!urn on in&e*!e( ca)i!a" -u*! a. A! "ea*! e8ua" !he a-oun! o' ca*h !o co&er in!ere*!* an( )rinci)a" )a#-en!* 'or an# (e$! o$!aine( !o nance !he )ro%ec! $. Genera!e *ucien! ca)i!a" !o )a# 'or i!*e"' i!hin !he econo-ic "i'e o' !he a**e!* co--iFe( !o !he )ro%ec! c. A! "ea*! e8ua" !o !he re!urn on in&e*!e( ca)i!a" curren!"# $eing genera!e( $# !he co-)an# (. Genera!e *ucien! ca)i!a" re*ource* !o %u*t'# an# a((itona" ca)i!a" e,)en(i!ure* an( re(uce i("e ca)aci!# i!hin !he co-)an#.
C
11. 7ha! ca)i!a" $u(getng -e!ho( a**u-e* !ha! 'un(* are rein&e*!e( a! !he co-)an#5* co*! o' ca)i!a": a. Pa#$ac -e!ho( $. Accountng ra!e o' re!urn c. Ne! )re*en! &a"ue -e!ho( (. Ti-e a(%u*!e( ra!e o' re!urn C 1/. 7hich ca)i!a" $u(getng -e!ho(* re8uire !he u*e o' )re*en! &a"ue !a$"e: a. Ne! )re*en! &a"ue an( Ti-e a(%u*!e( ra!e o' re!urn $. Pa#$ac an( Accountng ra!e o' re!urn
c. Accountng ra!e o' re!urn an( Ti-e a(%u*!e( ra!e o' re!urn (. Accountng ra!e o' re!urn an( Ti-e a(%u*!e( ra!e o' re!urn an( )a#$ac -e!ho( A 12. 7hich o' !he 'o""oing $e*! i(ente* !he rea*on 'or u*ing )ro$a$i"ite* in ca)i!a" $u(getng
16.
1;.
(eci*ion*: a. Uncer!ain!# $. Co*! o' ca)i!a" c. Ti-e &a"ue o' -one# (. Pro%ec!* i!h une8ua" "i&e* A The ne! )re*en! &a"ue o' a )ro)o*e( )ro%ec! re)re*en!* !he a. Ca*h 0o "e** !he )re*en! &a"ue o' !he ca*h 0o* $. Ca*h 0o "e** !he origina" in&e*!-en! c. Pre*en! &a"ue o' !he ca*h 0o* )"u* !he )re*en! &a"ue o' !he origina" in&e*!-en! (. Pre*en! &a"ue o' !he ca*h 0o* "e** origina" in&e*!-en! D The e+ect&ene** o' !he ne! )re*en! &a"ue4 -e!ho( ha* $een 8ue*tone( a* an e&a"uaton !echni8ue 'or ca)i!a" $u(getng (eci*ion* on !he $a*i* !ha! a. Pre(ictng 'u!ure ca*h 0o* i* oen (icu"! an( c"ou(e( i!h uncer!ainte* $. The accountng ra!e o' re!urn -e!ho( i* u*ua""# -ore accura!e an( u*e'u" c. The )a#$ac !echni8ue i* !heoretca""# -ore re"ia$"e (. The co-)u!aton in&o"&e* *o-e (icu"! -a!he-atca" a))"icaton* !ha! -o*! accoun!an!* canno! )er'or-
A 1<. The )a#$ac -e!ho( -ea*ure* a. Ho 8uic"# in&e*!-en! )e*o* -a# $e reco&ere( $. The ca*h 0o 'ro- an in&e*!-en! c. The econo-ic "i'e o' an in&e*!-en! (. The )ro!a$i"i!# o' an in&e*!-en! A
1@. A ca)i!a" $u(getng !echni8ue !ha! e,)"ici!"#4 incor)ora!e* an e*t-a!e( in!ere*! ra!e in!o i!* $a*ic co-)u!aton* i* !he a. Accountng $oo &a"ue -e!ho( $. Pa#$ac -e!ho( c. Ne! )re*en! &a"ue -e!ho( (. A&erage ra!e o' re!urn -e!ho( C 1. 7hen u*ing one o' !he (i*coun!e( ca*h 0o -e!ho(* !o e&a"ua!e !he (e*ira$i"i!# o' a ca)i!a" $u(getng )ro%ec!4 hich o' !he 'o""oing 'ac!or* genera""# i* no! i-)or!an!: a. The -e!ho( o' nancing !he )ro%ec! un(er con*i(eraton $. The t-e o' ca*h 0o* re"atng !o !he )ro%ec! c. The i-)ac! o' !he )ro%ec! on inco-e !a,e* !o $e )ai( (. The a-oun! o' ca*h 0o* re"atng !o !he )ro%ec! A
1. Sen*it&i!# ana"#*i* i* u*e( in ca)i!a" $u(getng !o 8uant'# !he a. A-oun! !ha! an a**u-e( 'ac!or u*e( in e&a"uatng a )ro%ec! cou"( $e &arie( an( *t"" )ro(uce acce)!a$"e re*u"!* $. Reacton i!hin !he -are!)"ace !o a ne )ro(uc! c. T#)e o' ca)i!a" !ha! i"" ha&e !o $e co--iFe( !o an antci)a!e( )ro%ec! (. Re"aton*hi) $e!een !he )a#$ac )erio( an( !he econo-ic "i&e* o' !he a**e!* u*e( in a )ro%ec! A /. Ho are !he 'o""oing u*e( in !he ca"cu"aton o' !he ne! )re*en! &a"ue o' a )ro)o*e( )ro%ec!:
Ignore inco-e !a, con*i(eraton* DEPRECIATION EPENSE SALAGE ALUE a. Inc"u(e inc"u(e $. Inc"u(e e,c"u(e c. E,c"u(e inc"u(e (. E,c"u(e e,c"u(e C /1. 7hich o' !he 'o""oing ca)i!a" $u(getng !echni8ue* re8uire !he u*e o' ca*h 0o* 'ro- )erio( !o )erio(: a. $. c. (.
INTERNAL RATE O3 RETURN e* e* No No
NP #e* no #e* no
A
//. 7hich o' !he 'o""oing i* nece**ar# in or(er !o ca"cu"a!e !he )a#$ac )erio( o' a )ro%ec!: a. U*e'u" "i'e $. Jini-u- (e*ire( ra!e o' re!urn c. Ne! )re*en! &a"ue (. Annua" ca*h 0o D /2. On ha! $a*i* i* !he co*! o' ca)i!a" (eri&e( 'ro- $on(* an( )re'erre( *!oc -ea*ure(4 re*)ect&e"#: a. Pre !a, ra!e o' in!ere*! 'or $on( an( *!a!e( annua" (i&i(en( ra!e "e** !he e,)ec!e( earning* )er *hare 'or )re'erre( *!oc $. Pre !a, ra!e o' in!ere*! 'or $on( an( *!a!e( annua" (i&i(en( 'or )re'erre( *!oc c. Aer !a, ra!e o' in!ere*! 'or $on(* an( *!a!e( annua" (i&i(en( ra!e "e** !he e,)ec!e( earning* )er *hare 'or )re'erre( *!oc (. Aer !a, ra!e o' in!ere*! 'or $on(* an( *!a!e( annua" (i&i(en( ra!e 'or )re'erre( *!oc D /6. On Ja# 14 /64 a co-)an# )urcha*e( a ne -achine !ha! i! (oe* no! ha&e !o )a# unt" Ja# 14 /1<. The !o!a" )a#-en! on Ja# 14 /<4 i"" inc"u(e $o!h )rinci)a" an( in!ere*!. A**u-ing
in!ere*! a! a 1K ra!e4 !he co*! o' !he -achine ou"( $e !he !o!a" )a#-en! -u"t)"ie( $# ha! t-e &a"ue o' -one# conce)!: a. 3u!ure a-oun! o' annui!# o' 1 $. 3u!ure a-oun! o' 1 c. Pre*en! &a"ue o' annui!# o' 1 (. Pre*en! &a"ue o' 1 D /;. On Ja# 14 /64 a co-)an# *o"( *o-e -achiner# !o ano!her co-)an#. The !o co-)anie* en!ere( in!o an in*!a""-en! *a"e* con!rac! a! a )re(e!er-ine( in!ere*! ra!e. The con!rac! re8uire( &e e8ua" annua" )a#-en!* i!h !he r*! )a#-en! (ue on Ja# 14 /6. 7ha! )re*en! &a"ue conce)! i* a))ro)ria!e 'or !hi* *i!uaton: a. Pre*en! &a"ue o' annui!# (ue o' 1 'or &e )erio(* $. Pre*en! &a"ue o' or(inar# annui!# o' 1 'or &e )erio(* c. 3u!ure a-oun! o' annui!# o' 1 'or &e )erio(* (. 3u!ure a-oun! o' 1 'or &e )erio(* A /<. I' inco-e !a, con*i(eraton* are ignore(4 ho i* (e)reciaton e,)en*e u*e( in !he 'o""oing ca)i!a" $u(getng !echni8ue*: INTERNAL RATE O3 RETURN PABAC a. E,c"u(e( e,c"u(e( $. E,c"u(e( inc"u(e( c. Inc"u(e( e,c"u(e( (. Inc"u(e( inc"u(e( A /@. I! i* a**u-e( !ha! ca*h 0o* are rein&e*!e( a! !he ra!e earne( $# !he in&e*!-en! in hich o' !he
/.
/.
'o""oing ca)i!a" $u(getng !echni8ue*: INTERNAL RATE O3 RETURN NP a. e* #e* $. e* No c. No No (. No e* B The (i*coun! ra!e >hur("e ra!e o' re!urn? -u*! $e (e!er-ine( a(&ance 'or !he a. In!erna" ra!e o' re!urn -e!ho( $. Ne! )re*en! &a"ue -e!ho( c. Pa#$ac )erio( -e!ho( (. Ti-e a(%u*!e( ra!e o' re!urn B The )re*en! &a"ue ca)i!a" $u(getng !echni8ue can $e u*e( hen ca*h 0o* 'ro- )erio( !o )erio( are
a. $. c. (. D
UNI3ORJ No No e* e*
UNEEN e* No No e*
2. I' inco-e !a, con*i(eraton* are ignore(4 ho i* (e)reciaton e,)en*e u*e( in !he 'o""oing ca)i!a" $u(getng !echni8ue*: INTERNAL RATE O3 RETURN a. E,c"u(e( $. E,c"u(e( c. Inc"u(e( (. Inc"u(e( A
NP e,c"u(e( inc"u(e( e,c"u(e( inc"u(e(
CAPITAL BUDGETING – PROBLEJS 1.i))ing Co-)an# in&e*!e( in an eigh! #ear )ro%ec!. I ! i* e,)ec!e( !ha! !he annua" ca*h 0o 'ro!he )ro%ec! ne! o' inco-e !a,e* i"" $e /4 . In'or-aton on )re*en! &a"ue 'ac!or* i* a* 'o""o*M Pre*en! &a"ue o' 1 a! 1/K 'or eigh! )erio(*
. 66
Pre*en! &a"ue o' an annui!# o' 1 in arrear* a! 1/K 'or eigh! )erio(*
6. <
A**u-ing !he i))ing $a*e( i!* in&e*!-en! (eci*ion on an in!ere*! ra!e o' 1/K4 ho -uch (i( !he )ro%ec! co*!: a.
<4
$. 4 2< c.
4
(. <64 <6
B.
)re*en! &a"ue o' ca*h 0o ne! o' inco-e !a,e*M >/4 , 6. <? 4 2< The co*! o' !he in&e*!-en! i* 4 2<
ITEJS / AND 2 ARE BASED ON THE 3OLLO7ING IN3ORJATIONM Han"e# co-)an# )urcha*e a -achine 'or1/;4 hich i"" $e (e)recia!e( on !he *!raigh! "ine $a*i* o&er a &e #ear )erio( i!h no *a"&age &a"ue. The re"a!e( ca*h 0o 'roo)eraton*4 ne! o' inco-e !a,e*4 i* e,)ec!e( !o $e 6;4 4 a #ear. A**u-e !ha! Han"e#5* e+ect&e inco-e !a, ra!e i* 6K 'or a"" #ear*. /.7ha! i* !he )a#$ac )erio(: a.
/. 1 #ear*
$. /. 2 #ear* c.
/. #ear*
(. 6. / #ear*
C.
Pa#$ac )erio(M >1/;4 ;#ear*?
/. #ear*
2.7ha! i* !he accountng >$oo &a"ue? ra!e o' re!urn on !he inita" increa*e in re8uire( in&e*!-en!: a.
1
$. /6K c.
/K
(. 2
A.
accountng ra!e o' re!urn 6;4 –>1/;4 ; #ear*? 1
6.On anuar# 14 /64 S!u( Co-)an# )urcha*e( a ne -achine 'or 14 i!h an e*t-a!e( u*e'u" "i'e o' &e #ear* an( no *a"&age &a"ue. 3or $oo an( !a, )ur)o*e*4 !he -achine i"" $e (e)recia!e( u*ing !he *!raigh! "ine -e!ho( an( i! i* e,)ec!e( !o )ro(uce annua" ca*h 0o 'roo)eraton*4 $e'ore inco-e !a,e*4 o' /64 . A**u-e !ha! S!u( u*e* a t-e a(%u*!e( ra!e o' 1/K an( !ha! i!* inco-e !a, ra!e i"" $e 6K 'or a"" #ear*. The )re*en! &a"ue o' 1 a! 1/K 'or &e )erio(* i* . ;@Q an( !he )re*en! &a"ue o' an or(inar# annui!# o' 1 a! 1/K 'or &e )erio(* i* 2. <1. The ne! )re*en! &a"ue o' !he -achine *hou"( $e a. 1;4 ;/ )o*it&e $. 1;4 ;/ negat&e c.
164 )o*it&e
(. 124 < negat&e
A.
annua" ca*h 0o $e'ore !a,e*
64
Le**M (e)reciaton M >14 ;?
/4
Ta,a$"e inco-e
/4
Inco-e !a, Annua" ca*h 0o aer !a,e*
64
, 6K
>4 ? 2/4
Pre*en! &a"ue o' ca*h 0o aer !a,e* >2/4 , 2. <1? 11;4 ;/ Inita" in&e*!-en!
14
Ne! )re*en! &a"ue= )o*it&e
1;4 ;/
;.Ha-i"!on Co-)an# in&e*!e( in a !o #ear )ro%ec! ha&ing an in!erna" ra!e o' re!urn o' 1/K. The )ro%ec! i* e,)ec!e( !o )ro(uce ca*h 0o 'ro- o)eraton*4 ne! o' inco-e !a,e*4 o' <4 in !he r*! #ear an( @4 in !he *econ( #ear. The )re*en! &a"ue o' 1 'or one )erio( a! 1/K i* .2 an( 'or !o )erio(* a! 1/K i* .@@. Ho -uch i"" $e !he )ro%ec! co*!: a.
124 <1
$. 14 2@ c.
11<4
(. 1//4 ;1
B.
!o!a" )re*en! &a"ue ><4 , .2? >@4 , .@@? 14 2@ The co*! o' !he )ro%ec! i* 14 2@ $a*e( on an in!erna" ra!e o' re!urn o' 1/K
<.7o-ac Co-)an# )urcha*e( a ne -achine on anuar# 14 /6 'or 4 i!h an e*t-a!e( u*e'u" "i'e o' &e #ear* an( a *a"&age &a"ue o' 14 . The -achine i"" $e (e)recia!e( u*ing !he *!raigh! "ine -e!ho(. The -achine i* e,)ec!e( !o )ro(uce ca*h 0o 'or- o)eraton*4 ne! o' inco-e !a,e*4 o' 2<4 a #ear in each o' !he ne,! &e #ear*. The )a#$ac )erio( ou"( $e a.
/./ #ear*
$. /. ; #ear*
c.
6. #ear*
(. 6. ; #ear*
B.
PABAC PERIOD 4 2<4 /.; #ear*
@.An oce e8ui)-en! re)re*en!at&e ha* a -achine 'or *a"e or "ea*e. I' #ou $u# !he -achine4 !he co*! a-oun!* !o @;4 <. I' #ou "ea*e !he -achine #ou i"" ha&e !o *ign a non cance""a$"e "ea*e an( -ae ; )a#-en!* o' /4 each. The r*! )a#-en! i"" $e )ai( on !he r*! (a# o' !he "ea*e. A! !he t-e o' !he "a*! )a#-en! #ou i"" recei&e t!"e !o !he -achine. The )re*en! &a"ue o' an or(inar# annui!# o' 1 i* a* 'o""o*M PRESENT ALUES AT No. o' )erio(*
1K
1/K
1
1
.
.2
./
/
1. @2<
1.<
1. <;
2
/. 6@
/. 6/
/. /6<
6
2. 1@
2. 2@
/. 1
;
2. @1
2. <;
2. /@6
The in!ere*! ra!e i-)"ici! in !hi* "ea*e i* a))ro,i-a!e"# a.
1K
$. 1/K c.
Be!een 1K an( 1/K
(. 1
D.
Annui!# >)a#$ac? 'ac!orM @;4 < /4 2. @ The )ro$"e- i* $a*e( on annui!# (ue $ecau*e !he r*! )a#-en! i* -a(e a! !he 1*! (a#. 3ac!or 2. @ 'or &e )a#-en!* i* $a*e( on or(inar# annui!#. To con&er! or(inar# annui!# !o annui!# >(ue in a(&ance?4 !ae one )erio( "e** an( a(( 1. . A! 1
ITEJS AND ARE BASED ON THE 3OLLO7ING IN3ORJATIONM 3"e-ing inc. i* )"anning !o ac8uire a ne -achine a! a !o!a" co*! o' 2<4 . The e*t-a!e( "i'e o' !he -achine i* *i, #ear* i!h no *a"&age &a"ue. The *!raigh! "ine -e!ho( o' (e)reciaton i"" $e u*e(. 3"e-ing e*t-a!e* !ha! !he annua" ca*h 0o 'ro- o)eraton*4 $e'ore inco-e !a,e*4 'rou*ing !hi* -achine a-oun!* !o 4 . A**u-e !ha! 3"e-ing5* co*! o' ca)i!a" i* K an( !he inco-e !a, ra!e i* 6K. The )re*en! &a"ue o' 1 a! K 'or *i, #ear* i* . <2. The )re*en! &a"ue o' an annui!# o' 1 in arrear* a! K 'or *i, #ear* i* 6.
B.
6 #ear*
$.
6. < #ear*
c.
;. @ #ear
(.
<.@ #ear
annua" ca*h 0o $e'ore !a,e*
4
4
Le**M (e)reciaton M >14 ;?
<4
Ta,a$"e inco-e
24
Inco-e !a,
, 6K
>1/4 ?
Annua" ca*h 0o aer !a,e*
@4
Pa#$ac )erio( 2<4 @4
6. < #ear*
. 7ha! ou"( $e !he ne! )re*en! &a"ue:
a.
;
$.
;<4 @
c.
14
(.
1214 6
A.
)re*en! &a"ue o' ca*h 0o aer !a,e*M >@4 , 6.
2<4
Ne! )re*en! &a"ue 1.
2<4 ; ;
Ro*a Co-)an# i* )"anning !o in&e*! 64 in a !hree #ear )ro%ec!. Ro*a5* e,)ec!e( ra!e
o' re!urn i* 1K. The )re*en! &a"ue o' 1 a! 1K 'or one #ear i* .4 'or !o #ear* i* ./<4 an( !he !hree #ear* i* .@;1. !he ca*h 0o4 ne! o' inco-e !a,e*4 i"" $e 1;4 'or !he r*! #ear >)re*en! &a"ue o' 124 <2;? an( 14 'or !he *econ( #ear >)re*en! &a"ue o' 164 <?. A**u-ing !he ra!e i* e,ac!"# 1K. 7ha! ou"( !he ca*h 0o4 ne! o' inco-e !a,e*4 $e 'or !he !hir( #ear: a. 4 <26 $. 114 c.
114 6@
(. 1;4 2
D.
co*! o' in&e*!-en!
64
Pre*en! &a"ue o' ca*h 0o*4 ne! o' !a,M #ear 1
124 <2;
ear / 164 <
11.
/4 ;2
Pre*en! &a"ue o' ca*h 0o* – #ear 2
114 6@
Pre*en! &a"ue o' 1 'or 2 #ear*
. @;1
Ca*h 0o4 ne! o' inco-e !a,e*= #ear 2
1;4 2
The enning* Co-)an# i* )"anning !o ac8uire a ne -achine. The )a#$ac )erio( i"" $e *i, #ear*. The ca*h 0o 'ro- o)eraton*4 ne! o' inco-e !a,e*4 i"" $e /4 a #ear 'or each o' !he r*! !hree #ear* o' !he )a#$ac )erio( an( 24 a #ear o' !he "a*! !hree #ear* o' !he )a#$ac )erio(. De)reciaton o' 1;4 a #ear i"" $e charge( !o inco-e 'or each o' !he *i, #ear* o' !he )a#$ac )erio(. Ho -uch i"" !he -achine co*!: a.
1;4
$. 1/4 c.
4
(. <4
A.
ca*h 0o4 ne! o' !a,M #ear 1=2 >/4 , 2? ear 6 =<
<4
>24 , 2?
Co*! o' -achine 1/.
4 1;4
The her$ Co-)an# ac8uire( a ne -achine 'or 1<4 4 hich i"" $e (e)recia!e( on a
*!raigh! "ine $a*i* o&er !en #ear )erio(. A 'u"" #ear 5* (e)reciaton a* !aen in !he #ear o' ac8ui*iton. The accountng >$oo &a"ue? ra!e o' re!urn i* e,)ec!e( !o $e 1/K on !he inita" increa*e in re8uire( in&e*!-en!. I' e a**u-e a uni'or- ca*h in0o4 !he annua" ca*h 0o 'ro- o)eraton*4 ne! o' inco-e !a,e*4 i"" $e a.
24 /
$. 1@4 / c.
14 /
(. 2;4 /
D.
accountng ra!e o' re!urn , – >1<4 1?
1/K
1<4 , – 1<4 14 / 2;4 / annua" ca*h 0o 12.
3i""-ore4 Inc. i* )"anning a )ro%ec! !ha! i"" co*! //4 . The annua" ca*h in0o ne! o' inco-e !a,e*4 i"" $e ;4 a #ear 'or *e&en #ear*. The )re*en! &a"ue o' 1 a! 1/K i* a* 'o""o*M PERIOD
P O3 P1 AT 1/K
1
.2
/
.@@
2
.@1/
6
.<2<
;
.;<@
<
.;@
@
.6;/
U*ing a ra!e o' re!urn o' 1/K4 ha! i* !he )re*en! &a"ue o' !he ca*h 0o genera!e( $# !hi* )ro%ec!: a.
//<4
$. //4 / c.
2614
(. 2;4
B.
)re*en! &a"ue o' ca*h 0o* ne! o' !a,M >;4 , 6. ;<6?
//4 /
>.2 . @@ .@1/ .<2< .;<@ .;@ .6;/? 6.;<6 16. Lu(ig Inc. )urcha*e( a ne -achine on anuar# 14 1 'or 2;4 . The -achine i* e,)ec!e( !o ha&e a u*e'u" "i'e o' #ear* an( no *a"&age &a"ue. S!raigh! "ine (e)reciaton i* !o $e u*e(. The )re*en! &a"ue o' !he ca*h 0o genera!e( $# !he -achine a* ca"cu"a!e( !o $e 2@14 1/ u*ing a
t-e a(%u*!e( ra!e o' re!urn o' 16K. The )re*en! &a"ue o' an or(inar# annui!# o' 1 in arrear* 'or )erio(* a! 16K i* 6. <2. The )re*en! &a"ue o' 1 'or )erio(* a! 16K i* . 2;1. 7ha! a* !he annua" ca*h 0o4 ne! o' inco-e !a,e*4 !ha! a* u*e( in ! he ca"cu"aton o' !he )re*en! &a"ue: a. 1//4 ; $.@;4 66@ c. 124 /<2 (. 4
D.
PRESENT ALUE O3 CASH 3LO7 AT 16K
2@14 1/
Pre*en! &a"ue o' an annui!# o' 1 'or )erio(*
6. <2
Annua" ca*h 0o
4
1;. Ja,e"" Co-)an# ha* an o))or!uni!# !o ac8uire a ne -achine !o re)"ace one o' i!* )re*en! -achine*. The ne -achine ou"( co*! 4 4 ha&e a &e #ear "i'e4 an( no E*t-a!e( *a"&age &a"ue. aria$"e o)eratng co*!* ou"( $e 14 )er #ear. The )re*en! -achine ha* a $oo &a"ue o' ;4 an( a re-aining "i'e o' &e #ear*. I!* (i*)o*a" &a"ue no i* ;4 $u! i! ou"( $e 9ero aer &e #ear*. aria$"e o)eratng co*!* ou"( $e 1/;4 )er #ear. Ignore )re*en! &a"ue ca"cu"aton* an( inco-e !a,e*. Con*i(ering !he &e #ear* in !o!a"4 ha! ou"( $e !he (i+erence in )ro! $e'ore inco-e !a,e* $# ac8uiring !he ne -achine a* o))o*e( !o re!aining !he )re*en! one:
D.
a. $. c. (. ne! co*! o' ne -achine >4 – ;4 ? O)eratng co*!*M >14 , ;? To!a" O)eratng co*!* o' o"( -achine >1/;4 , ;? Increa*e in )ro!
14 (ecrea*e 1;4 (ecrea*e 2;4 increa*e 64 increa*e ;4 ;4 ;;4
ITEJS 1< AND 1@ ARE BASED ON THE 3OLLO7ING IN3ORJATIONM He0in Inc. in&e*!e( in a -achine i!h a u*e'u" "i'e o' &e #ear* an( no *a"&age &a"ue. The -achine a* (e)recia!e( u*ing !he *!raigh! "ine -e!ho(. The annua" ca*h in0o 'roo)eraton*4 ne! o' inco-e !a,e*4 a-oun!* !o 14 . The )re*en! &a"ue o' an or(inar# annui!# o' 1 in arrear* 'or &e )erio(* a! 1/K i* 2. <;. The )re*en! &a"ue o' 1 'or &e )erio(* a* 1/K i* . ;<@. 1<. A**u-ing !ha! He0in u*e( a t-e a(%u*!e( ra!e o' re!urn o' 1/K4 ha! a* !he a-oun! o' !he origina" in&e*!-en!: a. $. c. (.
/24 ; 2<4 ; 664 ;<@4
1@.
B.
origina" in&e*!-en! M >14 , 2. <;?
2<4 ;
A**u-ing !ha! !he -ini-u- (e*ire( ra!e o' re!urn on !hi* in&e*!-en! a* 1/K an( !he a-oun! o' !he origina" in&e*!-en! a* 2;4 4 ha! ou"( $e !he ne! )re*en! &a"ue: a. $. 14 ; c. 14 (. ;4 <@ )re*en! &a"ue o' ca*h 0o*4 ne! o' !a,e* >14 , 2. <;? 2<4 ; B. Inita" in&e*!-en! 2;4 Ne! )re*en! &a"ue 14 ;
1.
Cora"4 Inc. recen!"# ac8uire( a -achine a! a co*! o' <64 . I! i"" $e (e)recia!e( on a *!raigh! "ine $a*i* o&er eigh! #ear* i!h no e*t-a!e( *a"&age &a"ue. Cora" e*t-a!e* !ha! !hi* -achine i"" )ro(uce annua" ne! ca*h 0o >$e'ore inco-e !a,e*? o' P14. A**u-ing an inco-e !a, ra!e o' ;K4 ha! i* !he a))ro,i-a!e )a#$ac )erio( on !hi* in&e*!-en!: a. 2.< #ear* $. 6. #ear* c. @.1 #ear* (.
B.
annua" ca*h 0o $e'ore !a,e*
14
Le**M (e)reciaton M ><64 ?
4
Ta,a$"e inco-e
14
Inco-e !a,
, ;K
Annua" ca*h 0o aer !a,e* Pa#$ac )erio( <64 124
1.
1/. #ear* 14
>;4 ? 124
6. #ear*
3ree(o- cor)oraton ac8uire( a ,e( a**e! a! a co*! o' P14. The e*t-a!e( "i'e a* 'our #ear* an( !here a* no e*t-a!e( *a"&age &a"ue. A**u-e a re"e&an! in!ere*! ra!e o' K an( an inco-e !a, ra!e o' 6K. The )re*en! &a"ue o' 1 a! K i* a* 'o""o*M No. o' )erio(* Pre*en! &a"ue No. o' )erio(* Pre*en! &a"ue 1 ./< 2 .@6 / .;@ 6 .@2; 7ha! i* !he )re*en! &a"ue o' !he !a, $ene!* re*u"tng 'ro- u*ing !he *u- o' !he #ear5* (igi!*
(e)reciaton a* o))o*e( !o *!raigh!="ine (e)reciaton on !hi* a**e!: a. $. 1 c. 1/@/ (. 21 C. ear *#( *."ine (i+erence !a, e+ec! 1 64 /;4 1;4 <4 / 24 /;4 ;4 /4 2 /4 /;4 >;4 ? >/4 ? 6 14 /;4 >1;4 ? ><4 ? TA BENE3ITS – SD DI33ERENCE 6K TA RATE
)& 'ac!or ./< .;@ . @6 .@2;
). &a"ue ;;;< 1@16 >14 ;? >64 61? 14 /@/
/.
George Co-)an# i* )"anning !o ac8uire a ne -achine a! a !o!a" co*! o' P2<44. The e*t-a!e( "i'e o' !he -achine i* < #ear* an( !he e*t-a!e( *a"&age &a"ue i* P<4.. George Co-)an# e*t-a!e* annua" ca*h *a&ing* 'ro- u*ing !hi* -achine i"" $e P4. A**u-e !he co-)an#5* co*! o' ca)i!a" i* K an( i!* inco-e !a, ra!e i* 6K. Pre*en! &a"ue o' 1 'or < #ear* i* .<2. !he )re*en! &a"ue o' an annui!# o' 1 in arrear* a! K 'or < #ear* i* 6.
D.
c.
P;64
annua" ca*h 0o $e'ore !a,e*
4
Le**M (e)reciaton M >2<4 – <4
;4
Ta,a$"e inco-e
24
Inco-e !a,
, 6K
Ca*h *a&ing* aer !a,e* /1.
(.
P<4 4
>1/4 ? <4
A**u-ing !he *a-e in'or-aton a* in no./4 i' !he annua" aer !a, ne! ca*h $ene!* o' in&e*!-en! ere P;4 ha! ou"( !he ne! )re*en! &a"ue o' !hi* in&e*!-en! $e: a. P@64; negat&e c. P@14@ )o*it&e $. P@14@ negat&e (. P@64; )o*it&e )re*en! &a"ue o' annua" ca*h *a&ing* >;4 , 6. <4 , .<2? 24 @ To!a" )re*en! &a"ue /264 2 Inita" in&e*!-en! 2<4 )re*en! &a"ue = negat&e >@14 @?
//.
A**u-ing !he *a-e in'or-aton in no./4 i' !he annua" aer !a, ne! ca*h $ene!* o' !he in&e*!-en! ere P;44 ha! ou"( $e !he )a#$ac )erio(: a. < #ear* $. <.1/ #ear* c. ;.; #ear* (. )a#$ac )erio( > 2<4 ;4 ? <. 1/ #ear* B.
/2.
6.6 #ear*
ar&i* Inc.4 a ca"en(ar #ear co-)an# 4 )urcha*e( a ne -achine 'or P/4 on anuar# 14 /6. The -achine ha* an e*t-a!e( u*e'u" "i'e o' #ear* i!h n o *a"&age &a"ue an( i* $eing (e)recia!e( u*ing !he *!raigh! "ine -e!ho(. The accountng >$oo &a"ue? ra!e o' re!urn i* e,)ec!e( !o $e 1;K on !he inita" increa*e in re8uire( in&e*!-en!. On !he a**u-)ton o' a uni'or- ca*h in0o4 !hi* in&e*!-en! i* e,)ec!e( !o )ro&i(e annua" ca*h 0o 'ro- o)eraton*4 ne! o' inco-e !a,e*4 o' a. 2;4 $. 64 /; c. 6/4 (. @@4 Accountng ra!e o' re!urn M , –> 4 ? 1;K D. /4 , – 2;4 6/4 , @@4 annua" ca*h 0o
/6.
Energ# co-)an# i* )"anning !o *)en( 64 'or a ne -achine hich i! i"" (e)recia!e on !he *!raigh! "ine $a*i* o&er !en #ear* i!h no *a"&age &a"ue. The re"a!e( ca*h 0o o)eraton*4 ne! o' inco-e !a,e*4 i* e,)ec!e( !o $e 14 a #ear 'or each o' !he r*! *i, #ear*4 an( 1/4 'or each o' !he ne,! 'our #ear* 7ha! i* !he )a#$ac )erio(: a. .6.6 #ear* $. @. < #ear* c. @. #ear* Ca*h 0o ne! o' !a,Q #ear 1=< >14 , 1/4 , /? E8ua" !o inita" in&e*!-en!
(. #ear* <4 /64 64
There'ore !he )a#$ac )erio( i* #ear* /;.
Hi""!o) Co-)an# in&e*!e( 14 in a !o #ear )ro%ec!. Hi""!o)5* e,)ec!e( ra!e o' re!urn a* 1/K. The ca*h 0o4 ne! o' inco-e !a,e*4 a* 64 'or !he r*! #ear. In'or-aton on )re*en! &a"ue an( 'u!ure &a"ue 'ac!or* i* a* 'o""o*M PRESENT ALUE PERIOD O3 1 AT 1/K 1 ./ / .@@/
3UTURE ALUE O3 1 AT 1/K 1.1/ 1./;66
A**u-ing !ha! !he ra!e ' re!urn a* e,ac!"# 1/K4 ha! a* !he ca*h 0o4 ne! o' inco-e
/<.
D.
!a,e*4 'or !he *econ( #ear o' !he )ro%ec!: a. ;14 /6@ $. ;4 c. <64 /6 (. 4 <2 inita" in&e*!-en! Pre*en! &a"ue o' ca*h 0o #ear 1>64 , ./? Pre*en! &a"ue o' ca*h 0o #ear / To con&er! !o 'u!ure &a"ue o' #ear / ca*h 0o Ca*h 0o – #ear 2
14 2;4 @1< <64 /6 , 1./;66 4 <2
The $rea( co-)an# i* )"anning !o )urcha*e a ne -achine !ha! i"" (e)recia!e on *!raigh! "ine $a*i* o&er a !en #ear )erio(. A 'u"" #ear5* (e)reciaton i"" $e !aen in !he #ear o' ac8ui*iton. The -achine i* e,)ec!e( !o )ro(uce ca*h 0o ne! o' inco-e !a,e* ' 24 in each o' !he !en #ear*. The accountng >$oo &a"ue? ra!e o' re!urn i* e,)ec!e( !o $e 1K on !he inita" increa*e in re8uire( in&e*!-en!. The co*! o' !he ne -achine i"" $e a. 1/4
$. 12;4 c. 1;4 (. 24 Co*! o' -achineM 24 – >, 1? 1K C. .1, 24 – >, 1? ./ , 24 /@.
, 1;4 co*! o' -achine
The Po"ar co-)an# i* )"anning !o )urcha*e a ne -achine 'or P24. The )a#$ac )erio( i* e,)ec!e( !o $e &e #ear*. The ne -achine i* e,)ec!e( !o )ro(uce ca*h 0o 'ro- o)eraton*4 ne! o' inco-e !a,e*4 o' P@4 a #ear in each o' !he ne,! !hree #ear* an( P;;4 in !he 'our!h #ear. De)reciaton o' P;4 a #ear i"" $e charge( !o inco-e 'or each o' !he &e #ear* o' !he )a#$ac )erio(. 7ha! i* !he a-oun! o' ca*h 0o 'ro- o)eraton*4 ne! o' !a,e*4 !ha! !he ne -achine i* e,)ec!e( !o )ro(uce in !he "a*! >h? #ear o' !he )a#$ac )erio(: a. P14 $. P2;4 c. P;4 (. B. inita" in&e*!-en! 24 Ca*h 0o*M #ear 1=2 >@4 , 2? /14 ear 6 ;;4 /<;4 CASH 3LO7 EAR ; 2;4
/.
P;4
SJ Su))"# i* con*i(ering !he )urcha*e o' a ne -achine. The e,)ec!e( aer !a, ca*h 0o* are "i*!e( a* 'o""o*M ear 1 / 2 6 ;
Ca*h 0o* aer !a,e* P/4 24 24 /4 14
I' SJ re8uire* a !arge! ra!e o' 1K on in&e*!-en! o' !hi* !#)e4 !he -a,i-u- SJ *hou"( )a# 'or !hi* -achine i* a. P114 $. P1/4 c. P<;4<< (. P@1466 D. ear P AT 1K CASH 3LO7S PRESENT ALUE 1 .6@ /4 1<4 6 / .@1 24 /14 ;6 2 .< 24 14 /@ 6 .;1< /4 14 2/ ; . 62< 14 64 2< SJ SHOULD PA @14 62 RE3ER TO PRESENT ALUE TABLEM
/.
Orien!a" Boo* i* con*i(ering !he )urcha*e o' a ne $in(ing e8ui)-en! !ha! i"" re(uce o)eratng co*!*. The co*! o' !he e8ui)-en! i"" $e P1@44 hich i"" $e (e)recia!e( *!raigh!="ine o&er &e=#ear* !o a 9ero *a"&age &a"ue. Sa"e* are e,)ec!e( !o increa*e P<;4 )er #ear4 i!h an e,)ec!e( ca*h 0o earning* $e'ore (e)reciaton an(4 !a,e**a"e* rato o' <K. The !a, ra!e i* 6K4 aer=!a, ca*h 0o* 'ro- !he )ro%ec! are e,)ec!e( !o $e a. P/;4 $. P1;4 c. P1;4 P/4
D.
annua" ca*h 0o $e'ore !a,e*><;4 <K?
14
Le**M (e)reciaton M >@4 ;?
4
Ta,a$"e inco-e
14
Inco-e !a,
, ;K
Annua" ca*h 0o aer !a,e*
2.
14
>;4 ? 124
The To) Co-)an# i* con*i(ering !o )urcha*e a ne !ruc !ha! i"" co*! P@4 an( i"" $e (e)recia!e( o&er &e #ear* . The ne !ruc i"" re)"ace ano!her !ha! ha* a $oo &a"ue o' P6;4 an( &e #ear* u*e'u" "i'e re-aining. The o"( !ruc can $e *o"( 'or P64. The curren! !a, ra!e i* 2;K. The ne! inita" in&e*!-en! 'or !he ne !ruc i* a. P24 $. P/;4 c.
P//4;
(.
P21@4;
