Luna, Jon Vincent Nico M. Engineering Economy/CPE-4!
Solved Problem
C"#P$E% 4 !. # Cor&oration 'old an i''ue o( )-year bond', *aving a total (ace value o( !,, (or +,,. $*e bond' bear intere't at !, &ayable 'emiannually. 'emiannually. $*e com&any i'*e' to e'tabli'* a 'in0ing (und (or retiring t*e bond i''ue and ill ma0e 'emiannual de&o'it t*at ill earn !), com&ounded 'emiannually. Com&ute t*e annual co't (or intere't and redem&tion o( t*e'e bond'. Solution1 23!,,
i 3 !) 3 r 3 ! 3 ) ) 5ntere't on t*e bond &er &eriod 3 2r 3 6!,,76.!73 !,,
# 3!,, 3 4,!.8 6!9.74-! . $otal $otal #nnual E:&en'e3 )64,!.879!,,3 !,;)+,)8.;!
). # com&any *a' i''ued !-year bond', it* (ace value o( !,, in !, unit'. 5ntere't at ! i' aid
8. # !,-bond *ic* ill mature in ! year' and it* a bond rate o( ! &ayable annually i' to be redeemed at &ar at t*e end o( t*i' &eriod. 5( it i' 'old no (or !,8+, determine t*e yield at t*i' &rice. >iven1 2 3 !, N 3 ! r 3 ! P 3 !,8+ Solution1 P3 2r6!-6!9i7 -!/i7 9 C6!9i7 !8+ 3 !+6.!7 6!-6!9i7 -!/i7 9 !6!9i7 3 .!6!7 .!6!7 3 !.
C*a&ter !. #n indu'trial engineer *a' de'igned to alternative met*od' (or accom&li'*ing a &roduction ?ob. @ot* met*od' involve t*e ac
Met*od @1
687687 9 6)76)7 3 !.) !-)
86)7 9 !6)7 3 !). -!
#n'er1 Met*od @ i' more economical. ). #n e:ecutive receive' an annual 'alary o( P, and *i' 'ecretary a 'alary o( P!,. # certain ta'0 can be &er(ormed by t*e e:ecutive or0ing alone in 4 *our'. 5( *e delegate' t*e ta'0 to *i' 'ecretary it ill re
#nnual Salary1 $ime to (ini'* t*e or01 #nnual Bor0ing *our'1
E:ecutive Bor0' , 4*r' 8,
Secretary Bor0' !, ),4
E:ecutive1 %ate &er *our1 6,&e'o'/yr7/68*r'/year7 6,&e'o'/yr7/68*r'/year7 3 ) &e'o'/*our Secretary1 %ate &er *our1 6!, &e'o'/yr7/6)4*r'/year7 &e'o'/yr7/6)4*r'/year7 3 ; &e'o'/*r E:ecutive Co't o( Per(orming t*e or0 ) &e'o'/*r64*r'7 3 &e'o' $otal $otal co't (or &er(orming t*e ta'0 6)&e'o'/*r76!.)*r'7 6)&e'o'/*r76!.)*r'7 9 4;. &e'o' 3 ;;. &e'o' #n'er1 ;;. &e'o' i' t*e co't (or &er(orming t*e '&eci(ic ta'0.
Secretary Co't o( Per(orming t*e or0 ;&e'o'/*r6.*r'73 4;. &e'o'.
8. # cement grinding mill #D it* a ca&acity o( ton' &er *our utilie' (orged 'teel grinding ball' co'ting P!), &er ton, *ic* *ave a ear rate o( ! gram' &er ton cement milled. #not*er cement mill @D o( t*e 'ame ca&acity u'e' *ig* c*rome 'teel grinding ball' co'ting P, &er ton it* a ear rate o( ) gram' &er ton cement milled. Aetermine t*e more economical grinding mill, con'idering ot*er (actor' to be t*e 'ame. Solution1 Mill # Mill @ Bear %ate1 !g6!ton/!g73.!ton )6!ton/!g73.)ton' Ca&acity1 ton' ton' Co't1 !) &e'o'/ton !) &e'o'/ton $otal $otal co't1 ton'6!) &e'o'/ton76 .!ton73 &e'o'/*r ton'6!) &e'o'/ton76.)73&e'o'/* &e'o'/ton76.)73&e'o'/*r r #n'er1 Mill @ i' more economical. 4. # cement cement 0iln it* &roduction ca&acity o( !8 ton' &er day 6)4 *our'7 o( clin0er *a' at it' burning one about 4 ton' o( magnetite c*rome bric0' being re&laced &eriodically, de&ending on 'ome o&erational (actor' and t*e li(e o( t*e bric0'. 5( locally &roduced bric0' co't' P), &er ton and *ave a li(e o( 4 mont*', *ile certain im&orted bric0' co'ting P8, &er ton and *ave a li(e o( mont*', determine t*e more economical bric0' and by *o muc*. Solution1 Co't1 Li(e1
Local @ric0' ), &e'o'/ton 4mont*'
5m&orted @ric0' 8,&e'o'/ton mont*'
Magnetite @ric0' &eriodically re&laced1 4ton' Co't o( local @ric0' &er mont* 6Local7
Co't o( @ric0' &er mont*65m&orted7
3 ),&e'o'/ton64ton7/4mont*' 3 )!,). &e'o'/mont*
38,&e'o'/ton64ton'7/mont*' 3 )), &e'o'/mont*
Saving'1 )!,)-)),3 ,) &e'o'/mont*. #n'er1 5m&orted @ric0' i' more economical. . # manu(acturer *a' been '*i&&ing *i' &roduct 6moderately *eavy mac*ine'7, mounted only on '0id' it*out com&lete crating. $o avoid crating *e mu't '*i& in (reig*t car' *ic* contain only *i' mac*ine'. $o do t*i' *e mu't &ay (reig*t on a car ca&acity load o( 4) ton' regardle'' o( *et*er or not t*e car i' com&letely (ull. 5n t*e &a't *e actually *a' '*ied only 8 ton' in eac* car. $*e car load (reig*t rate i' P4.! &er *undred &ound'. 5( t*e mac*ine' are crated 'o t*at t*ey can be '*ied in mi:ed car lot', along it* ot*er merc*andi'e, t*ey can be '*ied at a rate o( P4.) &er *undred &ound' it* t*e (reig*t bill com&uted only on t*e actual eig*t '*ied. $*e co't o( crating ould be P). &er mac*ine and ould increa'e t*e '*i&&ing eig*t (rom !,)- !)) &ound' &er mac*ine. B*ic* &rocedure '*ould be (olloed= 6! ton3 ),) lb'.7 Solution1 Crating1
B/o crating 64.!&e'o'/!lb'764)ton'76))lb'/ton7 3 8,;.4 &e'o'
B/crating No. o( mac*ine' to be '*i&&ed1 '*i&&ed1 8ton'6))lb'/ton7/!) 8ton'6))lb'/ton7/!)lb'3 lb'3 mac*ine' 5ncrea'e on Beig*t1 mac*ine'6!))lb'/mac*ine' F !)lb'/mac*ine73 !!lb' $otal co't it* crating Co't o( '*i&ment 3 co't o( crating Co't o( '*i&ment3 4.)&e'o'/!lb'68ton'76))lb'/to 4.)&e'o'/!lb'68ton'76))lb'/ton76!! n76!!lb'73 lb'73 )!.) &e'o' Co't o( Crating3 ) &e'o'/mac*ine6mac*ine'73 &e'o'/mac*ine6mac*ine'73 !8; &e'o'. $otal co't / crating3 )!.)9!8;3 4!+8.) &e'o' $otal $otal co't /o crating3 4!+8.)&e'o'-8,;.4 &e'o'3 44. &e'o' #n'er. S*i&&ing Bit*out Bit*out Crating i' more economical. . # mac*ine u'ed (or cutting material' in a (actory *a' t*e (olloing out&ut' &er *our at variou' 'eed' and re
C*a&ter -! # young mec*anical mec*anical engineer engineer i' con'ideri con'idering ng e'tabli' e'tabli'*ing *ing *i' on 'mall com&any com&any.. #n inve'tment inve'tment o( P4, ill be re
!, &e'o'/&er year ), &e'o'/&er year 4, 9! o( 'ale' &er year , &e'o'
$*e man ill give u *i' regular ?ob &aying P)!, &er year and devote (ull time to t*e o&eration o( t*e bu'ine''H t*i' ill re'ult in decrea'ing labor co't by P4, &er year, material co't by P), &er year and over*ead co't by P8), &er year. 5( t*e man e:&ect' to earn at lea't ) o( *i' ca&ital, '*ould *e inve't= Solution1 Com&ute (or t*e de&reciation value, 67/66!.)7!-!7/.) 67/66!.)7!-!7/.) 3P!!,!.+; 3P!!,!.+; Material'1 Labor1 Gver*ead1 Selling e:&en'e1 Sala Salary ry t*at t*at *e ill ill give give you1 ou1 Ae&reciation Ae&recia tion Value1 Value1 $otal #nnual Co't1
P!, F P), 3 P!8), P), F P4, 3 P)4, P!), F P8), 3 P, P, P)! P)!, , P!!,!.+; P!!,!.+ ; ;4;,!.+;
>etting t*e #nnual &ro(it1 , F ;4;,!.+; 3 ),+4.84!8 Com&uting t*e %ate o( %eturn1 6),+4.84!8/,76!7 6),+4.84!8/,76!7 3 .!! #n'er1 $*ere(ore, t*e man '*ould not inve't in t*e bu'ine''. -) $*e #@C com&any i' con'idering con'tructing a &lant to manu(acture a &ro&o'ed ne &roduct. $*e land co't' P!,,, t*e building co't' P8,,, t*e eiven1 #t t*e end o( !) year' Land !,,.&e'o' ),,. &e'o' @uilding 8,,. &e'o' !),,. &e'o' E
3 68,,-!,,7/6!.) 68,,-!,,7/6!.) !)-!7/.)7 6!),,-),7/6!.) 6!),,-),7/6!.) !)-!7/.)7 9 )8,;, 3 )4,8.8+.)! &e'o' Net #nnual #nnual Pro(it 3 #nnual #nnual Co't6a&&reciated Co't6a&&reciated - de&reciated7 3 !4,4;.;; 9 I - )4,8.8+.)! )4,8.8+.)! %ate G( %eturn1 Net #nnual &ro(it/ca&ital &ro(it/ca&ital inve'ted )3 6!4,4;.;; 9 I - )4,8.8+.)!7/),, I3 8+,;4,8.48 8+,;4,8.48 &e'o' 8 # man man (ormerly em&loyed e m&loyed a' c*ie( mec*anic o( an automobile re&air '*o& *a' 'aved P!,,. *ic* are no inve'ted in certain 'ecuritie' giving *im an annual dividend o( !. "e no &lan' to inve't t*i' amount in *i' on re&air '*o&. 5n *i' re'ent ?ob, *e i' earning P),. a mont*, but *e *a' to re'ign to run *i' on bu'ine''. "e ill need t*e 'ervice' o( t*e (olloing1 ) mec*anic' eac* earning P4. a day, and *el&er' eac* earning P). a day. $*e'e men ill or0 on t*e average 8 day' &er year. "i' ot*er e:&en'e' are t*e (olloing1 %ental Mi'cellaneou' Sale' ta: 5n'urance
P8,. a mont* P),. a mont* 8 o( gro'' income )
$*e lengt* o( *i' lea'e i' year'. 5( t*e average c*arge (or eac* car re&aired by *i' '*o& i' P!,.. Aetermine t*e number o( car' *e mu't 'ervice in one year 'o t*at *e ill obtain a &ro(it o( at lea't ) on *i' inve'tment= 2ind1 Number o( car' *e mu't 'ervice in one year N 3 year' %ental Mi'cellaneou' Sale' ta: 5n'urance ) mec*anic' *el&er'
5 3 ) P8,. a mont* P),. a mont* 8 o( gro'' income ) P4/day P)/day
Solution1 2ir't, com&ute (or t*e annual co'tH #nnual #nnual Co't3 Co't3 !)6P8, !)6P8,79 79 !)6P), !)6P),79 79.86> .86>ro'' ro''79.) 79.)6P!, 6P!,, ,79) 79)647 64768 68day' day'77 96)768day'79!,,/662/#, 96)768day'79!,,/662/#, !, 779!)6),7 #nnual #nnual Co't Co't3 3
P)48 P)48!. !.) )9 9.8 .86>r 6>ro'' o''77
$*en, (or t*e Net #nnual &ro(it and t*e >ro'' 5ncome i'H Net #nnual #nnual &ro(it3P!,,.6)7 &ro(it3P!,,.6)7 3P),. >ro'' 5ncome3 P),4,8!.)/6!-.87 P),4,8!.)/6!-.87 3P),!!!,.! $o com&ute (or t*e number o( car', 'im&ly divide t*e >ro'' 5ncome to t*e average c*arge o( eac* re&aired car. $*u', Number o( Car'3P),!!!,.!/! Car'3P),!!!,.!/!,. ,. 3)!!!. or )!!) car'
# (irm i' c*arged P! &er ton (or *auling it' ra material' by a truc0ing com&any. 2orty ton' &er day are *auled (or 8 day' a year. 5t i' de'ired to in'tall a railay 'y'tem *ic* ould bring don t*e co't o( *auling to P. &er ton. Maintenance co't o( t*i' i' P!), &er mont*. $a: i' !. #verage #verage rate i( earning i' ). a. 5( t*e com&any *a' t*e ca'* nece''ary (or t*e in'tallation, ould you recommend t*e c*ange= b. 5( t*e com&any *a' to (loat P,, ort* o( noncallable bond' at ! t*at ill mature in ! year' to *ave t*e ca&ital (or t*e &ro?ect, ould you recommend t*e c*ange= Solution1 a.
Ca'e !1 !ton'/&e'o' 4ton'/day 8day'/year $otal co't 3 6!:8:47 &*&/year 3 !,, &*&/year Ca'e )1 "auling 3 64:8:.7 3 ;+,) &*&/year Maintenance 36.!),:!)7 36.!),:!)7 3 !44, &*&/year &*&/year $a: 3 6.!:,,7 3 , &*&/year Ae&reciation 3 ,,/66!.! !-!7/.!7 3 )4,).8! &*&/year $otal Co't 3 !+,4.8! &*&/year #nnual Net Saving' 3 Ca'e ! F ca'e ) 3 !,, F !+,4.8! 3 !,),8+.+ &*&/year %G% 3 !,),8+.+/,, !,),8+.+/,, 3 .)!6!7 3 ).! #n'er1 $*e inve'tment i' Ju'ti(ied.
b. #3 ,,/6!-6!.!!7/.!7 3 ++,!.8! &*& "auling 3 64:8:.7 3 ;+,) &*&/year Maintenance 36.!),:!)7 36.!),:!)7 3 !44, &*&/year &*&/year $a: 3 6.!:,,7 3 , &*&/year #nnual Net Saving' 3 !,, F !,8+,8.8! 3 8,8+.; &*& %G% 3 8,8+.;/,, 3 .!!6!7 3 !.! #n'er1 $*e inve'tment i' not Ju'ti(ied.. # (ood &roce''ing &lant con'umed , 0B o( electric energy annually and &ay' an average o( P). &er 0B*. # 'tudy i' being made to generate it' on &oer to 'u&&ly t*e &lant t*e energy re
b. Gt*er e:&en'e' 3 !, !, &*& c. $a: $a: and and in'uran in'urance ce 3 ),, ),, : . . 3 !),& !),&*& *& ! d. Ae&rec Ae&reciat iation ion 3 6),, 6),,-) ), ,7/ 7/ 66!.! 66!.! -!7/.!7 3 8;,8.+4; &*&. #nnual net 'aving' 3 !,), F !,;,8.+ 3 !4),!+.8) &*& %G% 3 !4),!+.8)/),, 3 .;!6!7 3 ;.! #n'er1 $*e &oer &lant i' a good inve'tment # (i:ed ca&ital inve'tment o( P!, ,. i' reiven1 2i:ed Ca&ital Bor0 Ca&ital #nnu #nnual al Ae&r Ae&rec ecia iati tion on #nnual &ro(it
3 P!,,. 3 P),,. 3 P!, P!, , , . . 3 P),,.
Solution1 %ate o( %eturn 3 6#nnual 6#nnual Pro(it-#nnual Pro(it-#nnual Ae&reciation7/62i:ed Ae&reciation7/62i:ed Ca&ita9 Bor0 Bor0 ca&ital7 3 6P),,-P!,,.7/6P!,,. 6P),,-P!,,.7/6P!,,.9P),,.7 9P),,.7 3!). Payout Payout &eriod &eriod 3 !),, !),, . ./) /), ,, ,. . 3 4. year' #n'er1 !). and 4. year'
C*a&ter ; !. #n oil com&any i' being o((ered a '&ecial coating (or t*e ga'oline underground tan0 in'tallation in it' 'ervice 'tation' *ic* ill increa'e t*e li(e o( t*e tan0 (rom t*e u'ual ! year' to ! year'. $*e co't o( t*e '&ecial coating ill increa'e t*e co't o( t*e 4,-tan0 to ,. Co't o( in'tallation (or eit*er o( t*e tan0' i' P)4,. 5( t*e 'alvage value (or bot* i' ero, and intere't rate i' ), ould you recommend t*e u'e o( t*e '&ecial coating=
5ntere't rate 3 ) Solution1 Mac*ine /o coating1 Ae&reciation1 4,/6!.) !-!7/.) 3 !8!.4&*& Mac*ine / coating Ae&reciation1 ),/6!.) !-!7/.) 3 ;. &*& %G% 3 !8!.4 - ;./ ,-4, 3 .8 K ) #n'er 1 S&ecial coating '*ould not be u'e. ). #n electric coo&erative i' con'idering t*e u'e o( a concrete electric &ole in t*e e:&an'ion o( it' &oer di'tribution line'. # concrete &ole co't' !, eac* and ill la't ) year'. $*e com&any i' &re'ently u'ing creo'oted ooden &ole' *ic* co't !), &er &ole and ill la't ! year'. 5( money i' ort* !) &ercent, *ic* ole '*ould be u'ed= #''ume annual ta:e' amount to ! &ercent o( (ir't co't and ero 'alvage value in bot* ca'e'.
i 3 !) Solution1 Creo'oted Bood Pole' Ae&reciation1 !),/66!.!) !-!7/.!)7 #nnual $a:1 ),6.!7 $otal1 Concrete Pole Ae&reciation1 !,/66!.!) )-!7/.!)7 #nnual $a:1 !,6.!7
3 4&*& 3 !)&*& 3 4&*&
3 )&*& 3 !&*& 3 48&*& %G% 3 64-487/!,-!), 3 . .)8 #n'er1 Creo'oted Bood Pole' S*ould be u'ed.
8. 5t i' &ro&o'ed to &lace a cable on e:i'ting &ole line along t*e '*ore o( a la0e to connect to &oint' on o&&o'ite 'ide'. Land %oute Submarine %oute Lengt*/mile' ! 2ir't Co't/mile 4,&*& ,&*& #nnual Maintenance +&*& 8,&*& 5ntere't ! ! $a: 8 8 Net Salvage/mile !),&*& )),&*& Li(e/year' ! ! B*ic* i' more economical= Solution1 Land route Ae&reciation1 46!7-!)6!7/!.! 46!7-!)6!7/!.! !-!/.! 3 4+).;;+&*& Maintenance1 +6!7 3+,&*& $a:e'1 46!76.87 3!),&*& $otal 3 )+).;;+&*& Ae&reciation1 67-))67/!.! 67-))67/!.! !-!/ -!/.! .! Maintenance1 867 $a:e' 1 676.87 $otal 5ncome
3 8;;) ;;).8+ .8++ +&* &*& & 3 !;&*& 3 !).&*& 3 8!4;).8++&*& 8!4;).8++ &*&
%G% 3 8!4;).8++ - )+).;;+/46!7 F 67 3 .+6!7 3 .+ #n'er1 Submarine route i' more economical.
4. 5n a cold 'torage &lant, it i' de'ired to determine *et*er to u'e in'ulation to inc*e' t*ic0 or t*ree inc*e' in in'ulating t*e all' o( t*e cold 'torage are*ou'e. "eat ab'orbed t*roug* t*e all' it*out in'ulation ould co't P+. &er year &er '
Ball $*ic0ne'' Ball Bit*out in'ulation Bit*o Bit*out ut in'ula in'ulatio tion, n, &er m) "eat Lo'' 5ntere't on inve'tment Net Salvage value Li(e, year'
$o-inc*e' +. 8.4 8.4 + !
$*ree-inc*e' $*ree-inc *e' +. . . +) !
. 5n building t*eir &lant, t*e o((icer' o( t*e 5nternational Leat*er Com&any *ad t*e c*oice beteen alternative'1 Gne alternative i' to build in Metro Manila *ere t*e &lant ould co't P),,. Labor ould co't annually P!), and annual over*ead ould be 4,. $a:e' and in'urance ould total o( t*e (ir't co't o( t*e &lant. $*e 'econd alternative ould be to build in @ulacan a &lant co'ting P),),. Labor ould co't annually P!, and over*ead ould be P,. $a:e' $a:e' and in'urance ould be 8 o( t*e (ir't co't. $*e co't o( ra material' ould be t*e 'ame in neit*er &lant. 5( ca&ital mu't be recovered it*in ! year' and money i' ort* at lea't ), *ic* 'ite '*ould t*e o((icer' o( t*e com&any c*oo'e= Solution1 @y $*e %ate G( %eturn1 Metro Manila Plant Ae&reciation1 ),,6!.) !-!/.)7 3 ;;,4.!8&*& Labor1 3 !),&*& Gver*ead1 3 4,&*& $a:e' $a:e' and 5n'urance1 3 ),,6.7 3 !,&*& $otal #nnual Co't 3 88;,4.!&*& 88;,4. !&*& @ulacan Plant Ae&reciation1 ),),6!.) !-!/.)7 3 ,;.))+&*& Labor1 3 !,&*& Gver*ead1 3 ,&*& $a:e' $a:e' and 5n'urance1 3 ),),6.87 3 ;,&*& $otal #nnual Co't 3 8+,!;.))+&*& 8+,!;. ))+&*& #nnual Saving'1 88;,4.! - 8+,!;.))+ 3 );,+.8;!&*& #dditional 5nve'tment1 ),), - ),, 3 ),&*& %G%1 );,+,8;!/), 3 .!!!6!7 3 !!.! K ) #n'er1 t*e &lant '*ould be built in manila.
. # utility utility com&any i' con'idering t*e (olloing &lan' to &rovide a certain 'ervice re
Plan S #nnual co't 3 P4, #dditional annual co't a(ter year' 3 P, 9 P8,6.)7 3 P, Salvage value 3 P8,6.)7 9 P4,6.47 3 P)), Plan S 3 P8, 9 P4,6!-6!.!) -!7/.!7 F 4,6!.!) -!7 3 ),88;.4&*& ),88;.4&*& #n'er1 Since Plan S K Plan %, Plan S '*ould be c*o'en to &rovide t*e certain 'ervice.
C*a&ter
-!. $*e I com&any *a' to &lant' &roducing S&ecial'D. 5t *a' t*e (olloing e:&ected data (or t*e ne:t mont*O' o&eration'. Variable 6incremental7 co't' vary linearly (rom ero &roduction to ma:imum ca&acity &roduction.
a. &er(ormance *a' not been good, 'o t*e com&any e:&ect' to receive dome'tic order' (or only !,) unit' ne:t mont* at a rice o( !,4 &er unit. "o '*ould t*e &roduction be di'tributed beteen t*e &lant' (or o&timum economic oration= b. 5( t*e (riendly (oreign &oer &oer o((er' to buy 8 additional additional unit' at at !,! &er unit, '*ould '*ould t*e com&any acce&t t*e o((er= S*o t*e increment gain or lo''. Solution1 a. E:&ected order'3 !,) unit' Plant # !I3+, I3 + &er unit
Plant @ 3, 3 ! &er unit
$*ere(ore Plant # '*ould '*ould &roduce !, unit' and ) unit' (or Plant @.
b. 5ncrement %evenue (or 8 unit'1 unit'1 6876!,!7 3 8, 5ncrement co't1 Plant @ 86!7
3 8,
$*ere(ore, it* gain 8,, t*e com&any '*ould acce&t t*e o((er.
-). # com&any com&any *a' a ne &lant # and an old &lant @ in t*e 'ame metro&olitan area, eac* it* a ca&acity o( !) unit' o( &roduct &er mont*. 2i:ed e:&en'e at # i' 4, &er mont* and at @ are ), &er mont*. Variable Variable e:&en'e &er mont* at # i' !,:N), !,:N), *ere N 3 t*e number o( unit' &roduced. #t re'ent t*e 'ale' *ave been e'tabli'*ed at !4 unit' &er mont* it* eac* &lant &roducing ; unit'. S*ould t*e inter&lant load be redi'tributed= B*y= "o=
-8. #n a''et a' &urc*a'ed 'i: year' ago at a co't o( ;,. 5t a' e'timated to *ave a u'e(ul li(e o( ten year' it* a 'alvage value o( 8 at t*e end o( t*e time. 5t i' no o( no (uture u'e and can be 'old (or only . Aetermine t*e 'un0 co't i( t*e de&reciation *a' been com&uted by1 6a7 $*e 'traig*t-line met*od 6b7 $*e 'um-o(-t*e-yearO' digit' met*od Solution1 CG 3 ;,
CL 3 8
L3
6a7. d3 6;,-87/! 3 4,) C 3 Co F A 3 ;, F 4,) 3 ),+ Sun0 co't 3 boo0 value F re'ale value 3 ),+ F 3 ),!. 6b7. digit' 3 !9)9894999;99+9! !9)9894999;99+9! 3 A 3 / 6;, F 87 3 ,4!.) C3 ;, F ,4!.) 3 !,!.! Sun0 co't 3 !,!.! F 3 ;!.!
C*a&ter +
n 3 !
!. # reca&&ing reca&&ing &lant i' &lanning to ac
3 !),)4.! 3 !;,. 3!++,;4.!
%e&lacement #nnual co't'1 Ne generator 'et A3 !8,/6!.! !-!/.!7 Variable o&eration co't $otal annual co't
3 )),!!). 3 !,. !;),!!).
#nnual 'aving' 3 !++,;4.! F !;),!!). !;),!!). 3 );,;).! #dditional inve'tment inve'tment 3 !8, 9 !, F !;, 3 +,. %ate o( return on additional inve'tment 3 );,;).!/+, :! 3 ).)4 Since t*e rate o( return on additional inve'tment i' greater t*an t*e ort* o( money at ! rate o( return on additional additional inve'tment Q ort* ort* o( money ).)4 Q ! $*ere(ore it i' advi'able to buy t*e ne generating 'et. ). # com&any com&any t*at 'ell' *a' &ro&o'ed to a 'mall &ublic utility com&any t*at it &urc*a'e a 'mall electronic' com&uter (or !, , to re&lace ten calculating mac*ine' and t*eir o&erator'. #n annual 'ervice maintenance contract (or t*e com&uter ill be &rovided at acco't o( !, &er year. Gne o&erator ill be re
Solution:
2or t*e electronic com&uter1 #n inve'tment o( P!,, to &urc*a'e a 'mall electronic com&uter to re&lace ! calculating mac*ine' and t*eir o&erator'. Gt*er e:&en'e' (or t*e com&uter are1 Service Maintenance Salary o( t*e G&erator Salary o( t*e Programmer E'timated economical Li(e o( t*e com&uter
3 P!, 3 P+, 3 P!44, 3 ! year'
#nnual Co't 3 !, ,/!.)!-!/!.) 3 8,;). $otal $otal #nnual Co't 3 P!, 9P+,9P!44,9 P8,;).3 P8;,;). 2or t*e ! calculating mac*ine1 Co't o( eac* calculating mac*ine #nnua nnuall main aintena tenan nce o( eac* eac* calc calcul ulaating ting mac*i ac*ine ne #nnual ta:e' and in'urance Salary o( eac* o&erator 2ringe bene(it Salvage value
3 P;, 3 P P 3 ) 3 P4, 3 3 P!,
#(ter year', t*e co't o( t*e calculating mac*ine' are P), eac* 'o t*e total annual de&reciation ould be $otal $otal #nnual Ae&reciation 3 6P;, F P),7 6!7 3 6P,7 #nnual Co't 3 6;,-!,76!7/ 6 ;,-!,76!7/!.) !.) -!/!.) 9 P,9 P;,6! F .)7 9 P4,6! F .76!7 $otal #nnual Co't 3 P+4,4)8.+! #n'er1 Since t*e total annual co't o( t*e calculating mac*ine i' greater t*an t*e annual co't o( t*e com&uter, t*ere(ore, it i' advi'able to re&lace t*e calculating mac*ine'.
8. 5t i' de'ired to determine t*e re'ent economic Value Value o( an old mac*ine by con'idering o( *o it com&are' it* t*e be't modern mac*ine t*at could re&lace it. $*e old mac*ine i' e:&ected to re
2or t*e old mac*ine it* original co't o( P, (or 4 year' at ! and 'cra&ed value o( P, *a' a de&reciation value o( 3 ,-,/6!.! 4-!/.!7 3 !,)!.))!8 2or t*e ne mac*ine it* original co't o( P4, (or 4 year' and inve'tment o( P;+, ould *ave co't o( P3 ;+,6!.! -47 3 4,!. $*ere(ore t*e total co't o( t*e ne mac*ine ould be $otal $otal Co't 3 P4,!.+9P4,9!,)!.))!8 3 P!!,!+.!)!
$*ere(ore, t*e recent value o( t*e o( an old mac*ine i' P!,)!.))!8 C*a&ter !
!. # com&any i' con'idering to alternative' it* regard' to e
). Aata (or to -* motor' are (ollo'1 #l&*a Motor Griginal Co't 8;, #nnual Maintenance !, Li(e, year' ! E((iciency ; $a:e' and 5n'urance 8
@eta Motor 4, ; ! ; 8
Poer co't i' ). &er 0B*. 5( money i' ort* ), *o many *our' &er year ould t*e motor' *ave to be o&erated at (ull load (or t*em to be e
)./0*6*&76.;40*/*&76N7/.; )./0*6*&76.;40*/*&76N7/.; 3 .;4;!N $a:e' $a:e' and 5n'urance 3 8;,:.8 3 !,!) 5ntere't on Ca&ital 3 8;,:.) 3 ;, #nnual Co't #l&*a1 !!+.84 9 .;4;!N #nnual Co't o( @eta Motor A3 4,/6!.) !-!/.)7 3 !4+.+)8 #nnual Maintenance 3 ; Poer Con'um&tion )./0*6*&76.;40*/*&76N7/.+) )./0*6*&76.;40*/*&76N7/.+) 3 !.;N $a:e' $a:e' and 5n'urance 3 4,:.8 3 !,44 5ntere't on Ca&ital 3 4,:.) 3 +, #nnual Co't @eta1 !8,8+.+) 9 !.;N @rea0-even &oint #nnual Co't o( #l&*a Motor 3 #nnual Co't o( @eta Motor !!+.84 !!+.84 9 .;4;!N 3 !8,8+.+) 9 !.;N 4.!N 3 ),+.4+ N 3 444 *our'
8. # 'mall '*o& in bulacan (abricate' &ortable t*re'*er' (or &alay &roducer' in t*e locality. locality. $*e '*o& can &roduce eac* t*re'*er at labor co't o( P!. $*e co't o( material' (or eac* unit i' P), . $*e variable co't' amount to P &er unit, *ile (i:ed c*arge' incurred &er annum total' P+, . 5( t*e &ortable t*re'*er' are 'old at P;, &er unit, *o many unit' mu't be &roduced and 'old &er annum to brea0-even= Solution:
Let N3 number o( unit' mu't be &roduced and 'old &er annum to brea0-even. $otal 5ncome 3 $otal Co't ;,N 3 +, 9 6 9 ), 9 !,7 N Solving (or NH N 3 ) unit'
4. Com&ute (or t*e number o( bloc0' t*at an ice &lant mu't be able to 'ell &er mont* to brea0-even ba'ed on t*e (olloing data1 Co't o( electricity &er bloc0 P) $a: to be aid &er bloc0 P) %eal e'tate ta: P8, /mont* Salarie' and age' P), /mont* Gt*er' P!), /mont* Selling rice o( ice P/bloc0 Solution:
Let N 3 number o( bloc0' t*at an ice &lant mu't be able to 'ell &er mont* to brea0-even $otal 5ncome 3 $otal Co't N 3 6 8, 9 ), 9 !),7 9 6 ) 9 )7 N Solving (or NH
N 3 !,)) bloc0' . # local local com&any a''embling 'tereo radio ca''ette &roduce' 8 unit' &er mont* at a co't o( &er unit. Eac* 'tereo radio ca''ette 'ell' (or !,). 5( t*e (irm ma0e' a &ro(it o( ! on it' !, '*are' it* a &ar value o( ) &er '*are, and t*e (i:ed co't' are ), &er mont*. 6a7 B*at i' t*e brea0-even &oint= 6b7 "o muc* i' t*e lo'' or &ro(it i( only ! unit' are &roduced in a given mont*= Solution:
5ncome 3 !,) &er unit 2i:ed Co't' 3 ), &er mont* Variable Co't' 3 &er unit Aividend 3 ! &er year 6a7 Let N 3 no. o( radio ca''ette to &roduce (or brea0-even 5ncome 3 !,)6N7 $otal Co't 3 2i:ed Co't 9 Variable Co't 3 ), 9 6N7 5ncome 3 $otal Co't !,)N 3 ),/mont* 9 N N 3 unit' &er mont* 6b.7 Aividend 3 !,6)7.!/!) 3 !,.; &er mont* 5ncome 3 $otal Co't 9 Aividend 9 &ro(it/Lo'' 6!,)76!7 3 ), 9 67 6!7 9 &ro(it/Lo'' Pro(it 3 8,888.88 &er mont* . # &lant &roduce' 8 unit' o( e
5ncome 3 4, &er unit 2i:ed Co't' 3 !), &er mont* Variable Co't' 3 8, &er unit Aividend 3 ) &er year 6a7 Let N 3 no. o( e
Lo'' 3 !,888.88 C*a&ter !! !. $*e Ae&artment o( &ublic Bor0' Bor0' and "ig*ay' 6AB"7 i' con'idering t*e con'truction o( a ne *ig*ay t*roug* a 'cenic rural area. $*e road i' e:&ected to co't P million it* annual u'e e'timated at P4, . $*e im&roved acce''ibility i' e:&ected to re'ult in additional income (rom touri't' o( P; million &er year. $*e $*e road i' e:&ected to *ave a u'e(ul li(e o( ) year'. 5( 5 ( t*e rate o( intere't i' !, '*ould t*e road be con'tructed= Solution1 #nnual @ene(it #nnual Ai'bene(it #nnual Co't @ene(it-Co't %atio
3 ;,, 34, 3,,/6!-!.! !/.!7 3 ;,;84,+;.!) 3 ;,,-4,/;,;84,+;.!) 3 .88
#n'er1 b/c K ! t*e &ro?ect '*ould not be con'tructed. ). Aetermine t*e @/C ratio (or t*e (olloing &ro?ect. 2ir't Co't P!, Pro?ect li(e, year' Salvage value P!, #nnual bene(it' P, #nnual G and M P)), 5ntere't rate, ! Solution1 #nnual @ene(it 3 P , #nnual Ai'bene(it 3 P )), #nnual Co't 3 !,/6!.! --!/.!7 3 )+,8!. @ene(it-Co't %atio 3 ,/)+,8!.- P)), 3 !.!; #n'er1 b/c R !.! 8. Aata (or to alternative' are a' (ollo'1
'ing an intere't rate o( ), *ic* alternative '*ould be c*o'en= Solution1 Alternative A #nnual @ene(it 3 P), #nnual Ai'bene(it 3 P, 4 #nnual Co't 3 8,6.)/!-!.) -47 - 8,6.)/!-!.)47 3 P!4, !;).!8!! !;).!8!! Alternative B #nnual @ene(it 3 P),
#nnual Ai'bene(it 3 P!8, 8 #nnual Co't 3 8,6.)/!-!.) -7 F 3 P!8, 8.4;!!) @ene(it-Co't %atio 3 ), F !8,8/ !8, 8.4;!!) 3 .;) #n'er1 #lternative #lternative # i' re(erred over #lternative #lternative @ 'ince it *a' @/C ratio neare't to !..
4. t*ere i' (ive alternative' (or im&rovement o( a road. Aetermine *ic* alternative '*ould be c*o'en i( t*e *ig*ay de&artment i' illing to inve't money a' long a' t*ere i' a @/C ratio o( at lea't !.. #lternative' # @ C A E
#nnual @ene(it' P+, P!, 8, P), , P8, 8, P4, ),
#nnual Co't P!, , P!, 4, P), !, P), ;, P8, 4,
Solution1 By incremental incremental analysis: %earranging t*e value'1
!. Com&are E and A b/c 3 4,), F 8,8,/8,4, 8,8,/8,4, F ),;, 3 !.); !.); Since @/C Q !., 'elect alternative E
). Com&are E and C b/c 3 4,), F ),,/8,4, ),,/8,4, F ),!, 3 !.;+ !.;+ Since @/C Q !., 'elect alternative E
8. Com&are E and @ b/c 3 4,), F !,8,/8,4, !,8,/8,4, F !,4, 3 !.4 Since @/C Q !., 'elect alternative E 4. Com&are E and # b/c 3 4,), F +,/8,4, +,/8,4, F !,, 3 !.8; Since @/C Q !., 'elect alternative E #n'er1 Since bc , #lternative E i' re(erred
