CE303
Engi neer i ngEconomi csPr act i cePr obl ems
1.I nas i t uat i onwher et heeff ec t i v ei nt er es tr at epery eari s12%,bas edonmont hl y c ompoundi ng.Wh Whati st henomi nal i nt er es tr at epery ear ?
2.I f10% n omi nal ann ual i nt er es ti sc ompoundeddai l y ,whati st heeff ec t i v eannual i nt er es tr at e?
3.Ani ndi v i dual wi s hest odepos i tac er t ai nquant i t yofmone ynows ot hathewi l l ha v e $500att heendoffi v ey ear s .Whati st heamountoft hedepos i twi t hani nt er es tr at e o f4 %p ery e ar ,c o mp mp ou nd eds e mi mi a nn ua l l y ?
4 .A .Ac o ns ul t i n ge ng i n ee rb oug htaf a xmac h i ne .Th er ewi l l b en oma i n t e na nc ec os tf o r t hefi r s ty earasi twass ol dwi t honey ear ’ sf r eemai nt enanc e.I nt hes ec ondy eart he mai nt enanc ei ses t i mat edat$ 20.I ns ubs equ enty e ar st hemai nt enanc ec os twi l l r d t h i nc r eas e$20pery ear( t hati s ,3 y earmai nt enanc ewi l l be$40,4 y earwi l l be$60 ands of or t h) .Wh Whati st heamountt hatmus tbes etas i deno w at6 %i nt er es tt op ay t hemai nt enanc ec os t sont hef axma mac hi nef ort hefi r s ts i xy ear s ?
5.Apr oj ec thasani ni t i al c os tof$10, 000,uni f or m annual benefi t sof$2, 400,anda s al v agev al ueof$3, 000att heendofi t s10y earus ef ul l i f e.At12% i nt er es t ,whati s t henetpr es entwor t h( NPW)oft hepr oj ec t ?
6 .A .Ap er s o nb or r o ws$ 5, 0 00ata ni n t e r e s tr a t eof1 8%,c o mp mp ou nd edmo mo nt h l y .Mo Mo nt h l y pa y me me nt so f$ 16 7. 1 0we r eag r e edup on.Wh Wh ati st hel e ng t hoft h el oa n?
7 .A .Amac h i n ec o s t i n g$ 2, 0 00t ob uyan d$ 30 0p ery e art oo per at ewi l l s a v el a bo r ex pens esof$650pery earf or8y ear s .Thema mac hi newi l l bepur c has edi fi t ss al v age v al ueatt heendof8y ear si ss uffic i ent l yl ar get omak et hei nv es t mentec onomi c al l y at t r ac t i v e.I ft hei nt er es tr at ei s10%,whati st hemi ni mum s al v agev al ue?
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CE303
Engi neer i ngEconomi csPr act i cePr obl ems
8.Aneng i neerd epos i t ed$ 200quar t er l yi nhers av i n gsac c ountf ort hr eey ear sat6% i nt er es t ,c ompoundedquar t er l y .Thenf orfi v ey ear ss hemadenodepos i t sor wi t hdr awal s .Whati samounti nherac c ountaf t erei ghty ear s ?
9.Ani nv es t ori sc ons i der i ngt hei nv es t mentof$10, 000i napi ec eofl and.Thepr oper t y t ax esar e$100pery ear .Whati st hel owes ts el l i ngpr i c et hei nv es t ormus tr ec ei v ei f s hewi s hest oear n10% i nt er es tr at eaf t erk eepi ngt hepr oper t yf or10y ear s ? 10. T woal t er nat i v esar ebei ngc ons i der ed: A I ni t i al Cos t $500 Uni f or m Annual Benefi t $140 Us ef ul Li f e 8
B $800 $200 8
Whati st heBen efi tCos tRat i ooft hedi ff er enc ebe t weent heal t er nat i v e s,bas edon 12% i nt er es tr at e? 11. $20, 000i si nv es t edt oday .I ft heannual i nfl at i onr at ei s6% andt heeffec t i v eannual r et ur noni nv es t menti s10%,whatwi l l bet heappr o xi mat ef ut ur ev al ueoft he i nv es t ment ,adj us t edf ori nfl at i on,i n5y ear s ? 12. Af ac t or yt hatmanuf ac t ur esc hai r sc os t s$180, 000pery eart ooper at e,i nc l udi ng r ent ,depr ec i at i onc har gesonequi pment ,ands al ar i es .Eac hc hai rc os t s$31t o mak e,ands el l sf or$59.Whati st hef ac t or y ’ sbr eak ev ens al esv ol ume?
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CE303
Engi neer i ngEconomi csPr act i cePr obl ems
SOLUTI ONS
1.I nas i t uat i onwher et heeff ec t i v ei nt er es tr at epery eari s12%,bas edonmont hl y c ompoundi ng.Whati st henomi nal i nt er es tr at epery ear ? m Sol ut i on:i =( 1 +r / m) 1 e 12 0. 12=( 1+r / 12) 1 1 / 1 2 ( 1. 12) =( 1+r / 12) 1 . 0 094 9=( 1 +r / 12 ) r=0. 00949x12=0. 1138=11. 38%
2.I f10% n omi nal ann ual i nt er es ti sc ompoundeddai l y ,whati st heeff ec t i v eannual i nt er es tr at e? m 365 Sol ut i on:i =( 1 +r / m) 1=( 1+0. 10/ 365) 1=0 . 1 05 2=1 0. 5 2% e
3.Ani ndi v i dual wi s hest odepos i tac er t ai nquant i t yofmone ynows ot hathewi l l ha v e $500att heendoffi v ey ear s .Whati st heamountoft hedepos i twi t hani nt er es tr at e o f4 %p ery e ar ,c o mp ou nd eds e mi a nn ua l l y ? Sol ut i on:P=F( P/ F ,i ,n)=500( 0. 8203)=$410
4 .Ac o ns ul t i n ge ng i n ee rb oug htaf a xmac h i ne .Th er ewi l l b en oma i n t e na nc ec os tf o r t hefi r s ty earasi twass ol dwi t honey ear ’ sf r eemai nt enanc e.I nt hes ec ondy eart he mai nt enanc ei ses t i mat edat$ 20.I ns ubs equ enty e ar st hemai nt enanc ec os twi l l i nc r eas e$20pery ear( t hati s ,3rd y earmai nt enanc ewi l l be$40,4th y earwi l l be$60 ands of or t h) .Whati st heamountt hatmus tbes etas i deno w at6 %i nt er es tt op ay t hemai nt enanc ec os t sont hef axmac hi nef ort hefi r s ts i xy ear s ? Sol ut i on:Us i ngs i ngl epa ymentpr es entwor t hf ac t or s : P=2 0( P/ F ,6 %,2 )+4 0( P/ F ,6 %,3 )+6 0( P/ F ,6 %,4 )+8 0( P/ F ,6 %,5 )+1 00( P/ F ,6 %,6 )
=2 0( 0 . 8 90 0)+40( 0 . 8 39 6)+6 0( 0 . 7 92 1)+8 0( 0 . 7 47 3)+1 00( 0 . 70 50)=$ 22 9. 1 9 Anal t er nat i v es ol ut i oni st ous et hegr adi entpr es entwor t hf ac t or . P=2 0( P/ G,6 %,6 )=2 0( 1 1. 4 59 )=$ 22 9. 1 8 -3-
CE303
Engi neer i ngEconomi csPr act i cePr obl ems
5.Apr oj ec thasani ni t i al c os tof$10, 000,uni f or m annual benefi t sof$2, 400,anda s al v agev al ueof$3, 000att heendofi t s10y earus ef ul l i f e.At12% i nt er es t ,whati s t henetpr es entwor t h( NPW)oft hepr oj ec t ? Sol ut i on:NPW =PW ofBenefit s -PW ofCost =2, 4 00 ( P/ A, 1 2%, 1 0)+3, 0 00 ( P/ F , 12 %, 1 0)–10 , 0 00= =2 , 4 00 ( 5. 6 50 )+3, 0 00 ( . 3 220 )–1 0, 0 00=$ 4, 5 26 6 .Ap er s o nb or r o ws$5, 0 00ata ni n t e r e s tr a t eof1 8%,c o mp ou nd edmo nt h l y .Mo nt h l y pa y me nt so f$ 16 7. 1 0we r eag r e edup on.Wh ati st hel e ng t hoft h el oa n? Sol ut i on:PW ofBenefit s=PW ofCost $ 5, 0 00=$ 167 . 1 0( P , A, 1. 5 %, n ) ( P/ A, 1. 5%, n)=5, 000/ 167. 10=29. 92 Fr om 1½% Tabl en=40 7 .Amac h i n ec o s t i n g$ 2, 0 00t ob uyan d$ 30 0p ery e art oo per at ewi l l s a v el a bo r ex pens esof$650pery earf or8y ear s .Themac hi newi l l bepur c has edi fi t ss al v age v al ueatt heendof8y ear si ss uffic i ent l yl ar get omak et hei nv es t mentec onomi c al l y at t r ac t i v e.I ft hei nt er es tr at ei s10%,whati st hemi ni mum s al v agev al ue? Sol ut i on:NPW =PW ofBenefit s–PW ofCost=0 =( 6 503 00 ) ( P/ A, 10 %, 8 )+S8( P/ F , 10 %, 8 )– 2, 0 00=0 =3 50 ( 5 . 33 5)+S8( 0. 4665)–2, 000=0 S8 =$284. 57
8.Aneng i neerd epos i t ed$ 200quar t er l yi nhers av i n gsac c ountf ort hr eey ear sat6% i nt er es t ,c ompoundedquar t er l y .Thenf orfi v ey ear ss hemadenodepos i t sor wi t hdr awal s .Whati samounti nherac c ountaf t erei ghty ear s ? Sol ut i on:FW 200( F/ A, 1. 5%, 12) ( F/ P , 1. 5%, 20)=2 00( 13. 041) ( 1. 347)=$3, 513. 25 9. Ani n v es t ori sc ons i der i ngt hei n v es t mentof$10, 000i napi ec eofl and.Thepr oper t y t ax esar e$100pery ear .Whati st hel owes ts el l i ngpr i c et hei nv es t ormus tr ec ei v ei f s hewi s hest oear n10% i nt er es tr at eaf t erk eepi ngt hepr oper t yf or10y ear s ?
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CE303
Engi neer i ngEconomi csPr act i cePr obl ems
Sol ut i on:Mi nSal ePr i c e=10, 000( F/ P , 10%, 10)+100( F/ A, 10%, 10)= =1 0, 0 00 ( 2 . 5 94 )+1 00 ( 1 5. 9 37 )=$ 27 , 5 33 . 7 0
10. T woal t er nat i v esar ebei ngc ons i der ed: A I ni t i al Cos t $500 Uni f or m Annual Benefi t $140 Us ef ul Li f e 8
B $800 $200 8
Whati st heBenefi tCos tRat i ooft hei nc r ement al c as hfl owoft het woal t er nat i v es , bas edon12% i nt er es tr at e? Sol ut i on: B/ C=PW ofBenefit s/ PW ofCost=60( P/ A, 12%, 8) / 300=60( 4. 968) / 300=0. 99 Al t er nat i v e B/ C=EUAB/ EUAC=60/ 300( A/ P, 12%, 8)=60/ 300( 0. 2013)=0. 99 11. $20, 000i si nv es t edt oday .I ft heannual i nfl at i onr at ei s6% andt heeffec t i v eannual r et ur noni nv es t menti s10%,whatwi l l bet heappr o xi mat ef ut ur ev al ueoft he i nv es t ment ,adj us t edf ori nfl at i on,i n5y ear s ? Sol ut i on: Thei nt er es tr at eadj us t edf ori nfl at i oni sd=I+f+i * f=. 10+. 06+. 1* . 06=0. 166 n 5 SoF=P( i +d) =$20000( 1+0. 166) =$43105
12. Af ac t or yt hatmanuf ac t ur esc hai r sc os t s$180, 000pery eart ooper at e,i nc l udi ng r ent ,depr ec i at i onc har gesonequi pment ,ands al ar i es .Eac hc hai rc os t s$31t o mak e,ands el l sf or$59.Whati st hef ac t or y ’ sbr eak ev ens al esv ol ume? Sol ut i on:
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CE303
Engi neer i ngEconomi csPr act i cePr obl ems
Thebr eak e v enp oi nto cc ur swhenc os t sands al est o t al z er o.Le txbet henumberof c har spery earatbr eak v en. Cost s=$180000+$31* x Revenues=$59* x So,$180, 000+$31* x=$59* x X=6 42 9c h ai r s / y e ar
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