2001쓪6퓂뗚ꆡꆡJun.,200115뻭뗚3웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ뮪ꆡ뚫ꆡ뺭ꆡ볃ꆡ맜ꆡ샭EastChinaEconomicMꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ,맘폚춶뺻쿖횵폫붫살횵뗄쳖싛샮죙퇥,췵쏷헕(춬볃듳톧ꆡ뺭볃폫맜샭톧풺,짏몣ꆡ200092)[햪튪]놾컄믘맋뫍첽쳖쇋춶뺻쿖횵뫍붫살횵횮볤뗄맘쾵,횸돶쇋뺻쿖횵몯쫽뫍붫살횵몯쫽뗄닮틬,ퟅ훘횸쏷쇋헢훖닮틬뛔릤돌뺭볃럖컶뿉쓜듸살뗄룉죅ꆣ[맘볼듊]뺻쿖횵;붫살횵;춶쿮쒿움볛[훐춼럖샠뫅]F275ꆡꆡꆡ[컄쿗뇪쪶싫]Aꆡꆡꆡ[컄헂뇠뫅]1007ꆪ5097(2001)03ꆪ0107ꆪ02DiscussionontherelationshipbetweenpresentworthandfutureworthLIRong2yan,WANGMing2zhao(SchoolofEconomyandManagement,TongjiUniversty,Shanghai200092,China)Abstract:,causedbythedifferences,:presentworth;futureworth;evaluationofinvestedprojectꆡꆡ춶쿖횵(PresentWorth,PW)뫍붫살횵(Future랽낸뚼닉폃쿠춬뗄헛쿖싊,퓲늻싛쫇닉폃PW캪움에뇪ힼ뮹Worth,FW)쫇뛔춶쿮쒿뷸탐뺭볃킧맻움볛뗄훘튪횸뇪ꆣ쫇닉폃FW캪움에뇪ힼ,춶랽낸뗄폅쇓업탲쫇튻훂뗄ꆣ퓚볆쯣짏,솽헟뗄닮뇰뷶뷶뇭쿖캪붫튻쾵쇐뗄쿖뷰쇷솿내믹헢튻뷡싛죝틗컳떼돶헢퇹튻룶췆싛,벴PW뫍FW몯쫽ힼ쫕틦싊쿲붨짨웚돵믲붨짨웚쒩뮻쯣,솽헟뗄닮틬뇭쏦짏튲쫇췪좫뗈볛뗄ꆣ쪵볊짏,짏쫶뷡싛늢쎻폐횸돶PW뫍FW횮횻뇭쿖캪볆쯣쪱뗣뫍볆쯣뷡맻뗄늻춬,퓚쫽횵짏붫살횵뻍쫇볤뗄몯쫽쳘헷,폈웤쫇떱쿖뷰쇷솿룸뚨뗄쪱뫲,쪹PW듯떽뺻쿖횵돋짏튻룶뎣쫽(뢴샻쾵쫽),늢늻펰쿬뛠룶춶쿮쒿ퟮ듳뗄헛쿖싊i늢늻튻뚨튲쪹FW듯떽ퟮ듳횵,틲듋,뫜폐뺭볃킧맻뗄폅쇓업탲ꆣ뫜뛠뷌뿆쫩죏캪PW뫍FWퟷ캪춶뿉쓜뗄쟩뿶뻍쫇,떱i랢짺뇤뮯쪱(뇈죧쮵뻶닟헟룄뇤쇋뛔쿮쒿뺭볃킧맻뗄움에뇪ힼ뛸퇔쫇뗈킧뗄ꆣ놾컄춨맽럖컶횸쿮쒿뗄웚췻믘놨싊),붫퓶듳PW뛸복킡FW,믲헟룕뫃쿠돶,잰쫶뷡싛퓚튻냣쟩뿶쿂쫇헽좷뗄,떫헢튻쯆쫇뛸럇뗄뷡랴ꆣ헢쫇뫜훘튪뗄,틲캪헢튻쳘헷믡룸춶쿮쒿뗄톡폅듸살싛붫떼훂쿮쒿톡폅짏뗄쪧컳ꆣ뎣폃뗄볆쯣뺻쿖횵쒣탍쫇:룉죅ꆣ뿉틔쇮PW뫍FW뗄떼쫽캪0,듓뛸쟳뗃룷ퟔ뗄쿠뛔벫PW=ꇆNAj(1+-ji)ꆭꆭꆭꆭꆭꆭꆭꆭꆭꆭꆭꆭꆭ(1)j=0횵:웤훐Aj쫇쿮쒿퓚뗚j쓪뗄뺻쿖뷰쇷솿,N캪쿮쒿뗄쫙쏼d웚PW=ꇆN-j-1(-j)Adj(1+i)ꆭꆭꆭꆭꆭꆭꆭꆭ(3),i캪폐킧헛쿖싊,늢볙짨퓚헻룶쿮쒿쫙쏼쓚,i놣돖늻ij=1뇤ꆣ퓚뷶뷶뾼싇춶쿮쒿뗄뺭볃킧맻쪱,뛔떥튻쿮쒿뛸퇔,d죴FWN=(1+N-1i)ꇆ-1Aj(N-j)(1+-ji)ꆭꆭꆭꆭ(4)PWꇝ0,쿮쒿펦폨뷓쫜,죴PWꇜ0,쿮쒿펦폨뻜뻸;뛠dij=0랽낸뇈톡쪱,PW풽듳뗄랽낸쿠뛔풽폅ꆣ뎣폃뗄볆쯣붫살횵떱쟒뷶떱(3)쪽뫍(4)쪽폐쿠춬뗄뷢i0쪱FW뫍PW쒣탍쫇:몯쫽닅퓚춬튻룶헛쿖싊i0짏좡뗃벫횵ꆣ듓(3)쪽뫍(4)쪽뿉뾴돶,튻냣쟩뿶쿂헢룶뷡싛늻돉솢ꆣ(3)쪽뛀솢폚AFW0,=ꇆNAj(1+N-ji)ꆭꆭꆭꆭꆭꆭꆭꆭꆭꆭꆭꆭꆭ(2)j=0(4)쪽뛀솢폚AN,횻폐퓚Aj뗄쳘뚨ퟩ뫏쿂,PW뫍FW몯쪽훐럻뫅몬틥춬짏ꆣ퓚뷶뷶뾼싇춶쿮쒿뗄뺭볃킧맻쫽닅믡폐쿠춬뗄벫횵뗣i쪱0ꆣ,뛔떥튻쿮쒿뛸퇔,죴FWꇝ0,쿮쒿펦폨뷓쫜,죴FWꇜ컄쿗[3]쿪쾸퇐뺿쇋PW몯쫽뫍FW몯쫽ꆣ죋쏇맘탄0,쿮쒿펦폨뻜뻸;뛠랽낸뇈톡쪱,FW풽듳뗄랽낸쿠뛔풽뗄쫇PW몯쫽뫍FW몯쫽뛔뇤솿i뗄튻뷗떼쫽뗄럻뫅(쯼뇭폅ꆣ좻뛸,횵뗃힢틢뗄쫇,(2)쪽훐뗄헛쿖싊i쪵볊짏듺뇭쏷쇋몯쫽쫇뗝퓶뮹쫇뗝복뗄)뫍뛾뷗떼쫽뗄럻뫅(쯼뇭쏷쇋쇋볙쿫훐뗄퓙춶쫕틦싊,튲뻍쫇쿮쒿뻶닟헟뛔쿖폐뗄뇟볊몯쫽쫇춹뗄뮹쫇낼뗄),쿠뛔벫횵(벴뻖늿벫듳횵믲벫킡횵)춶믺믡믘놨싊욽뻹횵뗄맀볆ꆣ퓚췪좫쫐뎡뫍췪좫쿻돽쇋늻뫍떱iꇺ-1벰iꇺꇞ쪱뗄몯쫽뗄벫쿞횵ꆣ뇭1룸돶쇋PW몯좷뚨탔뗄볙짨쿂,퓙춶쫕틦싊뫍헛쿖싊퓚쫽횵짏쫇쿠뗈쫽뫍FW몯쫽뗄훷튪쳘헷ꆣ뗄ꆣ듓뇭1뿉틔뾴돶,죧맻웚돵듦퓚튻룶돵쪼춶,퓚틔뫳(튻)PW뫍FW횮볤뗄맘쾵뗄볆쯣웚훐돶쿖튻쾵쇐뗄헽뗄쿖뷰쇷솿(벴뎣맦춶뗄쟩PW뫍FW횮볤뗄맘쾵뿉볲떥뗄뇭쫶캪:ꋙ뛔튻쾵쇐룸뿶),퓲PW몯쫽늻듦퓚쇙뷧횵,떱i>-1쪱PW몯쫽쫇뗝뚨뗄쿖뷰쇷솿Aj,죧맻PW>0퓲FW>0;ꋚ퓚쟳뷢쓚늿쫕복뗄ꆣ좻뛸,FW몯쫽좴듦퓚쇙뷧횵ꆣ튲뻍쫇쮵,듦퓚쒳튻틦싊IRR쪱,늻싛쫇쇮PW=0뮹쫇FW=0,쟳뷢뷡맻뚼쫇룶횵i0,떱i<i0쪱FW몯쫽뗝퓶,뛸i>i0쪱FW몯쫽뗝복ꆣ쿠춬뗄;ꋛ룸돶튻쾵쇐쿠뮥업돢뗄춶랽낸,횻튪쎿룶춶죧맻Aj퓚럻뫅짏늻쫜쿞훆(벴럇뎣맦춶뗄쟩뿶),PW뫍[쫕룥죕웚]ꆡ2001ꆪ04ꆪ13[ퟷ헟볲뷩]ꆡ샮죙퇥(1976ꆪ),쓐,쮶쪿퇐뺿짺;췵쏷헕(1960ꆪ),쓐,뢱뷌쫚ꆣꆪ107ꆪ
FW몯쫽뗄쫽톧쳘헷뻍좡뻶폚i뫍Aj,쎻폐튻룶튻냣뗄맦싉ꆣ쫽뗄춼탎죧춼2쯹쪾ꆣ헢쪱뫲튲듦퓚쇙뷧횵,벴뻖늿벫듳횵뫍벫킡횵,떫쫇늻쓜놣듓춼1뫍춼2뿉틔뾴돶,쇮PW(i)=0뫍쇮FW(i)횤PW뫍FW몯쫽퓚쿠춬뗄i=i0뒦좡뗃벫횵ꆣ늻싛쫇뛔뎣맦=0쯹뗃떽뗄쓚늿쫕틦싊IRR뚼쫇쿠춬뗄,좻뛸PW(i)뫍춶뮹쫇럇뎣맦춶,뚼듦퓚ퟅ헢퇹뗄쿖뷰쇷솿ퟩ뫏Aj(jFW(i)좴퓚늻춬뗄i0짏듯떽쇋ퟮ듳횵ꆣ춼2듺뇭뗄쫇뎣맦=0,1,2ꆭꆭ,N),쪹뗃뛔튻뚨뗄iꇊU(a,ꛄ),PW(i)춶뗄쟩뿶,헢쮵쏷벴뇣쫇뎣맦춶,PW뫍FW튲뿉쓜퓚캪복몯쫽뛸FW(i)캪퓶몯쫽,믲헟룕뫃쿠랴ꆣ헢튻뷡싛퓚늻춬뗄i짏듯떽ퟮ듳믲ퟮ킡횵ꆣ릤돌뺭볃럖컶훐뗄뛔펦뗄쟩뿶뻍쫇,룸뚨튻ퟩ폐좷뚨쿖뷰쇷솿뗄춶랽낸,내쒳튻횸뚨뗄헛쿖싊i뛔랽낸폅쇓뷸탐업탲,늻싛쫇폃PW뮹쫇FWퟷ캪움에뇪ힼ뚼뿉틔뗃돶쿠춬뗄폅쿈듎탲,좻뛸,죧맻iꇊU(a,ꛄ),떱놾뷡릹랢짺뇤뮯,듓뛸떼훂뻶닟헟룄뇤쇋i쪱,뿉쓜믡돶쿖폃PW뫍FWퟷ캪움에틀뻝쪱룷랽낸뗄폅쿈쮳탲늻튻훂뗄쟩뿶ꆣ헢쫇평폚떱iꇊU(a,ꛄ)쪱몯쫽PW(i)뫍FW(i)뗄튻뷗뫍뛾뷗떼쫽럻뫅짏뗄닮틬,듓뛸튲뻍쫇퓚뻖늿랶캧쓚몯쫽뗄퓶복랽쿲ꆢ낼춹쟩뿶뗄닮틬쯹떼훂뗄ꆣ뇭1ꆡPW(i)몯쫽뫍FW(i)몯쫽뗄훷튪쳘헷쿖뷰쇷솿몯쫽쳘헷쿖횵(PW)붫살횵(FW)d(ꆤ)/di<0럱?쫇,복몯쫽좡뻶폚i뫍Ajd2(ꆤ)/d2i>0럱?쫇,춹몯쫽좡뻶폚춼1i뫍Aj뎣맦춶:쫇럱듦퓚쇙뷧횵늻듦퓚듦퓚A0<0,Aj>0lim(j=1,2,ꆭꆭiꇺꇞAN-1,N)limiꇺꇞA0-ꇞd(ꆤ)/di<0럱?좡뻶폚i뫍Aj좡뻶폚i뫍Ajd2(ꆤ)/d2i>0럱?좡뻶폚i뫍Aj좡뻶폚i뫍Aj쫇럱듦퓚쇙뷧횵듦퓚듦퓚럇뎣맦춶:Aj퓚럻뫅짏죴AN>0,컞쿞훆limPW(i)ꇺ+ꇞ;iꇺ-1죴AANN<0(j=0,1,2,ꆭꆭPW(i)ꇺ-ꇞ,N춼2)죴A0>0,솽룶샽ퟓ뇭쏷,뻍룸뚨뗄헛쿖싊뛸퇔,퓚춶쿮쒿업탲limAPW(i)ꇺ+ꇞ;컊쳢짏,늻싛쫇폃PW뮹쫇폃FWퟷ캪움에뇪ힼ,뗃돶뗄뷡0iꇺ-ꇞ죴A0<0,싛쫇튻훂뗄ꆣ좻뛸,죏캪PW(i)뫍FW(i)퓚쿠춬뗄헛쿖PW(i)ꇺ-ꇞ싊쟸볤짏폐쿠춬뗄뗝퓶믲뗝복쟷쫆퓲쫇늻뛔뗄,헢믡떼훂쿮힢쒿업탲쪱뗄쪧컳ꆣPW뫍FW퓚늻춬뗄i0짏듯떽ퟮ듳횵;떱:놾뇭닎뾼쇋컄쿗[2]ꆡꆡ(뛾)쪾ꆡ샽퓶듳헛쿖싊i쪱뿉쓜믡퓶듳PW뛸복킡FW,듓뛸쪹뗃춬튻틔쿂솽룶샽ퟓ쫇듓컄쿗[2]훐틽폃살뗄,쯼쏇횱맛뗘쿮쒿폃PW뫍FW캪에뻝뇪ힼ쪱쿮쒿뗄컼틽솦쮵쏷쇋짏쫶쟩뿶ꆣ(attractiveness)랢짺쿠랴랽쿲뗄뇤뮯ꆣ죧뇭3뗄샽2훐,볙쫗쿈뾼싇튻룶짨놸ퟢ쇞뗄쟩뿶ꆣ늻ퟢ폃짨놸뫍ퟢ폃짨놸뚨돵쪼뗄ퟮ뗍폐컼틽솦뗄쫕틦싊(MinimumAttractiveRateofReturn,MARR)캪20%,떫쫇평폚놾뷡릹믲헟춶믺뫳뗄쿖뷰쇷솿죧뇭2쯹쪾:믡돉놾뗄뇤뮯,떼훂MARR뇤캪30%,MARR뗄뇤뮯붫쪹뇭2뇭3훐뗄랽낸B폃PWퟷ캪움에틀뻝쪱웤뿉탐탔뷸튻늽뗍폚폃FWퟷ캪움에틀뻝쪱뗄뿉탐탔ꆣ헢쫇솽룶랽낸뗄뇈뷏쪱쓪쒩랽낸A뗄랽낸B뗄닮뛮춶쿖뷰쇷솿쿖뷰쇷솿쿖뷰쇷솿(ꚤ=B-A)PW뫍FWퟷ캪춶쿮쒿움볛뇪ힼ뛔랽낸뗄컼틽솦쿲쿠랴랽쿲뇤뮯뗄샽ퟓꆣ죧맻짦벰떽룼뛠랽낸뗄뇈뷏컊쳢쪱,PW(i)00-100-100뫍FW(i)뗄몯쫽쳘헷붫쪹뗃평폚i(믲헟쮵MARR)뗄뇤1-500-200300뚯뛸쪹춬튻ퟩ춶쿮쒿폃PW믲FWퟷ캪움에뇪ힼ쪱쿮쒿뗄2-600-200400폅쿈업탲돶쿖쎬뛜,헢헽쫇놾컄튪횸돶뗄ꆣ뇭3[닎뾼컄쿗]\[1\]믆폥쿩,탏낮랼.릤돌뺭볃톧\[M\].춬볃듳톧돶냦쓪쒩랽낸A뗄랽낸B뗄닮뛮춶쿖뷰쇷솿쿖뷰쇷솿쿖뷰쇷솿(ꚤ=B-A짧,1995.)\[2\]Fleischer,.,,OnFutureWorth00-100-100andItsRelationshiptoPresentWorthAsAnInvestment1-500-200300Criterion\[J\].TheEgnineeringEconomist,1990,(4):3232-600-200400-332.뇭\[3\]쇵쿾뻽.벼쫵뺭볃톧\[M\].컷놱듳톧돶냦짧,2쫇럇뎣맦춶뗄쟩뿶ꆣPW(i)뫍FW(i)뗄몯쫽뗄춼탎죧춼1쯹쪾ꆣ웤듎쫇솽룶놸톡랽낸뗄톡폅컊쳢,죧뇭1995.[퓰죎뇠벭:헅쓋쫩]3쯹쪾ꆣ뇭3쫇뎣맦춶뗄쟩뿶ꆣPW(i)뫍FW(i)뗄몯ꆪ108ꆪ
