ࡱ> _bjbj4bbRlrr87$.LFYYY4D PB$D$D$D$D$D$D$$&(<h$944h$YY$(((<YYB$(B$((:","Y%D@BH" .$$0$R"R) )"")B#Xl(z ~XXXh$h$XXX$)XXXXXXXXXr? :@5<5==0O :>=F5?F8O AB>8<>AB8 45=53. >=OB85 F5=K :0?8B0;0. 564C=0@>4=0O ?@0:B8:0 >F5=:8 M:>=><8G5A:>9 MDD5:B82=>AB8 :0?8B0;L=KE 2;>65=89 ACI5AB25==> 1078@C5BAO =0 :>=F5?F88 2@5<5==>9 AB>8<>AB8 45=53. A=>2=>9 ?@8=F8? :>=F5?F88  @C1;L A59G0A AB>8B 1>;LH5, G5< @C1;L, :>B>@K9 1C45B ?>;CG5= G5@57 3>4, B0: :0: >= <>65B 1KBL 8=25AB8@>20= 8 MB> ?@8=5A5B 4>?>;=8B5;L=CN ?@81K;L. !B>8<>ABL 45=53 A B5G5=85< 2@5<5=8 87<5=O5BAO A CG5B>< =>@<K ?@81K;8 =0 45=56=>< @K=:5.  :0G5AB25 =>@<K ?@81K;8 2KABC?05B =>@<0 AAC4=>3> ?@>F5=B0. !53>4=OH=89 @C1;L, ?><5I5==K9 2 ;N1K5 :><<5@G5A:85 >?5@0F88 (2;>65=85 2 F5==K5 1C<038, 8=25AB8F8>==K9 ?@>5:B, 10=:>2A:89 45?>78B 8 B.4.), G5@57 >?@545;5==K9 ?5@8>4 2@5<5=8 <>65B ?@52@0B8BLAO 2 1>;LHCN AC<<C 70 AG5B ?>;CG5==>3> A 53> ?><>ILN 4>E>40. Tax, 5A;8 ?>;>68BL =0 45?>78B=K9 2:;04 1000 @C1. ?>4 10% 3>4>2KE, G5@57 3>4 AC<<0 2:;040 A>AB028B 1000 + 1000 " 0,10 = 1100 @C1. A;8 45?>78B=K9 2:;04 =5 87K<0BL 87 10=:0, 0 >AB028BL 53> =0 2B>@>9 3>4, B> >:>=G0B5;L=0O AC<<0 ?>A;5 42CE;5B=53> ?5@8>40 A>AB028B 1000 (1 + 0,10) (1 + 0,10) = 1000 (1 + 0,10)2 = 1210 =25AB8@>20=85 ?@54AB02;O5B A>1>9, :0: ?@028;>, 4;8B5;L=K9 ?@>F5AA, ?>MB><C ?@8 >ACI5AB2;5=88 8=25AB8F8>==>9 45OB5;L=>AB8 ?@8E>48BAO A@02=820BL AB>8<>ABL A@54AB2 2 =0G0;5 8E 8=25AB8@>20=8O (=0AB>OICN AB>8<>ABL) A 8E AB>8<>ABLN ?@8 2>72@0B5 2 2845 1C4CI59 ?@81K;8, 0<>@B870F8>==KE >BG8A;5=89, 4@C38E 45=56=KE ?>B>:>2 (1C4CI59 AB>8<>ABLN). C4CI0O AB>8<>ABL 45=53 (future value  FV) ?@54AB02;O5B A>1>9 AC<<C A@54AB2, 2 :>B>@CN 2;>65==K5 A53>4=O A@54AB20 ?@52@0BOBAO G5@57 >?@545;5==K9 ?5@8>4 2@5<5=8. F5=:0 1C4CI59 AB>8<>AB8 45=53 A2O70=0 A ?@>F5AA>< =0@0I5=8O MB>9 AB>8<>AB8, :>B>@K9 ?@54AB02;O5B A>1>9 ?>AB5?5==>5 C25;8G5=85 ?5@2>=0G0;L=>9 AC<<K ?CB5< A>548=5=8O : =59 4>E>40, @0AAG8BK205<>3> A CG5B>< =>@<K 4>E>4=>AB8 (:0: ?@028;>, ?@>F5=B=>9 AB02:8). @>F5=B=0O AB02:0 2KABC?05B, A >4=>9 AB>@>=K, :0: 8=AB@C<5=B =0@0I5=8O AB>8<>AB8 45=56=KE A@54AB2, A 4@C3>9 AB>@>=K, :0: 87<5@8B5;L AB5?5=8 4>E>4=>AB8. "5:CI0O AB>8<>ABL 45=56=KE A@54AB2 (present value  PV) 2 8=25AB8F8>==KE @0AG5B0E @0AA<0B@8205BAO :0: ?5@2>=0G0;L=>5 7=0G5=85 B>9 AC<<K, :>B>@0O 8=25AB8@C5BAO @048 ?>;CG5=8O 4>E>40 2 1C4CI5< 8 >?@545;O5BAO :0: AC<<0 1C4CI8E 45=56=KE ?>ABC?;5=89, ?@82545==KE A CG5B>< >?@545;5==>9 AB02:8 ?@>F5=B0 (48A:>=B=>9 AB02:8) : =0AB>OI5<C 2@5<5=8. 0AG5B 1C4CI59 AB>8<>AB8 45=56=KE A@54AB2 2 =0AB>OI5< ?5@8>45 ?@>872>48BAO ?CB5< 48A:>=B8@>20=8O. 8A:>=B8@>20=85 - MB> A?>A>1 ?@82545=8O 1C4CI59 AB>8<>AB8 45=53 : 8E AB>8<>AB8 A53>4=O. => ?@54AB02;O5B A>1>9 ?@>F5AA, >1@0B=K9 =0@0I5=8N 45=56=KE A@54AB2, B.5. >?@545;5=85 B>3>, A:>;L:> =04> 8=25AB8@>20BL A53>4=O, GB>1K ?>;CG8BL >1CA;>2;5==CN AC<<C 2 1C4CI5<. @8 @0AG5B5 25;8G8=K 1C4CI59 AB>8<>AB8 8A?>;L7C5BAO D>@<C;0 FV = PV (1+k)t 0AG5B B5:CI59 AB>8<>AB8 >ACI5AB2;O5BAO ?> D>@<C;5 PV = FV/(1+k)t 345 k - =>@<0 4>E>4=>AB8 2;>65==KE A@54AB2, 2K@0605<0O 45AOB8G=>9 4@>1LN; t - G8A;> ?5@8>4>2 2@5<5=8, 2 B5G5=85 :>B>@KE 2;>65==K5 A@54AB20 1C4CB =0E>48BLAO 2 >1>@>B5. @8 @0AG5B5 =0@0I5=8O 8 48A:>=B8@>20=8O 45=56=KE A@54AB2 <>3CB 8A?>;L7>20BLAO <>45;8 ?@>ABKE 8 A;>6=KE ?@>F5=B>2. @>AB>9 ?@>F5=B ?@54AB02;O5B A>1>9 AC<<C, :>B>@0O =0G8A;O5BAO >B 8AE>4=>9 25;8G8=K AB>8<>AB8 2;>65=8O 2 :>=F5 >4=>3> ?5@8>40, >?@545;O5<>3> CA;>28O<8 2;>65=8O A@54AB2 (<5AOF, :20@B0;, 3>4). 0AG5B AC<<K ?@>AB>3> ?@>F5=B0 S 2 ?@>F5AA5 =0@0I5=8O 2;>65=89 ?@>2>4OB ?> D>@<C;5  EMBED Equation.3  > >:>=G0=88 :064>3> ?5@8>40 8=25AB8F8O C25;8G8205BAO =0 25;8G8=C kt. >MB><C 1C4CI0O AB>8<>ABL 8=25AB8F88 FV A CG5B>< =0G8A;5==KE ?@>F5=B>2 >?@545;O5BAO ?> D>@<C;5 FV= PV + S=PV(1 + kt). =>68B5;L (1 + kt) ?@54AB02;O5B A>1>9 :>MDD8F85=B =0@0I5=8O ?@>ABKE ?@>F5=B>2. @8 @0AG5B5 AC<<K ?@>AB>3> ?@>F5=B0 2 ?@>F5AA5 48A:>=B8@>20=8O, 8;8 AC<<K 48A:>=B0 D 8A?>;L7C5BAO D>@<C;0  EMBED Equation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k)t =07K20NB :>MDD8F85=B><t 8;8 <=>68B5;5< =0@0I5=8O, 0 B0:65 AB02:>9 ?@>F5=B0, =>@<>9 4>E>4=>AB8, =>@<>9 ?@81K;8, 0 :>MDD8F85=B 1/(1 + k)t - :>MDD8F85=B>< 48A:>=B8@>20=8O, 48A:>=B=>9 AB02:>9, 48A:>=B><, CG5B=>9 AB02:>9. G5284=>, GB> >10 :>MDD8F85=B0 A2O70=K <564C A>1>9, ?>MB><C, 7=0O >48= ?>:070B5;L, <>6=> >?@545;8BL 4@C3>9. ;O ?@>AB>BK 2KG8A;5=89 @07@01>B0=K A?5F80;L=K5 B01;8FK, A ?><>ILN :>B>@KE ?@8 7040==KE ?0@0<5B@0E C:070==KE :>MDD8F85=B>2 8 ?5@8>4>2 8=25AB8@>20=8O <>6=> >?@545;8BL B5:CICN 8 1C4CICN AB>8<>ABL 45=56=KE A@54AB2. >A:>;L:C ?@>F5AA 8=25AB8@>20=8O, :0: ?@028;>, 8<55B 1>;LHCN ?@>4>;68B5;L=>ABL 2 ?@0:B8:5 0=0;870 MDD5:B82=>AB8 :0?2;>65=89 >1KG=> ?@8E>48BAO 8<5BL 45;> =5 A 548=8G=K<8 45=56=K<8 AC<<0<8, 0 A ?>B>:0<8 45=56=KE A@54AB2. >B>: 45=56=KE A@54AB2 <>65B :;0AA8D8F8@>20BLAO :0: A<5H0==K9 ?>B>: ;81> :0: 0==C8B5BK. !<5H0==K9 ?>B>: - MB> ?>B>:8, E0@0:B5@ 42865=8O :>B>@KE =5 C:;04K205BAO 2 :0:CN-B> >?@545;5==CN A8AB5<C. ==C8B5B, =0?@>B82, ?@54AB02;O5B A>1>9 A8AB5<C A ?>ABC?;5=85< @02=KE 4>E>4>2. ==C8B5B - MB> ?>B>: @02=KE AC<< 45=56=KE A@54AB2, 2>7=8:0NI89 G5@57 @02=K5 ?@><56CB:8 2@5<5=8. !C<<0 2 1000 @C1;59, ?>;CG05<0O 2 :>=F5 :064>3> 3>40 5653>4=> 2 B5G5=85 10 ;5B - ?@8<5@ 0==C8B5B0. C4CI0O AB>8<>ABL 0==C8B5B0 <>65B 1KBL >?@545;5=0 A ?><>ILN B01;8FK 1. D0:B>@>2 =0@0I5=8O 4;O 0==C8B5B0 (FVwa). $0:B>@K =0@0I5=8O 4;O 0==C8B5B0 ?@54AB02;O5B A>1>9 AC<<C, 4> :>B>@>9 @53C;O@=K5 27=>AK 2 1 @C1;L, A45;0==K5 0 :>=F5 3>40, 2K@>A;8 1K ?@8 @07;8G=>9 :><18=0F88 ?5@8>4>2 8 AB02>: ?@>F5=B0. 0?@8<5@, 1 @C1;L, 2=5A5==K9 =0 10=:>2A:89 45?>78B, ?> :>B>@><C =0G8A;O5BAO 6% 2 :>=F5 :064>3> 3>40 =0 ?5@8>4 2 5 ;5B, 2K@>A 1K 4> 5,6371 @C1;O. A?>;L7CO D0:B>@ =0@0I5=8O 4;O 5-;5B=53> 0==C8B5B0 ?@8 AB02:5 6%, <>6=> =09B8 1C4CICN AB>8<>ABL ?>B>:0 45=56=KE A@54AB2, C<=>682 5653>4=>5 2;>65=85 A@54AB2 =0 A>>B25BAB2CNI89 D0:B>@ =0@0I5=8O.  A;CG05 8=25AB8@>20=8O 1000 @C1;59 2 :>=F5 :064>3> 3>40 2 B5G5=85 5 ;5B ?>4 6% 8B>3>20O 1C4CI0O AB>8<>ABL A>AB028B 5637,1 @C1;59:  EMBED Equation.3  "01;8F0 1. C4CI55 7=0G5=85 0==C8B5B0 2 B5G5=85 2@5<5=8 n ?5@8>4>2. 5@8>44%5%6%8%10%11,00001,00001,00001,00001,000022,04002,05002,06002,08002,100033,12163,15253,18363,24643,310044,24654,31014,37464,50614,641055,41635,52565,63715,86666,1051 @82545==0O AB>8<>ABL 0==C8B5B0 <>65B 1KBL =0945=0 A ?><>ILN B01;8FK 1. D0:B>@>2 48A:>=B8@>20=8O 4;O 0==C8B5B0 (PVwa). $0:B>@K 2 B0:8E B01;8F0E ?@54AB02;ONB A>1>9 ?@82545==CN AB>8<>ABL 0==C8B5B0, @02=>3> 1 @C1;N, A2O70==CN A @07;8G=K<8 :><18=0F8O<8 ;5B 8 AB02>: 48A:>=B8@>20=8O. "01;8F0 2. !>2@5<5==>5 7=0G5=85 0==C8B5B0 2 B5G5=85 2@5<5=8 n ?5@8>4>2. 5@8>44%5%6%8%10%10,96150,95240,94340,92590,909121,88611,85941,83341,78331,735532,77512,72322,67302,57712,486943,62993,54603,46513,31213,169954,45184,32954,21243,99273,7908 0?@8<5@, A>2@5<5==>5 7=0G5=85 0==C8B5B0 1000 @C1;59, 5653>4=> ?>;CG05<K5 2 B5G5=85 5 ;5B ?@8 AB02:5 10% @025=  EMBED Equation.3  @C1;59 &5=0 :0?8B0;0 - MB> AC<<0 8A?>;L7C5<KE 2 ?@>5:B5 D8=0=A>2KE @5AC@A>2, 2 ?@>F5=B0E : >1I59 ?>B@51=>9 AC<<5 45=56=KE A@54AB2 =0 ;CGHCN @50;870F8N 8=25AB8F8>==>3> ?@>5:B0. =0 >?@545;O5BAO CA;>28O<8 8AB>G=8:0 D8=0=A8@>20=8O 8=25AB8F8>==>3> ?@>5:B0. AB>G=8:0<8 D8=0=A8@>20=8O <>3CB 1KBL: 10=:>2A:85 :@548BK, 709<K C 4@C38E >@30=870F89, ?@828;538@>20==K5 8 ?@>ABK5 0:F88.  7028A8<>AB8 >B 8AB>G=8:0 D8=0=A8@>20=8O F5=0 :0?8B0;0 <564C A>1>9 <>65B <5=OBLAO <564C A>1>9. !CI=>ABL 8 284K 8=>AB@0==>3> :0?8B0;0. =>AB@0==K5 8=25AB8F88 ?@54AB02;ONB A>1>9 :0?8B0;L=K5 A@54AB20, 2K2575==K5 87 >4=>9 AB@0=K 8 2;>65==K5 2 @07;8G=K5 284K ?@54?@8=8<0B5;LA:>9 45OB5;L=>AB8 70 @C156>< A F5;LN 872;5G5=8O ?@54?@8=8<0B5;LA:>9 ?@81K;8 8;8 ?@>F5=B0. =>AB@0==K5 8=25AB8F88 <>3CB >ACI5AB2;OBLAO 2 @07;8G=KE D>@<0E. @8 0=0;875 MB8E D>@< <>3CB 1KBL 8A?>;L7>20=K >1I85 ?>4E>4K : :;0AA8D8:0F88 8=25AB8F89, ?@54?>;030NI85 8E 2K45;5=85 ?> >1J5:B0<, F5;O<, A@>:0< 2;>65=8O, D>@<0< A>1AB25==>AB8 =0 8=25AB8F8>==K5 @5AC@AK, @8A:0< 8 4@C38< ?@87=0:0<. <5AB5 A B5<, A?5F8D8:0 8=>AB@0==KE 8=25AB8F89 >?@545;O5B =5>1E>48<>ABL CB>G=5=8O @O40 :;0AA8D8:0F8>==KE ?@87=0:>2 ?@8<5=8B5;L=> : 40==><C B8?C 8=25AB8F89. "0:, ?> D>@<0< A>1AB25==>AB8 =0 8=25AB8F8>==K5 @5AC@AK 8=>AB@0==K5 8=25AB8F88 <>3CB 1KBL 3>AC40@AB25==K<8, G0AB=K<8 8 A<5H0==K<8. >AC40@AB25==K5 8=25AB8F88 ?@54AB02;ONB A>1>9 A@54AB20 3>AC40@AB25==KE 1N465B>2, =0?@02;O5<KE 70 @C156 ?> @5H5=8N ?@028B5;LAB25==KE 8;8 <56?@028B5;LAB25==KE >@30=870F89. -B8 A@54AB20 <>3CB ?@54>AB02;OBLAO 2 2845 3>AC40@AB25==KE 709<>2, :@548B>2, 3@0=B>2, ?><>I8. 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