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1p 2






1 Ǜԧ 10 11 1 1

1

2


1 2 future value F present value P () () 1 (F) (1+)?P n P (1+i) (F/P,i,n) ᨢ1 1 ҧ 1 (1+i)n F/Pin 2 F1+P1+in P F1+ F1+i-n 1 1 1+i-n P/Fin

2

Annuity n Ǧ 1 FA A i n

(1 ? i) n ? 1 FAA i
ۧ F/Ain A1 1 ҧ1 FAA(F/Ain) 2 PA A i n

1 i n 1 PAA * ???????? i

1 1 1 PA= AP/Ain 3 1 F A A= F 2 P A

3

A= P

NCF= 1 () ǧۧ 2 NCF =

4

3 1 100 10 10 100 10 10 NCF =100+10=110 =1101010=10 NCF0 = 100 NCF1 = 0 NCF2-10 = + = 10 + 10 = 20 NCF11= + + = 10+10+10 = 30( ֧ N=1+10=11

5

K =Wj Kj 3000 3 3



1 2 3 8% 1200 1050 900 10% 900 1350 1400 14% 900 600 700

1Kw = 1200/30008%+900/300010%+900/300014% =10.4% 2Kw = 1050/30008%+1350/300010%+600/300014% =10.1% 3Kw = 900/30008%+1400/300010%+700/300014% =10.3%





1 2 1


2

6

PP= N+ n / n+1 N NCF
NCF NCF -300 130 160 180 150 80 -300 140 140 140 140 140 5

NCF

?
NCF

3 000 000 ? ? 2.14 NCF 1 400 000

NCF



1 2 3 4 5

1,300,000 1,600,000 1,800,000 1,500,000 800,000

1,300,000 2,900,000 4,700,000 6,200,000 7,000,000

1,700,000 100,000

= 2+100,000/(4,700,000-2,900,000) = 2.06 2.14 2.06

7

5/2=2.5 1 2 ARR = 1

(t? t ?
t0 n

n

NCFt n ? ??[ NCFt ? ( P / Fit )] t t ?0 1 i t ?0
2 NPV NPV NPV NPV

8

1403.433=480.62 NPV = 480.62-300180.62 >0







114.01 123.04 121.50 88.80 41.52 488.87 300.00



188.87

3
9



PI ?



=1 + s 1 1 1 PI

?

480.62 ? ? 1.60 300 488.87 ? ? ? 1.63 300
1.63 1.60



IRR

10

NCF

= Or



I (P/A,IRR,n) = NCF

IRR NCF r1 NPV NPV=0 r1 NPV0 r1 NPV0 r1 r1 NPV0 r2 NPV0| r1 r2 |5% IRR

NCF 140
? 300 ? 2.143 140

NCF

2.143 36% 40% 2.143 36%40% i 36 40% 36% + 1.04% = 37.04% NCF 36% PVA5i 2.181 2.143 2.035

11



NCF

36% 95.55 86.56 71.64 43.80 17.20 314.75 300.00 14.75

40% 0.714 0.510 0.364 0.260 0.186 92.82 81.60 62.52 39.00 14.88 293.82 300.00 -6.18



130 160 180 150 80

0.735 0.541 0.398 0.292 0.215



14.75 ֦ 40% 6.18 36%~40% i 36 ? 40% IRR36%+2.82%=38.82% 37.04% 38.82% 14% NPV 14.75 0 (6.18)

12

NPV IRR
IRR NPV 0 IRR NPV 0 IRR NPV 0 IRR 1 NPV IRR NPV IRR r=10% 0 1 2 3 NPV IRR (%)

A

-23 000

10 000

10 000

10 000

1869

14.6

B

-8 000

7 000

2 000

1 000

768

17.7

NPV A B IRR B A C=A-B 0 -15000 1 3000 2 8000 3 9000 NPV 1101 IRR 13.5

2 1 IRR 2 IRR 0 to 4 : -$100 +$100 +$900 -$1,000 IRRs ? !! .


1 4 5 1000 8 10%ħ A 2848 B2165 C2354 D.2032
13



5 x*1.1 5 1.61x-1000 6 1.61x-10001.1-1000 7 1.771x-2100*1.1-1000 8 1.948x-3310*1.1-10000 2.1428x4641 x2165 2. 90 2 14 NCF=30 57 NCF=35 B A4 B5 C6 D7 71000 50000 100000 10 15000 10 12% 33% (1) (2) 1=100 00010=10 000 =71 000-50 000-10 0001-33%=7370 NCF0=-100 000 NCF110=10 000+7370=17 370 NPV=-100 000+17 370PA/A12%10=-100 000+17 370 5.65022=-1855.68<0 PA/AIRR10=100 00017 370=5.75705 : PA/A10%10=6.14457>5.75705 PA/A12%10=5.65022<5.75705 =10%+(6.14457-5.75705)(6.14457-5.65022) (12%-10%)=11.57%<12% 2NCF0=0 NCF110=71 000-50 000-15 0001-33%=4020 NPV=0+4020PA/A12%10=40205.65022=22713.88>0

14


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