金融学第二版课件Chapter04 Allocating Resources Over Time

1、Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 1 Objective Explain the concept of compounding and discounting and to provide examples of real life applications Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 2 Copyright 2009 Pearson Education, Inc. Publishing a

2、s Prentice Hall 3 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 4 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 5 1 Year$1.1 2 Years$1.21 3 Years$1.331 4 Years$1.4641 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 6 1 Year$5*(1+0.10)$5.5

3、2 years$5.5*(1+0.10)$6.05 3 years$6.05*(1+0.10)$6.655 4 Years$6.655*(1+0.10)$7.3205 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 7 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 8 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 9 n iPVFV)1

4、 (* FV with growths from -6% to +6% 0 500 1,000 1,500 2,000 2,500 3,000 3,500 02468101214161820 Years Future Value of $1000 6% 4% 2% 0% -2% -4% -6% Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 10 Your bank offers a CD with an interest rate of 3% for a 5 year investment. You wis

5、h to invest $1,500 for 5 years, how much will your investment be worth? 1111145.1738$ )03.01 (*1500$ )1 (* 5 n iPVFV n5 i3% PV1,500 FV? Result 1738.911111 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 11 This rule says that the number of years it takes for a sum of money to doub

6、le in value (“the doubling time”) is approximately equal to the number 72 divided by the interest rate expressed in percent per year Doubling Time = 72 Interest Rate Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 12 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Ha

7、ll 13 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 14 n n n n iFV i FV PV i iPVFV )1 (* )1 ( :obtain to)1 (by sidesboth Divide )1 (* Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 15 today55.293,34$ 55281.34293 )08. 01 ( 000,40 )1 ( 2 n i FV PV Copyright 200

8、9 Pearson Education, Inc. Publishing as Prentice Hall 16 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 17 1 )1 ( )1 ( )1 (* n n n n PV FV i PV FV i i PV FV iPVFV Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 18 point) basisnearest the(to %18. 7 071773463. 0

9、12121 15000 30000 1 10 1 10 10 n PV FV i Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 19 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 20 is Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 21 )ln()ln( )ln()ln()*ln( )ln( 0, )ln( xyx yxyx x

10、e xxe y x x Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 22 )ln(*)ln()ln( )ln()ln()ln()*ln( )ln()ln()/ln( yxyx zyxzyx yxyx Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 23 i PVFV i PV FV n ini PV FV i PV FV iPVFV n n n 1ln lnln 1ln ln 1ln*)1(lnln )1( )1(* C

11、opyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 24 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 25 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 26 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 27 Copyright 2009 Pearso

12、n Education, Inc. Publishing as Prentice Hall 28 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 29 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 30 A n n u a l P e r c e n t a g e r a t e F r e q u e n c y o f C o m p o u n d in g A n n u a l E f f e c t iv e

13、 R a t e 1 811 8 . 0 0 1 821 8 . 8 1 1 841 9 . 2 5 1 81 21 9 . 5 6 1 85 21 9 . 6 8 1 83 6 51 9 . 7 2 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 31 111 k m m m e m k LimEFF Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 32 Copyright 2009 Pearson Education,

14、Inc. Publishing as Prentice Hall 33 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 34 11* 11 11 1 1 m m EFFmk EFF m k m k EFF m m m m Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 35 A n n u a l E f f e c t i v e R a t e C o mp o u n d i n g F r e q u e n c y

15、 A n n u a l P e r c e n t a g e R a t e 1 211 2 . 0 0 1 221 1 . 6 6 1 241 1 . 4 9 1 21 21 1 . 3 9 1 25 21 1 . 3 5 1 23 6 51 1 . 3 3 1 2I n f i n i t y1 1 . 3 3 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 36 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 37

16、 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 38 Time Lines Future Value of a Stream of Cash Flow Present Value of a Stream of Cash Flows Investing with Multiple Cash Flows Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 39 Copyright 2009 Pearson Education, I

17、nc. Publishing as Prentice Hall 40 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 41 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 42 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 43 Copyright 2009 Pearson Education, Inc. Publishing as Pr

18、entice Hall 44 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 45 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 46 n n i pmt i pmt i pmt i pmt i pmt PV 111 11 13 21 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 47 1 1 1 1 1 1 1 1 1 1 * 13

19、21 nn iii ii pmtPV Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 48 1 1 1 1 1 1 1 1 1 1 *)1 (*)1 (* 13 21 nn iii ii ipmtiPV Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 49 n nnn nnnn i pmt iiii i pmt i pmt iiiii ii pmtiPV 1 1 1 1 1 1 1 1 1 1 1 1 * 1 1 * 1 1

20、 1 1 1 1 1 1 1 1 1 1 1 1 *)1 (* 122 10 122 10 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 50 n n n n ii pmt i i pmt PV i pmtpmtPViPV i pmtPV i pmtiPV 1 1 1* 1 1 1* 1 1 )1 (* 1 1 1 1 *)1 (* 0 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 51 n n ii pmt i i p

21、mt PV 1 1 1* 1 1 1* Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 52 n n n i iPV pmt i i pmt ii pmt PV 11 * 11* 1 1 1* Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 53 i pmt iPV n pmt iPV i pmt iPV in pmt iPV i i pmt iPV i i pmt PV n n nn 1ln * 1ln ; * 11 *

22、1ln1ln*; * 11 11 * ;11* Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 54 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 55 1)1(* )1 (*11* )1 (* 1 n n regdue ii i pmt ii i pmt iPVPV Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 56 11* 1* 1

23、 1 1*FV sum) (lump 1*FV annuity) (reg. 1 1 1* n n n n n i i pmt i ii pmt iPV ii pmt PV Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 57 11 * 11* n n i iFV pmt i i pmt FV Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 58 i pmt iFV n pmt iFV ini i pmt iFV i i p

24、mt FV n n n 1ln * 1ln * 1ln1ln*1ln 1 * 1 11* Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 59 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 60 n ii pmt PV 1 1 1* Let n - infinity with i 0: i pmt PV Copyright 2009 Pearson Education, Inc. Publishing as Prentic

25、e Hall 61 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 62 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 63 500,13$ 03.0*)1.01(*500000$Points 000,450$ )1.01(*500000$Loan Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 64 niPVFV PMTResult 3

26、60 0.5% 450,0000?-2,697.98 This is the monthly repayment Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 65 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 66 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 67 niPVFVPMTResult 360 .5% 450,000 0

27、?-2,697.98 300 .5%?0-2,697.98418,745 Outstanding 60 Months Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 68 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 69 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 70 Copyright 2009 Pearson Educatio

28、n, Inc. Publishing as Prentice Hall 71 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 72 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 73 Amortization of Principal 0.00 50000.00 100000.00 150000.00 200000.00 250000.00 300000.00 350000.00 400000.00 450000.00 0

29、24487296120144168192216240264288312336360 Months Outstanding Balance Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 74 After Tax Cash Flow $1,500 $1,700 $1,900 $2,100 $2,300 $2,500 $2,700 $2,900 024487296120144168192216240264288312336360 Monthly Cash Flow Month Copyright 2009 Pea

30、rson Education, Inc. Publishing as Prentice Hall 75 Percent of Interest and Principal 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 024487296120144168192216240264288312336360 Months Percent % Interest % Principal Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 76 10% Aditional Payme

31、nts 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000 024487296120144168192216240264288312336360 Months Principal Outstanding Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 77 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 78 $10,000 $11,0

32、00 1,000,000 1,030,000 Time 10% $/$ (direct) 0.01 $/ 3% / ? $/ U.S.A.Japan Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 79 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 80 $10,000 $11,124 $11,000 1,000,000 1,030,000 Time 10% $/$ (direct) 0.01 $/ 3% / 0.0108

33、 $/ U.S.A.Japan Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 81 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 82 $10,000 $10,918 $11,000 1,000,000 1,030,000 Time 10% $/$ (direct) 0.01 $/ 3% / 0.0106 $/ U.S.A.Japan Copyright 2009 Pearson Education, Inc. Publ

34、ishing as Prentice Hall 83 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 84 $10,000 $11,000 $11,000 1,000,000 1,030,000 Time 10% $/$ (direct) 0.01 $/ 3% / 0.01068 $/ U.S.A.Japan Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 85 Copyright 2009 Pearson Educatio

35、n, Inc. Publishing as Prentice Hall 86 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 87 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 88 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 89 Copyright 2009 Pearson Education, Inc. Publishing a

36、s Prentice Hall 90 r ri i r i i n r n r 11 1 1 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 91 %86. 20286. 0 05. 1 05. 008. 0 11 1 1 r n r n r i r ri i r i i Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 92 Copyright 2009 Pearson Education, Inc. Publishing

37、as Prentice Hall 93 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 94 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 95 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 96 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 97

38、Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 98 years48. 5 03. 1ln12. 1ln 03. 1*3000 03. 012. 020000 1ln 1ln1ln 1 1ln 1ln1ln 1ln1ln 1 1 1 1 1 1 0 00 0 n gr gX grP n rg gXgrPgX n r g P r g gr gX PV nn Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 99 Copyrigh

39、t 2009 Pearson Education, Inc. Publishing as Prentice Hall 100 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 101 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 102 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 103 Copyright 2009 Pearson E

40、ducation, Inc. Publishing as Prentice Hall 104 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 105 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 106 56.851,88$ )03. 01 (000,40 )1 ( 27 n iPF Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 107

41、 NIPVPMT FV 273% 40,0000? $88,851.56 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 108 Live! Blow the money on that red convertible! Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 109 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 110 Copy

42、right 2009 Pearson Education, Inc. Publishing as Prentice Hall 111 %87. 60687. 01 3287 4583 1)1 ( 5 1 1 i P F iiPF n n Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 112 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 113 Cyclical Price Movement 0 50 100 150 20

43、0 250 300 024681012 Year Price ($) Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 114 0 150 0150150 iodReturnHoldingPer StartCF DividendsStartCFEndCF %67.41%100%100%75%100 12 1 75 75150 75 75150 300 30075 150 150300 12 1 Compare with Average HPR Copyright 2009 Pearson Education,

44、Inc. Publishing as Prentice Hall 115 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 116 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 117 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 118 Copyright 2009 Pearson Education, Inc. Publishing

45、as Prentice Hall 119 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 120 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 121 %10. 1%096667999. 1 1 5 5000000000 11 1900 1 1 n P F niPF n n Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 122 niPV

46、 Pmt FV 1900? 1.09666% -505,000,000,000 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 123 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 124 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 125 Copyright 2009 Pearson Education, Inc. Publishi

47、ng as Prentice Hall 126 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 127 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 128 yearsn i P F niPF n 05.13 07. 01ln 284, 9 450,22 ln 1ln ln 1 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 129 Co

48、pyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 130 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 131 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 132 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 133 27.218, 2$ )01. 01

49、 ( 000, 6 )1 (* )1 ( )1 ( 100 P iF i F PiPF n n n Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 134 NIPVPMTFV 1001%? -2,218.27 06000 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 135 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 136 1 n

50、PFi Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 137 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 138 72. 0 1 2 ln 2 08. 02 * :8%i double, To ln 2 2 2 *2 ln 25 1 23 1 2 2 ln 1ln ln 1 53 in P F i i i i P F n i i i i i i P F i P F niPF n Copyright 2009 Pears

51、on Education, Inc. Publishing as Prentice Hall 139 %16. 7121 2 answerAccurate %20. 7% 10 72 72. 0* 10 1 1 n x x i i ni Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 140 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 141 Copyright 2009 Pearson Education, Inc.

52、Publishing as Prentice Hall 142 Doubling your Money 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00% 051015202530 Years Interest rule algebra Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 143 Absolute Error -30.00% -25.00% -20.00% -15.00% -10.00% -5.0

53、0% 0.00% 5.00% 051015202530 Years % Error error Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 144 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 145 Absolute Error -0.40% -0.35% -0.30% -0.25% -0.20% -0.15% -0.10% -0.05% 0.00% 0.05% 0.10% 51015202530 Years % E

54、rror Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 146 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 147 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 148 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 149 Copyright 2

55、009 Pearson Education, Inc. Publishing as Prentice Hall 150 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 151 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 152 Ten Years Growth 3% & 12% 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 01234567891

56、0 Holding Period in Years Value at end of Holding Period CDStock Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 153 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 154 48 Years Log scale 10000 100000 1000000 10000000 100000000 05101520253035404550 Holding Perio

57、d in Years Value at end of Holding Period (Log Scale) CDStock Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 155 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 156 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 157 Copyright 2009 Pearson Ed

58、ucation, Inc. Publishing as Prentice Hall 158 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 159 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 160 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 161 yearFlowAccumulation 8$30.00$30.00 7$70.0

59、0$97.27 6$90.00$178.43 5$130.00$292.21 4$140.00$405.64 3$140.00$508.77 2$110.00$572.52 1$90.00$610.47 0$0.00$554.97 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 162 rate0.1 RateFactor=1+rate yearFlowAccumulation 830=0 + B8 770=C8/RateFactor + B9 690=C9/RateFactor + B10 5130=C10

60、/RateFactor + B11 4140=C11/RateFactor + B12 3140=C12/RateFactor + B13 2110=C13/RateFactor + B14 190=C14/RateFactor + B15 00=C15/RateFactor + B16 Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall 163 year_Flow_Discounted 0$0.00$0.00 1$90.00$81.82 2$110.00$90.91 3$140.00$105.18 4$140.