Time Value of Money-kelompok 2 (Kelas a)

8/10/2019 Time Value of Money-kelompok 2 (Kelas a)

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TIME VALUE OF MONEY

Kelompok 2 / Kelas A

Roy Marthin

Yunita Selonika

Raja Valti Annur Fauzi

Zwilla Oktoriana

Jhon Alperdo H S

Adli Satria Sandika

Yesi Afriani


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TIME VALUE OF MONEY

An initial amount of money that is invested increases in value with

time

Compounding

Discounting


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Schematic of compundingand discounting


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DISCRETE C SH FLOW

cash flow pattern are often best perceived graphically.figure shows equal discrete cash flows occurring once per

month at the end of the month for a period of 1 year,

0

2,000

4,000

6,000

8,000

10,000

12,000

1 2 3 4 5 6 7 8 9 10 11 12

Equal end of month cash flow

Equal end of month cash flow


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figure shows unequal cash flows occurring at the end ofeach month for 1 year. the cash flows shown are

equivalent at a discount rate of 10 percent per year.

0

5,000

10,000

15,000

20,000

25,000

1 2 3 4 5 6 7 8 9 10 11 12

Unequal end-of-month cash flow

Unequal end-of-month cashflow


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PRESENT WORTH OF TWO DIFFERENT CASH FLOW PATTERNS

Ex.7-4

The cash flow patterns in figs. 7-3 and 7-4 are numerically shown in two table

below, if the interrest compounded monthly 10% per year, calculate the total amount of

the cash flow, the present worth at zero time, and future worth at 12 months for both

series of cash flow

Present worthfactor

Future worth factor


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EQUAL END OF MONTH CASH FLOW

End of month j Cash flow $ Present-worth factor Present worth $ Future worth factor Future worth $

1 10,000 0.991735537 9917.355372 1.095583207 10955.83207

2 10,000 0.983539376 9835.393757 1.086528801 10865.28801

3 10,000 0.975410951 9754.109511 1.077549224 10775.49224

4 10,000 0.967349704 9673.497036 1.068643858 10686.43858

5 10,000 0.959355078 9593.55078 1.059812091 10598.12091

6 10,000 0.951426524 9514.265236 1.051053313 10510.53313

7 10,000 0.943563494 9435.634945 1.042366922 10423.66922

8 10,000 0.935765449 9357.654491 1.03375232 10337.5232

9 10,000 0.92803185 9280.318503 1.025208912 10252.08912

10 10,000 0.920362166 9203.621656 1.016736111 10167.36111

11 10,000 0.912755867 9127.558667 1.008333333 10083.33333

12 10,000 0.90521243 9052.124298 1 10000

Total 120,000 113745.0843 125655.6809


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UNEQUAL END-OF-MONTH CASH FLOW

End of month j Cash flow $ Present-worth factor Present worth $ Future worth factor Future worth $

1 7,000 0.991735537 6942.14876 1.095583207 7669.082452

2 11,000 0.983539376 10818.93313 1.086528801 11951.81681

3 11,500 0.975410951 11217.22594 1.077549224 12391.81607

4 9,500 0.967349704 9189.822184 1.068643858 10152.11665

5 10,000 0.959355078 9593.55078 1.059812091 10598.12091

6 7,500 0.951426524 7135.698927 1.051053313 7882.89985

7 11,000 0.943563494 10379.19844 1.042366922 11466.03615

8 9,500 0.935765449 8889.771766 1.03375232 9820.647037

9 10,000 0.92803185 9280.318503 1.025208912 10252.08912

10 6,000 0.920362166 5522.172994 1.016736111 6100.416667

11 8,000 0.912755867 7302.046934 1.008333333 8066.666667

12 19,304 0.90521243 17474.22074 1 19304

Total 120,304 113745.1091 125655.7084


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Continuous Cash Flows

A continuous cash flows is one in which

receipts and expenditure occur continuouslyover time

A continuous, constant rate of cashflow Pin dollars per period (usually 1year).

The compound rate of earning onthe accumulated amount M that hasbeen invested at the rate r.


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Calculate the future worth at 6 years with Eq. (7-

42):

F = (F/,r,N) = ( )

= $450,000 = $3.465x106


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Notice that the total of the cash flow in 6 years of

$450,000 annualy is $2.7 million. The additional

$0.765 million shown in the future-worth calculationis interest earned on the cash flow itself and by

compounding the earned interest.

The present worth at time zero of the cash flow isgiven by Eq. (7-43):

P = ( )


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Notice that same result can be obtained by

multiplying the future worth obtained with Eq. (7-

42) By the discount factor ; thus

P = F

= ($3,465 x 106) x ( ) = 2.144 x 106


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Tabulation of the cash flow a year at a time with a

continuous cash flow of $450,000 per year is

presented here.

Year , $1000/yr F/, yr, Eq.(7-39b) Future worth Fat 6 yr, $1000 P/F, yr at 6yr, Eq. (7-33) Present worthP at 0 yr, $1000

1 450 1.5531 699 0.6188 432

2 450 1.4337 645 0.6188 399

3 450 1.3235 596 0.6188 369

4 450 1.2217 550 0.6188 340

5 450 1.1278 508 0.6188 314

6 450 1.0411 468 0.6188 290

Totals $2700 $3465 $2144


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Compounding

andDiscounting

Factor


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Continuous interest

compounding &continous cashflow

Continuousinterestcompounding& discrete or

cash flow

Discreteinterest

compounding &discrete or

continous cashflow


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Singleamount cashflow

Uniform series cashflow

Figure 7.5 Figure 7.6


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TABLE 7.3

CompoundingandDiscounting

Factors forDiscreteInterestCompoundingand Discreteor ContinuousCash Flow


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TABLE 7.4


Factors forContinuousInterestCompoundingand DiscreteCash Flow


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One-year continous

constant rate cash flow

Series of Continuous,constant rate cash flows

Figure 7.7

Figure 7.8


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TABLE 7.5


Factors forContinuousInterestCompoundingandContinuousCash Flow


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Example. 7.6


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SOLUTION


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EX: 7-7

Repeat EX 7-6 but require that the compoundingbe performed continously. Do the calculationtwo ways: first using the nominal interest rate r

= 0,1 and the using ieff = 0,1.

Solution :

The cash flow pattern is the same as in Example 7-6,but the appropriate equations are from Table 7-4.The future worth is given by


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Terima Kasih

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Time Value of Money-kelompok 2 (Kelas a)

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