1/19/2010 Pranoto.SA 1

Unsur-unsurDasar Ekonomi Rekayasa :

Investasi, Interest Rate, Cost,Benefit

Cash Flow Diagram

Time Value Eqivalent

1/19/2010 Pranoto.SA 2

The fee that a borrower pays to a leader for the use of his or her money.

INTEREST RATEINTEREST RATE

The percentage of money being borrowed that is paid to the lender on some time basis.Example : 10% per annum.

1/19/2010 Pranoto.SA 3

The total interest earned is linearly proportional to the initial amount of the loan (principal), the interest rate end the number of interest periods for which the principal is comitted.

When applied, total interest “I” may be found by :I = (P) (N) (i)

Where :P = principal amount lent or borrowed.N = number of interest periods (e.g. years).

i = interest rate per interest period.(eg. P=100,N=5,i=3% : I=100x5x0.03=15)

F=P (1+ni)=115

1/19/2010 Pranoto.SA 4

Interest charged for the current period is based on the remaining principal amount plus any accumulated interest charges up to the beginning of the period.

Period Amount owed

Interest for Amount owed

Start of period

Period (@ 10%) End of period

1 $ 1,000 $ 100 $ 1,100

2 $ 1,100 $ 110 $ 1,210

3 $ 1,210 $ 121 $ 1,331F=P(1+i)^n = 100(1.03)^10=134

1/19/2010 Pranoto.SA 5

Interest rate 3%

Amount owed (P + I)

Year Simple interest

Compound interest

0 100 100

1 103 103

2 106 106

3 109 109

4 112 113

5 115 116

10 130 134

15 145 156

20 160 181

25 175 209

30 190 243

35 205 281

40 220 326

45 235 378

50 250 438

Simple Interest:F=100+(100 x I x n)N=10 ; F=100+100x0.03x10=130

Compound Interest:F=100(1+i)^nN=10 ; F=100(1.03)^10=134

1/19/2010 Pranoto.SA 6

A student borrows Rp.3.000.000 from his uncle in order to finish study. His uncle agrees to charge him simple interest at the rate of 5.5% per year. Suppose the student waits two years and then repays the entire loan. How much will he have to repay?

F = P (1+ni) = 3.000.000(1+0.055*2)= Rp.3.330.000A student deposit Rp.1000.000 in a saving acount that pays interest at the rate of 6 % per year compounded annually. If all the money is allowed to accumulate, how much will the student have after 12 years?

F=P(1+i)^n = 1000.000(1+0.06)^12=Rp.2.012.000Compare with simple interest:F=1000.000(1+0.06*12)= Rp.1.720.000

1/19/2010 Pranoto.SA 7

Investment :

Funding or donation for invest in any project as Capital purpose, or fund is saved for received profit in the future.

Cost :Funding which have to paid for operation and maintenance of the project

Benefit:Out put or product can sold, or things which receiving profit income

1/19/2010 Pranoto.SA 8

Rehabilitation:The funding for repared to aim the think can remain perform

Normalization:The funding for service or small repared to reach the thing is normaly perform

InflationNational Economies frequently experience

inflation, in which the cost of goods and services increases from one year to the next. Normally, inflationary increases are expressed in term of percentages which are compounded annually. Thus, if the present cost of a commodity is PC, its future cost, FC will be:

FC= PC(1+i)^ni = annual inflation rate (expressed as a decimal)n= number of years

1/19/2010 Pranoto.SA 9

Example

An economy is experiencing inflation at the rate 6% per year. An item persently cost $.100. If the inflation rate continues, what will be price of this item in five years?

FC=$.100(1+0.06)^5=$.133.82

1/19/2010 Pranoto.SA 10

1/19/2010 Pranoto.SA 11

1. Time scale with progression of time moving from left to right; the numbers represent time periods (e.g., years, months, quarters, etc …) and may be presented within a time interval or at the end of a time interval.

2. Present expense (cash outflow) of $ 8,000 for lender.3. Annual income (cash inflow) of $ 2,524 for lender.4. Interest rate of loan.5. Dashed-arrow line indicates amount to be determined.

1

2 4

53

P = $8,000

1 2 3 4 5 = N

A = $2,524

i = 10% per year

1/19/2010 Pranoto.SA 12

i = effecive rate per interest period.N = number of compounding periods (e.g., years).P = present sum of money; the equvalent value of one or

more cash flows at the present time reference point.F = future sum of money; the equvalent value of one or

more cash flows at a future time reference point.A = end-of-period cash flows (or equvalent end-of-period

value) in a uniform series continuing for a specified number of periods, starting at the end of the first period and continuing through the last period.

G = uniform gradient amounts – used if cash flows increase by a constant amount in each period.

1/19/2010 Pranoto.SA 13

CASH FLOW

B2

CRCC

I

B2B1B1

4321

FV

I : invest R: Rehabilitation

B1: Benefit 1

C: Cost Benefit 2 FV: Future Value

1/19/2010 Pranoto.SA 14

•:

71 2 3 4 5 6

I1 I2 C C C C C

B B B B B

I1 = 4 M dan I2=10, (i investasi =15%)

Cost ( C ) = 2 M ( i = 20%)Benefit ( B ) = 6 M ( i = 10%)•Bagaimana kondisi keuangan proyek tersebut pada akhir tahun ke 7 ? (Hitung dengan kreteria NPV).•Bila hal tersebut masih rugi, dan kondisi C dan B tetap kapan proyek tersebut akan mulai untung (n=…th)?

Bila cashflow suatu proyek seperti berikut

Contoh Lapangan Futzal akan dibangun di daerah Tembalang pada

awal tahun 2011, dengan biaya investasi cost and benefit sebagai berikut :

Investasi I1 sebesar Rp. 10 Milyar , untuk pembangunan dan selesai dalam kurun waktu 2 tahun.

Operasional (C) diperkirakan Rp. 1 Milyar / tahun, dan meningkat menjadi 2M sejak Rehabilitasi.

Rehabilitasi pada awal th ke 5 dari saat mulai investasi sebesar 2M (waktu rehabilitasi abaikan=0)

Benefit untuk tahap I(pertama), sebesar Rp. 3 Milyar / tahun, dan meningkat setelah adanya rehabilitasi menjadi 6 M.

Bila Saudara sebagai investor diberi hak mengelola sampai tahun 2017, bagaimana pendapat Saudara ?

Tunjukkan analisa finansial Saudara (FV), diawali dengan gambar cashflow. (Gunakan asumsi bunga pengeluaran : I,R,C=15%, bunga pemasukan B;10%).

1/19/2010 Pranoto.SA 15

1/19/2010 Pranoto.SA 16