ENGINEERING ECONOMY EKONOMI TEKNIK...2! Ekonomi Teknik (Engineering Economy) Sesi 3! Dr. Ir. Manerep...

ENGINEERING ECONOMY EKONOMI TEKNIK

Dr. Ir. Manerep Pasaribu

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Ekonomi Teknik (Engineering Economy) Sesi 3

Dr. Ir. Manerep Pasaribu zDig


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Learning Objective Diharapkan peserta memiliki kompetensi dan kemampuan memahami dan menerapkann konsep-konsep ekonomi yang diperlukan di bidang teknik.

“An engineer who is unprepared to excel at engineering economy is not properly equipped for his or her job” (Sullivan, 2012)

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Goal of the Firm 1. Profit Maximization 2. Maximization of

Shareholder Wealth

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Foundation of Financial Management

• The2 Risk-Return Trade-off –We won’t take on additional risk unless we expect to be compesated with additional return

• The time value of money —a dollar received today is worth more than a dollar received in the future

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Life Cycle Step E

xpec

ted

Ret

urn

Risk

Expected return for delaying consumption

Expected return for taking added risk

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Principles of Money—Time Relationship The Following topics to be discussed is :

• Return to Capital • Origin of Interest • Simple Interest • The concept of equivalence • Cash flow diagrams/tables •  Interest formulas

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Introduction • Capital berkaitan dengan kekayaan (wealth) dalam

bentuk uang atau property(milik) yang dapat digunakan untuk menghasilkan lebih besar kekayaan

•  “Uang memancing Uang”. Dan engineering economy mempelajari tentang komitmen capital dalam periode yang panjang

• Uang satu dollar saat sekarang lebih berharga dari satu dollar pada waktu satu atau dua tahun yang akan datang karena ada bunga(laba) yang dapat dihasilkan

• Uang memiliki suatu nilai waktu (time value)

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Mengapa mempertimbangkan pengembalian terhadap modal? (1) •  Capital (modal) dalam bentuk uang untuk orang, mesin,

material, energi dan yang lainnya yang diperlukan dalam operasi dapat dikategorikan dalam 2 kategori yaitu : •  Modal ekuitas (equity capital) yang dimiliki individu yang

telah diinvestasikan uangnya dalam proyek atau joint venture (usaha) seharusnya menerima laba.

•  Modal hutang (debt capital), yang disebut juga modal pinjaman (borrowed capital), yang diperoleh dari pemberi pinjaman (lender), misalnya melalui surat-surat berharga atau pinjaman dari bank untuk investasi. Sebagai pengembaliannya seharusnya pemberi pinjaman menerima bunga (interest) dari peminjam.

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Mengapa mempertimbangkan pengembalian terhadap modal? (2) •  Terdapat hal yang sangat fundamental mengapa

pengembalian modal dalam bentuk bunga (interest) dan keuntungan (profit) yang menjadi bahan penting Ekonomi Teknik

•  Bunga (interest) dan laba (profit) terus menerus memberikan penghasilan pada pemberi modal selama modal digunakan.

•  Pengembalian terhadap modal sebagai suatu “incentives” dan merupakan penghasilan yang diberikan untuk resiko (risk) yang diambil oleh para investor dan pemberi pinjaman.

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Interest rate Rate of return

Interest earned Interest paid

Interest Rate interest accrued per time unit Interest Rate (%) = x 100%

original amount

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Asal mula bunga (interest) •  Seperti pajak (tax),maka bunga telah ada dalam

catatan sejarah manusia 2000 SM di Babilonia •  Tahun 575 SM gagasan bunga sudah begitu mapan di

Babilonia dengan kantor yang resmi dalam penggunaan uang untuk perdagangan internasional

•  Sejarah mencatat sudah ada tingkat suku bunga berkisar (6-25%) per tahun. Pengenaan tingkat suku bunga yang berlebih disebut dengan riba (usury)

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Bunga Sederhana (Simple Interest)

Dimana : I : Bunga Total P : Banyaknya Pinjaman N : Banyaknya periode Bunga i : tingkat biaya pa per periode bunga

I = (P) (N) (i)

Sistem bunga hanya didasarkan atas besarnya pinjaman semula dan bunga periode sebelumnya yang belum dibayar tidak termasuk faktor pengali bunga

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Bunga sederhana (Simple Interest)

Jumlah yang dipinjam P = $1,000 dalam N = 3 tahun dan tingkat suku bunga sebesar 10% per tahun, maka bunga yang didapat adalah ;

I = $,1000 x 3 x 0.10 = $300

Jadi, total hutang pada akhir tahun ketiga sebesar $1,000 + $300 = $1300

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Bunga Majemuk (Compund Interest)

Apabila bunga yang dibebankan untuk setiap periode (misalnya 1 tahun) didasarkan pada sisa pinjaman pokok ditambah setiap beban biaya yang terakumulasi sampai pada awal periode itu, seperti contoh pada pinjaman $1,000 selama 3 tahun pada tingkat biaya 10% per tahun. Perhitungan majemuk dapat dilihat pada contoh berikut ini......

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Bunga Majemuk (Compound Interest)

(1) (2) = (1) x 10% (3) = (1) + (2)

Amount Owed at Interest Amount Amount Owed Period Beginning of Period for Period at End of Period

1 $1,000 $100 $1,100 2 $1,100 $110 $1,210 3 $1,210 $121 $1,331

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Simple Interest Vs Compound Interest

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KONSEP KEINVALENAN (THE CONCEPT OF EQUIVALENCE)

• Plan 1 : At End of Each Year Pay $2,000 Principles Plus Interest Due

• Plan 2 : Pay Interest Due at End of Each Year and Principal at End of Four Year

• Plan 3: Pay in Equal End-‐of-‐Year Payments • Plan 4: Pay Principal and interest in One Payment of Four Year

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Four Plans for repayment of $8000 in four years with interest at 10% Per Year

(1) (2) (3) = 10% x (1) (4) = (2) + (3) (5) (6) = (3) + (5) Amount Owed at Interest Accrued Amount Owed Principal Total End of Year

Year Beginning of Year for Year at End of Period Payment Payment (Cash Flow) Plan 1 : At End of Each Year Pay $2,000 Principles Plus Interest Due

1 $8.000 $800 $8.800 $2.000 $2.800 2 $6.000 $600 $6.600 $2.000 $2.600 3 $4.000 $400 $4.400 $2.000 $2.400 4 $2.000 $200 $2.200 $2.000 $2.200

$20.000 $2.000 $8.000 $10.000 (total interest) (total amount repaid)

Plan 2 : Pay Interest Due at End of Each Year and Principal at End of Four Year 1 $8.000 $800 $8.800 $0 $800 2 $8.000 $800 $8.800 $0 $800 3 $8.000 $800 $8.800 $0 $800 4 $8.000 $800 $8.800 $8.000 $8.800


Plan 3: Pay in Equal End-‐of-‐Year Payments 1 $8.000 $800 $8.800 $1.724 $2.524 2 $6.276 $628 $6.904 $1.896 $2.524 3 $4.380 $438 $4.818 $2.086 $2.524 4 $2.294 $229 $2.523 $2.294 $2.524


Plan 4: Pay Principal and interest in One Payment of Four Year 1 $8.000 $800 $8.800 $0 $0 2 $8.800 $880 $9.680 $0 $0 3 $9.680 $968 $10.648 $0 $0 4 $10.648 $1.065 $11.713 $8.000 $11.713


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0

2000

4000

6000

8000

1 2 3 4

8000 6000

4000 2000

Years

Am

ount

Ow

ed ($

)

From Col. 2 of Table 3-1 for plan 1

Total Dollar-Years = 20,000

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The Sum of coloumn 3

Plan

Area Under Curve (Dollar-‐Years) (Sum of Col. 2 In table 3-‐1)

Total Interest Pain (Sum of Col. 3 In table 3-‐1)

Ratio of total interest to Dollar-‐Years

1 20,000 2,000 0.10 2 32,000 3,200 0.10 3 20,960 2,096 0.10 4 37,130 3.,713 0.10

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Notation and Cash Flow Diagrams/ Tables i = effective interest rate per interest period

N = number of compounding periods

P = present sum of money; the equivalent value of one or more cash flows at a reference point in time called the present

F = future sum of money; the equivalent value of one or more cash flows at a reference point in time called the present future

A = end-of-period cash flows (or equivalent end-of-period values) in a uniform series continuing for a specified number of periods, starting at the end of the first periods and continuing trough the last period

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Four Plans for repayment of $8000 in four years with interest at 10% Per Year (1) (2) (3) = 10% x (1) (4) = (2) + (3) (5) (6) = (3) + (5)

Amount Owed at Interest Accrued Amount Owed Principal Total End of Year Year Beginning of Year for Year at End of Period Payment Payment (Cash Flow)

Plan 1 : At End of Each Year Pay $2,000 Principles Plus Interest Due 1 $8.000 $800 $8.800 $2.000 $2.800 2 $6.000 $600 $6.600 $2.000 $2.600 3 $4.000 $400 $4.400 $2.000 $2.400 4 $2.000 $200 $2.200 $2.000 $2.200


Plan 2 : Pay Interest Due at End of Each Year and Principal at End of Four Year 1 $8.000 $800 $8.800 $0 $800 2 $8.000 $800 $8.800 $0 $800 3 $8.000 $800 $8.800 $0 $800 4 $8.000 $800 $8.800 $8.000 $8.800


Plan 3: Pay in Equal End-‐of-‐Year Payments 1 $8.000 $800 $8.800 $1.724 $2.524 2 $6.276 $628 $6.904 $1.896 $2.524 3 $4.380 $438 $4.818 $2.086 $2.524 4 $2.294 $229 $2.523 $2.294 $2.524


Plan 4: Pay Principal and interest in One Payment of Four Year 1 $8.000 $800 $8.800 $0 $0 2 $8.800 $880 $9.680 $0 $0 3 $9.680 $968 $10.648 $0 $0 4 $10.648 $1.065 $11.713 $8.000 $11.713


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Years i = 10% per year

Beginning of year 1

End of year 1

P = $8,000

F = $11,713

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Figure 4-3

Years i = 10% per year

P = $8,000

A = $2524

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ENGINEERING ECONOMY EKONOMI TEKNIK...2! Ekonomi Teknik (Engineering Economy) Sesi 3! Dr. Ir. Manerep...

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