Ekonomi Teknik

Ekonomi TeknikTeknik Industri UnsikaAhmad SurahmanEkonomiIlmu Ekonomi merupakan ilmu pengetahuan yang berhubungan dengan alokasi sumberdaya.Sumberdaya: Sumber daya alam Sumber daya manusia Sumber daya teknologi Sumber daya pembiayaanEkonomi TeknikEkonomi teknik merupakan suatu evaluasi sistematis terhadap keuntungan ekonomi dari setiap solusi permasalahan enjiniring(1). Ekonomi teknik merupakan aplikasi dari evaluasi desain dan alternatif solusi enjiniring. Peranan ekonomi teknik adalah untuk meninjau kesesuaian dari proyek yang diberikan, memperkirakan nilainya dan menilai dari sudutpandang enjiniring(2).

1 Lecture Notes by Randolph Kirchain, Engineering Economics: Comparing Financial Characteristics of Design Options. Massachusetts Institute of Technology, Department of Materials Science & Engineering2 ASTM E833, Definitions of Terms Relating to Building Economics,American Society for Testing and Materials, West Conshohocken, PA (1999).MasalahSimple problem, merupakan masalah yang solusinya tidak memerlukan terlalu banyak pertimbangan dan analisis karena masalah itu bukanlah sesuatu yang terlalu penting.Intermediate problem, merupakan masalah yang solusinya memerlukan pertimbangan dan analisis pada suatu bidang tertentu.Complex problem, merupakan masalah rumit yang solusinya memerlukan pertimbangan dan analisis pada berbagai bidang ilmu.

Analisa Ekonomi TeknikMasalah yg cocok:Cukup penting, memerlukan pemikiran dan upaya serius.Tidak bisa dikerjakan sendiri, masalah perlu dirumuskan, disusun dan dianalisa secara hati2 dengan berbagai akibatnya. Mempunyai aspek ekonomi yang dominan sebagai komponen analisa bagi pengambilan keputusan

Proses Pengambilan Keputusan (Engineering)Pengenalan masalah.Pendefinisian sasaran atau tujuan.Mengumpulkan data yang relevan.Mengidentifikasi aftematif-altematif yang mungkin,Seleksi Kriteria untuk memutuskan diantara altematif-altematif.Membangun model.Prediksi hasil untuk tiap altematif.Memilih aftematif terbaik untuk mencapai tujuan.Pemeriksaan Pasca Keputusan

61. Pengenalan MasalahMasalah bisa muncul dari luar organisasi bisnis/perusahaan : misal peraturan baru. dan/atau dari dalam perusahaan misal kesalahan produksi.Mengetahui masalah saja tidak cukup, perlu dikenali, siapa yang bisa melakukan sesuatu terhadap masalah tsbSeringkali masalah dikenali oleh sekelompok pekerja atau pada area/fungsi tertentu, tapi kurang dikenali oleh orang akan mengawali proses pengambilan keputusan

2. Definisikan Sasaran/Tujuan Tidak selaluharus besar dan menyeluruh/umum seperti menghasilkan laba; bisa sempit, terbatas, spesifik: Memproduksi 300 mobil dalam 2 minggu, melunasi cicilan mobil di bulan Juni 2013 Setiap hal yang bisa menghambat pencapaian sasaran/tujuan adalah masalah3. Pengumpulan Data yg RelevanSumber data penting untuk konsekuensi finansial: sistem akuntansi perusahaan, sistem keuangan dan akuntansi biaya menunjukkan aliran uang dan nilai akuntansi : biaya dan manfaat ( costs n benefits), biaya langsung, biaya tak langsung. ( exercise 3-1 Newnan )Memuaskan utk kepentingan akuntansi biaya, belum tentu untuk kepentingan analisa ekonomi. Perlu dicari true differences diantara pilihan2 , mungkin diperlukan beberapa penyesuaianKonsekuensi Pasar: Semua konsekuensiyangsudah mempunyai harga pasar, harga material, mesin, buruh dllKonsekuensi diLuar Pasar ( extra market) : tidak secara langsung harga pasar, tapi bisa dialokasikan ( shadow prices ), misal : machine breakdowns, kecelakaan kerja, perubahan waktu kerja dllKonsekuensi tak ternilai ( intangibles ) : analisis ekonomi numerik tidak selalu menggambarkan perbedaan antar alternatip secara penuh. Ada yang tidak bisa dikonversi ke nilai uang. Misal dampak lingkungan, dampak thd etos kerja, perubahan budaya kerja, etika dll

10Sudut pandang ahli EKTEK

AkuntanMelihat ke masa laluNOWAhli EktekMelihat ke masa datangManajer Teknik

4. Identifikasi Pilihan/AlternatipCari semua pilihan yang mungkin ( possible alternatives ), pilhan konvensional dan innovatip. brainstorming akan sangat membantu.Buat daftar pilihan yang praktis maupun tidak praktis.Buang pilihan yng tidak layak: misal tidak memenuhi kaidah2 ilmiah, melanggar hukum/etika, material tidak bisa diperoleh, target waktu tidak bisa dipenuhi. Pilihan yang layak dapat dianalisa lebih lanjut. Dua alternatip sering diabaikan: do-nothing alternative dan feasible but unglamorous alternatives.

5. Memilih Kriteria Keputusan 3 kategori masalah analisa ekonomi:Fixed Input ( Masukan Tertentu ) : Maksimasi manfaat ( benefit )Fixed Output ( Keluaran Tertentu ) : Minimasi biaya ( costs )Neither Input nor output fixed ( Masukan atau keluaran tidak menentu ) : Maksimasi Manfaat Costs atau Maksimasi Laba6. Pembuatan ModelSemua element dipadukan: tujuan/sasaran, data relevan, pilihan2 layak, kriteria keputusan. Hubungan bisa sederhana atau rumit. Bisa model fisik atau matematisAnalisa ekonomi : model matematis7. Prediksi Hasil (outcome) Tiap AltematifSemua hasil (outcomes) dari setiap pilihan harus diatur/disusun dengan cara yang bisa dibandingkan ( comparable way ).Buat perhitungan2 matematis untuk semua pilihan agar perbandingan bisa mempunyai arti.Nyatakan semua konsekuensi dalam uang.Mulai dari Biaya Manfaat, konsekuensi pasar dan diluar pasar. Intangibles umumnya sulit dimasukkan ke dalam perhitungan numerik, termasuk kapan ( timing) terjadinya.Buat table arus kas ( cash flow table ).Parameter ekonomi a.l. Present Worth, Annual Cost, Rate of Return, Payback Period adalah beberapa alat yang bisa digunakan untuk mengolah tabel arus kas , agar pilihan dapat dibandingkan.

8. Memilih Alternatip TerbaikSolusi model menggunakan kriteria keputusan dengan 7 tahap diatas memudahkan utk memilih alternatip terbaik secara numerik. Namun konsekuensi intangible belum masuk dalam perhitungan.Walaupun konsekuensi ekonomi dominan dan intangibles dianggap kurang penting, alternatip yang harus dipilih adalah yang terbaik yang memenuhi konsekuensi ekonomi dan konsekuensi yang tidak dihitung dengan nilai uang.9. Pemeriksaan Pasca Keputusan ( Post Audit of Results )Analisa ekonomi berdasarkan data proyeksi masa depan.Post Audit Review diperlukan untuk mengetahui apakah data proyeksi dapat dicapai. Mengantisipasi kesalahan yng mungkin terjadi di masa depan.Semua orang yang terlibat perlu diberitahu bahwa semua hasil akan diaudit.

InvestasiInvestasi atau penanaman modal adalah menyangkut penggunaan sumber-sumber yang diharapkan akan memberikan imbalan (pengembalian) yang menguntungkan di masa yang akan datang. (Suratman, 2001:6)Faktor yang terlibat dalam investasi :WaktuResikoSecara umum Investasi dibedakan menjadi dua jenis ;Investasi finansialInvestasi nyata

Faktor yang dipertimbangkan untuk pemilihan peralatan :faktor suku bunga (interest), biaya awal (first cost), biaya eksploatasi (exploatation cost=biaya operasi dan pemeliharaan) yang akan dikeluarkan setiap tahun, nilai jual kembali (resale value) peralatan pada akhir umur ekonomisnya, overhaul cost, pendapatan-pendapatan yang diterima selama umur ekonomis, perkiraan umur ekonomis dalam tahun atau periode pengembalian modal.

Parameter Ekonomi :laju pengembalian modal (rate of return), ekivalensi nilai bersih sekarang (net present value), indeks keuntungan (profitability index), berapa lama investasi akan kembali (payback period), ekivalensi nilai arus kas tahunan (uniform annual cash-flow), ratio pendapatan terhadap biaya (benefit-cost ratio).Principle 1: A nearby dollar is worth more than a distant dollar ( moneys time value = konsep nilai waktu uang , bunga )Principle 2: All it counts is the differences among alternativesPrinciple 3: Marginal revenue must exceed marginal costPrinciple 4: Additional risk is not taken without the expected additional return Prinsip Dasar Ekonomi TeknikChapter 3Interest and EquivalenceNilai Waktu UangMoney has valueMoney can be leased or rentedThe payment is called interestIf you put $100 in a bank at 9% interest for one time period you will receive back your original $100 plus $9Original amount to be returned = $100Interest to be returned = $100 x .09 = $9Simple InterestInterest that is computed only on the original sum or principalTotal interest earned = I = P i n , where:P = present sum of money, or principal (example: $1000)i = interest rate (10% interest is a .10 interest rate)n = number of periods (years) (example: n = 2 years)I = $1000 x .10/period x 2 periods = $200Future Value of a Loan With Simple InterestAmount of money due at the end of a loanF = P + P i n or F = P (1 + i n )Where,F = future valueF = $1000 (1 + .10 x 2) = $1200Simple interest is not used todayCompound InterestCompound Interest is used and is computed on the original unpaid debt and the unpaid interest. Year 1 interest = $1000 (.10) = $100Year 2 principal is, therefore: $1000 + $100 = $1100Year 2 interest = $1100 (.10) = $110Total interest earned is: $100 + $110 = $210This is $10 more than with simple interestCompound Interest (Contd)Future Value (F) = P + Pi + (P + Pi)i= P (1 + i + i + i 2) = P (1+i)2= 1000 (1 + .10) 2 = 1210In general, for any value of n:Future Value (F) = P (1+i)n Total interest earned = In = P (1+i)n - PWhere, P present sum of moneyi interest rate per periodn number of periodsCompound Interest Over TimeIf you loaned a friend money for short period of time the difference between simple and compound interest is negligible.If you loaned a friend money for a long period of time the difference between simple and compound interest may amount to a considerable difference.

Nominal and Effective InterestInterest rates are normally given on an annual basis with agreement on how often compounding will occur (e.g., monthly, quarterly, annually, continuous).Nominal interest rate /year ( r ) the annual interest rate w/o considering the effect of any compounding (e.g., r = 12%).Interest rate /period ( i ) the nominal interest rate /year divided by the number of interest compounding periods (e.g., monthly compounding: i = 12% / 12 months/year = 1%).Effective interest rate /year ( ieff or APR ) the annual interest rate taking into account the effect of the multiple compounding periods in the year. (e.g., as shown later, r = 12% compounded monthly is equivalent to 12.68% year compounded yearly.Interest Rates (contd)We use i for the periodic interest rateNominal interest rate = r (an annual rate)Number of compounding periods/year = mr = i * m, and i = r / mLet r = .12 (or 12%)

Interest Periodm = interest periods / yeari = interest rate / periodAnnual1.12Quarter4.03Month12.01Effective InterestIf there are more than one compounding periods during the year, then the compounding makes the true interest rate slightly higher. This higher rate is called the effective interest rate or Annual Percentage Rate (APR)ieff = (1 + i)m 1 or ieff = (1 + r/m)m 1 Example: r = 12, m = 12ieff = (1 + .12/12)12 1 = (1.01)12 1 = .1268 or 12.68%Consider Four Ways to Repay a DebtCompound and pay at end of loanInterest on unpaid balanceInterest on unpaid balanceRepay InterestDeclines at increasing rateEqual installments3Compounds at increasing rate until end of loanEnd of loan4ConstantEnd of loan2DeclinesEqual installments1Interest EarnedRepayPrincipalPlanPlan 1 Equal annual principal paymentsYearBalancePiPayment150001000500150024000100040014003300010003001300420001000200120051000100010011006500Plan 2 Annual interest + balloon payment of principalYearBalancePiPayment150005005002500050050035000500500450005005005500050005005007500Plan 3 Equal annual payments (installments)YearBalancePiPayment15000.00819.00500.00131924181.00900.90418.10131933280.10990.99328.01131942289.111090.09228.91131951199.021199.10119.9013196595Plan 4 Principal & interest at end of the loanYearBalancePiPayment150000500025500055003605006050466550665.50057320.500732.058052.558052.55Which plan would you choose?Total Principal + Interest PaidPlan 1 = $6500Plan 2 = $7500Plan 3 = $6595Plan 4 = $8052.55EquivalenceWhen an organization is indifferent as to whether it has a present sum of money now or, with interest the assurance of some other sum of money in the future, or a series of future sums of money, we say that the present sum of money is equivalent to the future sum or series of future sums.Each of the four repayment plans are equivalent because each repays $5000 at the same 10% interest rate. To further illustrate this concept, given the choice of these two plans which would you choose?$7000$6200Total540010805400116044001240340013202$400$14001Plan 2Plan 1YearTo make a choice the cash flows must be altered so a comparison may be made.Technique of EquivalenceDetermine a single equivalent value at a point in time for plan 1.Determine a single equivalent value at a point in time for plan 2.Both at the same interest rateJudge the relative attractiveness of the two alternatives from the comparable equivalent values. You will learn a number of methods for finding comparable equivalent values.Analysis Methods that Compare Equivalent ValuesPresent Worth Analysis (Ch. 5) - Find the equivalent value of cash flows at time 0.Annual Worth Analysis (Ch. 6) - Find the equivalent annual worth of all cash flows.Rate of Return Analysis (Ch. 7, 8) - Compare the interest rate (ROR) of each alternatives cash flows to a minimum value you will accept.Future Worth Analysis (Ch. 9) - Find the equivalent value of cash flows at time in the future.Benefit/Cost Ratio (Ch. 9) - Use equivalent values of cash flows to form ratios that can be easily analyzed.Interest FormulasTo understand equivalence the underlying interest formulas must be analyzed. We will start with Single Payment interest formulas.Notation:i = Interest rate per interest period.n = Number of interest periods.P = Present sum of money (Present worth, PV).F = Future sum of money (Future worth, FV).If you know any three of the above variables you can find the fourth one.For example, given F, P, and n, find the interest rate (i) or ROR Principal outstanding over time (P) Amount repaid (F) at n future periods from now We know F, P, and n and want to find the interest rate that makes them equivalent:

If F = P (1 + i)nThen i = (F/P)1/n - 1

This value of i is the Rate Of Return or ROR for investing the amount P to earn the future sum FCash Flow DiagramsWe use cash flow diagrams to help organize the data for each alternative. Down arrow - disbursement cash flowUp arrow - Income cash flown = number of compounding periods in the problemi = interest rate/period

Notation forCalculating a Future ValueFormula:F=P(1+i)n is the single payment compound amount factor.Functional notation:F=P(F/P, i, n) F = 5000(F/P, 6%, 10)F =P(F/P) which is dimensionally correct.Find the factor values in the tables in the back of the text. Using the Functional Notation and Tables to Find the Factor ValuesF = 5000(F/P, 6%, 10)To use the tables:Step 1: Find the page with the 6% tableStep 2: Find the F/P columnStep 3: Go down the F/P column to n = 10The Factor shown is 1.791, therefore:F = 5000 (1.791) = $8955Using EXCEL Spreadsheet FunctionsOn the menu bar select the fx iconSelect the Financial Function menuSelect the FV function to find the Future Value of a present sum (or series of payments): FV(rate, nper, pmt, PV, type) where:rate = inper = npmt = 0PV = Ptype = 0Notation forCalculating a Present ValueP=F(1/1+i)n=F(1+i)-n is the single payment present worth factorFunctional notation:P=F(P/F, i, n) P=5000(P/F, 6%, 10)

Example: P=F(P/F, i, n)F = $1000, i = 0.10, n = 5, P = ?

Using notation: P = F(P/F, 10%, 5) = $1000(.6209)= $620.90

Chapter 4More Interest Formulas

Components of Engineering Economic AnalysisCalculation of P and F are fundamental.Some problems are more complex and require an understanding of added components:Uniform series.Arithmetic or geometric gradients.Nominal and effective interest rates (covered in presentation #5 on Chapter 3).Continuous compounding.EGR 403 - Cal Poly Pomona - SA651Uniform Payment SeriesCapital Recovery FactorThe series of uniform payments that will recover an initial investment.A = P(A/P, i, n)

Uniform Payment SeriesCompound Amount Factor FThe future value of an investment based on periodic, constant payments and a constant interest rate. F = A(F/A, i, n)

Example 4-100$500$500$500$500$500Cash in-$276354321Cash outYearF = $500(F/A, 5%, 5) = $500(5.526) = $2763At 5%/year

Uniform Payment SeriesSinking Fund FactorThe constant periodic amount, at a constant interest rate that must be deposited to accumulate a future value.

A = F(A/F, i, n)Uniform Payment SeriesPresent Worth FactorThe present value of a series of uniform future payments.

P = A(P/A, i, n)Example 4-6F = $100(F/A, 15%, 3) = $347.25F = $347.25(F/P, 15%, 2) = $459.24F5$04$1003$1002$1001Cash flowYear

Example 4-7Finding the Present Value (P) for each cash flow is sometimes the easiest way to find the equivalent P.P = $20(P/F, 15%, 2) + $30(P/F, 15%, 3) + $20(P/F, 15%, 4) = $46.28$ 204$ 303$ 20201P0Cash flowYearArithmetic GradientA uniform increasing amount.The first cash flow is always equal to zero.G = the difference between each cash amount.

G = $10Arithmetic Gradient combined with a Uniform SeriesDecompose the cash flows into a uniform series and a pure gradient. Then add or subtract the Present Value of the gradient to the Present Value of the Uniform series

Example 4-8: Use P/G factor to find present value of the pure gradient portion of the cash flow

Arithmetic Gradient Uniform Series FactorA pure gradient (uniformly increasing amount) can also be converted into the equivalent present value of uniform series:

AG = G(A/G, i, n)

See Example 4-9: Notice that the uniform series portion of the cash flow was subtracted to separate the pure gradient.Geometric Series Present Worth FactorSometimes cash flows increase at a constant rate rather than a constant amount. Inflation, for example, could be reflected in a cash flow diagram that way. The equivalent present value of a geometrically increasing amount. g = the rate of increase (e.g., .05)

P = A(P/A, g, i, n) where (P/A, g, i, n) must be computed from equation 4-30 or 4-31Example 4-12 uses g = .10 and i = .08Sheet1Pni%F1000110%$1,100.001000210%$1,210.001000310%$1,331.0010001010%$2,593.7410002010%$6,727.5010003010%$17,449.4010004010%$45,259.26

Sheet2

Sheet3

]]]Chart1000150012500235003450045500-2763

YearCash InCash Out

]]]Sheet1YearCash InCash Out0015002500350045005500-2763

]]]Sheet1000000000000000000

YearCash InCash Out

]]]Sheet2

]]]Sheet3