TIN205 - Ekonomi Teknik Materi #10 Genap 2014/2015 TIN205 EKONOMI TEKNIK

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1 TIN205 - Ekonomi Teknik Materi #10 TIN205 EKONOMI TEKNIK Pendahuluan (1) 2 Seandainya anda menginvestasikan senilai ($1.650) dalam rekening tabungan 6% per tahun. Kemudian anda hanya memperoleh $9.477 pada Januari tahun Apa arti dari 6% interest disini? Ini adalah opportunity cost jika menyimpan uang pada rekening tabungan, dan merupakan suatu tindakan yang terbaik yang dapat dilakukan saat itu Taufiqur Rachman 1

2 TIN205 - Ekonomi Teknik Pendahuluan (2) 3 Kemudian, pada tahun 1970, anda memperoleh tawaran untuk investasi lain dengan interest lebih dari 6% untuk investasi lain, anda akan mengambil investasi tersebut? Dalam hal ini, 6% dipandang sebagai minimum attractive rate of return/marr (rate of return yang dibutuhkan). Maka, anda dapat menetapkan aturan keputusan berikut untuk memperoleh investasi yang diusulkan yang terbaik jika: ROR > MARR Definisi #1 ROR 4 Rate of return (ROR) merupakan interest rate yang diperoleh pada unpaid balance dari angsuran suatu pinjaman. Contoh: Sebuah bank meminjamkan $ dan menerima pembayaran pertahun sebesar $4.021 selama 3 tahun. Dalam hal ini, bank dikatakan memperoleh penghasilan kembali (return of) 10% dari pinjaman sebesar $10, Taufiqur Rachman 2

3 TIN205 - Ekonomi Teknik Loan Balance Calculation 5 Year A = $ (A/P, 10%, 3) = $4.021 Unpaid balance at beginning of year Return on unpaid balance (10%) Payment received Unpaid balance at the end of year 0 $ $ $ $ $4.021 $ $6.979 $698 +$4.021 $ $3.656 $366 +$ A return of 10% on the amount still outstanding at the beginning of each year Contoh #1 (ROR) 6 John membeli barang seni seharga $ dan menjual kembali seharga $53,9 juta pada 40 tahun kemudian. Berapa rate of return dari investasi John? $53,9juta 0 $ Taufiqur Rachman 3

4 TIN205 - Ekonomi Teknik Solusi Contoh #1 (ROR) 7 Diketahui: P = $ ; F = $53,9juta ; n = 40 tahun Ditanya: i Jawab: F P 1 i n $53,9juta $ i 40 i 17,69% Contoh #2 (ROR) 8 Pada awal 1985, suatu investasi dari 100 saham seharga $1.650 menjadikan sebuah perusahaan terbuka (go public). Investasi tersebut akan menjadi $ pada 31 Januari Berapa rate of return pada investasi tersebut? $ $ Taufiqur Rachman 4

5 TIN205 - Ekonomi Teknik Solusi Contoh #2 (ROR) 9 Diketahui: P = $1.650 ; F = $ ; n = 30 tahun Ditanya: i Jawab: F P 1 i n i 30 $ $ i 34,97% Definisi #2 ROR 10 Rate of return (ROR) is defined as breakeven interest rate (i*), which equates the present worth of a project s cash outflows to the present worth of its cash inflows. Mathematical Relation: Taufiqur Rachman 5

6 TIN205 - Ekonomi Teknik Definisi #3 ROR (Return on Invested Capital) 11 Return on invested capital is defined as the interest rate earned on the unrecovered project balance of an investment project. It is commonly known as internal rate of return (IRR). Contoh: A company invests $ in a computer and results in equivalent annual labor savings of $4.021 over 3 years. The company is said to earn a return of 10% on its investment of $ Project Balance Calculation Beginning project balance $ $6.979 $3.656 Return on invested capital $ $6.979 $3.656 Payment received $ $ $ $4.021 Ending project balance $ $6.979 $ The firm earns a 10% rate of return on funds that remain internally invested in the project. Since the return is internal to the project, we call it internal rate of return Taufiqur Rachman 6

7 TIN205 - Ekonomi Teknik Metode Perhitungan ROR 13 Metode Solusi Langsung (Log) Metode Solusi Langsung (Quadratic) Metode Trial & Error Metode Solusi Grafik Komputer n Proyek A Proyek B Proyek C Proyek D 0 $1,000 $2,000 $75,000 $10, ,300 24,400 20, ,500 27,340 20, ,760 25, ,500 Metode Solusi Langsung (Log) Proyek A 14 $1,000 = $1,500(P/F, i, 4) $1,000 = $1,500(1 + i) = (1 + i) 4 ln / 4 = ln (1 + i) = ln (1 + i) e 4 = (1 + i) i = e i = 10.67% Taufiqur Rachman 7

8 TIN205 - Ekonomi Teknik 15 Metode Solusi Langsung (Quadratic) Proyek B Metode Trial & Error Proyek C (1) 16 Langkah 1: Guess an interest rate, say, i = 15% Langkah 2: Compute PW(i) at the guessed i value. PW (15%) = $3,553 Langkah 3: If PW(i) > 0, then increase i. If PW(i) < 0, then decrease i. PW(18%) = $749 Langkah 4: If you bracket the solution, you use a linear interpolation to approximate the solution Taufiqur Rachman 8

9 TIN205 - Ekonomi Teknik Metode Trial & Error Proyek C (2) 17 3, ,553 i 15% 3% 3, i 17.45% % i 18% Metode Solusi Grafik Komputer Proyek D 18 Langkah (a): Create a NPW plot using Excel. Langkah (b): Identify the point at which the curve crosses the horizontal axis closely approximates the i*. Catatan: This method is particularly useful for projects with multiple rates of return, as most financial softwares would fail to find all the multiple i*s Taufiqur Rachman 9

10 TIN205 - Ekonomi Teknik Situasi Multiple Rates of Return 19 Aturan keputusan dasar, jika ROR > MARR, maka terima proyek. Aturan ini tidak berlaku untuk situasi dimana investasi mempunyai multiple rates of return. Contoh: Cari rate(s) of return dari CF diagram berikut. 0 $2, $2, 300 $1, PW( i) $1, i ( 1 i) 0 $1,000 $1,320 Solusi Contoh Multiple ROR 20 1 Let x. Then, 1 i $2, 300 $1, 320 PW( i) $1, ( 1 i) ( 1 i) $1, 000 $2, 300x $1, 320x 0 Solving for x yields, x 10 / 11 or x 10 / 12 Solving for i yields i 10% or 20% Taufiqur Rachman 10

11 TIN205 - Ekonomi Teknik Grafik Multiple ROR 21 NPW Plot for a Non-simple Investment with Multiple Rates of Return. Kalkulasi Kesetimbangan Proyek 22 i = 20% n = 0 n = 1 n = 2 Begining Balance $1,000 +$1,100 Interest $200 +$220 Payment $1,000 +$2,300 $1,320 Ending Balance $1,000 +$1,100 $0 Cash borrowed (released) from the project is assumed to earn the same interest rate through external investment as money that remains internally invested Taufiqur Rachman 11

12 TIN205 - Ekonomi Teknik Critical Issue Kesetimbangan Proyek 23 Can the company be able to invest the money released from the project at 20% externally in period 1? If your MARR is exactly 20%, the answer is yes, because it represents the rate at which the firm can always invest the money in its investment pool. Then, the 20% is also true IRR for the project. Suppose your MARR is 15% instead of 20%. The assumption used incalculating i* isno longer valid. Therefore, neither 10% nor 20% is a true IRR. How to Proceed Kesetimbangan Proyek 24 If you encounter multiple rates of return, abandon the IRR analysis and use the NPW criterion. If NPW criterion is used at MARR = 15%. PW(15%) = $1,000 + $2,300 (P/F, 15%, 1) $1,320 (P/F, 15%, 2 ) = $1.89 > 0 Investasi diterima Taufiqur Rachman 12

13 TIN205 - Ekonomi Teknik Aturan Keputusan Non-Simple Investment 25 Kemungkinan multiple ROR Jika PW(i) seperti Gambar 1, maka IRR = ROR. Maka jika IRR > MARR, terima proyek. i* i Jika PW(i) seperti Gambar 2, maka, IRR ROR (i*). Dapatkan IRR sebenarnya, atau Gunakan method PW. PW (i) i* i* i Aturan Keputusan Non-Simple Investment Taufiqur Rachman 13

14 TIN205 - Ekonomi Teknik Incremental Investment 27 n Proyek A1 Proyek A2 Incremental Investment (A2 A1) 0 $1,000 $5,000 $4,000 1 $2,000 $7,000 $5,000 ROR 100% 40% 25% PW(10%) $818 $1,364 $546 Assuming MARR of 10%, you can always earn that rate from other investment source, i.e., $4,400 at the end of one year for $4,000 investment. By investing the additional $4,000 in A2, you would make additional $5,000, which is equivalent to earning at the rate of 25%. Therefore, the incremental investment ina2 isjustified. Incremental Analysis (Procedure) 28 Langkah 1: Compute the cash flows for the difference between the projects (A,B) by subtracting the cash flows for the lower investment cost project (A) from those of the higher investment cost project (B). Langkah 2: Langkah 3: Compute the IRR on this incremental investment (IRR). Accept the investment B if and only if IRR B-A > MARR Taufiqur Rachman 14

15 TIN205 - Ekonomi Teknik Contoh Incremental ROR 29 Diketahui MARR = 10%, proyek mana yang menjadi pilihan terbaik? n B1 B2 B2 B $3,000 1,350 1,800 1,500 $12,000 4,200 6,225 6,330 $9,000 2,850 4,425 4,830 IRR 25% 17.43% 15% Karena IRR B2-B1 =15% > 10%, dan juga IRR B2 > 10%, pilih B2. IRR Increment Investment 3 Alternatif 30 n D1 D2 D3 0 $2,000 $1,000 $3, , , , , ,000 IRR 34.37% 40.76% 24.81% 1. Langkah 1: Tetapkan IRR untuk tiap proyek untuk mngeliminasi tiap project yang gagal memenuhi MARR. 2. Langkah 2: Bandingkan D1 dan D2 berpasangan. IRR D1 D2 =27.61% > 15%, pilih D1. 3. Langkah 3: Bandingkan D1 dan D3. IRR D3 D1 = 8.8% < 15%, pilih D1. 4. Kesimpulannya D1 adalah alternatif terbaik Taufiqur Rachman 15

16 TIN205 - Ekonomi Teknik Incremental Borrowing Analysis 31 Principle: Decision Rule: If the difference in flow (B-A) represents an increment of investment, then (A-B) is an increment of borrowing. When considering an increment of borrowing, the rate i* A-B is the rate we paid to borrow money from the increment. If BRR B-A < MARR, select B. If BRR B-A = MARR, select either one. If BRR B-A > MARR, select A. Borrowing Rate of Return 32 n B1 B2 B1 B2 0 $3,000 $12,000 +$9, ,350 4,200 2, ,800 6,225 4, ,500 6,330 4, Taufiqur Rachman 16

17 TIN205 - Ekonomi Teknik Incremental Analysis for Cost-Only Projects 33 Items CMS Option FMS Option Annual O&M costs: Annual labor cost $1,169,600 $707,200 Annual material cost 832, ,400 Annual overhead cost 3,150,000 1,950,000 Annual tooling cost 470, ,000 Annual inventory cost 141,000 31,500 Annual income taxes 1,650,000 1,917,000 Total annual costs $7,412,920 $5,504,100 Investment $4,500,000 $12,500,000 Net salvage value $500,000 $1,000,000 Incremental Cash Flow (FMS CMS) 34 n CMS Option FMS Option Incremental (FMS CMS) 0 $4,500,000 $12,500,000 $8,000, ,412,920 5,504,100 1,908, ,412,920 5,504,100 1,908, ,412,920 5,504,100 1,908, ,412,920 5,504,100 1,908, ,412,920 5,504,100 1,908, ,412,920 5,504,100 Salvage + $500,000 + $1,000,000 $2,408, Taufiqur Rachman 17

18 TIN205 - Ekonomi Teknik Solusi (FMS CMS) 35 PW(i) FMS CMS = $8,000,000 + $1,908,820(P/A, i, 5) + $2,408,820(P/A, i, 6) = 0 IRR FMS CMS = 12.43% < 15%, pilih CMS Predicting Multiple RORs % < i* < infinity Net Cash Flow Rule of Signs: No. of real RORs (i*s) No. of sign changes in the project cash flows Taufiqur Rachman 18

19 TIN205 - Ekonomi Teknik Contoh 37 n Net Cash flow 0 $100 1 $20 Sign Change 2 $ $60 5 $ $100 1 No. of real i*s = 3. This implies that the project could have (0, 1, 2, or 3) i*s but NOT more than 3. Accumulated Cash Flow Sign Test 38 Find the accounting sum of net cash flows at the end of each period over the life of the project. Period (n) Cash Flow (A n ) Sum (S n ) 0 A 0 S 0 = A 0 1 A 1 S 1 = S 0 + A 1 2 A 2 S 2 = S 1 + A 2 n A n S n = S n 1 + A n If the series S starts negatively and changes sign ONLY ONCE, there exists a unique positive i* Taufiqur Rachman 19

20 TIN205 - Ekonomi Teknik Contoh 39 n A n S n Perubanhan tanda 0 $100 $100 1 $20 $120 2 $50 $ $70 4 $60 $10 5 $30 $40 6 $100 $60 1 Jumlah tanda berubah = 1, indicating a unique i*. i* = 10.46% Contoh Incremental B/C Ratios 40 A1 A2 A3 I $5,000 $20,000 $14,000 B 12,000 35,000 21,000 C 4,000 8,000 1,000 PW(i) $3,000 $7,000 $6, Taufiqur Rachman 20

21 TIN205 - Ekonomi Teknik Solusi 41 A1 A2 A3 BC(i) Ranking Base A1 A3 A2 I +C $9,000 $15,000 $28,000 Cost-Effectiveness Studies (1) 42 General Procedure Step 1: Establish the goals to be achieved by the analysis. Step 2: Identify the imposed restrictions on achieving the goals, such as budget or weight. Step 3: Identify all the feasible alternatives to achieve the goals. Step 4: Identify the social interest rate to use in the analysis. Step 5: Determine the equivalent life-cycle cost of each alternative, including research and development, testing, capital investment, annual operating and maintenance costs, and salvage value Taufiqur Rachman 21

22 TIN205 - Ekonomi Teknik Cost-Effectiveness Studies (2) 43 Step 6: Determine the basis for developing the costeffectiveness index. Two approaches may be used; (1) the fixed-cost approach and (2) the fixed-effectiveness approach. If the fixed-cost approach is used, determine the amount of effectiveness obtained at a given cost. If the fixed-effectiveness approach is used, determine the cost toobtain the predetermined level of effectiveness. Step 7: Compute the cost-effectiveness ratio for each alternative based on the selected criterion in Step 6. Step 8: Select the alternative with the maximum cost-effective index. Cost-Effectiveness Decision Criterion 44 Fixed Cost Approach Fixed Effectiveness Approach Maximize Effectiveness Minimize Cost Subject to: Subject to: Budget Constraint Must meet the minimum effectiveness Taufiqur Rachman 22

23 TIN205 - Ekonomi Teknik Case Study Selecting An Weapon System 45 Weapon System Alternatives 46 Alternative A j Advantage Disadvantage A1: Inertial navigation system A2: Inertial navigation system (Global positioning system) A3: Imaging infrared (I 2 R) A4: Synthetic aperture radar A5: Laser detection / ranging A6: Millimeter wave (MMW) Low cost, mature technology. Moderate cost, nature technology Accurate, target recognition Accurate, target recognition Accurate, target recognition Moderate cost, accurate Accuracy, target recognition Probability of Kill 0.33 Target recognition 0.70 High cost, bunkered target detection 0.90 High cost 0.99 High cost, technical maturity 0.99 Target recognition Taufiqur Rachman 23

24 TIN205 - Ekonomi Teknik Life-Cycle Costs for Weapon Development Alternative 47 Expenditures in Million Dollars Phase Year A1* A2 A3 A4 A5 A FSD IOC PW(10%) , Cost-Effectiveness Index 48 Type Cost/Unit Probability of Kill Cost/Kill Kill/Cost A1 $31, $95, A2 49, , A3 88, , A4 82, , A5 122, , A6 61, , Taufiqur Rachman 24

25 Taufiqur Rachman Cost/kill TIN205 - Ekonomi Teknik Cost-Effectiveness Graph Unacceptable Region A Maximize Effectiveness A1 A2 A6 Fixed Cost A4 A Present value of life cycle cost ($ million) Taufiqur Rachman 25