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Bina Nusantara Contoh Soal Rate of Return: Contoh : Vincent Gogh’s painting “Irises” • John Whitney Payson membeli barang ...
Ardhianti Putri Follow Published on Jun 15, 2015
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Full Name Comment goes here. 12 hours ago Delete Reply Block Bina Nusantara Rate of Return • Diketahui: P =$80,000, F = $53.9juta, and N = 40 tahun • Cari : i • Solusi: $80,000 $53.9 ... Are you sure you want to Yes No Your message goes here
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D009452333 1. 1. Penggunaan ROR dan B/R Pertemuan 17 dan 18 Matakuliah : D 0094 Ekonomi Teknik Tahun : 2007 2. 2. Bina Nusantara Contoh Soal Rate of Return: Contoh : Vincent Gogh’s painting “Irises” • John Whitney Payson membeli barang seni ini seharga $80,000. • John menjual kembali seharga $53.9 juta 40 tahun kemudian. • Berapa rate of return dari investasi John ? 3. 3. Bina Nusantara Rate of Return • Diketahui: P =$80,000, F = $53.9juta, and N = 40 tahun • Cari : i • Solusi: $80,000 $53.9 Juta ( ) %69.17 1000.90$9.53$ 40 = += i ijuta 0 40 4. 4. Bina Nusantara Pada 1970, ketika Wal-Mart Stores, Inc. menjadi Perusahaan terbuka (go public), suatu investasi dari 100 saham seharga $1,650. Investasi tersebut akan menjadi $13,312,000 pada 31 January 2000. Berapa rate of return pada investasi tersebut ? Arti Rate of ReturnArti Rate of Return 5. 5. Solution: 0 30 $13,312,000 $1,650 Diketahui: P = $1,650 F = $13,312,000 N = 30 Cari i: $13,312,000 = $1,650 (1 + i )30 i = 34.97% N iPF )1( += Rate of Return 6. 6. Bina Nusantara Seandainya anda menginvestasikan senilai ($1,650) dalam rekening tabungan 6% per tahun. Kemudian anda hanya memperoleh $9,477 pada January, 2000. 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. Solution: 0 30 $13,312,000 $1,650 Diketahui: P = $1,650 F = $13,312,000 N = 30 Cari i: $13,312,000 = $1,650 (1 + i )30 i =... 7. 7. Bina Nusantara Kemudian, pada tahun 1970, anda memperoleh tawaran untuk investasi lain dengan interest lebih dari 6% untuk investasi lain, anda akan mengambil investasi tersebut. Oleh karena itu, 6% dipandang sebagai minimum attractive rate of return (rate of return yang dibutuhkan). Maka, anda dapat menetapkan aturan keputusan berikut untuk memperoleh investasi yang diusulkan adalah yang terbaik : ROR > MARR 8. 8. Bina Nusantara Rate of Return • Definisi 1: Rate of return (ROR) merupakan interest rate yang diperoleh pada unpaid balance dari angsuran suatu pinjaman. • Contoh: Sebuah bank meminjamkan $10,000 dan menerima pembayaran pertahun sebesar of $4,021 selama 3 tahun. Bank dikatakan memperoleh penghasilan kembali (return of) 10% dari pinjaman sebesar $10,000. 9. 9. Bina Nusantara Loan Balance Calculation: A = $10,000 (A/P, 10%, 3) = $4,021 Unpaid Return on Unpaid balance unpaid balance at beg. balance Payment at the end Year of year (10%) received of year 0 1 2 3 -$10,000 -$10,000 -$6,979 -$3,656 -$1,000 -$698 -$366 +$4,021 +$4,021 +$4,021 -$10,000 -$6,979 -$3,656 0 A return of 10% on the amount still outstanding at the beginning of each year 10. 10. Bina Nusantara Rate of Return: • Definition 2: Rate of return (ROR) is defined as break-even interest rate, i* , which equates the present worth of a project’s cash outflows to the present worth of its cash inflows. • Mathematical Relation: PW i PW i PW i( ) ( ) ( )* * * = − = cash inflows cash outflows 0 11. 11. Bina Nusantara Return on Invested Capital • Definition 3: 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). • Example: A company invests $10,000 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 $10,000. 12. 12. Project Balance Calculation: 0 1 2 3 Beginning project balance Return on invested capital Payment received Ending project balance -$10,000 -$6,979 -$3,656 -$1,000 -$697 $365 -$10,000 +$4,021 +$4,021 +$4,021 -$10,000 -$6,979 -$3,656 0 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. 13. 13. Bina Nusantara Period (N) Project A Project B Project C 0 -$1,000 -$1,000 +$1,000 1 -500 3,900 -450 2 800 -5,030 -450 3 1,500 2,145 -450 4 2,000 Project A is a simple investment. Project B is a nonsimple investment. Project C is a simple borrowing. 14. 14. Bina Nusantara Computational Methods Direct Solution Direct Solution Trial & Error Method Computer Solution Method Log Quadratic n Project A Project B Project C Project D 0 -$1,000 -$2,000 -$75,000 -$10,000 1 0 1,300 24,400 20,000 2 0 1,500 27,340 20,000 3 0 55,760 25,000 4 1,500 15. 15. Bina Nusantara Direct Solution Methods • Project A • Project B PW i i i x i PW i x x x x i i i i i i i ( ) $2, $1, ( ) $1, ( ) , ( ) , , , : . . . , * = − + + + + = = + = − + + = = + Õ = − = + Õ = − − < < ∞ = 000 300 1 500 1 0 1 1 2 000 1300 1500 08 08 1 1 25%, 1667 1 1 160% 100% 25%. 2 2 Let then Solve for or -1.667 Solving for yields Since the project's $1, $1, Bina Nusantara Seandainya anda menginvestasikan senilai ($1,650) dalam rekening tabungan 6% per tahun. Kemudian anda hanya... ( / , , ) $1, $1, ( ) . ( ) ln . ln( ) . ln( ) . . 000 500 4 000 500 1 0 6667 1 0 6667 4 1 0101365 1 1 1 4 4 0 101365 0 101365 = = + = + − = + = + = + = − = − − P F i i i i i e i i e 10.67% 16. 16. Bina Nusantara Trial and Error Method – Project C • Step 1: Guess an interest rate, say, i = 15% • Step 2: Compute PW(i) at the guessed i value. PW (15%) = $3,553 • Step 3: If PW(i) > 0, then increase i. If PW(i) < 0, then decrease i. PW(18%) = -$749 • Step 4: If you bracket the solution, you use a linear interpolation to approximate the solution 3,553 0 -749 15% i 18% ú û ù ê ë é + += 749553,3 553,3 %3%15i %45.17= 17. 17. Bina Nusantara Graphical Solution – Project D • Step 1: Create a NPW plot using Excel. • Step 2: Identify the point at which the curve crosses the horizontal axis closely approximates the i*. • Note: 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. 18. 18. Bina Nusantara Aturan Keputusan Dasar If ROR > MARR, terima Aturan ini tidak berlaku untuk situasi dimana invesrasi mempunyai ‘multiple rates of return’ 19. 19. Problem Multiple Rates of Return • Cari rate(s) of return: PW i i i ( ) $1, $2, $1, ( ) = − + + − − + = 000 300 1 320 1 0 2 $1,000 $2,300 $1,320 20. 20. Bina Nusantara Let Then, Solving for yields, or Solving for yields or 20% x i PW i i i x x x x x i i = + =− + + − + =− + − = = = = 1 1 000 300 1 320 1 000 300 320 0 10 11 10 12 10% 2 2 . ( ) $1, $2, ( ) $1, ( ) $1, $2, $1, / / 21. 21. Bina Nusantara NPW Plot for a Nonsimple Investment with Multiple Rates of Return 22. 22. Kalkulasi Kesetimbangan Proyek n = 0 n = 1 n = 2 Beg. Balance Interest Payment -$1,000 -$1,000 -$200 +$2,300 +$1,100 +$220 -$1,320 Ending Balance -$1,000 +$1,100 $0 i* =20% Cash borrowed (released) from the project is assumed to earn the same interest rate through external investment as money that remains internally invested. 23. 23. Bina Nusantara Critical Issue: 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 in calculating i* is no longer valid. Therefore, neither 10% nor 20% is a true IRR. 24. 24. Bina Nusantara • 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 How to Proceed: If you encounter multiple rates of return, abandon the IRR analysis and use the NPW criterion (or use the procedures outlined in Appendix A). 25. 25. Bina Nusantara Aturan Keputusan Untuk Nonsimple Investment • Kemungkinan multiple RORs. • Jika PW (i) plot looks seperti berikut, maka, IRR = ROR. If IRR > MARR, Terima • Jika PW(i) plot seperti berikut, maka, IRR ≠ ROR (i*). • Dapatkan IRR sebenarnya atau • Gunakan method PW PW(i) i* i i i* i* PW(i) 26. 26. Membandingkan Mutually Exclusive Alternatives Berdasarkan IRR • Issue: Dapatkah membuat ranking ‘mutually exclusive projects’ dengan besaran dari IRR?n A1 A2 0 1 IRR -$1,000 -$5,000 $2,000 $7,000 100% > 40% $818 < $1,364PW (10%) 27. 27. Incremental Investment • 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 in A2 is justified. n Bina Nusantara Kemudian, pada tahun 1970, anda memperoleh tawaran untuk investasi lain dengan interest lebih dari 6% untuk... Project A1 Project A2 Incremental Investment (A2 – A1) 0 1 -$1,000 $2,000 -$5,000 $7,000 -$4,000 $5,000 ROR PW(10%) 100% $818 40% $1,364 25% $546 28. 28. Bina Nusantara Incremental Analysis (Procedure) Step 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). Step 2: Compute the IRR on this incremental investment (IRR ). Step 3: Accept the investment B if and only if IRR B-A > MARR B-A 29. 29. Bina Nusantara Contoh - Incremental Rate of Return n B1 B2 B2 - B1 0 1 2 3 -$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% Diketahui MARR = 10%, project mana pilihan terbaik? Bila IRRB2-B1=15% > 10%, dan juga IRRB2 > 10%, pilih B2. 30. 30. Bina Nusantara IRR pada Increment Investment: Tiga Alternatif n D1 D2 D3 0 -$2,000 -$1,000 -$3,000 1 1,500 800 1,500 2 1,000 500 2,000 3 800 500 1,000 IRR 34.37% 40.76% 24.81% Step 1: Tetapkan IRR untuk tiap proyek untuk mngeliminasi tiap project yang gagal memenuhi MARR Step 2: Bandingkan D1 dan D2 berpasangan. IRRD1D2=27.61% > 15%, pilih D1. Step 3: Bandingkan D1 dan D3. IRRD3-D1= 8.8% < 15%, pilih D1. Kesimpulannya D1 adalah alternatif terbaik. 31. 31. Bina Nusantara Incremental Borrowing Analysis Decision Rule: • If BRR B-A < MARR, select B. • If BRR B-A = MARR, select either one. • If BRR B-A > MARR, select A. Principle: • 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. i* A B A BBRR− −= 32. 32. Bina Nusantara Borrowing Rate of Return n B1 B2 B1-B2 0 -$3,000 -$12,000 +$9,000 1 1,350 4,200 -2,850 2 1,800 6,225 -4,425 3 1,500 6,330 -4,830 33. 33. Bina Nusantara Incremental Analysis for Cost-Only Projects Items CMS Option FMS Option Annual O&M costs: Annual labor cost $1,169,600 $707,200 Annual material cost 832,320 598,400 Annual overhead cost 3,150,000 1,950,000 Annual tooling cost 470,000 300,000 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 34. 34. Bina Nusantara Incremental Cash Flow (FMS – CMS) n CMS Option FMS Option Incremental (FMS-CMS) 0 -$4,500,000 -$12,500,000 -$8,000,000 1 -7,412,920 -5,504,100 1,908,820 2 -7,412,920 -5,504,100 1,908,820 3 -7,412,920 -5,504,100 1,908,820 4 -7,412,920 -5,504,100 1,908,820 5 -7,412,920 -5,504,100 1,908,820 6 -7,412,920 -5,504,100 $2,408,820 Salvage + $500,000 + $1,000,000 35. 35. Bina Nusantara Solution: PW i P A i P F i IRR FMS CMS FMS CMS ( ) $8, , $1,908, ( / , , ) $2, , ( / , , ) .43% − − = − + + = = < 000 000 820 5 408 820 6 0 12 15%, select CMS. 36. 36. Bina Nusantara Ultimate Decision Rule: If IRR > MARR, Accept • Aturan berlaku untuk setiap situasi investasi. • Dalam beberapa situasi, IRR = ROR tapi hubungan ini tidak dapat digunakan untuk investasi dengan multiple RORs. Bina Nusantara Rate of Return • Definisi 1: Rate of return (ROR) merupakan interest rate yang diperoleh pada unpaid balanc... 37. 37. Bina Nusantara Predicting Multiple RORs - 100% < i * < infinity • Net Cash Flow Rule of Signs No. of real RORs (i*s) < No. of sign changes in the project cash flows 38. 38. Bina Nusantara Example n Net Cash flowSign Change 0 1 2 3 4 5 6 -$100 -$20 $50 0 $60 -$30 $100 1 1 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. 39. 39. Bina Nusantara Accumulated Cash Flow Sign Test Find the accounting sum of net cash flows at the end of each period over the life of the project Period Cash Flow Sum (n) (An ) Sn If the series S starts negatively and changes sign ONLY ONCE, there exists a unique positive i*. S A S S A S S A S S AN N N 0 0 1 0 1 2 1 2 1 = = + = + = +− A A A AN 0 1 2 0 1 2 N 40. 40. Bina Nusantara Contoh n An Sn Perubanhan tanda 0 1 2 3 4 5 6 -$100 -$20 $50 0 $60 -$30 $100 -$100 -$120 -$70 -$70 -$10 -$40 $60 1 • Jumlah tanda berubah = 1, indicating a unique i*. • i* = 10.46% 41. 41. Bina Nusantara Contoh: $2,145 $3,900 $5,030 $1,000 0 1 2 3 • Apakah ini simple investment? • Berapa RORs (i*s) dapat diharapkan dari menguji cash flows? • Apakah Investasi ini mempunyai rate of return yang unik ? 42. 42. Bina Nusantara Contoh Soal-soal Benefit Cost Ratio 43. 43. Bina Nusantara Contoh : Incremental Benefit-Cost Ratios 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 $6,000 44. 44. Solution A1 A2 A3 BC(i) 1.33 1.25 1.40 Ranking Base A1 A3 A2 I +C’ $9,000 $15,000 $28,000 BC i( ) $35, $21, ($20, $14, ) ($8, $1, ) . , 2 3 000 000 000 000 000 000 108 1 − = − − + − = > select A2. BC i( ) $21, $12, ($14, $5, ) ($1, $4, ) . , 2 1 000 000 000 000 000 000 15 1 − = − − + − = > select A2. 45. 45. Bina Nusantara General Procedure for Cost-Effectiveness Studies 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. 46. 46. Bina Nusantara • Step 6: Determine the basis for developing the cost-effectiveness index. Two approaches may be used; – (1) the fixed-cost approach and – (2) the fixedeffectiveness 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 to obtain 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. 47. 47. Bina Nusantara Cost-Effectiveness Decision Criterion • Fixed Effectiveness Approach • Fixed Cost Approach Maximize Effectiveness Subject to: Budget Constraint Minimize Cost Subject to: Must meet the minimum effectiveness 48. 48. Bina Nusantara Case Study - Selecting an Weapon System Bina Nusantara Loan Balance Calculation: A = $10,000 (A/P, 10%, 3) = $4,021 Unpaid Return on Unpaid balance unpaid balance... 49. 49. Weapon System Alternatives Alternative Aj Advantage Disadvantage Probability of Kill A1: Inertial navigation system Low cost, mature technology. Accuracy, target recognition 0.33 A2: Inertial navigation system: Global positioning system Moderate cost, nature technology Target recognition 0.70 A3: Imaging infrared (I2 R) Accurate, target recognition High cost, bunkered target detection 0.90 A4: Synthetic aperture radar Accurate, target recognition High cost 0.99 A5: Laser detection/ranging Accurate, target recognition High cost, technical maturity 0.99 A6: Millimeter wave (MMW) Moderate cost, accurate Target recognition 0.80 50. 50. Life-Cycle Costs for Weapon Development Alternative Expenditures in Million Dollars Phase Year A1* A2 A3 A4 A5 A6 FSD 0 $15 $19 $50 $40 $75 $28 1 18 23 65 45 75 32 2 19 22 65 45 75 33 3 15 17 50 40 75 27 4 90 140 200 200 300 150 5 95 150 270 250 360 180 IOC 6 95 160 280 275 370 200 7 90 150 250 275 340 200 8 80 140 200 200 330 170 PW(10%) $315.92 $492.22 $884.27 $829.64 $1,227.23 $612.70 51. 51. Bina Nusantara Cost-Effectiveness Index Type Cost/Unit Probability of Kill Cost/Kill Kill/Cost A1 $31,592 0.33 $95,733 0.0000104 A2 49,220 0.70 70,314 0.0000142 A3 88,427 0.90 98,252 0.0000102 A4 82,964 0.90 83,802 0.0000119 A5 122,723 0.99 123,963 0.0000081 A6 61,370 0.80 76,713 0.0000130 52. 52. $130,000 120,000 300 400 500 600 700 800 900 1000 1100 1200 1300 Unacceptable region Cost/kill Present value of life cycle cost ($ million) A1 A3 A6 A4 A5 110,000 100,000 90,000 80,000 70,000 A2 Fixed cost Maximize effectiveness
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Bina Nusantara Aturan Keputusan Dasar If ROR > MARR, terima Aturan ini tidak berlaku untuk situasi dimana invesrasi mempun...
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Bina Nusantara NPW Plot for a Nonsimple Investment with Multiple Rates of Return
Kalkulasi Kesetimbangan Proyek n = 0 n = 1 n = 2 Beg. Balance Interest Payment -$1,000 -$1,000 -$200 +$2,300 +$1,100 +$220...
Bina Nusantara Critical Issue: Can the company be able to invest the money released from the project at 20% externally in ...
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Description Add a brief description so others know what your Clipboard is about. Visibility Others can see my Clipboard Cancel Save Save this presentationTap To Close Bina Nusantara • If NPW criterion is used at MARR = 15% PW(15%) = -$1,000 + $2,300 (P/F, 15%, 1) - $1,320 (P/F, 15%, 2 ) =...
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Bina Nusantara Incremental Analysis (Procedure) Step 1: Compute the cash flows for the difference between the projects (A,...
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Bina Nusantara Solution: PW i P A i P F i IRR FMS CMS FMS CMS ( ) $8, , $1,908, ( / , , ) $2, , ( / , , ) .43% − − = − + +...
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Bina Nusantara Predicting Multiple RORs - 100% < i * < infinity • Net Cash Flow Rule of Signs No. of real RORs (i*s) < No....
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Bina Nusantara Contoh : Incremental Benefit-Cost Ratios A1 A2 A3 I $5,000 $20,000 $14,000 B 12,000 35,000 21,000 C’ 4,000 ...
Solution A1 A2 A3 BC(i) 1.33 1.25 1.40 Ranking Base A1 A3 A2 I +C’ $9,000 $15,000 $28,000 BC i( ) $35, $21, ($20, $14, ) (...
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Bina Nusantara Case Study - Selecting an Weapon System
Weapon System Alternatives Alternative Aj Advantage Disadvantage Probability of Kill A1: Inertial navigation system Low co...
Life-Cycle Costs for Weapon Development Alternative Expenditures in Million Dollars Phase Year A1* A2 A3 A4 A5 A6 FSD 0 $1...
Bina Nusantara Cost-Effectiveness Index Type Cost/Unit Probability of Kill Cost/Kill Kill/Cost A1 $31,592 0.33 $95,733 0.0...
$130,000 120,000 300 400 500 600 700 800 900 1000 1100 1200 1300 Unacceptable region Cost/kill Present value of life cycle...
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