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Module 8: Benefit-Cost Ratio
SI-4251 Ekonomi Teknik
Rani G. K. Pradoto
Outline Module 8 Benefit – Cost Ratio
8-2 SI-4251 Ekonomi Teknik
The Benefit – Cost Analysis The most commonly used method for
comparing economic alternatives.
This method is often considered as “supplementary” to present worth analysis.
The objective is to determine whether the benefit (gained) in return to any cost (spent) is favorable.
Basically it is desired that we will gain more than we have spent.
Benefit – Cost > 0 B/C > 1.08-3 SI-4251 Ekonomi Teknik
ClassificationBenefit (B) all favorable return/gain
or advantagesDisbenefit (D) negative benefit, any
negative (loss) result Cost (C) all things that one
pays/expends in order to have return
Benefit income from an investment, e.g., interest Disbenefit loss of value or (initial) income due to an
investment Cost expenditure
8-4 SI-4251 Ekonomi Teknik
B/C Analysis for A Single Project
Conventional B/C
Modified B/C- includes operation & maintenance cost- initial investment replaces cost as
denominator
8-5 SI-4251 Ekonomi Teknik
C
DBC/B
I
M&ODBC/B
Calculation can be made in present worth, future worth or annuity
B - C Analysis for A Single Project
Conventional B-C
Modified B-C- includes operation & maintenance cost
8-6 SI-4251 Ekonomi Teknik
Calculation can be made in present worth, future worth or annuity
C)DB(CB
I)M&ODB(CB
ExerciseA new machine having an initial investment of Rp 225 million and additional Rp 35 million a year for maintenance and operation cost, is estimated to generate Rp 95 million per year in revenue. On the other hand, installation of this new machine will cost the company to lose Rp 3.2 million per year from selling by product. The machine can latter be sold for Rp 75 million at the end of 5 year and the rate of return is set at 8%. Do the benefit cost analysis.
Muhamad Abduh, Ph.D.8-7 SI-4251 Ekonomi Teknik
Conventional method:
Cost C1 = Rp 225 million Cost C2 = Rp 35 million/year Benefit B1 = Rp 95 million/year Benefit B2 = Rp 75 million at end of 5 year
Disbenefit D = Rp 3.2 million/year
225 (A/P, 8, 5) = 56.3535
35 = 35
95 = 95
75 (A/F, 8, 5) = 12.7845
3 2 = 3.2
B/C = [(95 + 12.7845) – 3.2 - 35]/(56.3535) = 1.2348
B - C = [(95 + 12.7845) – 3.2 - 35] – [56.3535] = Rp 13.231 million
(A/P, 8, 5) = 0.25046 (A/F, 8, 5) = 0.17046
ExerciseA new machine having an initial investment of Rp 225 million and additional Rp 35 million a year for maintenance and operation cost, is estimated to generate Rp 95 million per year in revenue. On the other hand, installation of this new machine will cost the company to lose Rp 3.2 million per year from selling by product. The machine can latter be sold for Rp 75 million at the end of 5 year and the rate of return is set at 8%. Do the benefit cost analysis.
8-8 SI-4251 Ekonomi Teknik
Modified method:
Cost C1 = Rp 725 million Cost C2 = Rp 35 million/year Benefit B1 = Rp 95 million/year Benefit B2 = Rp 75 million at end of 5 year
Disbenefit D = Rp 3.2 million/year
225 (A/P, 8, 5) = 56.3535
35 = 35
95 = 95
75 (A/F, 8, 5) = 12.7845
3 2 = 3.2
(A/P, 8, 5) = 0.25046 (A/F, 8, 5) = 0.17046
B/C = [(95 + 12.7845) – 3.2]/(56.3535 + 35) = 1.1448
B - C = [(95 + 12.7845) – 3.2] – [56.3535 + 35] = Rp 13.231 million
Comparing two alternatives using B/C analysis
8-9 SI-4251 Ekonomi Teknik
Overpass A Tunnel B
Initial cost 1,250 million 3,500 millions
Yearly maintenance cost 27.50 million 55 million
Road user cost per year 425 million 350 million
Useful life 20 years 20 years
Interest rate 10%
COST:
EUAWA = 1,250 (A/P, 10, 20) + 27.50 = 1,250 (0.1175) + 27.50 = 174.375 million
EUAWB = 3,500 (A/P, 10, 20) + 55.00 = 3,500 (0.1175) + 55.00 = 466.250 million
Δ Cost = EUAWB – EUAWA = 466.250 – 174.375 = 291.875 million
BENEFIT:
EUAWA = 425 million EUAWB = 350 million Δ Benefit = 425-350 = 75 million
B/C = 75/291.875 = 0. 2570
B-C = 75 – 291.875 = -216.875
Selection form Mutually Exclusive Alternatives
Incremental B/C Analysis
8-10 SI-4251 Ekonomi Teknik
X Y Z
Initial cost - 250,000,00
0
-240,000,00
0
-320,000,00
0
Yearly expenses
- 135,000,00
0
-123,500,00
0
-130,000,00
0
Yearly revenues
390,000,000
381,000,000
420,500,000
Salvage value 45,000,000 52,000,000 202,000,000
period 5 5 5
Interest rate 12%
Selection form Mutually Exclusive Alternatives (benar)
Incremental B/C Analysis
8-11 SI-4251 Ekonomi Teknik
Y X Z
Initial cost, (I) -240,000,000
-250,000,000
-320,000,00
0
Yearly expenses, (C) -123,500,000
-135,000,000
-130,000,00
0
Yearly revenues, (B) 381,000,000 390,000,000 420,500,000
UAEW of Salvage value, (B)
52,000,000 45,000,000 202,000,000
Overall B/C
B – C
Alternative to compare
Incremental benefit
Incremental cost
Incremental B/C
Decision
Selection form Mutually Exclusive Alternatives (benar)
Incremental B/C Analysis
8-12 SI-4251 Ekonomi Teknik
Y X Z
Initial cost, (I) -240,000,000
-250,000,000
-320,000,00
0
Yearly expenses, (C) -123,500,000
-135,000,000
-130,000,00
0
Yearly revenues, (B) 381,000,000 390,000,000 420,500,000
UAEW of Salvage value, (B)
Overall B/C >1 <1
B – C
Alternative to compare YES Y to Z
Incremental benefit 262,219,000
Incremental cost 101,176,800
Incremental B/C 2.5
Decision Z
Homework #8A ready-mix concrete producer is considering to install a new
mixer system:
at rate of return 10% determine which system should be installed using B/C analysis?
8-13 SI-4251 Ekonomi Teknik
Operating characteristics System A System B System C
Installed cost ($) 2,250,000 2,950,000 2,750,000
Annual Operating cost ($) 320,000 495,000 401,500
Annual production (cm) 10,500 21,200 19,900
Unit price ($/cm) 122.50 122.50 122.50
Overhaul cost ($/ 2 years) 220,000 245,000 295,000
Salvage value ($) 221,500 308,000 367,500
Useful life (year) 3 4 4