Module 8: Benefit-Cost Ratio

SI-4251 Ekonomi Teknik

Rani G. K. Pradoto

Outline Module 8 Benefit – Cost Ratio

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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

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B/C Analysis for A Single Project

Conventional B/C

Modified B/C- includes operation & maintenance cost- initial investment replaces cost as

denominator

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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

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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.

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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

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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

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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

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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

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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?

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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