04 Cost Benefit Analysis 2020

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4 การวิเคระห,ต.นทุนและผลได.จากการลงทุนภาครัฐ (Cost-Benefit Analysis)

Public Finance, 8^th Edition

Rosen and Gayer, Chapter 8 Adapted by Chairat Aemkulwat for

Theory of Public Expenditures 2943410

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Outline

I. Introduction II. Present value

III. Private sector project evaluation

IV. Discount rate for government projects V. Valuing public benefits and costs

VI. Cost-benefit “games”

VII. Distributional considerations VIII. Uncertainty

ชัยรัตน์ เอี+ยมกุลวัฒน์ Theory of Public Expenditures 2943410

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I. Introduction

• การวิเคราะห์ต้นทุน - ผลประโยชน์

หมายถึง เครื;องมือที;ใช้ในทางปฏิบ ัติ

สําหร ับเป็นแนวทางในการต ัดสินใจการ ใช้จ่ายหรือการลงทุนภาคร ัฐ

– Cost-benefit analysis is a set of practical procedures for guiding public expenditure decisions.

I. Introduction

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II. Present Value

• Project evaluation usually requires comparing costs and benefits from

different

time periods

• Dollars or baht across time periods are not immediately comparable, because of

1) inflation and

2) returns in the market.

II. Present Value

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Present Value:

Present Dollars into the Future

• Suppose you invest $1000 today in the bank . .

R₀ = $1000

R₁ = $1000*(1+.01) = $1010

R₂ = $1010*(1+.01) = $1020.10 R₂ = $1000*(1+.01)² = $1020.10

R_T = R₀*(1+r)^T

II. Present Value

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Present Value:

• Define

– R = initial investment amount – r = rate of return on investment – T = years of investment

• The future value (FV) of the investment is:

( )

FV = R 1 + r

^T

II. Present Value

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Present Value:

Future Dollars into the Present

• Suppose someone promises to pay you $100 one year from now.

• What is the maximum amount you should be willing to pay today for such a promise?

• เรากําล ังสูญเสียผลประโยชน์ที6เราควรได้จาก การปล่อยกู้

– You are forgoing the interest that you could earn on the money that is being loaned.

II. Present Value

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Present Value:

• มูลค่าปัจจุบันของเงินก้อนในอนาคต คือ จํานวนเงิน ก้อนสูงสุดที7เรายินดีจ่ายวันนี< เพื7อสิทธิในการได้รับเงิน ก้อนในอนาคต

– The present value of a future amount of

money is the maximum amount you would be willing to pay today for the right to receive the money in the future.

II. Present Value

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Present Value:

• Define

– R = amount to be received in future – r = rate of return on investment

– T = years of investment

• The present value (PV) of the investment is:

( )

PV R

r

^T

= 1 +

II. Present Value

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Projecting Future Dollars into the Present

R₀ = R_T/(1+r)^T PV =

discount rate discount factor

In previous equation, r is often referred to as the discount rate,

and (1+r)^-T or 1/(1+r)^Tis the discount factor.

FV = R_T = R₀*(1+r)^T

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Present Value:

• Finally, consider a promise to pay a stream of money, $R₀ today, $R₁ one year from now, and so on, for T years.

( ) ( ) ( )

PV R R

r

R r

T

= + T

+ +

+ + +

0 1 2 +

1 1 2 ... 1

II. Present Value

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Present Value:

• Present value is an enormously important concept

• A $1,000,000 payment 20 years from now is only worth today:

– $376,889 if r=.05 – $148,644 if r=.10

II. Present Value

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Present Value:

Inflation

• Nominal amounts are valued according to the level of prices in the year the return occurs.

• Real amounts are valued according to the level of prices in one particular year.

• Inflation affects both the payout stream and the discount factor, and these two cancel each other out.

II. Present Value

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Present Value:

Inflation

II. Present Value

( ) ( ) ( )

1 2

0 2

(1 ) (1 ) (1 )

(1 ) 1 (1 ) 1 ... (1 ) 1

T

R R R

PV R

r r r

p p p

- - -

= + + + +

- + - + - +

• Inflation affects both the payout stream and the discount factor, and these two cancel each other out.

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11.4

4.9 4.3 10.2

4.5 5.0

9.3 9.8 10.3

5.4 5.2 5.9 5.4 5.6 5.8 4.6 5.5

9.5 13.3

12.2 11.2

8.6 8.1 8.3 8.0 8.1 5.7

(2.8)

(7.6) 4.6 4.5

3.4 6.1 7.2

6.3

4.2 5.0 5.4 1.7

(0.7) 7.5

0.8 7.2

2.7 1.0

3.0 3.3 3.9

(10.0) (5.0) 0.0 5.0 10.0 15.0 20.0

1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

GROWTH RATES 1970-2017 Thailand Korea, Rep.

Source: Tradingeconomicscom

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11.4

4.9 4.3 10.2

4.5 5.0

9.3 9.8 10.3

5.4 5.2 5.9 5.4 5.6 5.8 4.6 5.5 9.5

13.3 12.2

11.2

8.6 8.1 8.3 8.0 8.1 5.7

(2.8)

(7.6) 4.6 4.5

3.4 6.1 7.2

6.3

4.2 5.0 5.4 1.7

(0.7) 7.5

0.8 7.2

2.7 1.0

3.0 3.3 3.9

(10.0) (5.0) 0.0 5.0 10.0 15.0 20.0 25.0

1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

GROWTH RATE 1970-2019 Thailand China

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11.4

4.9 4.3

10.2

4.5 5.0

9.3 9.8 10.3

5.4 5.2 5.9

5.4 5.6 5.8 4.6

5.5 9.5

13.3 12.2

11.2

8.6 8.1 8.3 8.0 8.1

5.7

(2.8)

(7.6) 4.6 4.5

3.4 6.1

7.2 6.3

4.2 5.0 5.4

1.7

(0.7) 7.5

0.8 7.2

2.7 1.0

3.0 3.3 3.9

(10.0) (5.0) 0.0 5.0 10.0 15.0

1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Growth Rate 1970-2017 Thailand Malaysia

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Thailand vs Malaysia Compared

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Thailand vs Malaysia Compared

Source: www.bot.or.th EC_EI_027-2

2557 2558 2559 2560 2561 2562 2563 THB

2014 2015 2016 2017 2018 2019 2020

World economic rate 2.9 2.9 2.5 3.1 3.2 3.5 3.6

Malaysia 6.0 5.1 4.4 5.7 4.7 4.3 4.4-4.5%

Thailand 1.0 3.1 3.4 4.0 4.1 2.4 1.5-2.5%

Differnce 5.0 2.0 1.1 1.7 0.6 1.9

Economic Value

GDP (current price) 14,069,720 14,494,612 14,970,404 15,601,188 16,116,441 16,883,924

i=0% ^706,625 ^283,749 ^163,666 ^267,988 ^98,694 ^320,795 1,841,517 i=2% 780,171 307,139 173,684 278,815 100,668 320,795 1,961,272 i=5% ^901,852 ^344,899 ^189,464 ^295,457 ^103,629 ^320,795 2,156,096

5 4 3 2 1 0

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III. Private Sector Project Evaluation

• Suppose there are two projects, X and Y.

• Each entails certain benefits and costs, denoted as B^X, C^X, B^Y, and C^Y.

• Need to ask:

– Is the project admissible?

– Is the project preferable?

III. Present Sector Project Evaluation

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Private Sector Project Evaluation

• Admissible: Are the benefits greater than the costs?

• Preferable: Are the net benefits the highest?

• โครงการส่วนใหญ่เกี0ยวข้องก ับกระแส ผลประโยชน์และต้นทุนหลายช่วงเวลา

– Most projects involve a stream of benefits and costs over time.

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Private Sector Project Evaluation

• Define:

B

_tⁱ

=

C_tⁱ =

Benefits from project i at time t

Costs from project i at time t

• Then the present value of project i is:

( ) ( )

( )

PV B C B C

r

B C r

i i i

i i

T i

= - + - T

+ + + -

0 0 +

1 1

1 ... 1

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Private Sector Project Evaluation

• The present value criteria for project evaluation are that:

– A project is admissible only if its present value is positive.

– When two projects are mutually exclusive^,

the preferred project is the one with the highest present value.

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Private Sector Project Evaluation

• Two different projects (R&D or Advertising).

• The discount rate plays a key role in deciding what project to choose, because the cash inflows occur at different times.

• The lower the discount rate, the more valuable the back-loaded project

( โครงการที)มีผลประโยชน์สูง ในช่วงท้ายๆ -

advertising

)

^.

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Private Sector Project Evaluation

T T T

r C B

r C C B

B

PV ... (1 )

) 1

(

1 ²

3 3

2 2

1

1 +

+ - + +

+ + +

+ - -

=

Annual Net Return

Year R&D Advertising

0 - $1,000 - $1,000

1 600 0

2 0 0

3 550 1,200

Admissible Preferable

Present Value Criteria

PV

R = R&D Advertising

0 $150 $200

0.01 128 165

0.03 86 98

0.05 46 37

0.07 10 -21

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• Several other criteria are often used for project evaluation, but can give

misleading answers

– Internal rate of return (IRR)

– Benefit-cost ratio (B/C)

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Private Sector Project Evaluation

• The internal rate of return, ρ, is defined as the ρ that solves the equation:

( ) ( )

( )

0 ⁰ ⁰ 1 1

1 1

= - + -

+ + + -

B C B C B_T+ C_T r ^... r T

• The IRR is the discount rate that would make the present value of the project equal to zero.

– Admissible if ρ>r.

– The flawed analysis would choose an admissible project with the higher internal rate of return, ignoring scale.

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Internal Rate of Return

) 0 1

... ( )

1 (

1

²

3 3

2 1 2

1

-

+ + -

+ + + +

+ + -

-

= B C B C B

^T

C

_T^T

C B

PV r r r

Project Year 0 Year 1 ρ Profit PV

X -$100 $110 10% $4 3.77

Y -$1,000 $1,080 8% $20 18.87

Assume the firm can borrow and lend freely at a 6 percent rate of return

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• The benefit-cost ratio divides the discounted stream of benefits by the discounted stream of costs. In this case:

B=stream of benefits and C=stream of costs:

( ) ( )

B B B

r

B r

T

= + T

+ + +

0 1 +

1 ... 1

( ) ( )

C C C

r

C r

T

= + T

+ + +

0 1 +

1 ... 1

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Private Sector Project Evaluation

• Admissibility using the benefit-cost ratio requires:

B

C > 1

• This ratio is virtually useless for comparing across admissible projects, however.

• Ratio can be manipulated by counting benefits as “negative costs” and vice-versa.

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Project 1: Project waste Dump B=250; C=100

Project 2: Wastes sent to Saturn B=200; C=100

• Neglect seepage-induced crop damage of $40

– Reduction of dump benefits. B=210; B/C=2.1 – An increase in cost C=140; B/C = 1.79

Private Sector Project Evaluation

2.0 1

B B

C = C >

2.5 1

B B

C = C >

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Problems with the Benefit-cost Ratio

Method B C B/C

I $250 $100 2.5

II $200 $100 2.0

I: Subtract

$40 mistake from B

$210 $100 2.1

I: Add $40 mistake to C

$250 $140 1.79

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IV Discount Rate for Government Projects

• Government decision making involves present value calculations.

• Costs, benefits, and discount rates are somewhat different from private sector.

IV. Present Sector Project Evaluation

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Discount Rate for Government Projects

• Less consensus on appropriate discount rate in public sector. One possibility are rates based on returns in private sector.

– Assumes all of the money that is raised would have been invested in a private sector project.

– In reality, funding comes from a variety of sources – investment and consumption.

– Funding that come from consumption should be discounted at the after-tax discount rate.

– Hard in reality to determine what proportions of funding come from consumption or investment.

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Discount Rate for Government Projects

• Another possibility is the social rate of

discount – which measures the valuation

society place on consumption that is sacrificed in the present.

• Differs from market returns because it:

– Accounts for concern about future generations – Involves paternalism

– May solve some market inefficiency such as positive externalities

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Discount Rate for Government Projects

• In reality, federal agencies are required to use a real rate of return of 7%, on the assumption that this

measures the before-tax rate of return in the private sector.

• Some use 2% real return instead, thought to measure the after-tax rate of return.

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Thailand vs Malaysia Compared

Source: www.bot.or.th EC_EI_027-2

2557 2558 2559 2560 2561 2562 2563 THB

2014 2015 2016 2017 2018 2019 2020

World economic rate 2.9 2.9 2.5 3.1 3.2 3.5 3.6

Malaysia 6.0 5.1 4.4 5.7 4.7 4.3 4.4-4.5%

Thailand 1.0 3.1 3.4 4.0 4.1 2.4 1.5-2.5%

Differnce 5.0 2.0 1.1 1.7 0.6 1.9

Economic Value

GDP (current price) 14,069,720 14,494,612 14,970,404 15,601,188 16,116,441 16,883,924

i=0% ^706,625 ^283,749 ^163,666 ^267,988 ^98,694 ^320,795 1,841,517 i=2% 780,171 307,139 173,684 278,815 100,668 320,795 1,961,272 i=5% ^901,852 ^344,899 ^189,464 ^295,457 ^103,629 ^320,795 2,156,096

5 4 3 2 1 0

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V. Valuing Public Benefits and Costs

• Recall that the discount rate, benefits, and costs are needed to compute the present value of a project.

• For private company:

– Benefits = revenues received

– Costs = firm’s payments for inputs

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Valuing Public Benefits and Costs

• For public sector, market prices may not reflect social benefits and costs.

– Externalities, for example

• Several ways of measuring benefits and costs

– Market prices

– Adjusted market prices – Consumer surplus

– Inferences from economic behavior – Valuing intangibles

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Valuing Public Benefits and Costs

• Market prices

– In a properly functioning competitive

economy, the price of a good simultaneously reflects its marginal social cost of production and its marginal value to consumers.

– Ignores market imperfections – Easy to gather

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Valuing Public Benefits and Costs

• Adjusted market prices

– If markets are imperfect, prices generally do not reflect true marginal social cost.

– Shadow price of a commodity is its true, underlying marginal social cost, which can sometimes be estimated.

– Examples where insights can be gleaned include monopoly price, taxes, and

unemployment.

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Valuing Public Benefits and Costs

• Consumer surplus

– Public sector projects can be large and change market prices.

– Figure 8.1 measures the change in consumer surplus from a government irrigation project that lowers the cost of agricultural production.

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Valuing Public Benefits and Costs

Pounds of avocados per year

Price per pound of avocados

D_a

S_a d

A₀

S_a^’

$1.35

$2.89 b

c g

A₁ e

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• In this figure, the change in consumer surplus is area bcgd.

• Provided the government planner can accurately measure the demand curve, the project’s benefit can be measured with this change.

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Valuing Public Benefits and Costs

• Inferences from Economic Behavior

• Many times a good in question is not explicitly traded, so no market price exists.

• Examples:

– Value of time – Value of life

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• Value of time

• In cost-benefit analysis, need to estimate the value of time to take advantage of

theory of leisure-income choice.

– After-tax wage is often used

– But hours of work not always a “choice,” and not all uses of time away from job equivalent.

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Valuing Public Benefits and Costs

• Researchers have examined value of time by travel commuting choices.

– Trains are more expensive, but less time- consuming, than buses. The same is true about non-stop airline flights versus those with a layover.

– Estimates are that value of time

approximately half of the before-tax wage.

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Valuing Public Benefits and Costs

• Value of life

• The mindset that “life is priceless”

presents obvious difficulties for cost- benefit analysis.

• If the benefits of a saved life are infinite, any project that leads to even a single life saved has an infinitely high present

value.

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Valuing Public Benefits and Costs

• Economists use two methods to assign finite values to human life:

– Lost earnings: Net present value of individual’s after-tax earnings over lifetime.

• Taken literally, no loss for aged, infirm, or severely handicapped

– Probability of death: Most projects affect probability of death (e.g., cancer research). People are willing to accept increases in the probability of death for a finite amount of money.

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Valuing Public Benefits and Costs

• Examples:

– Purchasing a more expensive, safer car with a lower probability of death versus a less

expensive, less safe car.

– Occupational choice: Riskier jobs have higher wages, all else equal

– Willingness to pay for safety devices like smoke alarms.

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Valuing Public Benefits and Costs

• Estimates suggest value of a life between

$4,000,000-$9,000,000

• Can contrast this versus the cost per life saved:

– Emergency floor lights on airplanes cost about $900,000 per life saved

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• Valuing intangibles

– National prestige, others

• Can be used to subvert entire cost-benefit analysis

• Could use difference between costs and

benefits to make an argument on how large intangibles would have to be to make the project admissible

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จริง / ไม่จริง ต้องพิสูจน์

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ใช้

Cost-Benefit Analysis

ดีกว่าไหม

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Cost Benefit Analysis หรือ ม . 44 (1)

• ม.44 "ปิดประตูหลายชั0นในการตรวจสอบ"

• ส่วนมุมมองของนักวิชาการด้านกฎหมายมหาชน คณะนิติศาสตร์ จุฬา ฯ รศ.ดร.ณรงค์เดช สรุโฆษิต หนีไม่พ้นความกังวลเรืGองการใช้

"อํานาจพิเศษ" ตามมาตรา 44 ของรัฐธรรมนูญฉบับชัGวคราว ซึGงถูก

รับรองโดยรัฐธรรมนูญปี 2560 ออกคําสัGงเร่งรัดโครงการนีY เขา

ชีYให้เห็นว่า แม้ในคําสัGงหัวหน้า คสช. จะอ้างถึงการดําเนินการต้อง เป็นไปตาม "ข้อตกลงคุณธรรม" หากผู้เกีGยวข้องไม่ปฏิบัติตาม

ข้อตกลงนีYให้ดําเนินการตามกฎหมาย แต่ปรากฎว่าคําสัGงหัวหน้าคสช. ฉบับเดียวกัน กลับยกเว้นการบังคับใช้กฎหมายรวม 7 ฉบับ

Source: https://www.bbc.com/thai/thailand-40369155 59

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Cost Benefit Analysis หรือ ม . 44 (2)

• ม.44 "ปิดประตูหลายชั0นในการตรวจสอบ"

• "กฎหมายที, คสช.ให้ยกเว้น เป็นกฎหมายมุ่งขจัดการทุจริตทั@งสิ@น ความหมายคือเจ้าหน้าที,รัฐไทยทําผิด ยังโดนลงโทษตามกฎหมาย แต่

ถ้าคนเสนอราคาทําผิด หลุดหมด ถือเป็นการยกเว้นการบังคับใช้

กฎหมายที,ไม่ควรยกเว้น นอกจากนี@ยังมีความไม่ชัดเจน หาก

รัฐวิสาหกิจจีนต้องการให้บริษัทใดบริษัทหนึ,งของไทยมารับงานต่อ จะสามารถเข้ามาได้โดยอัตโนมัติหรือไม่" รศ.ดร.ณรงค์เดชโยนคําถาม ขึ@นกลางวงเสวนา

Source: https://www.bbc.com/thai/thailand-40369155 60

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Cost/Benefit Analsis หรือ ม 44 (3)

• เขาบอกด้วยว่า คําสั4งตามมาตรา 44 ไม่เพียงตรวจสอบไม่ได้ เพราะถูก รับรองโดยรัฐธรรมนูญ และแนวบรรทัดฐานการพิจารณาคดีของศาล ในประเด็นที4เกี4ยวข้องกับมาตรา 44 ยังให้ความคุ้มครองการรถไฟแห่ง ประเทศไทย (รฟท.) ในการสั4งการ การปฏิบัติ ถือเป็นการ "ปิดประตู

หลายชัQนในการตรวจสอบ"

• "ต่อให้การออกคําสั4งนีQเริ4มต้นด้วยเจตนาดี อยากสลายข้อติดขัด อยาก พัฒนาประเทศ ซึ4งทางกฎหมายมีคําพูดว่าทําอย่างไรก็ได้ให้ถึง

เป้าหมาย แต่แม้เป้าหมายดี แต่วิธีการไม่ถูก ก็จะไปอย่างนั4นหรือ" รศ.

ดร.ณรงค์เดชระบุ

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VI. Cost-Benefit “Games”

• Chain-Reaction game

– Include secondary benefits to make a proposal appear more favorable, without also including the secondary costs

• Double counting game

– Benefits are erroneously counted twice

1) the increase in value of land

2) the present value of the stream of net income obtained from farming

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Cost-Benefit “Games”

• Labor game

– Wages are viewed as benefits rather than costs of the project

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VII. Distributional Considerations

• Hicks-Kaldor Criterion – a project should be undertaken if it has positive net present value, regardless of distributional consequences

• The Hicks-Kaldor criterion bases project selection on whether there is a potential Pareto improvement

VII. Distribution Considerations

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Distributional Considerations

• Others view some groups in population as “more deserving” and argue this should be taken into account in project selection

• Government costlessly corrects any undesirable distributional aspects

VII. Distribution Considerations

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Ans.

d. The subway project has a higher present value. If a dollar to the “poor” is valued the same as a dollar to the “middle class,” choose the subway project.

e. Let l = distributional weight. set

– 220,000 = -68,750 + l[(62,500/1.25) + (62,500/1.25²)]

– l= 3.21

– This distribution weight means that $1 of income to a poor person must be viewed as more important than $3.21 to the middle class for the legal services to be done.

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VIII. Uncertainty

• The results of many projects are uncertain (e.g., AIDS vaccine research or defense research).

• In risky projects, benefits or costs must be

converted into certainty equivalents – the amount of certain income the individual would trade for a set of uncertain outcomes generated by project.

VIII. Uncertainty

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Uncertainty

• Requires information on distribution of returns and risk aversion.

• Figure 8.2 shows a risky project (E,E+y) and a certain project (C) that give the

same expected utility.

VIII. Uncertainty

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Figure 11.2 70

Calculating the Certainty Equivalent Value

VIII. Uncertainty

• ลูกตานา – บัณฑิตศึกษาที่จุฬาลงกรณ:

มหาวิทยาลัย คาดวAาจะทำใหEรายไดEสูงเพิ่มขึ้น y บาท

– Probability of ½

• Expected Income รายไดEเฉลี่ยของลูกตานา = E+y/2 หรือจุด

• Expected Utility = ½ U(E) + ½ U(E+y) หรือ จุด C

• Risk premium =

• The project’s expected value be reduced by a risk premium that depends on the shape of the utility function.

I

I C-

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Recap of Cost-Benefit Analysis

• Present value

• Private sector project evaluation

• Discount rate for government projects

• Valuing public benefits and costs

• Cost-benefit “games”

• Distributional considerations

• Uncertainty

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