sustainable project management

Debate 1

Topic: Monetary valuation is essential in the project evaluation phase in order to bring environmental effects to the forefront of decision-making

AGREE

Participant 1: Martin

Participant 2: Marly

Participant 3: Mark

DISAGREE

Participant 1: Anna

Participant 2: Garth

Participant 3: Jessica

Debate 2

Topic: Philosophical debate on the preservation of the environment based on the intrinsic value of natural resources vs. extrinsic value (i.e. value to humans)

AGREE

Participant 1: Raphael Dumas

Participant 2: Graeme

Participant 3: Rebecca

DISAGREE

Participant 1: Elle

Participant 2: Thomas

Participant 3: Alex

CIV324 Week 4 Feb 3, 2012

Single objective and multiple objective evaluation methods Feb 10: Case-study of a CBA for high-speed rail in the Quebec-Windsor Corridor & guest lecture. Feb 17: Sample problems, wrapping-up evaluation stage March 2: Midterm exam, in-class, 3 hours. Course notes and slides are allowed (in hard copy only)

M. Hatzopoulou

Methods of evaluating project alternatives

I. Economic evaluation techniques

Benefit-Cost Ratio

Net Present Value

Annual Worth

Rate of Return

II. Use of weighing schemes that produce a score for each alternative

III. (To a lesser extent) Cost-Effectiveness Analysis illustrates trade-offs but does not indicate which alternative is the best

Economic evaluation techniques

These techniques estimate the monetary value of the benefits and costs for individual projects (or project alternatives) and their comparative worth

Costs and benefits for each year of the useful life of a project are estimated, discounted to a base year, and then compared on the basis of some decision rule (e.g. ratio of benefits and costs must be greater than 1)

Being able to compare different streams of monetary benefits and costs over time requires that there be some method for a fair comparison. This is found in the concepts of discounting and capital recovery.

Economic concepts of discounting and capital recovery

The worth of an alternative is determined by estimating the monetary return on capital investment. To do this, one needs to estimate the Real Value of Money

If one invests $10,000 today with an interest rate of 10% per year; at the end of year 1, the investment will be worth: 10,000 + (10,000 x 0.1) = 11,000

$10,000 now is equivalent to a future sum of $11,000 after 1 year

$10,000 is the present or discounted value of the future $11,000

Interest rate used when determining a future value

Discount rate used when discounting to the present


If one invests $10,000 today with an interest rate of 10% per year:

At the end of year 1, the investment will be worth: 10,000 + (10,000 x 0.1) = 11,000

At the end of year 2, the investment will be worth: 11,000 + (11,000 x 0.1) = 12,100 or: [10,000 + (10,000 x 0.1)] + 0.1 [10,000 + (10,000 x 0.1)]= = 10,000 + 10,000 x 0.2 + 10,000 x 0.12 = 10,000 x (1 + 0.1)2

At the end of year n, the investment will be worth: 10,000 x (10,000 + 0.1)n

The equation used to compare sums of money that exist at two distinct times is: F = P x (1 + i)n F= future amount; P = present amount; i = interest rate per period; n= periods of repayment


The future value of present costs or benefits is: F = P x (1 + i)n

The present value of future costs or benefits is: P = F / (1 + r)n

i is the interest rate, r the discount rate

In P = F / (1 + r)n, 1/(1 + r)n is called the Present Worth Factor

Year PWF @ r=5% PWF @ r=10% PWF @ r=15%

1 0.95 0.90 0.87

2 0.90 0.82 0.75

3 0.86 0.75 0.65

4 0.82 0.68 0.57

5 0.78 0.62 0.49

10 0.61 0.38 0.24

20 0.37 0.15 0.06


An important investment consideration is the present value of a constant stream of equal payments over several periods (common to home and auto mortgages)

F = A + A (1+ i) + A (1 + i)2 + A (l + i)3 + ...+ A (1 + i)n-1

F = future value sought through a series of equal payments

A = uniform payments required over n periods

We can write F = A [1 + (1 + i) + (1 + i)2 + (1 + i)3 + + (l + i)n-1]

This is a geometric ratio series equal to:

F = A [(1 - (1 + i)n / 1 - (1 + i)) 1]

Simplifies to F = A ((1 + i)n 1) / i


Lets go back to: F = P x (1 + i)n

And lets replace F by A ((1 + i)n 1) / i

We obtain: A ((1 + i)n 1) / i = P x (1 + i)n

A will be equal to: A = P [ i x (1 + i)n ] / [(1 + i)n 1]

Capital Recovery Factor represents the proportion of an initial investment that has to be recouped as benefits in each of n periods in order to return the same value as was invested

E.g. The annual payment required over 10 years to return the value of a present amount of $10,000 is:

A = 10,000 [0.1 x 1.110] / [1.110 - 1] = 1,627


10,000 Annual

payment Capital

year 1 11,000 1,627 9,373

year 2 12,100 1,627 10,310 8,682

year 3 13,310 1,627 9,551 7,923

year 4 14,641 1,627 8,715 7,088

year 5 16,105 1,627 7,797 6,169

year 6 17,716 1,627 6,786 5,159

year 7 19,487 1,627 5,675 4,047

year 8 21,436 1,627 4,452 2,825

year 9 23,579 1,627 3,107 1,480

year 10 25,937 1,627 1,627 0

Capital Recovery Factor (CRF)

Year CRF @ r=5% CRF @ r=10% CRF @ r=15%

1 1.05 1.10 1.15

2 0.54 0.57 0.61

3 0.37 0.40 0.44

4 0.28 0.31 0.35

5 0.23 0.26 0.30

10 0.13 0.16 0.20

20 0.08 0.12 0.16

Concluding remarks on the concepts of discounting and capital recovery

The value of money concept and associated equations are extremely important components of project evaluation

In most cases, the time streams of benefits and costs of alternatives are expressed in terms of present values (that is, one discounts to the present time) or as equivalent annual costs

The selection of a discount rate can have a significant impact on the level of discounted benefits and costs. The discount rate provides a relative weighing of present costs vs. future benefits a value judgement related to the alternatives being considered

It is often suggested that project evaluation should include a sensitivity analysis with different discount rates (e.g. starting from a low rate that reflects the current government borrowing rate for capital to a high-rate that represents and expected private sector return on capital)

Economic evaluation techniques 1. Present worth method: Discount the costs and benefits of each

project alternative to their equivalent present value and obtain a net worth

2. Annual worth method: Determine the discounted annual equivalent benefits and costs for each alternative and then obtain an annual worth

3. Benefit/Cost methods: Separating costs from benefits, discount to their equivalent annual (or present) values and develop a benefit/cost ratio

4. Return-on-investment method: Find the interest rate that balances present and future cash flows and compare it to a minimum return rate

Economic evaluation techniques Considering the example time stream of benefits and costs shown in Figure 1. Costs represent the capital costs for construction, continuing costs of operation and maintenance, and future costs of rehabilitation. Benefits represent changes in the user and non-user benefits.

-8

-6

-4

-2

0

2

4

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Benefits

Costs

Present Worth Method

Calculate Net Present Value:

NPVy,r = (pwfr,t)(benefitsy,t) - (pwfr,t)(costsy,t)

NPVy,r = net present value of project y with a discount rate r

pwfr,t = present worth factor with discount rate r and time t

benefitsy,t = benefits of project y in time period t

costsy,t = costs of project y in time period t

n = economic life of project y

If NPV is positive, the project/alternative is feasible from an economic efficiency perspective

Illustrating the Present Worth Method year Benefits Costs pwf Discounted Benefits Discounted Costs

1 0 6 0.9091 0.0000 5.4545 2 1 4 0.8264 0.8264 3.3058 3 1 2 0.7513 0.7513 1.5026 4 3 1 0.6830 2.0490 0.6830 5 3 1 0.6209 1.8628 0.6209 6 3 1 0.5645 1.6934 0.5645 7 3 1 0.5132 1.5395 0.5132 8 3 1 0.4665 1.3995 0.4665 9 3 2 0.4241 1.2723 0.8482

10 4 1 0.3855 1.5422 0.3855 11 4 1 0.3505 1.4020 0.3505 12 4 1 0.3186 1.2745 0.3186 13 4 1 0.2897 1.1587 0.2897 14 4 2 0.2633 1.0533 0.5267 15 4 2 0.2394 0.9576 0.4788 16 4 3 0.2176 0.8705 0.6529 17 4 2 0.1978 0.7914 0.3957 18 5 2 0.1799 0.8993 0.3597 19 5 2 0.1635 0.8175 0.3270 20 5 2 0.1486 0.7432 0.2973 21 5 2 0.1351 0.6757 0.2703

23.5801 18.6119

NPV = 23.5801 - 18.6119 NPV= 4.9682

Annual Worth Method

Discounted costs are summed and multiplied by the appropriate Capital Recovery Factor

Recall that A = P x CRF; so we need first the present value

Same applies for the discounted benefits

In the previous example:

Equivalent Annual Costs = 18.6119 x CRF@20yrs = 2.1869

Equivalent Annual Benefits = 23.5801 x CRF@20yrs = 2.7707

Equivalent Annual Worth = 2.7707 - 2.1869 = + 0.5838

Useful to compare two project alternatives with unequal lives, in other methods, alternatives have to be expanded to a common life

Rate of Return Method Determines the discount rate at which the present value of both

the present and future costs will equal the present value of both the present and future benefits

We are trying to determine the discount rate r in which:

(pwfr,t)(benefitsy,t) = (pwfr,t)(costsy,t)

When the discount rate is identified, it can be compared to a predefined acceptable rate of return. If the calculated rate of return is greater than the acceptable rate, the project can be considered economically feasible.

In the previous example, it is 16% which means that if the desired rate of return was set at less than 16%, the project would be feasible

Benefit/Cost (B/C) Method

Develops a ratio of discounted benefits to discounted costs [B/C] = (pwfr,t)(benefitsy,t) / (pwfr,t)(costsy,t)

If an alternative has a B/C ratio of less than 1, it is a likely candidate for rejection

In the previous example, B/C = 23.5801 / 18.6119 = 1.267 which means that this project is economically feasible. BUT when two projects are compared, it does not mean that the project with the higher B/C ratio is the one to select!

B/C method requires steps beyond the initial calculation of B/C ratios for each alternative

Incremental Benefit/Cost Method Assessment between any pair of alternatives a and b is:

[B/C]b-a = [Bb - Ba] / [Cb Ca] where b is the higher cost alternative which should be greater than 1 if alternative b is preferred over alternative a

The best choice is the highest-cost alternative whose B/C ratios with all lower-cost alternatives are greater than 1

This method assumes that the relative merit of a project is measured by its change in benefits and costs, compared to the next lower-cost alternative. Is a cost increment worth it compared to the increment in benefits?

Steps for using the incremental B/C method

1. Determine the benefits, costs, and the resulting B/C ratio for each alternative

2. Ignore alternatives with a B/C1.0 in order of increasing cost

4. Calculate the incremental B/C of the second lowest-cost alternative compared to the lowest-cost alternative

5. If the incremental B/C >1, then pick the second lowest cost alternative, else pick the lowest cost alternative

6. Continue in order of increasing costs to calculate the incremental B/C for each alternative compared to the last-picked alternative

Illustration of incremental B/C method

Alternative Benefit Cost B/C

A 40,000 21,000 1.9

B 15,000 1,500 10.0

C 12,800 1,700 7.5

D 52,000 24,500 2.1


B 15,000 1,500 10.0

C 12,800 1,700 7.5

A 40,000 21,000 1.9

D 52,000 24,500 2.1

Illustration of incremental B/C method

Comparison between B and C (12,800 15,000) / (1,700 1,500) = -11 (Pick B, the lower cost)

Comparison between B and A (40,000 15,000) / (21,000 1,500) = 1.28 (Pick A, the higher cost)

Comparison between A and D (52,000 40,000) / (24,500 21,000) = 3.42 (Pick D, the higher cost)


B 15,000 1,500 10.0

C 12,800 1,700 7.5

A 40,000 21,000 1.9

D 52,000 24,500 2.1

HOMEWORK 3 (Part 1)

Rank the following alternatives based on the NPV and B/C methods (at a discount rate of 10%). Also, use the incremental B/C to find the best project alternative. Comment.

Project Altern.

Year 1 Year 2 Year 3 Year 4

B C B C B C B C

A 20 200 50 100 150 50 110 15

B 35 90 90 90 120 90 140 30

C 20 200 50 50 200 50 260 45

D 100 300 200 200 300 100 345 65

E 50 100 100 100 200 100 420 100


I. Economic evaluation techniques SINGLE OBJECTIVE

Benefit-Cost Ratio

Net Present Value

Annual Worth

Rate of Return

II. Use of weighing schemes that produce a score for each alternative MULTIPLE ATTRIBUTES


Multi-Attribute Assessment Methods

The economic evaluation techniques introduced today have one major characteristic in common: the many dimensions of a project are reduced to dollar terms to maximize the net benefit. While these frameworks are capable of incorporating environmental and social impacts, it is necessary to quantify them in economic terms (monetary valuation)

To overcome the need to assign a dollar value to non-market goods and services, rating approaches have been proposed. These rely on the development of Measures of Effectiveness characterizing different sustainability impacts of a given project

Multi-Attribute Assessment Methods

Multiple Attribute Decision Making (MADM) refers to making preference decisions over project alternatives that are characterized by multiple, usually conflicting attributes

MADM problems are diverse and share the following common characteristics:

Alternatives: A finite number of project alternatives

Attributes: Each problem has multiple attributes or criteria

Incommensurable units: Each attribute has different units of measurement

Attribute weights: Expressing the relative importance of each attribute

Decision matrix: where columns indicate attributes considered in a given problem and rows list project alternatives

MADM Decision Matrix

Project Alternative

Attributes

Cost

(x1,000$)

GHG (tons)

Noise (dBA)

Land consumption

(x 1,000 sq ft)

Benefits ($)

0 Do nothing 0 50 65 80 2,000

1 2,000 20 55 100 4,000

2 3,000 12 75 50 4,000

3 5,000 18 50 80 8,000

What else is needed to start evaluating this matrix?

MADM Decision Matrix

Project Alternative

Attributes

Cost

(x1,000$)

GHG (tons)

Noise (dBA)

Land consumption

(x 1,000 sq ft)

Benefits ($)

Weight of attribute 0.25 0.20 0.15 0.15 0.25

0 Do nothing 500 50 65 80 2,000

1 2,000 20 55 100 4,000

2 3,000 12 75 50 4,000

3 5,000 18 50 80 8,000

So which is the best project alternative? How do we evaluate the different alternatives?

Step 1: Attribute normalizing

Normalized ratings have dimensionless units and the larger the rating, the more preference an attribute has.

For cost attributes offering decreasing monotonic utility, take inverse ratings. The transformed benefit attribute (from cost) follows the same normalization process:

Linear normalization: rij = xij / xj* where xj* is the maximum value of the jth attribute.

Vector normalization: rij = xij/sqrt(sumi (xij2))

xij xij2 rij

50 2500 0.897 20 400 0.359 12 144 0.215

8 64 0.143

sumi (xij2) 3108

Sqrt (sumi (xij2)) 55.75

Step 2: Attribute weighting

The role of weight serves to express the importance of each attribute relative to the others. Often, weights from ranks are generated:

Arrange attributes in a simple rank order (most important first) and assign 1 to the most important and n to the least important attribute (assuming n attributes). If two attributes are tied, their mean ranking can be taken. The weights can be obtained from:

Rank reciprocal weights

Rank sum weights

Ranking n attributes at the same time may be difficult, rankings can be obtained from a set of pair-wise judgements

Step 3: Scoring Methods

Involve an index formulation of a system

The two most commonly used scoring methods are:

Simple additive weighing (SAW)

Involves taking the weighted sum of the normalized, weighted, attributes

Vi is the value of alternative i

wj is the weight of attribute j

rij is the normalized rating of alternative i with respect to attribute j

Weighted Product Method

Normalization is not necessary if the attributes are connected by multiplication

The weights become exponents associated with each attribute value; a positive power for benefit attributes and a negative power for cost attributes

Step 3: Weighted Product Method

Involves taking the weighted sum of the normalized, weighted, attributes

Vi is the value of alternative i

wj is the weight of attribute j

This method requires that all ratings be greater than 1. If an attribute has fractional ratings, all ratings in that attribute are multiplied by 10Z to meet this requirement

Alternative values obtained by the multiplicative method do not have a numerical upper bound

It is often convenient to compare each alternative value with a standard or ideal value by computing a value ratio

HOMEWORK 3 (continued)

Use the weighted sum and the weighted product method to rank the different project alternatives. Does the best alternative remain the same under the two methods?

Project Alternative

Attributes

Cost

(x1,000$)

GHG (tons)

Noise (dBA)

Land consumption

(x 1,000 sq ft)

Benefits ($)

Weight of attribute 0.25 0.20 0.15 0.15 0.25

0 Do nothing 500 50 65 80 2,000

1 2,000 20 55 100 4,000

2 3,000 12 75 50 4,000

3 5,000 18 50 80 8,000

Multi-objective Assessment Methods Limitations

Just like the economic evaluation approaches, multi-objective methods are associated with limitations:

Subjective weighing procedures raise the question of whose values are being applied in the assessment. If the weights do not reflect the true preference of the (project owner, community, politicians?); the entire approach may not be very helpful

The rating approach does not provide useful information on whether the costs of alternatives are justified by the benefits expected


I. Economic evaluation techniques SINGLE OBJECTIVE

Benefit-Cost Ratio

Net Present Value

Annual Worth

Rate of Return

II. Use of weighing schemes that produce a score for each alternative MULTIPLE ATTRIBUTES


Cost Effectiveness Evaluation

Estimates the level of goals and objectives attainment per dollar of net expenditure e.g.

Kg of GHG reduced/$

sq ft or decontaminated land / $

CE evaluation lies in the development of an efficiency frontier

Choosing an alternative over another depends on the willingness of the decision-maker to trade-off a level of effectiveness for cost (is the additional benefit worth the added costs?)

Cost Effectiveness Evaluation

GHG Cost

(Kg) $

P1 20 1

P2 70 20

P3 30 1

P4 20 5

P5 25 5

P6 50 15

P7 40 20

P8 100 20 0

20

40

60

80

100

120

0 5 10 15 20 25

GH

G

Cost ($)

P1

P3

P4

P5 P6 P7

P2

P8

Learning outcomes and the muddiest point

Five volunteers to prepare each a 3 min presentation, 5 slides illustrating:

What they learnt the best over the past few weeks, their own highlights

Their muddiest point

Volunteer 1:

Volunteer 2:

Volunteer 3:

Volunteer 4:

Volunteer 5:

sustainable project management

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