Investment Analysis for private and Public sector projects Timing is everything To have money sooner rather than later increases the range of alternatives open to us.

Value of futurity we continually return to the idea of the value of futurity - a far off cost or benefit must be marked down or discounted ; its value is always greater now. The basic question tackled by investment appraisal methods is whether to incur an expense now so that benefits can be enjoyed in later periods (investment), or whether the funds should be used to generate immediate benefits, now ( consumption ) . In economic terms, we are considering the "time preference for consumption”. Definition: Any project which requires an outlay of money or other resources and which then generates a flow of costs and benefits in subsequent periods should be regarded as an investment. Whether the initial outlay is funded out of a capital or a current expenditure account is of no relevance in this context.

we continually return to the idea of the value of futurity - a far off cost or benefit must be marked down or discounted ; its value is always greater now.

The basic question tackled by investment appraisal methods is whether to incur an expense now so that benefits can be enjoyed in later periods (investment), or whether the funds should be used to generate immediate benefits, now ( consumption ) .

In economic terms, we are considering the "time preference for consumption”.

Definition:

Any project which requires an outlay of money or other resources and which then generates a flow of costs and benefits in subsequent periods should be regarded as an investment. Whether the initial outlay is funded out of a capital or a current expenditure account is of no relevance in this context.

Basic Managerial Questions When projects are put forward for funding approval, sufficient information needs to be presented in order to answer the following types of questions: • What is the project designed to do? • Why are the project's aims desirable? • Is there a better way of achieving these aims? • Why must the project proceed now? • Who benefits and who loses as a result of the project?

When projects are put forward for funding approval, sufficient information needs to be presented in order to answer the following types of questions:

• What is the project designed to do?

• Why are the project's aims desirable?

• Is there a better way of achieving these aims?

• Why must the project proceed now?

• Who benefits and who loses as a result of the project?

The Relative Value of Futurity and the Role of Interest Rates Interest paid on forgone consumption, that is, saving, is the reward of thrift and the interest rate is in effect, its price. If interest rates are considered to be high, individuals will be tempted to forgo current consumption. If interest rates are low, individuals will not be induced to save. On the other hand, investors (private companies or public agencies) who wish to use these savings will find that low interest rates render more projects viable - its now more worthwhile to transform interest earning money into a profit making investment - and the demand for funds will thus increase. High interest rates will work in the opposite direction. Thus, interest rates perform an important role in determining the amount of saving and investment in the economy at large. The investment analyst’s tools recognise this "time cost" of tying up funds in long-lived projects.

Interest paid on forgone consumption, that is, saving, is the reward of thrift and the interest rate is in effect, its price. If interest rates are considered to be high, individuals will be tempted to forgo current consumption. If interest rates are low, individuals will not be induced to save.

On the other hand, investors (private companies or public agencies) who wish to use these savings will find that low interest rates render more projects viable - its now more worthwhile to transform interest earning money into a profit making investment - and the demand for funds will thus increase. High interest rates will work in the opposite direction. Thus, interest rates perform an important role in determining the amount of saving and investment in the economy at large. The investment analyst’s tools recognise this "time cost" of tying up funds in long-lived projects.

The Nature of Decision Making in the Public Sector So far we have made no real distinction between the type of financial evaluation normally encountered in the private sector and that special type of appraisal that needs to be employed in the government sector. Discounted cash flow techniques are used in both domains to ensure that the estimates of net benefits of alternative courses of action are strictly comparable over time. However, the interpretation of "net benefits" is considerably more complex in the government sector. Private firms usually seek to optimise the use of their own shareholder’s funds to generate their own financial returns. In a war against other firms, the issue is what did this decision do to advance the interest of the firm in which I have voluntarily invested. By contrast, the government sector is concerned to use community resources (ultimately appropriations from taxes levied compulsorily) to generate community benefits.

So far we have made no real distinction between the type of financial evaluation normally encountered in the private sector and that special type of appraisal that needs to be employed in the government sector.

Discounted cash flow techniques are used in both domains to ensure that the estimates of net benefits of alternative courses of action are strictly comparable over time.

However, the interpretation of "net benefits" is considerably more complex in the government sector. Private firms usually seek to optimise the use of their own shareholder’s funds to generate their own financial returns. In a war against other firms, the issue is what did this decision do to advance the interest of the firm in which I have voluntarily invested. By contrast, the government sector is concerned to use community resources (ultimately appropriations from taxes levied compulsorily) to generate community benefits.

The Aim of Cost Benefit Analysis (CBA) The function of public investment is to increase community welfare. The aim of CBA is thus to ensure that the community’s resources are used in such a way as to maximise community welfare over time. The advantages of CBA though are that: • a consistent approach can be applied to a wide range of government projects - after all, resources are limited and outlays across very different portfolios must be compared • the discounting techniques, that are used to reduce money outlays at different times to true comparability, have become generally well understood • the concept of economic welfare provides an alternative basis for the appraisal of government projects and is the parallel concept to financial return in the private sector evaluations

The function of public investment is to increase community welfare. The aim of CBA is thus to ensure that the community’s resources are used in such a way as to maximise community welfare over time.

The advantages of CBA though are that:

• a consistent approach can be applied to a wide range of government projects - after all, resources are limited and outlays across very different portfolios must be compared

• the discounting techniques, that are used to reduce money outlays at different times to true comparability, have become generally well understood

• the concept of economic welfare provides an alternative basis for the appraisal of government projects and is the parallel concept to financial return in the private sector evaluations

Pareto Improvement Pareto Improvement hinges 1) on how much the gainers would value their prospective gain and 2) what the losers would be willing and able to accept to compensate them for their prospective loss. Examples of situations in transport where there are positive and negative effects of a change are listed in the following table. Positives / Negatives Time savings -Increases in noise levels Vehicle operating cost savings -Loss of dwelling Accident reductions-Materials used in construction

Pareto Improvement hinges 1) on how much the gainers would value their prospective gain and 2) what the losers would be willing and able to accept to compensate them for their prospective loss.

Examples of situations in transport where there are positive and negative effects of a change are listed in the following table.

Positives / Negatives

Time savings -Increases in noise levels

Vehicle operating cost savings -Loss of dwelling

Accident reductions-Materials used in construction

Consumers Surplus represents the difference between what consumers collectively would be willing and able to pay for a given volume of a good or service and the actual collective expenditure dispersed on it.

Consumers Surplus represents the difference between what consumers collectively would be willing and able to pay for a given volume of a good or service and the actual collective expenditure dispersed on it.

Project Acceptance and Capital Programming In deciding to recommend investments on the basis of economic merit the fundamental rule is: If the project does not preclude other projects and if unlimited funds are available, undertake all projects with a Net Present Value, NPV, greater than or just equal to zero. but If funds are limited, it will be necessary to rank projects and to select the better projects until the budget is exhausted . The Net Present Value, may be thought of as the amount I would be prepared to pay today - a single sum - to have the stream of returns (less their associated costs) from a given investment over the foreseeable future.

In deciding to recommend investments on the basis of economic merit the fundamental rule is:

If the project does not preclude other projects and if unlimited funds are available, undertake all projects with a Net Present Value, NPV, greater than or just equal to zero.

but

If funds are limited, it will be necessary to rank projects and to select the better projects until the budget is exhausted .

The Net Present Value, may be thought of as the amount I would be prepared to pay today - a single sum - to have the stream of returns (less their associated costs) from a given investment over the foreseeable future.

Discounted Cash Flow Analysis As a professional at work you will be expected by your manager to competently perform the calculations, so learning the technique thoroughly while still a student is essential. If your future managers are not “economists”, you may even have to convince them of the correctness of the procedure. The relationship between future dollar value (FV) and present dollar value (PV) is as follows : (1) FV = PV (1 + i)n where i is the interest rate and n is the number of time periods (say years) elapsing between the present and future date. This relationship should be familiar to most people who have an interest earning account at a bank. For instance, if a sum of money PV = $1000 is deposited in a bank for n = 2 years at an interest rate i = 10%, then the maturing value of the deposit is given by : FV = $1210 = $1000(1.10)2

As a professional at work you will be expected by your manager to competently perform the calculations, so learning the technique thoroughly while still a student is essential. If your future managers are not “economists”, you may even have to convince them of the correctness of the procedure.

The relationship between future dollar value (FV) and present dollar value (PV) is as follows :

(1) FV = PV (1 + i)n

where i is the interest rate and n is the number of time periods (say years) elapsing between the present and future date.

This relationship should be familiar to most people who have an interest earning account at a bank. For instance, if a sum of money PV = $1000 is deposited in a bank for n = 2 years at an interest rate i = 10%, then the maturing value of the deposit is given by :

FV = $1210 = $1000(1.10)2

Net present value ( NPV ) Net present value ( NPV ) is a standard method for evaluating competing long-term projects in capital budgeting. It measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met. One way of ranking projects with a budget constraint is to calculate the NPV gained per unit of limited capital. That is in effect a ratio of benefits to costs. Using the NPV method a potential investment project should be undertaken if the present value of all cash inflows minus the present value of all cash outflows (which equals the net present value) is greater than zero.

Net present value ( NPV ) is a standard method for evaluating competing long-term projects in capital budgeting. It measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met. One way of ranking projects with a budget constraint is to calculate the NPV gained per unit of limited capital. That is in effect a ratio of benefits to costs.

Using the NPV method a potential investment project should be undertaken if the present value of all cash inflows minus the present value of all cash outflows (which equals the net present value) is greater than zero.

NPV A key input into this process is the interest rate which is used to discount future cash flows to their present values. If the discount rate is equal to the shareholder’s required rate of return, any NPV > 0 means that the required return has been exceeded, and the shareholders will expect an additional profit that has a present value equal to the NPV. Thus if the goal of the firm is to maximize shareholder wealth, managers should undertake all projects that have an NPV > 0, or if two projects are mutually exclusive, they should choose the one with the highest positive NPV.

A key input into this process is the interest rate which is used to discount future cash flows to their present values. If the discount rate is equal to the shareholder’s required rate of return, any NPV > 0 means that the required return has been exceeded, and the shareholders will expect an additional profit that has a present value equal to the NPV. Thus if the goal of the firm is to maximize shareholder wealth, managers should undertake all projects that have an NPV > 0, or if two projects are mutually exclusive, they should choose the one with the highest positive NPV.

NPV Income received in the future is worth less now than income received now. That's because income you get now can earn interest and grow. The net present value of an investment tells you how this investment compares either with your alternative investment or with borrowing, whichever applies to you. A positive net present value means this investment is better. A negative net present value means your alternative investment, or not borrowing, is better. The future value of an amount you get now is Future Value = Present Value ×( 1 + Interest Rate )ª, where a is the number of years it grows. Therefore, the present value of a future income amount a years in the future is: Present Value = (Future Value) / ( 1 + Interest Rate )ª The discount rate is another name for the interest rate, so Present Value = (Future Value) / ( 1 + Discount Rate )ª When the discount rate goes up, present values go down. When the discount rate goes down, present values go up.

Income received in the future is worth less now than income received now. That's because income you get now can earn interest and grow.

The net present value of an investment tells you how this investment compares either with your alternative investment or with borrowing, whichever applies to you. A positive net present value means this investment is better. A negative net present value means your alternative investment, or not borrowing, is better.

The future value of an amount you get now is Future Value = Present Value ×( 1 + Interest Rate )ª, where a is the number of years it grows.

Therefore, the present value of a future income amount a years in the future is: Present Value = (Future Value) / ( 1 + Interest Rate )ª

The discount rate is another name for the interest rate, so Present Value = (Future Value) / ( 1 + Discount Rate )ª

When the discount rate goes up, present values go down. When the discount rate goes down, present values go up.

Internal Rate of Return (IRR) An alternative way of comparing projects is to calculate the internal rates of return. This method is widely used in business applications, its main advantage being that rate of return is a familiar concept in business Generally speaking the higher the IRR, the better the project. Provided that the IRR exceeds the target rate of return, the project is a good one. (An exception is when The internal rate of return is not a good way evaluate an investment that has costs later rather than just earlier. An example of that would be an investment that generates an environmental problem that will require a cleanup at the end of the income stream. For some such investments, the worse investments have higher internal rates of return. ) To evaluate investments and calculate an internal rate of return, we need the concept of income stream . An income stream is a series of amounts of money. Each amount of money comes in or goes out at some specific time, either now or in the future.

An alternative way of comparing projects is to calculate the internal rates of return. This method is widely used in business applications, its main advantage being that rate of return is a familiar concept in business

Generally speaking the higher the IRR, the better the project. Provided that the IRR exceeds the target rate of return, the project is a good one.

(An exception is when The internal rate of return is not a good way evaluate an investment that has costs later rather than just earlier. An example of that would be an investment that generates an environmental problem that will require a cleanup at the end of the income stream. For some such investments, the worse investments have higher internal rates of return. )

To evaluate investments and calculate an internal rate of return, we need the concept of income stream .

An income stream is a series of amounts of money. Each amount of money comes in or goes out at some specific time, either now or in the future.

Net Present Value (NPV) of an income stream The net present value of an income stream is the sum of the present values of the individual amounts in the income stream. Each future income amount in the stream is discounted , meaning that it is divided by a number representing the opportunity cost of holding capital from now (year 0) until the year when income is received or the outgo is spent. The opportunity cost can either be how much you would have earned investing the money elsewhere,or how much interest you would have had to pay if you borrowed money. The present value of an investment is the amount of money you'd need now to be able to duplicate the investment's income stream The internal rate of return is the interest rate that makes the present value of the investment's income stream -- its costs and payoffs -- add up to 0. The internal rate of return is a measure of the worth of an investment. The present value of a future amount of income is: Present Value = (Future Value)/(1 + Discount Rate)ª, where the exponent ª is the number of years in the future that the future value will be received. The discount rate is the same as the interest rate.

The net present value of an income stream is the sum of the present values of the individual amounts in the income stream. Each future income amount in the stream is discounted , meaning that it is divided by a number representing the opportunity cost of holding capital from now (year 0) until the year when income is received or the outgo is spent. The opportunity cost can either be how much you would have earned investing the money elsewhere,or how much interest you would have had to pay if you borrowed money.

The present value of an investment is the amount of money you'd need now to be able to duplicate the investment's income stream

The internal rate of return is the interest rate that makes the present value of the investment's income stream -- its costs and payoffs -- add up to 0.

The internal rate of return is a measure of the worth of an investment.

The present value of a future amount of income is: Present Value = (Future Value)/(1 + Discount Rate)ª, where the exponent ª is the number of years in the future that the future value will be received. The discount rate is the same as the interest rate.

Optimal Timing "Why undertake the project now? " For the present purposes, it is sufficient to note the usefulness of the "first-year rate of return" rule for deciding optimal timing. First-Year Rate of Return A project should be postponed if the benefits that would have occurred in the first year of the project’s life would have been less than the interest incurred on the capital in that year Of course, it is only necessary to defer commencement when insufficient funds are available for worthwhile projects in the first place

For the present purposes, it is sufficient to note the usefulness of the "first-year rate of return" rule for deciding optimal timing.

First-Year Rate of Return

A project should be postponed if the benefits that would have occurred in the first year of the project’s life would have been less than the interest incurred on the capital in that year

Of course, it is only necessary to defer commencement when insufficient funds are available for worthwhile projects in the first place

Alternative Decision Methods The preference in these notes is to use the NPV method supplemented by the B/C method for project ranking suitably modified for consideration of mutually exclusive projects and postponement. Recommended practice of the NSW and Victorian Treasuries, bodies whose instructions guide the appraisal of the majority of transport investment in Australia is also strongly in favour of the NPV criterion, because in practice governments wish to maximise aggregate NPV from the total of available funds. This is possible by admitting projects to the program with the highest NPV per dollar outlaid, until the available budget is exhausted.

The preference in these notes is to use the NPV method supplemented by the B/C method for project ranking suitably modified for consideration of mutually exclusive projects and postponement.

Recommended practice of the NSW and Victorian Treasuries, bodies whose instructions guide the appraisal of the majority of transport investment in Australia is also strongly in favour of the NPV criterion, because in practice governments wish to maximise aggregate NPV from the total of available funds. This is possible by admitting projects to the program with the highest NPV per dollar outlaid, until the available budget is exhausted.

common variants of the NPV rule : • annual equivalent method where a project’s cash flows are converted to an annuity over the life of the project • terminal value method - instead of discounting back to the present, a terminal value is at some future date is estimated. The earning power of returns as they re received are calculated by forward compounding. The former method is used in an assessment known as Cost Effectiveness Analysis . Such analysis is recommended for the case where the costs of the alternative options may be estimated but the intrinsic value of the returns are unquantifiable. Examples arise commonly in areas of public spending with social impacts and certainly include public health and safety as well as social welfare. In practice, two alternative means of attaining the same objective are selected and costed over their whole life time. The present value of these cost streams are then compared. In addition there are non-discounted cash flow methods such as the Pay-Back Criterion

:

• annual equivalent method where a project’s cash flows are converted to an annuity over the life of the project

• terminal value method - instead of discounting back to the present, a terminal value is at some future date is estimated. The earning power of returns as they re received are calculated by forward compounding.

The former method is used in an assessment known as Cost Effectiveness Analysis . Such analysis is recommended for the case where the costs of the alternative options may be estimated but the intrinsic value of the returns are unquantifiable. Examples arise commonly in areas of public spending with social impacts and certainly include public health and safety as well as social welfare. In practice, two alternative means of attaining the same objective are selected and costed over their whole life time. The present value of these cost streams are then compared.

In addition there are non-discounted cash flow methods such as the Pay-Back Criterion

Discounted Cash Flow Analysis As a professional at work you will be expected by your manager to competently perform the calculations, so learning the technique thoroughly while still a student is essential. If your future managers are not “economists”, you may even have to convince them of the correctness of the procedure. The relationship between future dollar value (FV) and present dollar value (PV) is as follows : (1) FV = PV (1 + i)n where i is the interest rate and n is the number of time periods (say years) elapsing between the present and future date. This relationship should be familiar to most people who have an interest earning account at a bank. For instance, if a sum of money PV = $1000 is deposited in a bank for n = 2 years at an interest rate i = 10%, then the maturing value of the deposit is given by : FV = $1210 = $1000(1.10)2

As a professional at work you will be expected by your manager to competently perform the calculations, so learning the technique thoroughly while still a student is essential. If your future managers are not “economists”, you may even have to convince them of the correctness of the procedure.

The relationship between future dollar value (FV) and present dollar value (PV) is as follows :

(1) FV = PV (1 + i)n

where i is the interest rate and n is the number of time periods (say years) elapsing between the present and future date.

This relationship should be familiar to most people who have an interest earning account at a bank. For instance, if a sum of money PV = $1000 is deposited in a bank for n = 2 years at an interest rate i = 10%, then the maturing value of the deposit is given by :

FV = $1210 = $1000(1.10)2

Discounted Cash Flow Analysis Page13 notes onward Effects of High Discount Rates So, high discount rates favour projects which generate quick returns. In addition, net worth will increase if the project continues to generate benefits for a longer rather than a shorter period, although it is very often the case that the project life cannot be predicted with any great certainty. For example an engineer might predict that a road may have a useful life of 20 years but experience could show that similar roads range in life from 10 to 30 years. It is typical for railway assets to be long-lived. Railway tunnels and structures typically have useful lives exceeding 40 years. It has not been uncommon for some passenger rolling stock to see over 60 years in service. Some railway formations and cuttings and some harbour dredging amount to a perpetual alteration to the landscape From the foregoing discussion about discount rates, it should be clear that the present value of $1 in the future diminishes considerably as the time period increases.

Page13 notes onward

Effects of High Discount Rates

So, high discount rates favour projects which generate quick returns.

In addition, net worth will increase if the project continues to generate benefits for a longer rather than a shorter period, although it is very often the case that the project life cannot be predicted with any great certainty.

For example an engineer might predict that a road may have a useful life of 20 years but experience could show that similar roads range in life from 10 to 30 years.

It is typical for railway assets to be long-lived. Railway tunnels and structures typically have useful lives exceeding 40 years. It has not been uncommon for some passenger rolling stock to see over 60 years in service. Some railway formations and cuttings and some harbour dredging amount to a perpetual alteration to the landscape

From the foregoing discussion about discount rates, it should be clear that the present value of $1 in the future diminishes considerably as the time period increases.

Principles of Cost Benefit Analysis for Public Sector Projects All evaluation passes through 4 phases. In practice you should be able to: 1. Write down the objective to be attained. This is not the activity itself. It is what we wish to see happen as a result. 2. Specify at least 2 alternative ways of achieving that objective 3. Estimate the costs and benefits of the alternatives 4. Pick the better (or best) alternative and say why it is preferred.

All evaluation passes through 4 phases. In practice you should be able to:

1. Write down the objective to be attained. This is not the activity itself. It is what we wish to see happen as a result.

2. Specify at least 2 alternative ways of achieving that objective

3. Estimate the costs and benefits of the alternatives

4. Pick the better (or best) alternative and say why it is preferred.

Identification and Specification of Alternatives in Practice The essence of a social CBA is that it sets out to ascertain whether or not a change can potentially raise community welfare . Thus, implementation of a project at least requires that the benefits of undertaking the project outweigh the benefits of doing nothing at all. For example, the community must be better off by undertaking a road improvement over and above leaving the road as it is.

The essence of a social CBA is that it sets out to ascertain whether or not a change can potentially raise community welfare .

Thus, implementation of a project at least requires that the benefits of undertaking the project outweigh the benefits of doing nothing at all. For example, the community must be better off by undertaking a road improvement over and above leaving the road as it is.

Do-Nothing Case Good CBA practice requires that the benefits and costs of a course of action must be compared with not undertaking the project at all. In practice however, definition of a “do- nothing” case is often difficult. For example, reconstruction of a failing railway bridge must be compared with not repairing the bridge. The do-nothing case here could mean total closure of the line. This might be unrealistic as a point of comparison, and some more practical definition of a do-nothing case might be required. Sometimes a “ do-minimum” base case is compared with the project case, in recognition of the unreasonableness of a future in which absolutely nothing occurred.

Good CBA practice requires that the benefits and costs of a course of action must be compared with not undertaking the project at all.

In practice however, definition of a “do- nothing” case is often difficult. For example, reconstruction of a failing railway bridge must be compared with not repairing the bridge. The do-nothing case here could mean total closure of the line. This might be unrealistic as a point of comparison, and some more practical definition of a do-nothing case might be required. Sometimes a “ do-minimum” base case is compared with the project case, in recognition of the unreasonableness of a future in which absolutely nothing occurred.

consider all alternatives? Although there is an obligation to consider the ‘do-nothing’ case, other alternatives should also be examined to ensure that the design project is the best way of achieving project aims. For example, it is desirable to consider: • alternative scale or standard of project (Are most of the benefits attainable from part of the proposal ? Would a lesser quality be adequate?) • alternative phasing or location (Do the most pressing parts first ? Consider a reestablishment as an alternative to a new distribution scheme?) • alternative operating methods ( Contract out, stop doing it in house - or vice versa ) • alternative types of project ( Not always another capital investment. Is there a change to operating practice that can better the desired objective?) In practice, it is often simply not feasible to consider all alternatives

Although there is an obligation to consider the ‘do-nothing’ case, other alternatives should also be examined to ensure that the design project is the best way of achieving project aims. For example, it is desirable to consider:

• alternative scale or standard of project (Are most of the benefits attainable from part of the proposal ? Would a lesser quality be adequate?)

• alternative phasing or location (Do the most pressing parts first ? Consider a reestablishment as an alternative to a new distribution scheme?)

• alternative operating methods ( Contract out, stop doing it in house - or vice versa )

• alternative types of project ( Not always another capital investment. Is there a change to operating practice that can better the desired objective?)

In practice, it is often simply not feasible to consider all alternatives

special points Two special points should be made regarding alternative futures. 1. The estimates of future impacts may be supplied by transport and traffic engineers or made by the economist directly. The important point is that they must be for “with and without” the proposal cases, not just “before and after”. Our aim is to isolate the difference of having one future versus its alternative, not the difference between now and a general future. 2. Unlike the private sector manager, the public policy analyst must also be mindful of a “project” it is all too easy to forget. An ultimate test, which all proposals must beat, is a tax reduction. Would society be better off without the project under consideration and a little less public debt or lighter taxes? In CBA inflation is generally ignored. Provided that the discount rate is expressed in real terms, and provided that the inflation does not affect benefit

Two special points should be made regarding alternative futures.

1. The estimates of future impacts may be supplied by transport and traffic engineers or made by the economist directly. The important point is that they must be for “with and without” the proposal cases, not just “before and after”. Our aim is to isolate the difference of having one future versus its alternative, not the difference between now and a general future.

2. Unlike the private sector manager, the public policy analyst must also be mindful of a “project” it is all too easy to forget. An ultimate test, which all proposals must beat, is a tax reduction. Would society be better off without the project under consideration and a little less public debt or lighter taxes?

In CBA inflation is generally ignored. Provided that the discount rate is expressed in real terms, and provided that the inflation does not affect benefit

Treatment of Risk and Uncertainty The environment within which projects are undertaken is forever changing. The estimates that are made about benefits and costs are often be based upon sets of quite debatable assumptions. However reasonable these assumptions might be, it is clearly important to distinguish between two projects that, say, have the same NPV, but for which we have different degrees of confidence about underlying assumptions. Risk and uncertainty are therefore important dimensions of a project's desirability. Conceptually, we can distinguish between: • risk - probabilities of outcome are known, • uncertainty - probabilities of outcomes (or even, the outcomes themselves ) cannot be predicted

The environment within which projects are undertaken is forever changing. The estimates that are made about benefits and costs are often be based upon sets of quite debatable assumptions. However reasonable these assumptions might be, it is clearly important to distinguish between two projects that, say, have the same NPV, but for which we have different degrees of confidence about underlying assumptions.

Risk and uncertainty are therefore important dimensions of a project's desirability. Conceptually, we can distinguish between:

• risk - probabilities of outcome are known,

• uncertainty - probabilities of outcomes (or even, the outcomes themselves ) cannot be predicted

Risk and Uncertainty (cont) A number of methods have been used to account for these dimensions, including: • attaching a risk premium to the discount rate, • using probability theory to estimate expected values, • using gaming methods, • simulation studies

A number of methods have been used to account for these dimensions, including:

• attaching a risk premium to the discount rate,

• using probability theory to estimate expected values,

• using gaming methods,

• simulation studies

Sensitivity Analysis One of the simplest, and most widely used approaches is to simply test how sensitive results are to key assumptions, tabulating the effect on final NPV of an x% increase or decrease in a given key input price or quantity One of the significant areas of uncertainty in transport studies is in the forecasting of future traffic volumes. Experience with traffic forecasts has been that actual traffic volumes have frequently turned out to be markedly different from forecast levels. Although it should be of concern that forecasting methods should be refined, it should also be clear that the effect of forecasting errors is reduced by the discounting process Provided that forecasts in the early years of the project's life are reasonably accurate, the estimated net present value can be more confidently relied upon. The higher the discount rate, the more confident we can be.

One of the simplest, and most widely used approaches is to simply test how sensitive results are to key assumptions, tabulating the effect on final NPV of an x% increase or decrease in a given key input price or quantity

One of the significant areas of uncertainty in transport studies is in the forecasting of future traffic volumes. Experience with traffic forecasts has been that actual traffic volumes have frequently turned out to be markedly different from forecast levels.

Although it should be of concern that forecasting methods should be refined, it should also be clear that the effect of forecasting errors is reduced by the discounting process Provided that forecasts in the early years of the project's life are reasonably accurate, the estimated net present value can be more confidently relied upon. The higher the discount rate, the more confident we can be.

Valuation of Non-Market Impacts Value of Time Savings Time is a highly 'valued' fixed resource because it provides the opportunity to undertake desirable activities. For this reason time savings are valued. Indeed, a significant proportion of the total benefits emanating from transport investments - up to 80% in some cases - are attributable to travel time savings that accrue to the 'users' of such facilities. A major difficulty however is that the dollar value of such benefits can only be imputed indirectly because no identifiable market exists for travel time savings.

Time is a highly 'valued' fixed resource because it provides the opportunity to undertake desirable activities.

For this reason time savings are valued. Indeed, a significant proportion of the total benefits emanating from transport investments - up to 80% in some cases - are attributable to travel time savings that accrue to the 'users' of such facilities. A major difficulty however is that the dollar value of such benefits can only be imputed indirectly because no identifiable market exists for travel time savings.