# Ideal Approach - Step 4 - Comparing Costs and Benefits

## Determining Present Value of Project Costs and Benefits

Project costs and benefits are incurred at different times during a project’s life. As such, the process of discounting allows the expression of a stream of costs or benefits as one number in present value terms.

## Comparing Costs and Benefits

Benefit and cost streams form the basis of several measures of project viability:

Net Present Value (NPV): NPV is the value resulting from subtracting the expected cost from the expected benefits. Projects with a NPV greater than zero are worth undertaking.

Benefit – Cost Ratio (BCR): the BCR is the ratio of the present value of benefits to the present value of costs. The ratio should be greater than 1.0 for a project to be acceptable[1]. For example, a BCR of 1.25 indicates that for every \$1 of cost, the project will return \$1.25 of benefit. BCR is a relative measure of viability.

Internal Rate of Return (IRR): the IRR is the discount rate at which the present value of costs equals the present value of benefits. Alternatively, IRR is the discount rate at which NPV = 0 and BCR = 1.0. If IRR exceeds the opportunity cost of the capital, the project is considered to be economically sound and worth pursuing. [2]

## Using Excel to calculate cost-benefit

 Value to Calculate Excel Function Function Help PVBenefit & PVCost NPV() Excel help Net Present Value NPV() Excel help Benefit Cost Ratio n/a n/a Internal Rate of Return IRR() Excel help

References:

[1] It is not in any way inconsistent for a project to have a low positive NPV (because it is a small project) at the same time as it has a high BCR.

[2] The IRR is a criteria to be used with caution because: (i) it cannot be calculated for all projects (e.g. projects where the stream of net benefits is strictly positive for each year or projects with multiple IRR); and, (ii) “it is a mathematical concept and not an investment criterion for evaluating alternative cash flows. When the cash flows are irregular, with net costs occurring in the later years of the project, it will give unreliable results in the ranking of alternative options”(Treasury Board of Canada 2007).

Costs and Benefits are compared using measures of project viability
Source: Migikata
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The text passage provides an overview of cost-benefit analysis methods, including Net Present Value (NPV), Benefit-Cost Ratio (BCR), and Internal Rate of Return (IRR). It explains how these measures are used to evaluate the economic viability of projects and mentions the use of Excel functions for calculations.
no_question

the passage does not contain any specific mathematical questions or provide answers to such questions. it is primarily descriptive, explaining concepts and methods.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Ideal Approach - Step 4 - Comparing Costs and Benefits

## Determining Present Value of Project Costs and Benefits

Project costs and benefits are incurred at different times during a project’s life. As such, the process of discounting allows the expression of a stream of costs or benefits as one number in present value terms.

## Comparing Costs and Benefits

Benefit and cost streams form the basis of several measures of project viability:

Net Present Value (NPV): NPV is the value resulting from subtracting the expected cost from the expected benefits. Projects with a NPV greater than zero are worth undertaking.

Benefit – Cost Ratio (BCR): the BCR is the ratio of the present value of benefits to the present value of costs. The ratio should be greater than 1.0 for a project to be acceptable[1]. For example, a BCR of 1.25 indicates that for every \$1 of cost, the project will return \$1.25 of benefit. BCR is a relative measure of viability.

Internal Rate of Return (IRR): the IRR is the discount rate at which the present value of costs equals the present value of benefits. Alternatively, IRR is the discount rate at which NPV = 0 and BCR = 1.0. If IRR exceeds the opportunity cost of the capital, the project is considered to be economically sound and worth pursuing. [2]

## Using Excel to calculate cost-benefit

 Value to Calculate Excel Function Function Help PVBenefit & PVCost NPV() Excel help Net Present Value NPV() Excel help Benefit Cost Ratio n/a n/a Internal Rate of Return IRR() Excel help

References:

[1] It is not in any way inconsistent for a project to have a low positive NPV (because it is a small project) at the same time as it has a high BCR.

[2] The IRR is a criteria to be used with caution because: (i) it cannot be calculated for all projects (e.g. projects where the stream of net benefits is strictly positive for each year or projects with multiple IRR); and, (ii) “it is a mathematical concept and not an investment criterion for evaluating alternative cash flows. When the cash flows are irregular, with net costs occurring in the later years of the project, it will give unreliable results in the ranking of alternative options”(Treasury Board of Canada 2007).

Costs and Benefits are compared using measures of project viability
Source: Migikata
 Search: Home | About the Toolkit | Toolkit Summary | Glossary | Site Map funded by the Canadian POPs Trust Fund through the
Not logged on: log on here
user
The text passage provides an overview of cost-benefit analysis methods, including Net Present Value (NPV), Benefit-Cost Ratio (BCR), and Internal Rate of Return (IRR). It explains how these measures are used to evaluate the economic viability of projects and mentions the use of Excel functions for calculations.

TYPE: NO_QUESTION

The passage does not contain any specific mathematical questions or provide answers to such questions. It is primarily descriptive, explaining concepts and methods.