Benefit Cost Ratio (BCR) - Revision history

Efthymist: /* Limitations of BCR */

2023-05-09T09:45:10Z

Limitations of BCR

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	3. The project's potential externalities or spillover effects are not taken into account by the BCR technique. The BCR result, for instance, may not account for unanticipated negative effects a project may have on the environment or nearby communities.		3. The project's potential externalities or spillover effects are not taken into account by the BCR technique. The BCR result, for instance, may not account for unanticipated negative effects a project may have on the environment or nearby communities.

	4. The BCR is commonly used in conjunction with other financial metrics, in order to format a well-informed decisions about project feasibility~~.<ref name=" Xavier"/>~~		4. The BCR is commonly used in conjunction with other financial metrics, in order to format a well-informed decisions about project feasibility.

	5. This method relies heavily an accurate forecasting of future costs and benefits, which can be difficult to predict with certainty. This may result in overly optimistic benefits estimates or underestimated costs, which may compromise the reliability of the BCR result.

			5. This method relies heavily an accurate forecasting of future costs and benefits, which can be difficult to predict with certainty. This may result in overly optimistic benefits estimates or underestimated costs, which may compromise the reliability of the BCR result. <ref name=" Xavier"/>

	== Annotated Bibliography ==		== Annotated Bibliography ==

Efthymist: /* Other formulas of CBA */

2023-05-09T09:44:44Z

Other formulas of CBA

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	1.''' Payback Period ''' = Initial Investment / Annual Cash Inflow		1.''' Payback Period ''' = Initial Investment / Annual Cash Inflow

	The payback period is the length of time it takes for the initial investment to be recovered through the annual cash inflows generated by the investment.		The payback period is the length of time it takes for the initial investment to be recovered through the annual cash inflows generated by the investment.<ref name="Žižlavský"/>

	For example, if the project requires an initial investment of $10,000 and generates annual cash inflows of $2,000, the payback period would be:		For example, if the project requires an initial investment of $10,000 and generates annual cash inflows of $2,000, the payback period would be:
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	} = \frac{$2,000}{$11,000}\times 100% = 18,18 % </math>		} = \frac{$2,000}{$11,000}\times 100% = 18,18 % </math>

	Net income is the amount of money gained from an investment after all expenses have been paid. The initial investment includes all costs associated with the investment, such as purchase price, fees, and any other expenses. A higher ROI suggests a more profitable investment, whereas a lower ROI can imply a less successful investment.		Net income is the amount of money gained from an investment after all expenses have been paid. The initial investment includes all costs associated with the investment, such as purchase price, fees, and any other expenses. A higher ROI suggests a more profitable investment, whereas a lower ROI can imply a less successful investment.<ref name="Žižlavský"/>


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	4. '''Internal Rate of Return ''' = Internal Rate of Return / Discount Rate		4. '''Internal Rate of Return ''' = Internal Rate of Return / Discount Rate

	Internal Rate of Return (IRR) is a tool of measurement of the profitability of a project and is defined as the discount rate that makes the net present value (NPV) from a particular project to be zero. The purpose is to determine the rate i that balances the benefits and costs. The IRR of each project must be higher than the discount rate and the project with higher IRR value, are more desirable. An important benefit of IRR is the fact that IRR considers the time value of money and offers a more precise indicator of an investment's profitability over time.		Internal Rate of Return (IRR) is a tool of measurement of the profitability of a project and is defined as the discount rate that makes the net present value (NPV) from a particular project to be zero. The purpose is to determine the rate i that balances the benefits and costs. The IRR of each project must be higher than the discount rate and the project with higher IRR value, are more desirable. An important benefit of IRR is the fact that IRR considers the time value of money and offers a more precise indicator of an investment's profitability over time.<ref name="Investopedia "/>

Efthymist: /* Advantages of BCR */

2023-05-09T09:16:40Z

Advantages of BCR

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	== Advantages of BCR ==		== Advantages of BCR ==

	1. The BCR ~~translates~~ the absolute amounts of benefits and costs into a ratio and ~~allows~~ a direct comparison of the benefits and costs of a project. It is financial metric that compares the total present value of benefits to the total present value of costs for a project.		1. The BCR uses the absolute amounts of benefits and costs into a ratio and can achieve a direct comparison of the benefits and costs of a project. It is financial metric that compares the total present value of benefits to the total present value of costs for a project.

	2. The BCR is a relatively simple ~~method~~ and a good starting point for the financial analysis to determine if a project ~~is feasible or not~~.		2. The BCR is a relatively a simple tool to use and a good starting point for the financial analysis to determine the desirability of a project.

	3. ~~For~~ the ~~calculation of~~ BCR the time value of money through the discount rate is considered. By taking into account the ~~fact that money in the future has less~~ value ~~than~~ money ~~today~~, ~~as a result this provide a~~ more accurate assessment of the project's profitability.<ref name=" Xavier"/>		3. To calculate the BCR, the time value of money through the discount rate must be considered. By taking into account the time value of money, the results are more accurate about of the assessment of the project's profitability. <ref name=" Xavier"/>

	== Limitations of BCR ==		== Limitations of BCR ==

Efthymist: /* Other formulas of CBA */

2023-05-09T09:16:05Z

Other formulas of CBA

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	The payback period is the length of time it takes for the initial investment to be recovered through the annual cash inflows generated by the investment.		The payback period is the length of time it takes for the initial investment to be recovered through the annual cash inflows generated by the investment.

	For example, if ~~an investment~~ requires an initial ~~outlay~~ of $10,000 and generates annual cash inflows of $2,000, the payback period would be:		For example, if the project requires an initial investment of $10,000 and generates annual cash inflows of $2,000, the payback period would be:

	<math> Payback Period = \frac{Initial Investment}{Annual Cash Inflow		<math> Payback Period = \frac{Initial Investment}{Annual Cash Inflow
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	2. '''Return on Investment ''' = Annual Net Income / Initial Investment		2. '''Return on Investment ''' = Annual Net Income / Initial Investment

	It is a financial metric used to measure the profitability of an investment. It is ~~typically~~ expressed as a percentage and is calculated ~~by dividing~~ the net profit or benefit of an investment by the cost of the investment.		It is a financial metric used to measure the profitability of an investment. It is expressed as a percentage and is calculated as the ratio of the net profit or benefit of an investment and the cost of the investment.

	For example, an investment cost is $10,000 in a stock and it is sold it for $12,000, the profit would be $2,000. The total cost of investment including fees and taxes was $11,000, ROI would be:		For example, an investment cost is $10,000 in a stock and it is sold it for $12,000, the profit would be $2,000. The total cost of investment including fees and taxes was $11,000, ROI would be:
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	} = \frac{$2,000}{$11,000}\times 100% = 18,18 % </math>		} = \frac{$2,000}{$11,000}\times 100% = 18,18 % </math>

	Net income is the amount of money gained from an investment after all expenses have been paid. ~~Initial~~ investment includes all costs associated with the investment, such as purchase price, fees, and any other expenses. A higher ROI suggests a more profitable investment, whereas a lower ROI can imply a less successful investment.		Net income is the amount of money gained from an investment after all expenses have been paid. The initial investment includes all costs associated with the investment, such as purchase price, fees, and any other expenses. A higher ROI suggests a more profitable investment, whereas a lower ROI can imply a less successful investment.


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	Where:		Where:

	B: is the ~~cash inflow~~ in period t		B: is the Benefits in period t

	C: is the ~~cash outflow (cost)~~ in period t		C: is the Cost in period t

	r: is the discount rate		r: is the discount rate

	n: ~~is the last~~ period of the project		n: The calculation period of the project in years



	4. '''Internal Rate of Return ''' = Internal Rate of Return / Discount Rate		4. '''Internal Rate of Return ''' = Internal Rate of Return / Discount Rate

	IRR is a profitability ~~metric~~ and is defined as the discount rate that makes the net present value (NPV) from a particular project to be zero. The ~~IRR of each project must be higher than~~ the ~~discount~~ rate and ~~the project with higher IRR value, are more preferable~~ The IRR of each project must be higher than the discount rate and the project with higher IRR value, are more ~~preferable~~. ~~The~~ fact that IRR considers the time value of money and offers a more precise indicator of an investment's profitability over time ~~is one of its benefits~~.		Internal Rate of Return (IRR) is a tool of measurement of the profitability of a project and is defined as the discount rate that makes the net present value (NPV) from a particular project to be zero. The purpose is to determine the rate i that balances the benefits and costs. The IRR of each project must be higher than the discount rate and the project with higher IRR value, are more desirable. An important benefit of IRR is the fact that IRR considers the time value of money and offers a more precise indicator of an investment's profitability over time.

Efthymist: /* What is BCR? */

2023-05-09T09:13:45Z

What is BCR?

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	== What is BCR? ==		== What is BCR? ==

	The Benefit Cost Ratio is a profitability indicator, and it is the ratio of the present value of the benefit of the project to the present value of the cost. It is usually used to summarize the results of the cost benefit analysis (CBA) during the financial analysis of a proposed program, project or portfolio.<ref name="Gerald"/> The origins of BCR can be traced back to the early 20th century when economists and engineers first began developing methods to evaluate the costs and benefits of public infrastructure projects. One of the earliest known applications ~~of BCR~~ was in the United States in the 1920s, when the Bureau of Public Roads began to use it to evaluate the economic benefits of ~~road construction~~ projects. BCR began to be used as more in the 1930s and 1940s, when economists and engineers needed to refine and standardize methods for estimating costs and benefits.		The Benefit Cost Ratio is a profitability indicator, and it is the ratio of the present value of the benefit of the project to the present value of the cost. It is usually used to summarize the results of the cost benefit analysis (CBA) during the financial analysis of a proposed program, project or portfolio.<ref name="Gerald"/> The origins of BCR can be traced back to the early 20th century when economists and engineers first began developing methods to evaluate the costs and benefits of public infrastructure projects. . One of the BCR’s earliest known applications was in the United States in the 1920s, when the Bureau of Public Roads began to use it to evaluate the economic benefits of transportation projects. BCR began to be used as more in the 1930s and 1940s, when economists and engineers needed to refine and standardize methods for estimating costs and benefits.

	Today, the BCR is widely used by the public and private sectors to assess the economic viability of ~~various~~ projects and investments, such as transportation infrastructure, power generation facilities and public health initiatives.		Today, the BCR is widely used by the public and private sectors to assess the economic viability of many projects and investments, such as transportation infrastructure, power generation facilities and public health initiatives etc.

	BCR is another way of comparing the present value of a project’s costs with the present value of its benefits. If the value of BCR of a project is greater than 1.0, the project is expected to have also a positive NPV and to have an internal rate of return (IRR) higher than the discount rate used in the calculations. When the BCR has a value equal to 1.0, indicates that the NPV of expected profits equals the costs. If BCR of a project is less than 1.0, the project's costs outweigh the benefits, and it should not be feasible. <ref name=" Investopedia"/>		BCR is another way of comparing the present value of a project’s costs with the present value of its benefits. If the value of BCR of a project is greater than 1.0, the project is expected to have also a positive NPV and to have an internal rate of return (IRR) higher than the discount rate used in the calculations. When the BCR has a value equal to 1.0, indicates that the NPV of expected profits equals the costs. If BCR of a project is less than 1.0, the project's costs outweigh the benefits, and it should not be feasible. <ref name=" Investopedia"/>
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	'''Example 2'''		'''Example 2'''

	The government is considering building a new ~~highway~~, and they want to calculate the Benefit-Cost Ratio (BCR) of the project. ~~They estimate that the~~ construction cost will be $100 million and the ~~highway will~~ generate 30 million in benefits for each year over the next 4 years. The discount Ratio is 3%.		The government is considering building a new railway, and they want to calculate the Benefit-Cost Ratio (BCR) of the project to determine if the project is feasible. The construction cost will be $100 million and the railway is expected to generate 30 million in benefits for each year over the next 4 years. The discount Ratio is 3%.


	<math>B = \frac{30,000,000}{(1+0.03)^1} + \frac{30,000,000}{(1+0.03)^2} + \frac{30,000,000}{(1+0.03)^3} + \frac{30,000,000}{(1+0.03)^4}</math>		<math>B = \frac{30,000,000}{(1+0.03)^1} + \frac{30,000,000}{(1+0.03)^2} + \frac{30,000,000}{(1+0.03)^3} + \frac{30,000,000}{(1+0.03)^4}</math>
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	<math>BCR = \frac{B}{C} = \frac{111,780,000}{100,000,000} = 1.1178</math>		<math>BCR = \frac{B}{C} = \frac{111,780,000}{100,000,000} = 1.1178</math>

	~~This means that for every dollar spent on the project, there will be $1.1178 in benefits over the next 4 years. A~~ BCR of greater than 1 indicates that the project is economically viable.		The BCR is greater than 1 indicates that the project is economically viable.

	=== Comparison Between BCR and NPV ===		=== Comparison Between BCR and NPV ===

Efthymist: /* Cost Benefit Analysis */

2023-05-09T09:11:30Z

Cost Benefit Analysis

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	== Cost Benefit Analysis ==		== Cost Benefit Analysis ==

	'''Cost-benefit analysis (CBA)''' is a method of economic ~~assessment~~ that ~~seeks~~ to ~~quantify~~ the positive and negative impacts of a proposed ~~decision or project~~. ~~The technique~~ has been used for centuries, with the ~~earliest known~~ examples dating back to the 1700s. However, ~~the use~~ of CBA ~~were mandatory only after regulations were established by~~ the ~~US government~~ in the 1930s ~~CBA is often used to determine whether or not a proposed decision or project is worth investing~~ in~~. It is also used to compare different options or to determine which option will provide the greatest benefit to its stakeholders~~.<ref name="Mishan"/> ~~One of~~ the earliest applications ~~of cost-benefit analysis~~ was in the transportation ~~sector~~, where it was used to evaluate the ~~feasibility~~ and desirability of public infrastructure projects.<ref name="European "/>		'''Cost-benefit analysis (CBA)''' is a method of economic appraisal that aims to measure the positive and negative impacts of a proposed projects. This tool has been used for centuries, with the examples dating back to the 1700s. However, wider applications of CBA dates back to the USA in the 1930s, where the methodology was developed in connection with large water projects. <ref name="Mishan"/> CBA was ‘exported’ to Europe in the 1950s and was used for decisions about building motorways CBA’s earliest applications was in the transportation area, where it was used to evaluate the profitability and desirability of public infrastructure projects.<ref name="European "/>

	In the 1960s, ~~there were~~ economists such as Kenneth Arrow, Milton Friedman, and Richard Musgrave, who supported that CBA could be an important method for evaluating the efficiency of government programs.<ref name="Kenneth Arrow "/>		In the 1960s, CBA obtained a status as a more or less objective tool which could guide the subjective politicians, with the help of economists such as Kenneth Arrow, Milton Friedman, and Richard Musgrave, who supported that CBA could be an important method for evaluating the efficiency of government programs.<ref name="Kenneth Arrow "/>

	After that, CBA was refined over the next decades due the advent of computers and still		After that, CBA was refined over the next decades due the advent of computers and still
	more sophisticated prediction ~~modelsand~~ is widely used in a variety of fields, including environmental regulation, health care, and transportation planning.<ref name="Schmalensee "/>		more sophisticated prediction models and is widely used in a variety of fields, including environmental regulation, health care, and transportation planning.<ref name="Schmalensee "/>

	The last years the goal is to link CBA with other methods (hard and soft operation research techniques) and setting a focus on wider impacts,		The last years the goal is to link CBA with other methods (hard and soft operation research techniques) and setting a focus on wider impacts,
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	===Microeconomic approach===		===Microeconomic approach===
	CBA is often a microeconomic approach that enables the calculation of economic performance indicators, offering an assessment of predicted welfare improvements, to analyze the project's influence on society as a whole. While the project's direct employment or external environmental consequences are recognized in the ENPV, indirect and broader effects (such as those on secondary markets, public funds, employment, regional growth, etc.) should be disregarded. <ref name="European "/>		CBA is often a microeconomic approach that enables the calculation of economic performance indicators, offering an assessment of predicted welfare improvements, to analyze the project's influence on society as a whole. While the project's direct employment or external environmental consequences are recognized in the ENPV, indirect and broader effects (such as those on secondary markets, public funds, employment, regional growth, etc.) should be disregarded. <ref name="European "/>
	This is because of two ~~key~~ factors:		This is because of two factors:

	1. The majority of indirect and/or wider effects are typically capitalized, redistributed, and altered versions of direct effects. This has as a result for benefits to be double-counted.		1. The majority of indirect and/or wider effects are typically capitalized, redistributed, and altered versions of direct effects. This has as a result for benefits to be double-counted.
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	===Project appraisal steps===		===Project appraisal steps===

	A Typical CBA is structured in ~~seven~~ steps:<ref name="Gerald"/>		A Typical CBA is structured in six steps:<ref name="Gerald"/>

	1. '''Description of the ~~context~~''': ~~The problem or opportunity~~, ~~such as~~ a ~~proposed investment, policy change, or project~~ that ~~the CBA is trying~~ to ~~solve must~~ be ~~identified in this step. It also includes identifying~~ the ~~relevant stakeholders~~.		1. '''Description of the Context''': A presentation and discussion of the socio-economic context and objectives of the project. To be more specific, the first step of the appraisal is a qualitive discussion of the socio-economic context and the objectives that are expected to be attained through the investment, both directly and indirectly.

	2. '''Identification of ~~alternatives~~''': This step involves identifying and evaluating ~~different alternatives~~ and ~~options. Also, in this step the baseline scenario is defined, which the alternatives will~~ be ~~compared~~.		2. '''Identification of the Project''': This step involves identifying and evaluating whose costs and benefits must be considered and what indirect and network effects are going to be adequately covered.

	3. '''~~Development~~ of ~~criteria~~''': In this step, different ~~criteria or indicators~~ are identified, ~~which will be used to evaluate the alternatives~~.		3. '''Identification of the alternatives''': In this step, different alternatives are identified and there is a Justification of the project design (scale, location, etc.) against alternative scenarios.

	4. '''Analysis ~~of impacts~~''': After identifying the ~~criteria~~, the next step is ~~to define~~ the ~~impacts of each alternative. Also, in this step~~ the ~~benefits~~ and ~~costs~~ of ~~each alternative are calculated~~.		4. '''Financial Analysis''': After identifying the alternatives, the next step is financial analysis which is based on the discounted cash flow approach and contains the traditional inflows and outflows of the project.

	5. '''~~Comparison of alternatives~~''': In this step, the ~~alternatives are compared against the criteria developed in step 3. The comparison can be done using different techniques, such as~~ cost~~-effectiveness~~ analysis~~, multi-criteria analysis, or~~ a ~~combination of these~~.		5. ''' Economic Analysis''': In this step, the cost benefit analysis is implemented. CBA requires an investigation of a project’s net impact on economic welfare.

	6. '''~~Sensitivity analysis~~''': In this step, the ~~impact~~ of ~~different assumptions is assessed, finding~~ the ~~most critical assumptions and uncertainties~~.		6. '''Risk Assessment''': In this step, the project appraisal document must include an assessment of the project risks. This can be achieved by Sensitivity analysis, Probability distribution on important impacts, Performance indicators. Finally, there must be a discussion of the results compared to risk levels and a discussion how to mitigate the risks.

	7. ~~'''Conclusions and recommendations''': In the final step~~, the results of the ~~analysis are summarized, and conclusions are drawn~~.

	== What is BCR? ==		== What is BCR? ==

Efthymist: /* Annotated Bibliography */

2023-05-01T14:26:55Z

Annotated Bibliography

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	'''Shively G., An Overview of Benefit-Cost Analysis., (Gerald Shively, Purdue University, 2012)'''		'''Shively G., An Overview of Benefit-Cost Analysis., (Gerald Shively, Purdue University, 2012)'''

			This comprehensive book on cost-benefit analysis (CBA) covers the concepts and techniques used to evaluate the economic efficiency of policies and projects. The authors explore how to identify, measure, and value the costs and benefits of different policy options, including social welfare, environmental impacts, and public health outcomes.

	'''Häcker J. and Ernst D., Ch. 8 - Investment Appraisal. In: Financial Modeling. Global Financial Markets, (Palgrave Macmillan, London, 2017), pp. 343-384'''		'''Häcker J. and Ernst D., Ch. 8 - Investment Appraisal. In: Financial Modeling. Global Financial Markets, (Palgrave Macmillan, London, 2017), pp. 343-384'''
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	'''Dupuis Xavier , Applications and limitations of cost-benefit analysis as applied to cultural development, (1985)'''		'''Dupuis Xavier , Applications and limitations of cost-benefit analysis as applied to cultural development, (1985)'''

			This book on cost-benefit analysis (CBA) presents the limitation of the different tools used on the financial appraisal. The author, Dupuis Xavier, provides an in-depth analysis of CBA as applied to cultural development and examines its strengths and weaknesses.

	== References ==		== References ==

Efthymist: /* Annotated Bibliography */

2023-05-01T14:17:53Z

Annotated Bibliography

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	'''Shively G., An Overview of Benefit-Cost Analysis., (Gerald Shively, Purdue University, 2012)'''		'''Shively G., An Overview of Benefit-Cost Analysis., (Gerald Shively, Purdue University, 2012)'''



	'''Häcker J. and Ernst D., Ch. 8 - Investment Appraisal. In: Financial Modeling. Global Financial Markets, (Palgrave Macmillan, London, 2017), pp. 343-384'''		'''Häcker J. and Ernst D., Ch. 8 - Investment Appraisal. In: Financial Modeling. Global Financial Markets, (Palgrave Macmillan, London, 2017), pp. 343-384'''

			The investment appraisal chapter in the financial modeling book by Häcker J. and Ernst D. presents the concept of financial assessment and provides a good overview of methodologies used in assessing a project, program, or portfolio. The concept of NPV, the concept of BCR, how to calculate NPV and BCR are all well explained in this book.

	'''H. Lopez ., The Social Discount Rate: Estimates for Nine Latin American Countries, (H. Lopez , 2012)'''		'''H. Lopez ., The Social Discount Rate: Estimates for Nine Latin American Countries, (H. Lopez , 2012)'''

			This article presents information about the discount rate, providing more in-depth knowledge. It highlights the importance of the time value of money and approaches used to select the suitable discount rate.

	'''Dupuis Xavier , Applications and limitations of cost-benefit analysis as applied to cultural development, (1985)'''		'''Dupuis Xavier , Applications and limitations of cost-benefit analysis as applied to cultural development, (1985)'''

Efthymist: /* Annotated Bibliography */

2023-05-01T13:47:40Z

Annotated Bibliography

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	== Annotated Bibliography ==		== Annotated Bibliography ==

	Shively G., An Overview of Benefit-Cost Analysis., (Gerald Shively, Purdue University, 2012)		'''Shively G., An Overview of Benefit-Cost Analysis., (Gerald Shively, Purdue University, 2012)'''


	Häcker J. and Ernst D., Ch. 8 - Investment Appraisal. In: Financial Modeling. Global Financial Markets, (Palgrave Macmillan, London, 2017), pp. 343-384		'''Häcker J. and Ernst D., Ch. 8 - Investment Appraisal. In: Financial Modeling. Global Financial Markets, (Palgrave Macmillan, London, 2017), pp. 343-384'''


	H. Lopez ., The Social Discount Rate: Estimates for Nine Latin American Countries, (H. Lopez , 2012)		'''H. Lopez ., The Social Discount Rate: Estimates for Nine Latin American Countries, (H. Lopez , 2012)'''


	Dupuis Xavier , Applications and limitations of cost-benefit analysis as applied to cultural development, (1985)		'''Dupuis Xavier , Applications and limitations of cost-benefit analysis as applied to cultural development, (1985)'''

	== References ==		== References ==

Efthymist: /* Time value of money */

2023-05-01T13:47:16Z

Time value of money

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	The values of each year need to be discounted to calculate the present value (PV), that can happen by multiplying each year's cash flow by a discount factor, which is determined by the discount rate and the number of years into the future the cash flow occurs. There is an example for these calculations making the usual assumption that the discount rate is constant from year to year.		The values of each year need to be discounted to calculate the present value '''(PV)''', that can happen by multiplying each year's cash flow by a discount factor, which is determined by the discount rate and the number of years into the future the cash flow occurs. There is an example for these calculations making the usual assumption that the discount rate is constant from year to year.