Net Present Value (NPV) - Revision history

Valdemar Vium: /* Discount rate */

2023-04-06T17:37:05Z

Discount rate

← Older revision		Revision as of 17:37, 6 April 2023
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	=== Discount rate ===		=== Discount rate ===
	[[File:~~discountrate~~.png\|thumb\|300px\|right\|Figure 1: NPV vs. Discount rate (i). Own creation inspired from <ref name="Ferrari" />.]]		[[File:NPV-vs-i.png\|thumb\|300px\|right\|Figure 1: NPV vs. Discount rate (i). Own creation inspired from <ref name="Ferrari" />.]]

	The discount rate is the rate used to determine the present value of future cash flows in NPV calculation. The choice of the discount rate can dramatically change the NPV since the NPV is an inverse function of the discount rate (i) <ref name="Ferrari" />. The selection of discount rate will be company-specific since it is related to how the company finds its funds <ref name="Žižlavský" />. If an investment is financed completely with equity, the discount rate can be obtained from a cost of equity. On the other hand, if the investment is completely debt-financed it can be analyzed using the cost of debt. If an investment depends on both equity and debt financing, the discount rate is the weighted average cost of capital (WACC) and can be calculated as the weighted average of the cost of equity and cost of debt <ref name="Žižlavský" />. WACC is often used in companies as the discount rate <ref name="Häcker" />. For small projects, where it is hard to identify the equity and debt used for financing a single project, the WACC of the whole company is usually assumed as the discount rate <ref name="Žižlavský" />.		The discount rate is the rate used to determine the present value of future cash flows in NPV calculation. The choice of the discount rate can dramatically change the NPV since the NPV is an inverse function of the discount rate (i) <ref name="Ferrari" />. The selection of discount rate will be company-specific since it is related to how the company finds its funds <ref name="Žižlavský" />. If an investment is financed completely with equity, the discount rate can be obtained from a cost of equity. On the other hand, if the investment is completely debt-financed it can be analyzed using the cost of debt. If an investment depends on both equity and debt financing, the discount rate is the weighted average cost of capital (WACC) and can be calculated as the weighted average of the cost of equity and cost of debt <ref name="Žižlavský" />. WACC is often used in companies as the discount rate <ref name="Häcker" />. For small projects, where it is hard to identify the equity and debt used for financing a single project, the WACC of the whole company is usually assumed as the discount rate <ref name="Žižlavský" />.

Valdemar Vium: /* Discount rate */

2023-04-06T17:36:23Z

Discount rate

← Older revision		Revision as of 17:36, 6 April 2023
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	=== Discount rate ===		=== Discount rate ===
	[[File:~~Discointrate~~.png\|thumb\|300px\|right\|Figure 1: NPV vs. Discount rate (i). Own creation inspired from <ref name="Ferrari" />.]]		[[File:discountrate.png\|thumb\|300px\|right\|Figure 1: NPV vs. Discount rate (i). Own creation inspired from <ref name="Ferrari" />.]]

	The discount rate is the rate used to determine the present value of future cash flows in NPV calculation. The choice of the discount rate can dramatically change the NPV since the NPV is an inverse function of the discount rate (i) <ref name="Ferrari" />. The selection of discount rate will be company-specific since it is related to how the company finds its funds <ref name="Žižlavský" />. If an investment is financed completely with equity, the discount rate can be obtained from a cost of equity. On the other hand, if the investment is completely debt-financed it can be analyzed using the cost of debt. If an investment depends on both equity and debt financing, the discount rate is the weighted average cost of capital (WACC) and can be calculated as the weighted average of the cost of equity and cost of debt <ref name="Žižlavský" />. WACC is often used in companies as the discount rate <ref name="Häcker" />. For small projects, where it is hard to identify the equity and debt used for financing a single project, the WACC of the whole company is usually assumed as the discount rate <ref name="Žižlavský" />.		The discount rate is the rate used to determine the present value of future cash flows in NPV calculation. The choice of the discount rate can dramatically change the NPV since the NPV is an inverse function of the discount rate (i) <ref name="Ferrari" />. The selection of discount rate will be company-specific since it is related to how the company finds its funds <ref name="Žižlavský" />. If an investment is financed completely with equity, the discount rate can be obtained from a cost of equity. On the other hand, if the investment is completely debt-financed it can be analyzed using the cost of debt. If an investment depends on both equity and debt financing, the discount rate is the weighted average cost of capital (WACC) and can be calculated as the weighted average of the cost of equity and cost of debt <ref name="Žižlavský" />. WACC is often used in companies as the discount rate <ref name="Häcker" />. For small projects, where it is hard to identify the equity and debt used for financing a single project, the WACC of the whole company is usually assumed as the discount rate <ref name="Žižlavský" />.

Valdemar Vium: /* Discount rate */

2023-04-06T17:34:31Z

Discount rate

← Older revision		Revision as of 17:34, 6 April 2023
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	=== Discount rate ===		=== Discount rate ===
	[[File:~~NPV-vs-i~~.png\|thumb\|300px\|right\|Figure 1: NPV vs. Discount rate (i). Own creation inspired from <ref name="Ferrari" />.]]		[[File:Discointrate.png\|thumb\|300px\|right\|Figure 1: NPV vs. Discount rate (i). Own creation inspired from <ref name="Ferrari" />.]]

	The discount rate is the rate used to determine the present value of future cash flows in NPV calculation. The choice of the discount rate can dramatically change the NPV since the NPV is an inverse function of the discount rate (i) <ref name="Ferrari" />. The selection of discount rate will be company-specific since it is related to how the company finds its funds <ref name="Žižlavský" />. If an investment is financed completely with equity, the discount rate can be obtained from a cost of equity. On the other hand, if the investment is completely debt-financed it can be analyzed using the cost of debt. If an investment depends on both equity and debt financing, the discount rate is the weighted average cost of capital (WACC) and can be calculated as the weighted average of the cost of equity and cost of debt <ref name="Žižlavský" />. WACC is often used in companies as the discount rate <ref name="Häcker" />. For small projects, where it is hard to identify the equity and debt used for financing a single project, the WACC of the whole company is usually assumed as the discount rate <ref name="Žižlavský" />.		The discount rate is the rate used to determine the present value of future cash flows in NPV calculation. The choice of the discount rate can dramatically change the NPV since the NPV is an inverse function of the discount rate (i) <ref name="Ferrari" />. The selection of discount rate will be company-specific since it is related to how the company finds its funds <ref name="Žižlavský" />. If an investment is financed completely with equity, the discount rate can be obtained from a cost of equity. On the other hand, if the investment is completely debt-financed it can be analyzed using the cost of debt. If an investment depends on both equity and debt financing, the discount rate is the weighted average cost of capital (WACC) and can be calculated as the weighted average of the cost of equity and cost of debt <ref name="Žižlavský" />. WACC is often used in companies as the discount rate <ref name="Häcker" />. For small projects, where it is hard to identify the equity and debt used for financing a single project, the WACC of the whole company is usually assumed as the discount rate <ref name="Žižlavský" />.

DeepthiTharaka: /* Decision rule */

2022-03-20T16:24:45Z

Decision rule

← Older revision		Revision as of 16:24, 20 March 2022
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	\|-		\|-
	\|If NPV < 0		\|If NPV < 0
	\|Investment would ~~destroy~~ value (profit) in an amount equal to the negative NPV.		\|Investment would decrease value (profit) in an amount equal to the negative NPV.
	\|The investment can be rejected.		\|The investment can be rejected.
	\|}		\|}

DeepthiTharaka: /* Decision rule */

2022-03-20T16:24:07Z

Decision rule

← Older revision		Revision as of 16:24, 20 March 2022
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	\|-		\|-
	\|If NPV = 0		\|If NPV = 0
	\|No increase or decrease in ~~wealth results~~.		\|No increase or decrease in value of the company.
	\|This project adds no monetary value. Difficult to get the decision whether to accept or reject the project. Decisions should be based on other criteria.		\|This project adds no monetary value. Difficult to get the decision whether to accept or reject the project. Decisions should be based on other criteria.
	\|-		\|-

DeepthiTharaka at 16:22, 20 March 2022

2022-03-20T16:22:38Z

← Older revision		Revision as of 16:22, 20 March 2022
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	\|}		\|}

	~~Since both NPV > 0, the~~ company can accept the investment in both projects since it has the ability to invest in both.		The company can accept the investment in both projects since both NPV > 0 and the company has the ability to invest in both.

	=== Mutually exclusive projects ===		=== Mutually exclusive projects ===
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	\|}		\|}

	Even though both projects give positive NPV, the company cannot invest in both since they are mutually exclusive. Therefore it has to select the project which gives the highest NPV ~~based on the relative profitability criteria discussed in the decision rule section above~~. Hence, in this case, the rubber manufacturing plant can be selected.		Even though both projects give positive NPV, the company cannot invest in both since they are mutually exclusive. Therefore it has to select the project which gives the highest NPV. Hence, in this case, the rubber manufacturing plant can be selected.

	=== Contingent projects ===		=== Contingent projects ===

DeepthiTharaka: /* Big idea */

2022-03-20T15:47:04Z

Big idea

← Older revision		Revision as of 15:47, 20 March 2022
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	== Big idea ==		== Big idea ==

	According to ISO 21502, a ~~'''~~business case~~'''~~ is a documented justification to support decision-making about the commitment to a project, program or portfolio <ref name="ISO_21502"/>. Development of a business case is a critical point in a project, program or portfolio where it uses to obtain the approval by presenting the benefits, cost, and risk associated with alternative options <ref name="PRINCE2"/> <ref name="PRINCE2_program"/> <ref name="PRINCE2_portfolio"/>. The business case is produced by the client or the sponsor of the project, program or portfolio and the directorate of an organization uses this document to accept or reject the case. <ref name="Ing" />. In a business case, financial appraisal plays a key role to answer the main questions of whether an investment should be made and which project should be chosen among a selection of different alternatives. Because the task of financial appraisal is to predict the financial effects of planned investment and to present the data to get critical investment decisions <ref name="Häcker" />. NPV method is one of the most frequently used approaches in the financial appraisal of a project, program, or portfolio <ref name="Häcker" /> <ref name="Konstantin" />.		According to ISO 21502, a business case is a documented justification to support decision-making about the commitment to a project, program or portfolio <ref name="ISO_21502"/>. Development of a business case is a critical point in a project, program or portfolio where it uses to obtain the approval by presenting the benefits, cost, and risk associated with alternative options <ref name="PRINCE2"/> <ref name="PRINCE2_program"/> <ref name="PRINCE2_portfolio"/>. The business case is produced by the client or the sponsor of the project, program or portfolio and the directorate of an organization uses this document to accept or reject the case. <ref name="Ing" />. In a business case, financial appraisal plays a key role to answer the main questions of whether an investment should be made and which project should be chosen among a selection of different alternatives. Because the task of financial appraisal is to predict the financial effects of planned investment and to present the data to get critical investment decisions <ref name="Häcker" />. NPV method is one of the most frequently used approaches in the financial appraisal of a project, program, or portfolio <ref name="Häcker" /> <ref name="Konstantin" />.

	=== What is NPV? ===		=== What is NPV? ===
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	* '''Relative profitability''': If there are several positive NPV options, the one with the highest NPV should be selected.		* '''Relative profitability''': If there are several positive NPV options, the one with the highest NPV should be selected.


	== Other NPV formulas for special scenarios ==		== Other NPV formulas for special scenarios ==

DeepthiTharaka at 15:38, 20 March 2022

2022-03-20T15:38:39Z

← Older revision		Revision as of 15:38, 20 March 2022
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	Contingent projects are dependent projects where the acceptance or rejection of one project affects the acceptance or rejection of one or more other projects <ref name="Bora" />. For Example, the decision to invest in a medical testing laboratory may depend on the decision to build a private hospital nearby. The cash inflows of the medical testing laboratory will be enhanced by the presence of a nearby hospital and vice versa. This enhancement of the cashflows from the contingent projects must consider when calculating the NPV and to get the right decision.		Contingent projects are dependent projects where the acceptance or rejection of one project affects the acceptance or rejection of one or more other projects <ref name="Bora" />. For Example, the decision to invest in a medical testing laboratory may depend on the decision to build a private hospital nearby. The cash inflows of the medical testing laboratory will be enhanced by the presence of a nearby hospital and vice versa. This enhancement of the cashflows from the contingent projects must consider when calculating the NPV and to get the right decision.


	== Limitations ==		== Limitations ==
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	The research paper, 'comparison between net present value and internal rate of return' by Bora, B. provides a comprehensive discussion on the NPV method. This critically highlights the benefits and limitations of the NPV method and its applications in different investments.		The research paper, 'comparison between net present value and internal rate of return' by Bora, B. provides a comprehensive discussion on the NPV method. This critically highlights the benefits and limitations of the NPV method and its applications in different investments.


	== References ==		== References ==

DeepthiTharaka: /* Limitations */

2022-03-20T15:38:08Z

Limitations

← Older revision		Revision as of 15:38, 20 March 2022
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	* It does not consider the non-cash benefits and costs generated from a project while making decisions. NPV method is purely quantitive in nature and does not consider qualitative factors. However, it is important to consider both quantitative and qualitative benefits and costs associated with a project when taking the final decisions <ref name="ISO_21502"/>.		* It does not consider the non-cash benefits and costs generated from a project while making decisions. NPV method is purely quantitive in nature and does not consider qualitative factors. However, it is important to consider both quantitative and qualitative benefits and costs associated with a project when taking the final decisions <ref name="ISO_21502"/>.


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

DeepthiTharaka: /* Other NPV formulas for special scenarios */

2022-03-20T15:28:59Z

Other NPV formulas for special scenarios

← Older revision		Revision as of 15:28, 20 March 2022
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	Net cash flows can be interpreted as an annuity, if they are constant, equidistant and occur at the end of each period <ref name="Häcker" />. Using the formula for the present value of an ordinary annuity, NPV can be calculated as follows <ref name="Häcker" />:		Net cash flows can be interpreted as an annuity, if they are constant, equidistant and occur at the end of each period <ref name="Häcker" />. Using the formula for the present value of an ordinary annuity, NPV can be calculated as follows <ref name="Häcker" />:

	<math>N P V=-I_{0}+N C \cdot\left[\frac{(1+i)^{n}-1}{i \cdot(1+i)^{n}}\right]+\frac{L_{n}}{(1+i)^{n}}</math> <ref name="Häcker" />,		<math>N P V=-I_{0}+N C \cdot\left[\frac{(1+i)^{n}-1}{i \cdot(1+i)^{n}}\right]+\frac{L_{n}}{(1+i)^{n}}</math> <ref name="Häcker" />

	~~where <math> N C </math> is the constant net cash flow.~~

	=== NPV of a perpetuity ===		=== NPV of a perpetuity ===
	Net cash flow is considered as perpetuity, when they occur constantly and infinitely. For this case, NPV can be expressed as follows <ref name="Häcker" />:		Net cash flow is considered as perpetuity, when they occur constantly and infinitely. For this case, NPV can be expressed as follows <ref name="Häcker" />:

	<math>N P V=-I_{0}+\frac{N C}{i}</math> <ref name="Häcker" />,		<math>N P V=-I_{0}+\frac{N C}{i}</math> <ref name="Häcker" />

	~~where <math> N C </math> is the constant net cash flow.~~


	== Applications ==		== Applications ==