Project viability assessment through Net Present Value (NPV)

Revision as of 09:54, 5 April 2023

Abstract

The Net Present Value (NPV) is a widely used financial metric in project management. Its purpose is to evaluate the profitability of a proposed project by aggregating the streams of costs and benefits into a single value. This makes for an effective indicator of identifying profitable projects when assessing multiple projects at a time. For a given project to be considered a profitable investment, its NPV must be larger than zero. ^[1]

Central to the calculation of the NPV is assigning varying weights, dependent on time, to the benefits and costs through the utilization of a so-called discount factor, which is calculated using a discount rate. The discount rate represents the rate of interest that is used to discount all future costs and benefits. ^[2] By incorporating this principle, the NPV accounts for and subscribes to the paradigm of the time value of money, referring to the idea that money has a different value at different points in time.^[3]

This article explores central concepts connected to the calculation and application of NPV in the assessment of projects, programs, or portfolios. For demonstration purposes, an example of the calculation of an emulated project's NPV will be given. Moreover, the advantages and disadvantages of using NPV as an indicator of project profitability will be addressed.

NPV Formula

The net present value achieves comparability of all costs and benefits by discounting them to the beginning of the investment period. The NPV is amongst the most frequent and sophisticated tools when it comes to assessing the profitability of projects and investments. ^[4] The formula used to calculate the net present value is presented below:

$NPV = \sum_{t=0}^{N}\frac{B_t-C_t}{(1+r)^t}$

$N$ :The calculation period of the project in years.

$B_t$ : The aggregated amount of benefits (both positive and negative) in year t

$C_t$ : The amount of investments costs in year t

$r$ : The discount rate

There are two inherent principles to the NPV as a tool. The first principle is the time value of money, which postulates that an uncertain Danish Crown tomorrow is less valuable than a Danish Crown today.^[5] This is modulated by the use of the discount factor $(1+r)^t$ , where a discount rate is used.^[2]Therefore, the NPV achieves comparability of the costs and benefits that happen at different points in time by determining their present values by discounting them to $t = 0$ . The second principle considers all future costs and benefits affiliated with the project or investment. The project’s worth is evaluated by assessing its ability to generate economic value in the specified time horizon, $N$ .^[5].For a given project assessed, the streams of costs and benefits are aggregated into a single number, the NPV index value. This allows for quick and effective comparisons of projects, programs, and portfolios. The NPV index value, used as a proxy of the future benefits from commencing the project, can be estimated as either zero, negative, or a positive number, with the positive number serving as an estimate of the project’s potential long-term value. This makes for a

Time value of money

Brief explanation time value of money and how it relates to NPV

Discount rate

The discount rate is the interest rate used to convert future cash flows into an equivalent one-off upfront sum or present value (article 18). As the discount rate increases, the lower the present value of a given future amount becomes. Hence the magnitude of the discount rate exerts a significant influence on the net present value. For instance, if the selected discount rate level is set too high, it may make potentially good projects, programs or portfolios seem unattractive, whereas if set too low, it might result in the opposite.

The selection of an appropriate discount rate can be a very exhaustive and challenging task, as the decision is dependent on multiple factors, to name a few:

- The situational circumstances under which the investment project is taking place are characterized by fundamental uncertainty, computable risk, or certainty. The first, driving the discount rate to increase the most. Reference, chapter 8 paper) Furthermore, the jurisdiction and location of the project being commenced also play a role in the choice of a discount rate. (See EU reference) - The duration of the time horizon, especially in a socio-economic context, numerous countries have opted to differentiate between projects that span less than or more than 30-50 years, with the latter receiving a lower discount rate. (Chapter 8) - Private versus public and government bodies. Discounting from a firm’s or individual perspective is inherently different than that of government bodies.

In relation to state-aided projects, the European Commission calculates and issues base rates each month for countries within the union. The discount rate can be found by adding a margin of a 100 basispoints to the base rate. The base rate for the first four months of 2023 is depicted in the table below.

	Base rates as of 1.4.2023
From	To	AT	BE	BG	CY	CZ	DE	DK	EE	EL	ES	FI	FR	HR	HU	IE	IT	LT	LU	LV	MT	NL	PL	PT	RO	SE	SI	SK	UK
1.4.2023	…	3.06	3.06	1.51	3.06	7.43	3.06	3.54	3.06	3.06	3.06	3.06	3.06	3.06	15.10	3.06	3.06	3.06	3.06	3.06	3.06	3.06	7.62	3.06	8.31	3.21	3.06	3.06	3.52
1.3.2023	31.3.2023	3.06	3.06	1.10	3.06	7.43	3.06	2.92	3.06	3.06	3.06	3.06	3.06	3.06	15.10	3.06	3.06	3.06	3.06	3.06	3.06	3.06	7.62	3.06	8.31	2.96	3.06	3.06	3.52
1.2.2023	28.2.2023	2.56	2.56	0.79	2.56	7.43	2.56	2.92	2.56	2.56	2.56	2.56	2.56	2.56	15.10	2.56	2.56	2.56	2.56	2.56	2.56	2.56	7.62	2.56	8.31	2.44	2.56	2.56	2.77
1.1.2023	31.1.2023	2.56	2.56	0.36	2.56	7.43	2.56	2.92	2.56	2.56	2.56	2.56	2.56	2.56	15.10	2.56	2.56	2.56	2.56	2.56	2.56	2.56	7.62	2.56	8.31	2.44	2.56	2.56	2.77

The weighted average cost of capital (WACC) is another way to determine and select an appropriate discount rate for firms, in the appraisal process of a proposed investment or project using the NPV. The WACC represents the risk to the future cashflows received by an organization from its operations including equity and debt. It weighs the cost of each capital source by its relevant weight by market value and adds it together to determine the total. The gist of using the WACC besides it representing a minimum rate of return that a firm must achieve is that it can be used as a proxy for a suitable discount rate (Article 19). The WACC is calculated as follows:

$WACC = (\frac{E}{V}\cdot Re)+(\frac{D}{V}\cdot Rd \cdot (1-Tc))$

Financial Appraisal

Why do we make financial appraisals of projects, programs, and portfolios? Where do NPV fit?

Application and decision making

In the following paragraph, the application of NPV in regard to assessing the profitability of a project prior to commencing it will be outlined.

Example

A practical example on how to calculate the NPV of a construction project.

Advantages

Disadvantages

Annotated Bibliography

References

↑ Investopedia. (2023). Net Present Value (NPV): What It Means and Steps to Calculate It. Investopedia, 1–8. https://www.investopedia.com/terms/n/npv.asp
↑ ^2.0 ^2.1 Barfod, M. B., & Leleur, S. (2019). Decision Support and Strategic Assessment DTU Management Compendium.
↑ Gardner, N.D. 2004. The Time Value of Money: A Clarifying and Simplifying Approach. Journal of College Teaching & Learning (TLC). 1, 7 (Jul. 2004).
↑ Häcker, J., & Ernst, D. (2017). Financial Modeling. In Financial Modeling.
↑ ^5.0 ^5.1 Žižlavský, O. (2014). Net Present Value Approach: Method for Economic Assessment of Innovation Projects. Procedia - Social and Behavioral Sciences, 156(April), 506–512.

[NPV-0] Investopedia. (2023). Net Present Value (NPV): What It Means and Steps to Calculate It. Investopedia, 1–8. https://www.investopedia.com/terms/n/npv.asp

[DSSA-1] 2.0 ^2.1 Barfod, M. B., & Leleur, S. (2019). Decision Support and Strategic Assessment DTU Management Compendium.

[TVM-2] Gardner, N.D. 2004. The Time Value of Money: A Clarifying and Simplifying Approach. Journal of College Teaching & Learning (TLC). 1, 7 (Jul. 2004).

[NPV_H-3] Häcker, J., & Ernst, D. (2017). Financial Modeling. In Financial Modeling.

[NPV_P-4] 5.0 ^5.1 Žižlavský, O. (2014). Net Present Value Approach: Method for Economic Assessment of Innovation Projects. Procedia - Social and Behavioral Sciences, 156(April), 506–512.

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Project viability assessment through Net Present Value (NPV)

Revision as of 09:54, 5 April 2023

Contents

Abstract

NPV Formula

Time value of money

Discount rate

Financial Appraisal

Application and decision making

Example

Advantages

Disadvantages

Annotated Bibliography

References

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 The selection of an appropriate discount rate can be a very exhaustive and challenging task, as the decision is dependent on multiple factors, to name a few:
--	The situational circumstances under which the investment project is taking place are characterized by fundamental uncertainty, computable risk, or certainty. The first, driving the discount rate to increase the most. Reference, chapter 8 paper) Furthermore, the jurisdiction and location of the project being commenced also play a role in the choice of a discount rate. (See EU reference)
+- The situational circumstances under which the investment project is taking place are characterized by fundamental uncertainty, computable risk, or certainty. The first, driving the discount rate to increase the most. Reference, chapter 8 paper) Furthermore, the jurisdiction and location of the project being commenced also play a role in the choice of a discount rate. (See EU reference)
--	The duration of the time horizon, especially in a socio-economic context, numerous countries have opted to differentiate between projects that span less than or more than 30-50 years, with the latter receiving a lower discount rate.  (Chapter 8)
+- The duration of the time horizon, especially in a socio-economic context, numerous countries have opted to differentiate between projects that span less than or more than 30-50 years, with the latter receiving a lower discount rate.  (Chapter 8)
--	Private versus public and government bodies. Discounting from a firm’s or individual perspective is inherently different than that of government bodies.
+- Private versus public and government bodies. Discounting from a firm’s or individual perspective is inherently different than that of government bodies.
 In relation to state-aided projects, the European Commission calculates and issues base rates each month for countries within the union. The discount rate can be found by adding a margin of a 100 basispoints to the base rate. The base rate for the first four months of 2023 is depicted in the table below.