Project viability assessment through Net Present Value (NPV)

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.

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. 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.

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. 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. This is modulated by the use of the discount factor $(1+r)^t$, where a discount rate is used.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, $N$..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

Figure 1: Discount factor versus 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

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