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# Net Present Value of an Investment Project

The Net present value (NPV) of a project refers to the present value of all cash inflows minus the present value of all cash outflows, evaluated at a given discount rate. The difference between the two represents the income generated by a project. A project whose cash inflows outweigh its cash outflows is generally considered financially viable, as it generates a positive return. However, there are projects in which the present value of cash outflows exceeds the present value of cash inflows. Such a project is not financially viable. To help you understand the NPV concept, consider the following example:

Suppose the local government in a given location decides to build a bridge that will connect two cities, A and B. At the start of this project, the government will have to spend a considerable amount of money to acquire necessary construction material and also pay the constructor. Assume a risk discount rate of 10% per annum. After construction, more, but smaller amounts of money, will cater for maintenance costs. All these expenses constitute the cash outflows of the project. The project is then expected to generate a continuous stream of income in the form of toll fees paid by the users of the bridge. To simplify matters, let’s assume that the project will generate income for ten years. Fees paid will constitute the project’s cash inflows. Therefore, the government should only proceed with the project if the NPV is positive.

## Net Present Value Formula

$$NPV=\sum { C_{ t }(1+r)^{ t } } \text { for all } t\ge 0$$

Where: Ct is the cash flow at time t

And r is the risk discount rate

## Question

A project generates the following cash flows;

Beginning of years:

1 – ($100,000) (contractors’ fees) 2 – ($200,000) (contractors’ fees)

3 –  ($200,000) (contractors’ fees) End of Year 3 :$1,000,000 (sales)

Calculate the NPV of the project using a risk discount rate of 20% per year.

A. $500,000 B.$173,148

C. \$166,667

Solution

r = 0.2

\begin{align*} \text{NPV} & = – 100,000 – 200,000(1 + 0.2)^{-1} – 200,000(1 + 0.2) ^{-2} + 1000,000(1 + 0.2)^{-3} \\ & = – 100,000 – 166,667 – 138,889 + 578,704 \\ & = 173,148 \\ \end{align*}

Note that we do not discount cash flows occurring at the beginning of a project. Hence, the discount should be zero at t = 0.

## Advantages of the NPV method

– NPV tells us whether a project will increase the value of a company, and by how much in terms of dollars.

– The method takes into account all the cash flows associated with a particular project.

– It considers the time value of money.

– Net present value method offers a convenient tool during appraisal of any given project.

Calculate and interpret the net present value (NPV) and the internal rate of

return (IRR) of an investment

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