More about this Net Present Value Calculator (NPV) with steps

The net present value (\(NPV\)) of a stream of cash flows \(F_t\) depends on the discount interest rate \(r\), and the cash flows themselves. It corresponds to the sum of the present values of ALL cash flows associated to a project.

How do you calculate net present value? What formula do you use?

The net present value (\(NPV\)) can be computed using the following formula:

\[ NPV = \displaystyle \sum_{t=0}^n \frac{F_t}{(1+i)^t} \]

where \(F_t\) corresponds to the total sum of cash flows for period \(t\). Such sum can be negative or positive. The factor \((1+i)^t\) in the denominator is part of the discount factor used to bring the value of future cash flows into present values.

What is NPV discount rate?

The discount rate corresponds to \(i\) in the above equation, and represents the interest rate, or more precisely, the cost of capital, which is used to bring future values into present values.

How to compute the net present value excel

Excel has a built in function, the =NPV() function that allows you to compute the present value of cash flows.

What other calculators can I use to evaluate a project?

There are other metrics used to evaluate a projects, which use different angles to assess profitability. You can also use our internal rate of return calculator , the payback period calculator , or our profitability index calculator .

How to calculate Present Value step by step? Here is an example

Question: You are the manager of a new project that requires $10,000 of upfront outlay. It is expected that the project will bring a revenue of $3,000 at the end of the first year, and $4,000 at the end of the following 3 years. Assuming that the discount rate is 4%, compute the net present value (NPV) of the project.

Solution:

This is the information we have been provided with:

• The cash flows provided are: -10000,3000,4000,4000,4000 and the discount rate is \(r = 0.04\).

Therefore, the net present value (NPV) associated to these cash flows are computed using the following formula

\[ NPV = \displaystyle \sum_{i=0}^n {\frac{F_i}{(1+i)^i}} \]

The following table shows the cash flows and discounted cash flows:

Period	Cash Flows	Discounted Cash Flows
0	-10000	\(\displaystyle \frac{ -10000}{ (1+0.04)^{ 0}} = -\text{\textdollar}10000\)
1	3000	\(\displaystyle \frac{ 3000}{ (1+0.04)^{ 1}} = \text{\textdollar}2884.62\)
2	4000	\(\displaystyle \frac{ 4000}{ (1+0.04)^{ 2}} = \text{\textdollar}3698.22\)
3	4000	\(\displaystyle \frac{ 4000}{ (1+0.04)^{ 3}} = \text{\textdollar}3555.99\)
4	4000	\(\displaystyle \frac{ 4000}{ (1+0.04)^{ 4}} = \text{\textdollar}3419.22\)
		\(Sum = 3558.04\)

Based on the cash flows provided the NPV is computed as follows:

\[ \begin{array}{ccl} NPV & = & \displaystyle \frac{ -10000}{ (1+0.04)^{ 0}}+\frac{ 3000}{ (1+0.04)^{ 1}}+\frac{ 4000}{ (1+0.04)^{ 2}}+ \frac{ 4000}{ (1+0.04)^{ 3}}+\frac{ 4000}{ (1+0.04)^{ 4}} \\\\ \\\\ & = & -\text{\textdollar}10000+\text{\textdollar}2884.62 +\text{\textdollar}3698.22+\text{\textdollar}3555.99+\text{\textdollar}3419.22 \\\\ \\\\ & = & \text{\textdollar}3558.04 \end{array} \]

Therefore, the net present value associated to the provided cash flows and the discount rate of \(r = 0.04\) is \( NPV =\text{\textdollar}3558.04\).