# Calculation of NPV and IRR

### Net Present Value (NPV)

This is one of the widely used methods for evaluating capital investment proposals. In this technique the cash inflow that is expected at different periods of time is discounted at a particular rate. The present values of the cash inflow are compared to the original investment. If the difference between them is positive (+) then it is accepted or otherwise rejected. This method considers the time value of money and is consistent with the objective of maximizing profits for the owners. However, understanding the concept of cost of capital is not an easy task.

The NPV formula is a way of calculating the Net Present Value (NPV) of a series of cash flows based on a specified discount rate.  The NPV formula can be very useful for financial analysis and financial modeling when determining the value of an investment (a company, a project, a cost-saving initiative, etc.).

What is the Math behind the NPV Formula?

Here is the mathematical formula for calculating the present value of an individual cash flow.

NPV = F / [(1 + i) ^n]

Where,

PV = Present Value

F = Future payment (cash flow)

i = Discount rate (or interest rate)

n = the number of periods in the future cash flow.

### INTERNAL RATE OF RETURN (IRR)

This is defined as the rate at which the net present value of the investment is zero. The discounted cash inflow is equal to the discounted cash outflow. This method also considers time value of money. It tries to arrive to a rate of interest at which funds invested in the project could be repaid out of the cash inflows. However, computation of IRR is a tedious task.

It is called internal rate because it depends solely on the outlay and proceeds associated with the project and not any rate determined outside the investment.

If IRR > WACC then the project is profitable.

If IRR > k = accept

If IR < k = reject

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