Question

Explain the net present value formula and also explain what the net present value represents.

Answer 1

Net Present value is computed by using the below formula:

Net Present Value = (Initial Investment) + Present value of future cash flows

As can be seen NPV is computed by adding the present value of future cash flows with the initial investment in the project.

If the NPV of a project is positive, then it denotes that the project's initial investment is recovered from the present value of future cash flows and hence the project should be accepted and vice-versa i.e. if the project's NPV is negative then it denotes that the project's initial investment is not recovered by the present value of future cash flows and hence the project should not be accepted.

Net Present Value represents the sum of initial investment and present value of future cash flows and it is very helpful in judging that whether the project should be accepted or not. Further since it discounts the future cash flows by an appropriate discount rate conveys that it also takes in to account the time value of money.

Let us understand this with an example:

Suppose a project has an initial investment of $ 100,000 and the cash flows are as follows:

Year 1 cash flow = $ 30,000

Year 2 cash flow = $ 40,000

Year 3 cash flow = $ 80,000

Now we shall compute the NPV of this investment as follows:

= ( Initial Investment ) + Year 1 cash flow / (1 + required rate of return )¹ + Year 2 cash flow / ( 1 + required rate of return )² + Year 3 cash flow / ( 1 + required rate of return )³

In this question these are the following figures that we need to insert in the above mentioned function:

Initial Investment = $ 1,00,000

Year 1 cash flow = $ 30,000

Year 2 cash flow = $ 40,000

Year 3 cash flow = $ 80,000

Required rate of return = 0.10 or 10%

Now we shall plug these figures in the above function to get the net present value as follows:

= (1,00,000) + 30,000 / (1.10¹) + 40,000 / (1.10²) + 80,000 / (1.10³)

= $ 20,435.76 or $ 20,436 Approximately

So this denotes that the project should be accepted since the NPV of the project is positive.

Feel free to ask in case of any query relating to this question