Get instant live expert help with Excel or Google Sheets
“My Excelchat expert helped me in less than 20 minutes, saving me what would have been 5 hours of work!”

Post your problem and you’ll get expert help in seconds.

Your message must be at least 40 characters
Our professional experts are available now. Your privacy is guaranteed.

Learn How to Find the NPV of a Perpetuity in Excel

When calculating the net present value, a situation might arise where you are face with a constant series of payments without an end. This is what we refer to as NPV for a perpetuity.

To find the net present value of a perpetuity, we need to first know the future value of the investment.

General syntax of the formula

NPV(perpetuity)= FV/i

Where;

  • FV- is the future value
  • i – is the interest rate for the perpetuity

Example

To understand how the NPV of a perpetuity works in excel, we need to consider the example below;

Figure 1: Finding NPV of perpetuity in excel

To better understand the above NPV, we need to consider a real case study;

Imagine you are evaluating a firm based on its future profits. The firm’s expected profit per year is $100 as shown in cell B2, without an end. The cash flow is then discounted at the rate of 4% as shown in cell B3. To get the NPV, we simply divide the Future value, which is $100, by the rate.

=$100/0.04

=$2,500

What if the cash flow grows at a constant rate?

In a perpetuity case, a scenario might emerge where the cash flow increases at a given constant rate. To find the NPV in such a case, we proceed as follows;

NPV= FV/(i-g)

Where;

  • FV– is the future value of the cash flows
  • i – is the discount rate
  • g- is the growth rate of the firm

Example

Assume that a firm anticipates a profit of $100 per year without an end. The discounted rate is 4% and the profit is expected to grow at a rate of 2% every year. What is the NPV of the perpetuity?

Answer

NPV(perpetuity)= $100/(0.04-0.02)

Figure 2: NPV of perpetuity with growth rate

Notice that when we have the growth rate given, the NPV is higher than that of when we don’t have a growth rate.

Most of the time, the problem you will need to solve will be more complex than a simple application of a formula or function. If you want to save hours of research and frustration, try our live Excelchat service! Our Excel Experts are available 24/7 to answer any Excel question you may have. We guarantee a connection within 30 seconds and a customized solution within 20 minutes.

Solution examples
I have a figure which is the sum of 9 months of payments. Each payment decreases by the same amount (X) so the first payment is Y, second payment is Y-X, third is Y-(Xx2), forth is Y-(Xx3) and so on. I am trying to calculate what each of the 9 payments should be.
Solved by A. W. in 60 mins
how do I calculate daily interest in excel? for instance if I have $20,000 in a bank that gives .5% interest and calculates it daily, I want to create a spreadsheet that will show what I will have at the end of a 30 day month
Solved by O. A. in 21 mins
how would i do this question on excel? An investment will generate £15,000 a year for 20 years. If you require a rate of compensation of 10% and the investment costs £100,000, show whether it is worth buying? If expected inflation is instead estimated to be 2% higher, show how this impacts on your recommendation.
Solved by V. W. in 60 mins

Leave a Comment

avatar

Subscribe to Excelchat.co

Get updates on helpful Excel topics

Subscribe to Excelchat.co
Trusted by people who work at
Amazon.com, Inc
Facebook, Inc
Accenture PLC
Siemens AG
Macy's
The Allstate Corporation
United Parcel Service
Dell Inc