Skip to main content

Time value of money, Present Value (PV), Future Value (FV), Net Present Value (NPV), Internal Rate of Return (IRR)

Why do I use my current money to invest in the stock market? Because I expect to have more money in the future. Why do I need more money in the future than now? Because of many reasons, the same amount of money will have less purchasing power than today. Therefore my investment needs to generate more money than today to protect my purchasing power in the future. That is the main concept of the time value of money where one dollar today is worth more than one dollar in the future.

Present Value (PV), Future Value (FV)

At 10% annual growth rate, an investment of 1000$ will be worth 1000 * 110% = 1100$ after 1 year, and will be worth 1000 * 110% * 110% = 1210$ after 2 years.

  • The future value of 1000$ after 2 years at the rate of 10% is 1210$.
  • Inversely, the "present value" of 1210$ 2 years ago at the rate of 10% is 1000$.
Present value and future value formula

Net Present Value (NPV)

Let's say I have 1000$ now and a bank offers me a saving account at a 10% annual rate. At the same time, a public company attracts my attention because it pays a very good amount of dividend each year and has potential growth in the future. The scenario is that I would buy 100 shares at the cost of 10$ each now and hold them for 5 years. Each year I would receive a fairly good and stable amount of dividends, at least 5% yield. After 5 years, I would sell all shares with the expectation that the share price would grow 20%. The table below shows the scenario of cash flows if I buy stocks of that company. Which investment should I choose?

YearAmountType
0-$1,000.00Buy
1$50.00Dividend
2$55.00Dividend
3$60.00Dividend
4$65.00Dividend
5$1,200.00Sell

To make that decision, let put it this way: I want to have the same scenario of cash flows as investing into the stock market but by putting money into a saving account at a 10% annual rate. How much money do I need to put into that saving account now? Let's do the math:

  • At a 10% rate, to have 50$ after 1 year, I need to invest 45.45$ now. Because 50$ is the future value of 45.45$ after 1 year at a 10% rate.
  • At a 10% rate, to have 55$ after 2 years, I need to invest 45.45$ now. Because 55$ is the future value of 45.45$ after 2 years at a 10% rate.
  • At a 10% rate, to have 60$ after 3 years, I need to invest 45.08$ now. Because 60$ is the future value of 45.08$ after 3 years at a 10% rate.
  • At a 10% rate, to have 65$ after 4 years, I need to invest 44.40$ now. Because 65$ is the future value of 44.40$ after 4 years at a 10% rate.
  • At a 10% rate, to have 1200$ after 5 years, I need to invest 745.11$ now. Because 1200$ is the future value of 745.11$ after 5 years at a 10% rate.

Totally, to have the same scenario of cash flows as investing in the stock market, I need to invest 45.45 + 45.45 + 45.08 + 44.40 + 745.11 = 925.49$ now in a saving account at a 10% rate. In other words, to have the same result in the future, investing in the stock market costs me 1000$ now, whereas investing in the saving account at a 10% rate costs me only 925.49$ now. Therefore, in this case, I should better put money in the saving account at 10% rate.

Let's suppose that the share prices would grow 50% during the 5 years, which means the last cash flow would be 1500$ in the 5th year. In this case, at a 10% rate, to have 1500$ after 5 years, I need to invest 931.38$ now. Because 1500$ is the future value of 931.38$ after 5 years at a 10% rate. Totally, to have the same scenario of cash flows as investing in the stock market, I need to invest 45.45 + 45.45 + 45.08 + 44.40 + 931.38 = 1089.88$ now in a saving account at a 10% rate. In other words, to have the same result in the future, investing in the stock market costs me only 1000$ now, whereas investing into the saving account at a 10% rate costs me 1089.88$ now. Therefore, in this case, I have a better deal to invest in the stock market than to put money in a saving account at a 10% rate.

Moreover, because at year 0 future value equals to present value, I can do like that:

  • For the first scenario, sum of all present values of future cash flows is: -1000 + 45.45 + 45.45 + 45.08 + 44.40 + 745.11 = -96.40 < 0
  • For the second scenario, sum of all present values of future cash flows is: -1000 + 45.45 + 45.45 + 45.08 + 44.40 + 931.38 = 89.88 > 0

What's I have calculated so far is to sum the present values of future cash flows at a defined discount rate and compare it with 0. That's what they call Net Present Value (NPV). If Net Present Value (NPV) is positive, the investment is worth pursuing.

Net Present Value - NPV formula

Discount rate

In this example, I have chosen the saving account at a 10% annual rate as a benchmark to evaluate my investment in the stock market. The 10% annual rate of that saving account is therefore the discount rate in my evaluation. My investment in the stock market must beat 10% annually, otherwise, it is not worth my time and effort because I can easily save that money at 10% annually. The choice of a discount rate is important and depends on personal preferences. Here are a few examples:

  • A minimum required rate of return for an investment that one sets for herself/himself
  • An expected rate of return if investing in an alternative asset such as: saving account, real estate, buying a business, etc.
  • A reference rate of return of the market: S&P 500, CAC 40, etc.

Internal Rate of Return (IRR)

The discount rate that makes Net Present Value (NPV) equal to zero is called the Internal Rate of Return (IRR).

Internal Rate of Return - IRR formula
  • For the first scenario of cash flows above, that internal rate of return is 8.13%.
    • At a 8.13% rate, sum of all present values of future cash flows is: -1000 + 46.24 + 47.04 + 47.46 + 47.54 + 811.72 = 0.
    • Because 8.13% < 10%, it confirms once again that the saving account at a 10% rate is a better choice.

YearAmountTypePresent Value
0-$1,000.00Buy-$1,000.00
1$50.00Dividend$46.24
2$55.00Dividend$47.04
3$60.00Dividend$47.46
4$65.00Dividend$47.54
5$1,200.00Sell$811.72
  • For the second scenario of cash flows above, that internal rate of return is 12.57%.
    • At a 12.57% rate, sum of all present values of future cash flows is: -1000 + 44.42 + 43.40 + 42.06 + 40.47 + 829.66 = 0.
    • Because 12.57% > 10%, it confirms once again that investing in the stock market is a better choice.
YearAmountTypePresent Value
0-$1,000.00Buy-$1,000.00
1$50.00Dividend$44.42
2$55.00Dividend$43.40
3$60.00Dividend$42.06
4$65.00Dividend$40.47
5$1,500.00Sell$829.66

Conclusion

In summary, Net Present Value (NPV) and Internal Rate of Return (IRR) are two methods that help me to evaluate the performance of an investment.

To evaluate an investment with Net Present Value (NPV), I follow the steps below:

  • Identify all cash flows
  • Pick a discount rate
  • Calculate Net Present Value (NPV) by summing all present values of those cash flows
  • If Net Present Value (NPV) is positive, the investment is worth pursuing

To evaluate an investment with Internal Rate of Return (IRR), I follow the steps below:

  • Identify all cash flows
  • Pick a discount rate
  • Calculate the Internal Rate of Return (IRR) rate that makes Net Present Value (NPV) equal to 0
  • If Internal Rate of Return (IRR) is bigger than the discount rate, the investment is worth pursuing

Performing those steps requires many calculations, and I don't perform them manually. I have leveraged the built-in functions of Google Sheets to do those tasks. In the next posts, I will explain how to calculate Net Present Value (NPV) and Internal Rate of Return (IRR) in Google Sheets, particularly in the context of a stock portfolio.

Comments

Popular posts from this blog

Create personal stock portfolio tracker with Google Sheets and Google Data Studio

I have been investing in the stock market for a while. I was looking for a software tool that could help me better manage my portfolio, but, could not find one that satisfied my needs. One day, I discovered that the Google Sheets application has a built-in function called GOOGLEFINANCE which fetches current or historical prices of stocks into spreadsheets. So I thought it is totally possible to build my own personal portfolio tracker with Google Sheets. I can register my transactions in a sheet and use the pivot table, built-in functions such as GOOGLEFINANCE, and Apps Script to automate the computation for daily evolutions of my portfolio as well as the current position for each stock in my portfolio. I then drew some sort of charts within the spreadsheet to have some visual ideas of my portfolio. However, I quickly found it inconvenient to have the charts overlapped the table and to switch back and forth among sheets in the spreadsheet. That's when I came to know the existen

Create a dividend income tracker with Google Sheets by simply using pivot tables

As my investment strategy is to buy stocks that pay regular and stable dividends during a long-term period, I need to monitor my dividends income by stocks, by months, and by years, so that I can answer quickly and exactly the following questions: How much dividend did I receive on a given month and a given year? How much dividend did I receive for a given stock in a given year? Have a given stock's annual dividend per share kept increasing gradually over years? Have a given stock's annual dividend yield been stable over years? In this post, I explain how to create a dividend tracker with Google Sheets. Manage stock transactions with Google Sheets Create dividend tracker with Google Sheets Track annual dividend amount of stocks Track dividend amount by month and by year Track annual dividend per share of stocks Track annual dividend yield of stocks Demo Conclusion References Manage stock transactions with Google Sheets I use a spreadsheet on Goo

How to copy data in Google Sheets as HTML table

I often need to extract some sample data in Google Sheets and present it in my blog as an HTML table. However, when copying a selected range in Google Sheets and paste it outside the Google Sheets, I only get plain text. In this post, I explain how to copy data in Google Sheets as an HTML table by writing a small Apps Script program. Concept Implementation Source Code Demo HTML table code HTML table visualization Getting Started Concept On a spreadsheet, users select a range that they want to copy as HTML table. With the selected range, users trigger a command Copy AS HTML table . The command can be added to the toolbar, or to the contextual menu, or accessed via a keyboard shortcut. The command is executed to transform the selected range into HTML code for table. The HTML code can be added to the clipboard or can be displayed somewhere so users can copy it manually. The HTML table must consist of all displayed cells of the selected range and the widths between c

Stock Correlation Analysis With Google Sheets

Correlation is a statistical relationship that measures how related the movement of one variable is compared to another variable. For example, stock prices fluctuate over time and are correlated accordingly or inversely to one another. Understanding stock correlation and being able to perform analysis are very helpful in managing a stock portfolio investment. In this post, we will look at how to perform stock correlation analysis with Google Sheets. Understanding correlation and its applications in stock investing Stock correlation analysis with Google Sheets Getting started User guide Conclusion Understanding correlation and its applications in stock investing The most familiar correlation measure is the Pearson product-moment correlation coefficient . The strength of the relationship between two variables is expressed numerically between -1 and 1. For example: Two stocks are positively correlated when their prices always go up or go down together. Their coefficient

Demo stock portfolio tracker with Google Sheets

As explained in the post Create personal stock portfolio tracker with Google Sheets and Google Data Studio , a personal stock portfolio tracker consists of 2 main elements: a spreadsheet in Google Sheets and an interactive dashboard in Google Data Studio. You can take a look at the sample spreadsheet below to have an idea of how the data is organized and related. It is possible to make a copy of the spreadsheet to study it thoroughly. NOTE: An enhanced version was published at Create personal stock portfolio tracker with Google Sheets and Google Data Studio . Make a copy Note Disclaimer Make a copy Click here to make a copy Note To better understand the overall concept, please check out this post Create personal stock portfolio tracker with Google Sheets and Google Data Studio . Disclaimer The post is only for informational purposes and not for trading purposes or financial advice.

Manage Stock Transactions With Google Sheets

The first task of building a stock portfolio tracker is to design a solution to register transactions. A transaction is an event when change happens to a stock portfolio, for instance, selling shares of a company, depositing money, or receiving dividends. Transactions are essential inputs to a stock portfolio tracker and it is important to keep track of transactions to make good decisions in investment. In this post, I will explain step by step how to keep track of stock transactions with Google Sheets. Define the structure of transactions Use Google Sheets to register transactions Demo Note References Define the structure of transactions In the example, I assume that a transaction generally has 5 main attributes: Date : It is the moment when a transaction happened. Type : It can be one of the following values: DEPOSIT : When money is added to the portfolio BUY : When money in the portfolio is used to buy shares of a company SELL : When money is added into