*Anthony Aparicio*Show bio

Tony taught Business and Aeronautics courses for eight years; he holds a Master's degree in Management and is completing a PhD in Organizational Psychology

Lesson Transcript

Instructor:
*Anthony Aparicio*
Show bio

Tony taught Business and Aeronautics courses for eight years; he holds a Master's degree in Management and is completing a PhD in Organizational Psychology

The value of money changes over time. If you spoke to your parents or grandparents about what things cost when they were children, you will see a big difference. This concept is called net present value.
Updated: 03/24/2021

**Net present value (NPV)** refers to the concept that the value of money changes over time. Even though one dollar in 1920 is still called a dollar today, the amount of things that one dollar buys has changed. Something that cost $20 back in 1920 would cost around $239 today because of the rate of inflation.

NPV is a common technique used in business to determine how to select the best investment based on its value at one point in time (usually the present). Companies prefer to get their money back from their initial investment as quickly as possible so that they can do the same thing again with future investments. In order to figure out whether an investment will be worthwhile, the manager or accountant must calculate the value of future revenue in today's dollars.

Simple NPV is when you are dealing with one investment and return with no payments in between. To give an example of simple NPV, say that you are asked to loan your brother $4,000 for a car, and he said that he will pay you back in two years when he graduates college.

Before calculating the NPV, you will have to first discuss the cost of capital. The **cost of capital** is what the firm pays for its funds. If you are thinking of lending money, you also have the option to keep that $4,000 in an investment that could have earned you interest. Use the example of an expected 5% return on your investment. Therefore, 5% is your cost of capital.

If you do decide to loan your brother the money and you have determined that 5% is your cost of capital, what is the value of that $4,000 two years from now?

Compute NPV by first:

- Determine the amount. In this example, the amount is $4,000.
- Then, determine the cost of capital (5%) and the number of periods. The period is 2 years because that is how long it will be until your brother pays you back.
- Next, look up the present value of 1 table at the intersection of the percentage and the period.
- Finally, multiply the decimal found on the table by the initial amount.

If you search the Internet, you will find a special table called the Present Value of 1. Once you have found it, look at the intersection between the 5% column and 2 periods (years in this case). You will see that there is a decimal number of 0.9070.

Take the amount you are going to loan your brother ($4,000) and multiply that by the decimal number you found at the intersection of the appropriate column and row (0.9070).

$4,000 x 0.9070 = $3,628

Based on this example, if your brother paid you back exactly $4,000 in two years, it will only be worth the equivalent of what $3,628 dollars is now.

A company has two investment choices that cost $3,000 each: one that brings in $10,000 in revenue at 8% interest in two years, and another that brings in $11,000 revenue at the same interest rate in five years. Use the Present Value of 1 table to compute the value of each investment and see how they compare.

What is the present value of $10,000 revenue in two years?

- $10,000 x 0.8573 (intersection of 8% and 2 periods) = $8,573.00 - $3,000 (original investment) = $5,573.00.

What is the present value of $11,000 revenue in five years?

- $11,000 x 0.6806 (intersection of 8% and 5 periods) = $7,486.60 - $3,000 (original investment) = $4,486.60.

Even though the second investment brings in more money, the value of that investment is less due to the amount of time it takes to earn it.

The formula for computing multiple year investments with returns is much more extensive than the simple version above. The formula is:

This is the way that you would compute the formula manually. Luckily, there is also a table called the Present Value for an Annuity of 1 that you would use in the same way as in the simple version. The difference is that you have to multiply the number of periods by the amount of each payment.

As an example, instead of your brother paying back the entire $4,000 at the end of two years, use the Present Value of an Annuity of 1 table to see how much it would be worth if he paid you $2,000 payments each year.

This time, when you use the table, you see 1.8594 at the intersection of the 5% and the 2 periods row. Take the $2,000 payment and multiply it by that number to see how much it is worth. Notice that by making yearly payments, it has increased that value of what you would be getting back to $3,718.80 (compared to $3,628). The higher amount shows that this would be a better investment than the first option.

**Net present value (NPV)** refers to the concept that the value of money changes over time.

Simple and multiple year NPV can be calculated in much the same way. For a simple (one-time) NPV payment, take the total amount and multiply it by the result of the number at the intersection of the rate and number of periods in the Present Value of 1 table.

For a multiple year NPV calculation, multiply the payment amount by the appropriate number found in the Present Value for an Annuity of 1 table. If this is for a business investment, remember to subtract the amount of the original investment in order to see how much that specific project would be worth to the company.

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