### How to Calculate NPV | How It Works. How It's Done.

In
the business world, Net present value (or NPV) is one of the most
helpful tools available for financial decision making. Usually, NPV is
used to estimate whether a certain purchase or investment is worth more
in the long run than simply investing an equivalent amount of money in
the bank. While it is often used in the world of corporate finance, it
can also be used for everyday purposes. Generally, NPV can be calculated
as the sum of (P / (1 + i)t) - C for all positive integer values up to t

where t is your number of time periods, P is your cash inflow, C is your initial investment, and i is your discount rate. For a step-by-step breakdown, get started with Step 1 below!

NPV Calculator

In the world of business, purchases and investments are often made with the goal of earning money in the long run. For instance, a construction company might buy a bulldozer so that it can take on bigger projects and make more money over time than it would have if it had saved the money and only taken small projects. These sorts of investments usually have a single initial cost — to begin to find your investment's NPV, identify this cost.

As an example, let's imagine that you operate a small lemonade stand. You are considering buying an electric juicer for your business which will save you time and effort compared to juicing the lemons by hand. If the juicer costs $100,$100

is your initial investment. Over time, this initial investment will hopefully allow you to make more money than you would have without making it. In the next few steps, you'll use your $100 initial investment value to calculate NPV and determine whether it's "worth it" to buy the juicer.

As noted above, businesses and individuals make investments with the goal of making money in the long run. For instance, if a sneaker factory buys a shoe-making machine, the "goal" of this purchase is for the machine to generate enough money to pay for itself and turn a profit before it breaks or wears out. To determine the NPV for your investment, you'll need to specify a time period during which you're trying to determine whether the investment will pay for itself. This time period may be measured in any unit of time, but for most serious financial calculations, years are the unit used.

In our lemonade stand example, let's say that we've researched the juicer we intend to buy online. According to most reviews, the juicer works great, but usually breaks after about 3 years. In this case, we'll use 3 years

as the time period in our NPV calculation to determine whether the juicer will pay for itself before it's likely to break.

Next, you'll need to estimate how much money your investment will make you during each time period for which it's earning you money. These amounts (or "cash inflows") can be specific, known values, or they can be estimates. In the latter case, companies and financial firms sometimes devote a great deal of time and effort to getting an accurate estimate, hiring industry experts, analysts, and so on.

Let's continue with our lemonade stand example. Based on your past performance and your best future estimates, you assume that implementing the $100 juicer will bring in an extra $50 the first year, $40 the second year, and $30 the third year by reducing the time your employees need to spend juicing (and thus saving you money on wages) In this case, your expected cash inflows are: $50 in year 1, $40 in year 2, and $30 in year 3

.

In general, a given amount of money is worth more now than it is in the future. This is because the money you have today can be invested in an interest-earning account and gain value over time. In other words, it's better to have $10 today than $10 one year in the future because you can invest your $10 today and have more than $10 in a year. For NPV calculations, you need to know the interest rate of an investment account or opportunity with a similar level of risk to the investment you're analyzing. This is called your "discount rate" and is expressed as a decimal, rather than a percent.

In corporate finance, a firm's weighted-average cost of capital is often used to determine the discount rate. In simpler situations, you can usually just use the return rate on a savings account, stock investment, etc. that you might put your money in instead of making the investment you're analyzing.

In our lemonade stand example, let's say that if you don't purchase the juicer, you'll invest the money in the stock market, where you feel confident that you can earn 4% annually on your money. In this case, 0.04

(4% expressed as a decimal) is the discount rate we'll use in our calculation.

Next, we'll weight the value of our cash inflows for each time period we're analyzing against the amount of money we'll make from our alternate investment in the same period. This is called "discounting" the cash flows and is done using the simple formula P / (1 + i)t

, where P is the amount of the cash flow, i is the discount rate, and t represents time. We don't need to worry about our initial investment yet — we'll use this in the next step.

In our lemonade example, we're analyzing three years, so we'll need to use our formula three times. Calculate your yearly discounted cash flows as follows:

Year One: 50 / (1 + 0.04)1 = 50 / (1 .04) = $48.08

Year Two: 40 / (1 +0.04)2 = 40 / 1.082 = $36.98

Year Three: 30 / (1 +0.04)3 = 30 / 1.125 = $26.67

Finally, to get the total NPV for the project, purchase, or investment you're analyzing, you'll need to add up all of your discounted cash flows and subtract your initial investment. The answer you get for this calculation represents your NPV — the net amount of money that your investment will make compared to the alternate investment that gave you the discount rate. In other words, if this number is positive, you'll make more money than if you had spent it on an alternative investment, and if it's negative, you'll make less money. Remember, however, that the accuracy of your calculation hinges on how accurate your estimates for your future cash inflows and your discount rate were.

For our lemonade stand example, the final projected NPV value of the juicer would be:

48.08 + 36.98 + 26.67 - 100 = $11.73

In general, if the NPV for your investment is a positive number, then your investment will be more profitable than putting the money in your alternate investment and you should accept it. If the NPV is negative, your money is better invested elsewhere, and your proposed investment should be rejected. Note that these are generalities — in the real world, much more usually goes into the process of determining whether a certain investment is a wise idea.

In the lemonade stand example, the NPV is $11.71. Since this is positive, we'll probably decide to buy the juicer.

Note that this doesn't mean that the electric juicer only made you $11.71. In fact, this means that the juicer made you the required return rate of 4% annually, plus an additional $11.71 on top of that. In other words, it's $11.71more profitable than your alternate investment.

Finding the NPVs for multiple investment opportunities allows you to easily compare your investments to determine which are more valuable than others. In general, the investment with the highest NPV is the most valuable because its eventual payout is worth the most in present dollars. Because of this, you'll usually want to pursue the investments with the highest NPVs first (assuming you don't have enough resources to pursue every investment with a positive NPV).

For instance, let's say that we have three investment opportunities. One has an NPV of $150, one has an NPV of $45, and one has an NPV of -$10. In this situation, we'd pursue the $150 investment first because it has the greatest NPV. If we have enough resources, we'd pursue the $45 investment second because it's less valuable. We wouldn't pursue the -$10 investment at all because, with a negative NPV, it will make you less money than investing in an alternative with a similar level of risk.

Using a slightly modified form of the standard NPV formula, it's possible to quickly determine how much a present sum of money will be worth in the future (or how much a future sum of money is worth in the present). Simply use the formula PV = FV / (1+i)t, where i is your discount rate, t the number of time periods being analyzed, FV is the future money value, and PV is the present value. If you know i, t, and either FV or PV, it's relatively simple to solve for the final variable.

For instance, let's say we want to know how much $1,000 will be worth in five years. If we know that, at bare minimum, we can get a return rate of 2% on this money, we'll use 0.02 for i, 5 for t, and 1,000 for PV and solve for FV as follows:

1,000 = FV / (1+0.02)5

1,000 = FV / (1.02)5

1,000 = FV / 1.104

1,000 × 1.104 = FV = $1,104

.

The Internal Rate of Return (or IRR) is the discount rate that gives you an NPV of zero. In other words, it's the discount rate at which an alternate investment is exactly as valuable as the one you're analyzing. This can be another useful tool for judging which investments are the wisest. In general, investments with high IRRs are more valuable than ones with low IRRs because this means that the rate of return on an alternate investment would need to be higher to generate the same amount of value.

For example, if we have one possible investment with an IRR of 5% (i = 0.05) and one with an IRR of %10 (i = 0.10), we should take the %10 investment because an alternate investment would have to have a higher return rate to be as valuable — in other words, it's the more profitable investment.

You can find your investment's IRR with the NPV equation by solving for i when NPV = 0, but this requires complex math if you're analyzing more than one time period (t >1). An easier solution is to use a simple online IRR calculator, like this one.

As noted above, the accuracy of any NPV calculation basically depends on the accuracy of the values you use for your discount rate and your future cash inflows. If your discount rate is close to the actual return rate you can get on your money for an alternate investment of similar risk and your future cash inflows are close to the amounts of money you'll actually make from your investment, your NPV calculation will be right on the money. To get your estimates for these values as close to their corresponding real-world values as possible, you may want to take a look at corporate valuation techniques. Because large corporations often have to make enormous multi-million dollar investments, the methods they use to determine whether the investments are sound or not can be quite sophisticated.

A variety of financial resources are available online that can introduce the somewhat tricky fundamentals of corporate valuation to novices. For instance,this short beginner's guide is a great place to start.

where t is your number of time periods, P is your cash inflow, C is your initial investment, and i is your discount rate. For a step-by-step breakdown, get started with Step 1 below!

## NPV Calculator

NPV Calculator

## Part 1 of 2: Calculating NPV

### 1. Determine your initial investment.

In the world of business, purchases and investments are often made with the goal of earning money in the long run. For instance, a construction company might buy a bulldozer so that it can take on bigger projects and make more money over time than it would have if it had saved the money and only taken small projects. These sorts of investments usually have a single initial cost — to begin to find your investment's NPV, identify this cost.

As an example, let's imagine that you operate a small lemonade stand. You are considering buying an electric juicer for your business which will save you time and effort compared to juicing the lemons by hand. If the juicer costs $100,$100

is your initial investment. Over time, this initial investment will hopefully allow you to make more money than you would have without making it. In the next few steps, you'll use your $100 initial investment value to calculate NPV and determine whether it's "worth it" to buy the juicer.

### 2. Determine a time period to analyze.

As noted above, businesses and individuals make investments with the goal of making money in the long run. For instance, if a sneaker factory buys a shoe-making machine, the "goal" of this purchase is for the machine to generate enough money to pay for itself and turn a profit before it breaks or wears out. To determine the NPV for your investment, you'll need to specify a time period during which you're trying to determine whether the investment will pay for itself. This time period may be measured in any unit of time, but for most serious financial calculations, years are the unit used.

In our lemonade stand example, let's say that we've researched the juicer we intend to buy online. According to most reviews, the juicer works great, but usually breaks after about 3 years. In this case, we'll use 3 years

as the time period in our NPV calculation to determine whether the juicer will pay for itself before it's likely to break.

### 3. Estimate your cash inflow for each time period.

Next, you'll need to estimate how much money your investment will make you during each time period for which it's earning you money. These amounts (or "cash inflows") can be specific, known values, or they can be estimates. In the latter case, companies and financial firms sometimes devote a great deal of time and effort to getting an accurate estimate, hiring industry experts, analysts, and so on.

Let's continue with our lemonade stand example. Based on your past performance and your best future estimates, you assume that implementing the $100 juicer will bring in an extra $50 the first year, $40 the second year, and $30 the third year by reducing the time your employees need to spend juicing (and thus saving you money on wages) In this case, your expected cash inflows are: $50 in year 1, $40 in year 2, and $30 in year 3

.

### 4. Determine the appropriate discount rate.

In general, a given amount of money is worth more now than it is in the future. This is because the money you have today can be invested in an interest-earning account and gain value over time. In other words, it's better to have $10 today than $10 one year in the future because you can invest your $10 today and have more than $10 in a year. For NPV calculations, you need to know the interest rate of an investment account or opportunity with a similar level of risk to the investment you're analyzing. This is called your "discount rate" and is expressed as a decimal, rather than a percent.

In corporate finance, a firm's weighted-average cost of capital is often used to determine the discount rate. In simpler situations, you can usually just use the return rate on a savings account, stock investment, etc. that you might put your money in instead of making the investment you're analyzing.

In our lemonade stand example, let's say that if you don't purchase the juicer, you'll invest the money in the stock market, where you feel confident that you can earn 4% annually on your money. In this case, 0.04

(4% expressed as a decimal) is the discount rate we'll use in our calculation.

### 5. Discount your cash inflows.

Next, we'll weight the value of our cash inflows for each time period we're analyzing against the amount of money we'll make from our alternate investment in the same period. This is called "discounting" the cash flows and is done using the simple formula P / (1 + i)t

, where P is the amount of the cash flow, i is the discount rate, and t represents time. We don't need to worry about our initial investment yet — we'll use this in the next step.

In our lemonade example, we're analyzing three years, so we'll need to use our formula three times. Calculate your yearly discounted cash flows as follows:

Year One: 50 / (1 + 0.04)1 = 50 / (1 .04) = $48.08

Year Two: 40 / (1 +0.04)2 = 40 / 1.082 = $36.98

Year Three: 30 / (1 +0.04)3 = 30 / 1.125 = $26.67

### 6. Sum your discounted cash flows and subtract your initial investment.

Finally, to get the total NPV for the project, purchase, or investment you're analyzing, you'll need to add up all of your discounted cash flows and subtract your initial investment. The answer you get for this calculation represents your NPV — the net amount of money that your investment will make compared to the alternate investment that gave you the discount rate. In other words, if this number is positive, you'll make more money than if you had spent it on an alternative investment, and if it's negative, you'll make less money. Remember, however, that the accuracy of your calculation hinges on how accurate your estimates for your future cash inflows and your discount rate were.

For our lemonade stand example, the final projected NPV value of the juicer would be:

48.08 + 36.98 + 26.67 - 100 = $11.73

### 7. Determine whether or not to make the investment.

In general, if the NPV for your investment is a positive number, then your investment will be more profitable than putting the money in your alternate investment and you should accept it. If the NPV is negative, your money is better invested elsewhere, and your proposed investment should be rejected. Note that these are generalities — in the real world, much more usually goes into the process of determining whether a certain investment is a wise idea.

In the lemonade stand example, the NPV is $11.71. Since this is positive, we'll probably decide to buy the juicer.

Note that this doesn't mean that the electric juicer only made you $11.71. In fact, this means that the juicer made you the required return rate of 4% annually, plus an additional $11.71 on top of that. In other words, it's $11.71more profitable than your alternate investment.

## Part 2 of 2: Using the NPV Equation

### 1. Compare investment opportunities by their NPV.

Finding the NPVs for multiple investment opportunities allows you to easily compare your investments to determine which are more valuable than others. In general, the investment with the highest NPV is the most valuable because its eventual payout is worth the most in present dollars. Because of this, you'll usually want to pursue the investments with the highest NPVs first (assuming you don't have enough resources to pursue every investment with a positive NPV).

For instance, let's say that we have three investment opportunities. One has an NPV of $150, one has an NPV of $45, and one has an NPV of -$10. In this situation, we'd pursue the $150 investment first because it has the greatest NPV. If we have enough resources, we'd pursue the $45 investment second because it's less valuable. We wouldn't pursue the -$10 investment at all because, with a negative NPV, it will make you less money than investing in an alternative with a similar level of risk.

### 2. Use PV = FV / (1+i)t to find present and future values.

Using a slightly modified form of the standard NPV formula, it's possible to quickly determine how much a present sum of money will be worth in the future (or how much a future sum of money is worth in the present). Simply use the formula PV = FV / (1+i)t, where i is your discount rate, t the number of time periods being analyzed, FV is the future money value, and PV is the present value. If you know i, t, and either FV or PV, it's relatively simple to solve for the final variable.

For instance, let's say we want to know how much $1,000 will be worth in five years. If we know that, at bare minimum, we can get a return rate of 2% on this money, we'll use 0.02 for i, 5 for t, and 1,000 for PV and solve for FV as follows:

1,000 = FV / (1+0.02)5

1,000 = FV / (1.02)5

1,000 = FV / 1.104

1,000 × 1.104 = FV = $1,104

.

### 3. Use the Internal Rate of Return.

The Internal Rate of Return (or IRR) is the discount rate that gives you an NPV of zero. In other words, it's the discount rate at which an alternate investment is exactly as valuable as the one you're analyzing. This can be another useful tool for judging which investments are the wisest. In general, investments with high IRRs are more valuable than ones with low IRRs because this means that the rate of return on an alternate investment would need to be higher to generate the same amount of value.

For example, if we have one possible investment with an IRR of 5% (i = 0.05) and one with an IRR of %10 (i = 0.10), we should take the %10 investment because an alternate investment would have to have a higher return rate to be as valuable — in other words, it's the more profitable investment.

You can find your investment's IRR with the NPV equation by solving for i when NPV = 0, but this requires complex math if you're analyzing more than one time period (t >1). An easier solution is to use a simple online IRR calculator, like this one.

### 4. Research valuation methods for more accurate NPVs.

As noted above, the accuracy of any NPV calculation basically depends on the accuracy of the values you use for your discount rate and your future cash inflows. If your discount rate is close to the actual return rate you can get on your money for an alternate investment of similar risk and your future cash inflows are close to the amounts of money you'll actually make from your investment, your NPV calculation will be right on the money. To get your estimates for these values as close to their corresponding real-world values as possible, you may want to take a look at corporate valuation techniques. Because large corporations often have to make enormous multi-million dollar investments, the methods they use to determine whether the investments are sound or not can be quite sophisticated.

A variety of financial resources are available online that can introduce the somewhat tricky fundamentals of corporate valuation to novices. For instance,this short beginner's guide is a great place to start.

### Tips

- Always remember that there may be other, non-financial factors (such as environmental or social concerns) to consider when making any investment decision.
- NPV can also be calculated using a financial calculator or a set of NPV tables, which are useful if you don't have a calculator to perform the cash flow discounts.