# What is NPV and How Does It Work?

The Net Present Value, abbreviated simply as NPV, is one of the most important concepts in finance and commercial real estate. Compared to the Internal Rate of Return, the concept of NPV is easy to understand, yet it’s also still commonly misunderstood by many commercial real estate and finance professionals. In this article we’ll discuss the concept NPV in depth and leave you with a solid understanding of the logic and intuition behind the Net Present Value.

## What Is NPV?

First of all, what exactly is NPV? Net present value (NPV) is defined as an investment measure that tells an investor whether the investment is achieving a target yield at a given initial investment. NPV also quantifies the adjustment to the initial investment needed to achieve the target yield assuming everything else remains the same. Formally, the net present value is simply the summation of cash flows (C) for each period (n) in the holding period (N), discounted at the investor’s required rate of return (r):

If all of this math scares you don’t worry, we’ll walk through some detailed examples next that will leave you with a solid intuition and understanding of NPV.

## NPV Intuition

What’s the intuition behind NPV? Here’s a simple way to think about the net present value:

### NPV = Present Value – Cost

The net present value is simply the present value of all future cash flows, discounted back to the present time at the appropriate discount rate, less the cost to acquire those cash flows. In other words NPV is simply value minus cost.

What’s does NPV mean? When NPV is viewed as value minus cost, then it’s easy to see that the NPV tells you whether or not what you are buying is worth more or less than what you’re paying.

There are only 3 possible categories NPV will fall into:

• Positive NPV. If NPV is positive then it means you’re paying less than what the asset is worth.
• Negative NPV. If NPV is negative then it means that you’re paying more than what the asset is worth.
• Zero NPV. If NPV is zero then it means you’re paying exactly what the asset is worth.

## NPV Examples

Let’s take a look at a few examples to see exactly how to calculate and interpret the net present value or the NPV. First of all, let’s take a look at a sample set of cash flows:

The above set of cash flows shows an upfront investment of -\$100,000 (this is a negative number because it’s money leaving our pocket) that returns \$10,000 at the end of each year for 5 years, and then at the end of year 5 the original \$100,000 investment is also returned. As shown, when an internal rate of return or IRR is calculated on this set of cash flows, we get 10%. That means that the percentage rate earned on each dollar invested for each period it is invested is exactly 10%. So, what about the NPV, the other commonly used discounted cash flow measure?

As shown in the diagram above, when we calculate an NPV on this set of cash flows at an 8% discount rate, we end up with a positive NPV of \$7,985. As clearly demostrated above, NPV is calculated by discounting each of the cash flows back to the present time at the 8% discount rate. Then, each of these present values are added up and netted against the initial investment of \$100,000 in order to find the net present value. This is exactly how NPV is calculated, step by step.

Let’s take another example of calculating NPV using the same set of cash flows, except with a different discount rate.

In this second example the same exact process is followed in order to calculate the net present value. However, this time we are using a 12% discount rate instead of an 8% discount rate. As shown above, each future cash flow is discounted back to the present time at a 12% discount rate. Then each of these present values are added up and netted against the original investment amount of \$100,000, resulting in an NPV of -\$7,210.

Notice that when the discount rate is lower than the internal rate of return, our NPV is positive (as shown in the first example above). Conversely, when the discount rate is higher than the IRR, the resulting net present value is negative (as shown in the second example above). Intuitively this makes sense if you think about the discount rate as your required rate of return. The IRR tells us what “return” we get based on a certain set of cash flows. If our required rate of return (discount rate) is higher than the IRR, then that means we want to earn more on the set of cash flows that we actually earn (the IRR). So, in order for us to earn more on a given set of cash flows we have to pay less to acquire those cash flows. How much less? Exactly the amount of the net present value.

Let’s take a final example to see what happens when the discount rate is exactly equal to the IRR:

As shown above, when the discount rate is exactly equal to the IRR, then the resulting NPV is exactly equal to zero. Why is this? Well, intuitively if you think about the IRR as the actual return you get from a given set of cash flows, and the discount rate as what you want the return to be from the same set of cash flows, then when these are both equal, NPV will be zero. This means what you want to earn on an investment (discount rate) is exactly equal to what the investment’s cash flows actually yield (IRR), and therefore value is equal to cost.

## NPV and The Discount Rate

In order to fully understand how to calculate the net present value you’ll first need a solid understanding of the time value of money. Assuming you’re comfortable with the time value of money and specifically with calculating present values, then you’ll be quick to recognize that the discount rate used has a big impact on determining the present value of future cash flows.

So, what discount rate should you use when calculating the net present value? One easy way to think about the discount rate is that it’s simply the required rate of return that you want to achieve. The discount rate is what you want, the IRR is what you get, and the NPV quantifies the difference. Check out our article on the discount rate for a much more in depth look at this concept.

## Conclusion

What is NPV? In this article we discussed what NPV is, detailed how it’s calculated as well as the intuition behind what it means. We also covered some common misconceptions and mistakes and finally we tied it all together with some relevant examples. Once you look at how NPV works, step-by-step, it’s easy to see that NPV is simply value minus cost.