If you work in finance you will inevitably spend time calculating and reviewing the return on different investments. Some of the most common methods for calculating these valuations are net present value (NPV) and Internal Rate of Return (IRR).

If you learn better through video check out our NPV Explanation video here:

If you went to college or university, you probably learned what NPV and IRR were and you may have even memorized the formula. If it’s been awhile since you have last thought through these calculations we are here to help dust off the cobwebs and give you a bit of a refresher. If it is new to you, we hope our lesson in plain English will help you understand quickly and be able to start to use these methods of measurement right away.

In order to understand Net Present Value and Internal Rate of Return (NPV and IRR), there are a few foundational concepts that you will need to understand first. So, let’s dig into “Time Value of Money”, “Discounted Cash Flows”, and “Discount Rates” or “Hurdle Rates”

**First…. The concept of “time value of money**

Time value of money is the concept that having $100 today is worth more than having $100 in one year or some other time in the future. The reason is, if you have $100 today you can put it to work for you and add some sort of return on that investment. For an individual that might mean, depositing your $100 in a high-yield savings account earning 5% interest rate, buying stocks or bonds, or some other investment like real estate or starting a business.

An example:

if you have $100 today and you put it into a savings account and earn $5 of interest over the next year, you would have $105 in one year vs. $100 today. Your present value is $100 and your future value is $105. Let’s demonstrate with two people…

Person X: We give Person X $100 today. Person X invests that as mentioned in the example above and earns $5 of interest. *Exactly one year from now, Person X has $105.*

Person Y: We give Person Y $0 today. But one year from now we give Person Y $100. *Exactly one year from now, Person Y has $100. *

**To recap, the concept of time value of money says that getting $1 now is worth more than getting $1 sometime in the future. **

**Second…. The Discounted Cash Flow Model**

A technical definition of Discounted Cash Flow Model (sometimes abbreviated as a “DCF”) is: A method of analysis to determine the value of a project, investment, or company using expected future cash flows discounted back (using cost of capital or a hurdle rate) to get to a present value.

A Net Present Value calculation is effectively a Discounted Cash Flow model but also takes into account the investment or overhead cost

A simpler explanation is: You take the cash that you think an project/investment/company will generate over its life and try to see what it’s worth today.

Discounted cash flow models are useful to help businesses (or even individuals) make decisions. Here are some examples of when it is commonly used for:

- To understand what the value of a company or product line is if you are working an acquisition or divestiture
- To value an initiative or project at a company
- To understand the value of an investment
- To value stocks / bond

**Third… Discount Rate**

The discount rate is a rate used to determine the __current__ value of __future__ cash flows (AKA the NPV or net present value). Sometimes you hear a discount rate referred to as a “hurdle rate”. A discount rate could represent some sort of opportunity cost or risk rating. The discount rate is OFTEN based on a company’s *weighted-average cost of capital (WACC… click HERE for the definition)*. The discount rate is a critical component of a discounted cash flow model (like NPV).

Put more simply, the discount rate is usually either the cost a person or company incurs to borrow money OR the rate of return a person or company expects to earn. The discount rate will be specific to the person or company who is evaluating a project

The discount rate can vary based on when you are evaluating a project, the time horizon of that project, who is evaluating the project.

Ok. We have covered the building blocks of NPV and IRR, now we can get into two of the big methods for understanding return on investment. Let’s start with NPV…

__Net Present Value (NPV)__

__Net Present Value (NPV)__

A technical definition of Net Present Value (NPV) is a “time value of money” metric that uses a discounted cash flow approach to evaluate projects / investments.

Put more simply, NPV tells you what the present value of an investment or project (specifically the cash flows) is at a required rate of return (discount rate or hurdle rate).

__When to use NPV?__

NPV is used to evaluate projects or investments to tell you what your return will be. Companies use NPV to evaluate or compare projects, to make “go” or “no go” decisions. It can be used for something large like an acquisition or something smaller like whether or not to buy a new machine or piece of software. You don’t really have to know how to calculate it by hand… just learn the excel function and you are set! You do, however, need to UNDERSTAND it in order to be dangerous enough to use it and interpret it!

__How does NPV it work?__

A discounted cash flow model takes the concept to time value of money and creates a model to tell you what those future cash flows are worth today. What the NPV metric does is it looks at a landscape of cash inflows and outflows over the life of the investment (in intervals of months, quarters, or years), it then “discounts” those cash flows back to today so you know what all of those __future__ cash flows are worth __today__ (AKA the PRESENT… hence the term “net PRESENT value”).

__A simple example of Net Present Value (NPV)__

__A simple example of Net Present Value (NPV)__

There are essentially three steps to calculating an NPV (and the first two can be done in either order)

Step 1 – decide on (or calculate) a discount rate

Step 2 – estimate or map out the cash inflows and outflows

Step 3 – Calculate NPV

__Step 1 – Decide on (or calculate) a discount rate__

A company will often look to use a “cost of capital” or a “weighted-average cost of capital” (or WACC) as their discount rate. WACC is the average cost that the company has to pay to acquire the capital to use in the investment. So, if you are a company that manufactures chairs and you would need to get a loan from your local bank at a 8% interest rate in order to a do project, you might use 8% as your discount rate. For larger companies the WACC is going to be made up of various types of funding (commercial paper, equity, debt, etc…) If you work at a larger corporation you should understand what your company’s WACC is and how to that in your modeling.

*For this example, let’s use 8% as our discount rate.*

The higher the discount rate, the lower the NPV. One way to think through this fact is to understand that if your WACC is high, that means it costs your company a lot to get capital to fund a project… which makes the returns on a project less attractive.

__Step 2 – Define the series of cash flows __

We will start with a very simple example then move onto something a little more detailed. For this first project we are going to assume each year as an even cash flow of $1,000.

__Step 3 – Calculate the NPV__

This is where we use our friend Microsoft Excel to help us do the calculation extremely quickly! If you look at the image below you can see the template shows your $1,000 for each of 7 years and it lists out the 8% discount rate that we determined in Step 1. In Microsoft Excel the formula for NPV is: “NPV(rate,value1,value2,…)”

For that formula here is what those fields mean:

Rate = discount rate

Value1, Value 2, … = each period’s cash flow

Once you plug that into the .xls (If you look in row 12 in the image you can see the exact formula used) it .xls will give the answer that the value of those $1,000 cash flows, over the 7 years, discounted at 1.08% is $5,206.

*(While I don’t think you will ever need to calculate this by hand, I do think it is worth understanding how the formula works… to get to present value you simply take 1 / (1 + discount rate)^(# of years)… so for year one you use 1, for year 2 you use ^2, year 3 you use ^3, etc… for DCF you do that for each year, then sum them up)*

__A slightly more complicated NPV example__

__A slightly more complicated NPV example__

Step 1 – decide on (or calculate) a discount rate

Step 2 – estimate or map out the cash inflows and outflows

Step 3 – Calculate NPV

__Step 1 – Decide on (or calculate) a discount rate__

We talked above about various ways a company might get to a discount rate (include WACC) but for this example, let’s calculate this project with a 12% discount rate.

__Step 2 – Define the series of cash flows __

When defining a series of cash flows you will usually have something more complicated than the simple example above where there is no initial investment and there is set cash flow each year. There are often items like:

- Initial investment
- Value each year
- Terminal value

For this example, let’s set those parameters

** Initial investment** = ($294,500) This number is a cash outflow and it is the amount that is required to initially invest in the project

** Cash values by year** = (see screen shot below)

The numbers starting in column D (year 1) show the expected cash inflows for each year in the future.

** Terminal value** = $330,000 You may have noticed in year 7 there is a spike in the cash inflow. A terminal value is a value in the last year of a discounted cash flow model that represents either (1) what an exit value would be (i.e. what the business / equipment could be sold for) or (2) you could use the present value of all the rest of the future cash flows. (one way of doing this is the perpetuity growth formula… feel free to google how to calculate that)

The story…

In this example, we will say a company which owns a number of laundromats is looking to acquire another location for their portfolio by buying a laundromat in a neighboring city. The company believes they can buy that existing laundromat for $294,500 (This would be their Initial investment found in cell C4). They then projected out future sales based on the information they know about the past cash flows of the laundromat and the growth rates they hope for going forward (these are in columns D:J or “years” 1 – 7). As mentioned above, If you look in year 7 you will see a much bigger value, that is the “terminal value”. In this example they think they could sell the laundromat in 7 years for 3x cash flows (year 6 cash flow is $110,000 * 3 = $330,000).

__Step 3 – Calculate the NPV__

We again plug everything into .xls using the formula below…

Rate = discount rate

Value1, Value 2, … = each period’s cash flow

*while this example has a few additional complexities, the formula is the same. You just happen to have a negative cash flow at the beginning and a big bump for terminal value at the end.

Once you plug that into the .xls (If you look in row 12 in the image you can see the exact formula used) you will learn this project clearly has a great return. Despite an investment of almost $300k, the present value of the future cash flows is just under $200k even with a discount rate of 12%!

__Net Present Values … Pros & Cons, some thoughts, and a summary__

__Net Present Values … Pros & Cons, some thoughts, and a summary__

#### NPV is not a perfect tool. There are a few drawbacks.

- You need a good discount rate / hurdle rate in order for NPV to make sense
- The formula only allows for one discount rate over the life of the investment. For some companies this could change drastically over time, especially in a start-up
- You have to forecast (i.e. educated guess) what future cash inflows/outflows will be
- It can be difficult to compare projects with different lives or different sizes. If you have one project that is a multimillion-dollar projects vs. one that is only a few hundred thousand, naturally the multi-million dollar project will have a higher return in NPV dollars, but it might not be a better return on your investment.

#### A few things to remember and some interesting points

- The higher the NPV the better a project or investment is to undertake
- The higher the discount rate, the lower the NPV
- An NPV of zero does not mean there is no value on the project, rather it means the return of the project or investment is equal to what you used for your discount rate
- Cash flows in early years matter more than cash flows in out years
- No decision should be made in a vacuum. One NPV analysis should not be the determining factor in decision making. A company needs to evaluate if a project or investment is consistent with its companies goals and objectives, they need to compare against other projects / investments, and a host of other factors that should be considered

Regardless of some of the disadvantageous associated with it, NPV is a great tool to use to understand the value of a project, company, or investment. In general, if you have a discount rate that makes sense for you or your business, then any project with a positive NPV is probably worth doing (assuming you have cash or can secure funding). NPV gives a good measure of the current value of a project, it factors in risks and trade-offs through the discount rate, and it captures time value of money. NPV is one of the key tools in the tool belt of a finance person. It is something every financial analyst should know how to do inside and out.