# NPV Analysis

**What is Discount Rate?**

The **discount rate**, in general, is the cost of capital but there might be exceptions to this. So more often than not, we can think of this as the **cost of capital** for companies that are operating in just one country, or companies that have only one division, or manufacture only one specific product or service the cost of capital is a typical discount rate.

**Do we need different discount rates for different countries and different divisions if we operate in many different countries or we have many different divisions? **

And again we’ll deal with that a little bit later on, but for now, we can think of that discount rate as being the cost of capital and whether it is the cost of capital or not, what stands clear is that ** the discount rate is always going to be positively related to risk**. And that basically means that the riskier the investment that we have or the riskier the company for which we’re evaluating this project, then the higher that discount rate is going to be, and everything else equal the lower the net price in value is going to be.

There are two reasons for discounting, and it is important that you keep both of them in mind.

- We typically think of discounting whenever you see a present value expression or a net present value expression and let me open a quick parenthesis here. The only difference between a present value and a
**net present value**is that initial cash flow, the CF 0 that you are seeing in the expression. And remember, some people called it net simply because they take out, or that they actually include the initial investment that you need to make in order to forecast the project. So, if you were only discounting what you expect to get out of this project, then that typically is something that we call the**present value**of all the**cash flows**that we expect to get. But if we actually take into account the initial investment that we need to expect those**cash flows**, then many people would call that the**net present value**. At the end of the day, there is not a whole lot of difference but because the tool is known as**NPV**or**net present value**, that is the name that we are going to use. So press in value unit, press in value for our purposes is indistinguishable in terms that what we really care about is foreseeing all the money that needs to go out of the company and all the money that is expected to come into the company. - Most people focus on discounting because of the passage of time. That is, the further away you get those dollars, then the higher the discount rate that you need to apply. And that is perfectly correct. But there is one other thing that we mentioned before and you do need to keep into account that is a reason for discounting, and that is a risk.

Remember if you look at the expression once again of the **NPV** the further away the cash flow, then the higher it’s going to be the discount rate, because the higher is the power at which we’re raising 1 plus DR 2, 3, 4 all the way to T. But also, the higher risk of the company, the higher the require return, and the higher is going to be the discount rate. Therefore, there are **two reasons for discounting:**

**One is because we are not getting all the cash flows at the same time.****And two, because of risk matters. And the riskier the investment opportunity everything else equal, then the lower will be the NPV.**

So keep that in mind, because there are two, not just one the reason for discounting. As for the rule, the rule is somewhat straightforward. What are we doing when we discount? Well, we are bringing future dollars into current value. So if I discount, adjusting by time and by risk a dollar that I expect to get a year from now, when I discount that I am expressing that dollar in today’s currency. And so now we can compare the money that we need to put down today with the present value of the money I expect to get in the future. So now instead of comparing dollars today and dollars a year from now, which would be like comparing apple and oranges, we are actually comparing apples and apples after the proper discounting. So after discounting all the **cash flow**, what we are doing is expressing all the future cash flows in current and present value. And now when we actually aggregate all these numbers, then we say something very simple. Look,** if the net inflows and outflows of cash out of this company is positive, then we are going to invest in the project**. In other words, the net press in values project, it is positive, go for this project and if the net present value is negative, then do not go for, for this project. But you can only do that after properly adjusting all the expected cash flows by when you are going to get them and by the risk of expecting those cash flows in the future. But having done that, the rule is very simple.

*If you get a positive NPV, you should go ahead with the project. If you get a negative NPV, you should not go ahead with this with this project.*

**What happens if ****you are**** comparing more than one ****project?**

Let’s suppose that your capital is restricted and you have two projects in ways that initially the investment is more or less the same but the expected cash flows are different. The discount rate may be different too, and therefore you end up with different net present values. Well, the rule, as you might imagine, actually extends in a very simple way. And the way that the rule extends is simply that, you know, the higher the net present value, then the more you want to invest in a project. So if you are comparing project a and project b and you can only invest in either one or the other. That’s the standard definition of competing projects, is not that you can invest, invest in both, but you can invest in either one or the other, then you’re going to invest in one, in the one with the higher NPV. And that is another way of saying that, you know, the net of all the money coming in and all the money coming out, properly adjusted by risk and properly adjusted by when you are getting those cash flows; well one has a higher value for the company than the other.

So, the rule for one individual project is very clear, positive or negative NPV, you go or do not go for this project. If you are evaluating competing projects, the higher than that present value the more you want to invest in a project compared to all the others. Thereof project a higher than NPV or project B, then you go for project A. And, and one final thing before, because we’re going to look at an example and then I think it’s going to look a little bit simpler than it really is in real life, is highlighting once again when you look at that formula, the NPV, it doesn’t look all that complicated. If you are evaluating a long-term project, it might be a messy calculation about that seed. You throw the numbers into Excel, and Excel will give you the NPV in the blink of an eye. So, that’s not really the problem. The problem in real life, once again, and that is something important for you to keep in mind, is foreseeing what those cash flows are going to be. That is the key to determining properly what the NPV actually is.