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Â The discount rate, as we said before this is in general the, the cost of capital.

Â We're going to discuss a little bit later that there might be exceptions to this.

Â So more often than not, we can think of this as the cost of capital for

Â companies that are operating just one country, or

Â companies that have only one division, or manufacture only one specific product of

Â service the cost of capital is a typical discount rate.

Â Now, there's a question again that we threw a couple times already at the end of

Â last session and at the beginning of this one.

Â What happens if you operate in many different countries or

Â you have many different divisions?

Â Then there's a question to be made here whether we need different discount rates

Â for different countries and different divisions.

Â And again we'll deal with that a little bit later on,

Â but for now we can think of that discount rate as being the cost of capital.

Â And whether it is the cap, the cost of capital or not what, what stands clear

Â is that, that discount rate is always going to be positively related to risk.

Â And that basically means that the riskier the investment that we have or

Â the riskier the company for which we're evaluating this project,

Â then the higher that discount rate is going to be, and

Â everything else equal the lower the net price in value is going to be.

Â 1:26

The idea of discounting, well we already discussed this.

Â There's two reasons for discounting, and

Â it's important that you keep both of them in mind.

Â We typically think of discounting whenever you see a present value expression or

Â a net present value expression, and let me open a quick parenthesis here.

Â The only difference between a present value and a net present value is

Â that initial cash flow, the CF 0 that you're seeing in the expression.

Â And remember, some people called it net simply because they take out, or

Â that they actually include,

Â the initial investment that you need to make in order to forecast the project.

Â So, you know, if you were only discounting what you expect to get out of

Â this project, then that typically is something that we

Â call the present value of all the cash flows that we expect to get.

Â But if we actually take into account the initial investment that we need to expect

Â those cash flows, then many people would call that the net present value.

Â At the end of the day, there's not a whole lot of difference but

Â because the tool is typically known as NPV or

Â net present value, that's the name that that we're going to use.

Â So press in val unit, press in value for our purposes is indistinguishable in

Â terms that what we really care about is foreseeing all the money that needs to

Â go out of the company and all the money that is expected to come into the company.

Â But back now to the issue of discounting.

Â Most people focus on discounting because of the passage of time.

Â That is, the further away you get those dollars,

Â then the higher the discount rate that you need to apply.

Â And that is perfectly correct.

Â But there's one other thing that we mentioned before and you do need to

Â keep into account that is a reason for discounting, and that is risk, right.

Â Remember if you look at the expression once again of the NPV the higher excuse me

Â the further away the cash flow, then the higher it's going to be the discount rate,

Â because the higher is the power at which we're raising 1 plus DR 2, 3,

Â 4 all the way to T.

Â But also, the higher risk of the company,

Â the higher the require return, and the higher is going to be the discount rate.

Â So there's two reasons, not just one, two reasons for discounting.

Â One, is because we're not getting all the cash flows at the same time.

Â And two, because risk matters.

Â And the riskier the investment opportunity everything else equal,

Â then the lower will be the NPV.

Â So keep that in mind,

Â because there are two, not just one, reason for, for discounting.

Â As for the rule, the rule is kind of straightforward.

Â What are we doing when we discount?

Â Well, we're basically bringing future dollars into current value.

Â So if I discount, properly discount, adjusting by time and

Â by risk a dollar that I expect to get a year from now, when I

Â discount that I'm basically I'm expressing that dollar in today's currency.

Â And so now we can compare the money that we need to

Â put down today with the present value of the money I expect to get in the future.

Â So now instead of comparing dollars today and

Â dollars a year from now, which would be like comparing apple and

Â oranges, we're actually comparing apples and apples after the proper discounting.

Â So after discounting all the cash flow, what we're doing is

Â expressing all the future cash flows in current and present value.

Â And now when we actually aggregate all these numbers,

Â then we say something very simple.

Â Look, if the net inflows and outflows of cash out of this company is positive,

Â then we're going to invest in the project.

Â In other words, the net press in values project, it, it's positive, go for

Â this project and if the net present value is negative, then do not go for, for

Â this project.

Â But you can only do that after properly adjusting all the expected cash

Â flows by when are you going to get them and

Â by the risk of expecting those cash flows in the future.

Â But having done that, the rule is very simple.

Â If you get a positive NPV, you should go ahead with the project.

Â If you get a negative NPV you should not go ahead with this with this project.

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One more thing on this.

Â What happens if you're comparing more than one project?

Â Lets suppose that your capital is restricted and

Â you have two projects in ways that initially the investment is more or

Â less the same but the expected cash flows are different.

Â The discount rate may be different too, and

Â therefore you end up with different net present values.

Â Well, the rule, as you might imagine, actually extends in a very simple way.

Â And the way that the rule extends is simply that, you know,

Â the higher the net present value, then the more you want to invest in a project.

Â So if you're comparing project a and

Â project b and you can only invest in either one or the other.

Â That's the, the, the standard definition of competing projects,

Â is not that you can invest, invest in both, but you can invest in either one or

Â the other, then you're going to invest in one, in the one with the higher MPV.

Â And that is another way of saying that, you know, the net of all the money

Â coming in and all the money coming out, properly adjusted by risk and

Â properly adjusted by when you're getting those cash flows,

Â well one has a higher value for the company than the other.

Â So, the rule for one individual project is very clear, positive or

Â negative NPV, you go or don't go for this project.

Â If you're evaluating competing projects, the higher than that

Â present value the more you want to invest in a project compared to all the others.

Â So, NPV there of project A higher than NPV or project B, then you go for project A.

Â And, and one final thing before, because we're going to look at an example and

Â then I think it's going to look a little bit simpler than it really is in

Â real life, is highlighting once again when you look at that formula, the NPV,

Â it doesn't look all that complicated.

Â If you're evaluating a long-term project it might be a messy calculation

Â about that seed.

Â You throw the numbers into Excel, and

Â Excel will give you the NPV in the blink of an eye.

Â So, so that's not really the problem.

Â The problem in real life, once again, and that is something important for

Â you to keep in mind, is foreseeing what those cash flows are going to be.

Â That is the key of determining properly what the NPV actually is.

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Â