Hi, welcome back to finance for non-finance professionals. In this video, I'd like to talk to you about one of our capital budgeting tools, net present value. Net present value is going to be the standard bearer for a lot of the capital budgeting stuff that we're going to talk about in week two. It's one of our main capital budgeting tools, the net present value pulls right out of the work that we've done in week one about compounding and discounting and using rates of return. The net present value, the basic idea, is to add up the present value of all future cash flows and like a lot of what we did with the annuity and bond examples in week one. We're going to add up that present value, the future stream of all future cash flows, and we're going to weigh that against the initial investment. And we're going to ask a very simple question. Does all the present value of the money coming in over the life of the project, does it outweigh how much money we have to spend in order to do the project? Net present value is just that, it's the net between the present value of these two streams, money going out and money coming in. We're going to ask a present values since whether that NPV is greater than zero. If it's greater than zero, then the costs are less than the benefit. The benefits exceed the costs we should do the project, make the investment, that's our decision rule. Is the NPV bigger than zero, we can write down the formula for NPV very simply as following along very closely with what we did in our discounting in week one. The NPV is equal to the initial cost, which has a minus sign in front of it. Make that bigger. Plus, what? What's coming in off the project is cash flows. Cash flow in period one, discounted one period back plus the cash flow in period two, discounted to periods back. You get the idea. Plus maybe the cash flow in period three, discounted back. Three periods plus maybe more cash flow's coming in. What we're going to do is take that initial cost up here and we're going to weigh that against the present value of all the cash coming in. We're going to net the two. There's a minus sign here. Plus signs on all of these and we're going to ask where they're sort of like a seesaw. Whether all that money going out, ways against all the money coming and ask whether that's bigger than zero or less than zero. You can think of this sort of like seesaw. If I think of that red minus sign over on the left being an initial investment and that stream of green plus sign being the money coming in off the project in the future, we can measure the NPV as the difference between the two, the net between those two streams. Right now you can see the seesaw's kind of balance against during the project because the initial investment is sort of outweighing those positive plus signs. But the larger those plus signs become, or the smaller that red negative becomes, that balance tends to tip and the NPV becomes larger. If that initial investment is much larger the NPV becomes smaller. And you can see that the NPV whether it's bigger than zero or less than zero, depends on sort of that balance between the money going out and the money coming in. Let's work a problem together and compute an NPV impractice. So let's think of this table of cash flows that I've got and at a discount rate of 10%, let's think about whether it's worth it to do the project. So what have I got? I've got here in period 0 I'm going to spend how much? $1,500. And the question now is is it worth it to spend that $1,500? Well, what's coming in off the project. I've got a cash flow of $900 coming in at the end of year 1 and I've got a cash flow of $750 coming in at the end of year 2. And if I just sum up the cash flows, if I just say 15 minus 1,500 plus 900 plus 750, I get an answer of $150. So this project is generating cash. It's profitable. The money coming in is bigger than the money going out. This is a key concept here. The money coming in is bigger than the money going out. 150 is bigger than 0. That's the sum of all the cash flows, but that's without any discounting. We haven't accounted for the fact that I have to wait a year to get the $900, and then wait another year to get the $750. We remember from week one that if you ask me to be patient, you have to pay me. So what do we have to pay? In this case, we have to pay that 10% discount rate. So now if we take those cash flows and discount them, to the present value I take that 900 and discount at 1 period at 10%, I get 818.18. If I take that 750 and discount it 2 periods at 10% I get 619, less than 750. Now, when I sum the present value of all those cash flows, I get -61, which suggests that the project destroys value, it's not worth doing. It's a profitable project, but we don't want to do it. Now why would we ever not want to do a project that's profitable? And the answer is it really all comes down to this 10% up here. What is that 10% tell me? That 10% tells me what the hurdle rate is for the profitability of the project. This project might be profitable but it is not profitable enough to justify a 10% return, and that's what net present value tells me. Net present value discounting those cash flows at 10%, tells me with a 10% return baked in through the discounting does that balance between cash going out and cash coming in. Net together to create value for the firm. In this case, the project was clearly profitable. But it's not profitable enough to get over the 10% discount. In other words, we're not making at least 10% on the project. If our investors require a 10% return to take the risk of that project, we're not going to be able to deliver it to them with a project like this. Let's think about what some of the main drivers are in net present value calculation. First is cash flow. Obviously, more cash is better than less. The second is the timing. The further the cash flow out is out in the future, the harder it gets discounted, the less it sort of counts the further it is out on that seesaw. And the third thing is the discount rate. The higher the discount rate, the further those cash flows get pushed down, lower the NPV. The lower the discount rate, the less discounting, the better the project. Lower discount rates, higher NPV. Higher discount rates, lower NPV. Okay, good. Let's think about this Net Present Value metric. This is really going to be our best, our standard bearer, our benchmark, our best capital budgeting tool. It incorporates the timing of the cash flows, it incorporates the opportunity cost, because that discount rate says, hey, what else could I do with my money? The fact that we're discounting implicitly incorporates the opportunity cost. And it incorporates risk. If the we think the project is a lot riskier, what could we do? We could always jack up the discount rate to reflect that risk, a concept we'll get back to in week four. It's objective, in the sense that if we have good forecast and good discount rates, we can do this in a way that I can explain it to anybody, its arms length that those discount rates and forecast are coming from someone that isn't making the decision, then it's an arms-length metric and it's transparent. We could sit down together with a spreadsheet and go over it together and explain the metric to each other. So net present value weighs the costs and benefits of cash coming in versus cash going out, and gives us an objective, arms-length, and transparent metric for capital budgeting.
