So now let's consider net present value analysis. As you will see, net present value analysis relies upon what we just covered in discounted cash flow analysis. In order to motivate this session, let's think about what chief financial officers, CFOs, actually do out there on a day to day basis. So what we have here is evidence from the US on a survey of Fortune 500 companies, as well as from Australia in a similar survey of the very largest listed companies on the Australian securities exchange. Very simply, CFOs were asked what technique they always or almost always use when evaluating new projects. And what you'll see is that net present value analysis is the second ranked of the project evaluation techniques. So I guess you're wondering, why not start with a discussion of internal rate of return? Well, we get to internal rate of return in our next video. But as you'll see, internal rate of return is simply an alternative way most of the time of looking at net present value analysis. So let's get into it. There are four simple steps associated with the NPV approach to project evaluation. Step 1 is to forecast the expected cash flows that we expect from the project. That is, we need to know both the amount we expect the asset to produce or the project to produce, the net amount. So, inflows minus outflows, as well as very importantly, the timing of that cash flow. The second step is to discount the expected cash flows back to their present values using a discount rate that reflects the time value of money. Recalling the time value of money reflects risk, opportunity cost, and expected inflation. The third step is very simple. Having adjusted future expected cash flows back to their present value today, we aggregate them all, subtracting the initial investment cost. Finally we apply the appropriate decision rule. And as we'll discuss today, the decision rule changes depending upon whether you're dealing with an independent project or if you're ranking mutually exclusive projects. Let's get into it. So let's assume that your firm, Kellogg's say, has to decide whether to invest in a new machine for packaging cereals. Let's call it the Boxolator. So step 1 is to forecast the expected cash flows. So we estimate that the initial cost of the machinery is $2 million. The machinery will last for four years, and you will expect that at the end of each of those years, you'll generate net cash flows, cash inflows minus cash outflows of $800,000. We also estimate that the appropriate discount rate is 10% per annum. So we often use timelines when we're dealing with net present value analysis, just to make sure that we've got all the cash flows down, and we understand exactly when those cash flows are occurring. So here we have -$2 million as a negative cash flow at the start, and then a series of four subsequent payments of $800,000, expected payments that is. We employed discounted cash flow analysis to discount those future cash flows back to their present value today. Then, once we subtract the initial investment outlay, we end up with the NPV, that is the net present value of the project, very simple. So that's what we're doing on this slide. The present value, of course, of $2 million dollars, that we need to spend today, well, there's no time for the time value of money to have an effect. Okay, so the present value of $2 million dollars received today is equal to $2 million dollars. $800,000 that we expect to occur at the end of the first year, in present value terms equates to $727,723 today. In two years' time, of course, the $800,000 in present value terms, that second cash flow, second net cash flow, in two years' time is worth less, $661,157. The third cash flow, $601,052 and the cash flow, the $800,000 net cash flow that we expect to occur in four years' time translates to $546,411 today. Let's just pause for a sec. So intuitively what's going on here? Let's consider that final cash flow. As an investor, I'm indifferent between $546,411 in my hand immediately or the promise of $800,000 in four years' time, assuming the appropriate discount rate is 10% per annum. Or if we switch that around a little bit, if you invest $546,411 today, at 10% per annum for four years, it will accumulate to $800,000. So the next step, the third step, is to add all those cash flows together, because now they are recorded on a consistent, more comparable basis that is in terms of their present value today. So when we do this, we end up with an NPV of $535,893, okay, a positive NPV. What does that figure actually represent? So the final step is to apply the appropriate decision rule. And the decision rule varies depending upon whether we're talking about independent projects or projects that are mutually exclusive. When dealing with independent projects, the acceptance of one project doesn't impact upon the acceptability of any other projects. So, for example, imagine you're Kellogg's and there are two projects that land on your desk or two proposals for projects that land on your desk. Firstly, do we buy retail outlets in Japan? And at the same time, another proposal is to upgrade underperforming factories. Now that we've got four alternatives available to us, we could accept both projects. We could buy retail outlets in Japan, and we could also upgrade our underperforming factories. Our second alternative is to buy our retail outlets in Japan and reject the underperforming factories if they don't meet our minimum benchmark. Third alternative is to upgrade our underperforming factories, forget about the retail outlets in Japan, or we could reject both projects. Independent projects, the acceptance of one doesn't impact upon the acceptability of another. So let's assume we are dealing with an independent project in this case. The decision rule is very straightforward. We accept all projects with a positive NPV. We know this particular project has an NPV of $535,893. That is the sum of the present values of the cash flows promised by the project exceed the initial investment outlay by $535,893. So intuitively what's going on here? So let's assume that prior to this project, the firm had assets in place with a value of $10 million, and $2 million of that was cash. So the firm accepts the new project because it meets the minimum benchmark of zero in net present value terms. And it has a present value of net cash flows of $2,535,893, but it's gotta pay $2 million for the project. So the market value of the firm's assets increase by only $535,893. The take away here is that the NPV reflects the incremental wealth created by accepting a project. So think about that. If you pay $2 million for an asset that's worth only worth $2 million, all you've done is converted cash into an asset. And from an accounting perspective, nothing's happened to the market value of the firm. So the lesson from NPV analysis is we need to be buying something that creates more value than what we pay for it, which makes perfect sense. So what would happen if this was a project that wasn't independent but was mutually exclusive to another project? Let's define what we mean by mutually exclusive projects. This occurs where acceptance of one project necessarily leads to the rejection of the other. The decision rule here is to accept the project with the highest positive NPV. So for example, let's say we had an alternative to the Boxolator. It's called the Packomatic. And let's say that the Packomatic had an NPV of $409,070. Well, because the NPV of the Boxolator exceeds the NPV of the Packomatic, and is positive, we would always go with the Boxolator. So that's the net present value technique. The net present value technique is highly popular, and we know that it's based upon discounted cash flow principles. It results in a calculation of the net change in the value of the firm's assets as a result of taking on the project. There are four simple steps. You forecast cash flows, timing in and out. You discount those cash flows back to present values. You aggregate them, you add them up. You apply the appropriate decision rule. And we understand that the decision rule changes slightly depending on whether we're dealing with mutually exclusive or independent projects.