In this video, we assess three more tools very useful for assessing renewable energy projects. Discounted cashflow, net present value, and internal rate of return. These are widely used in important project financial metrics. Again, they're discounted cashflows, DCF, net present value, NPV, and internal rate of return, IRR. You'll see these over and over again whenever a financial analysis is done of a project. First off, what's a cashflow and what's a discounted cash flow? A cash flow is at time series sequence of cash inflows and outflows from a project. Here is the cashflow for the 20 year annuity we looked at in the previous video. One thousand dollars paid out every year over 20 years, starting in year 1. A discounted cash flow is a cash flow in each period which is discounted back to today to determine its present value. This is what it looks like. You can see that in year 1, we've discounted the $1,000 of debt because it's being paid out a year from now. In year 20 is discounted a great deal because it's being paid out in 20 years, every year in-between increases the discounted value of the cash flow in the present. When we add these all up, that gives us our discounted cashflow value. Net present value is very similar to discounted cashflow. It is a present value sum of all project cash flows. Net present value calculations include the present value of inflows minus the present value of the outflows. The calculations for discounted cashflows and NPV are the same. Here's our example. Solar PV project cost $10,000. We save $1,000 per year in power costs but now we're going to include $500 maintenance every five years. Plus we're going to have $1,000 salvage value in year 20, meaning that we can sell off the old panels and equipment for $1,000 in year 20, they still have some value. If we run the numbers, the net profit is $9,500, $20,000 in revenues, another $1,000 in salvage minus the initial cost of $10,000 minus $1,500 in maintenance over the years, that gives us a net profit of $9,500. In contrast, the NPV of these cashflows, if you do the math, is $1,900 at a five percent discount rate. That is the difference between net profit and NPV. Net profit is just adding up the revenues and the costs. NPV takes the discounted cashflows and brings them back to the present. Here's the mathematical representation for NPV. Here's our problem statement that we just looked at and here we're going to assign r as the interest rate as usual, CF_n, that's the cashflow in period n. The net cash flow in period n it's the revenues minus expenses. The discounted cashflow is the net cash flow in year n. We use our discounting methods in order to bring that cost back to the present and n is the final year of the project that is, in this case, 20 years. Here's the calculation for net present value. We take the sum of all of the cashflows, the absolute value of the cashflows in n divided by one plus the interest rate to the nth power for each of those cashflows. Now, if you're not familiar with this summation sign, the big Sigma, that's just mathematical laziness or shorthand to represent that in this case, 20 different ratios that needed to be added together. If you're not familiar with this, is just shorthand for what would be a very long addition statement and [inaudible] of additions if we wrote it all out. In summary, it's the net present value of all those discounted cashflows, positive and the negative. When you write it out term by term, we'd have 20 different additions to do from the first, the 0th year start to the very last year, the 20th. Now happily, we do not need to do these NPV calculations by hand. Instead, we can use a spreadsheet. NPV calculations are shown here. This is our sample problem we've been looking at. Then here's the spreadsheet that summarizes the problem. We have in the first column, the years from 0-20. In the second column we see the revenues starting in year 1 after the project is built of a $1,000 per year or $21,000 in aggregate. In the third column, we have the expenses which area $10,000 in year zero. That's the cost of getting the project built. Then we have expenses in year 5, 10, and 15, and $500 in each of those years for maintenance. If we add up each year, we get the net cash flows, $10,000 expense in year 1, and then $1,000 in every year after that, except for years 5, 10, and 15, when we only have revenues or net revenues of 500 because of the maintenance expenses. In year 20 we have net revenues of $2,000 because we get an extra $1,000 for salvage. We add all those up, we get $9,500 net profit. Now, in the last row or last column rather, if we take the present value of each of the net cashflows for each year, we get that column. It's a full $10,000 in year zero, no discounting and in the 20th year our $2,000 in net cash flow comes back to the present as $754. Add those up and we get the $1,900 NPV. The NPV always will be less than the net cash flow if there's any discounting at all. How do we interpret NPV values? What do they actually mean? NPV greater than zero means the project earns discounted profits greater than alternatives. It means that we are clearing our discount rate or earning money beyond what we might earn elsewhere beyond that discount rate. The NPV equals zero, that means that project earns discounted profits at exactly the discount rate or equal to alternatives that did establish the discount rate. If NPV is less than zero, the project clearance discounted profits that are less than alternatives. It means that we probably have alternatives that may be better than this particular project if the discount rate reflects what we think we could earn from those other projects. But note that the NPV less than zero does not imply that net profits are zero. It just means that this particular project will not earn profits that are an excess of the discount rate or an excess of alternative projects that we've identified. Comparing projects, we can choose the project with the greatest NPV, all else equal. I want to say something about all else equal. We're looking now at financial measurements of projects, that's only one of many different criteria that we want to use to evaluate a project. It's not just about the money. There may be ecological reasons to choose a project, environmental reasons. There may be risk reasons to choose a project. Some projects may align better with the strategy of our firm or our own value system. Financing in the financial metrics that we use to evaluate projects are only financial. They're only a piece of the decisions do. They are not everything. Let's not at anytime imply that the finances dominate everything else. That's just not the case. This brings us to internal rate of return, IRR. The internal rate of return is the annualized compounded rate of return on a project. That's quite a mouthful. What does it meaning? IRR is the discount rate for which NPV equals zero or another way of saying it, it's the project break-even discount rate, the discount rate that gives us an NPV equal to zero. An example, suppose the project IRR, internal rate of return is 15 percent. Then almost by definition, the project NPV is equal to zero using net 15 percent discount rate. For project discount rates r, if IRR is less than r, then the NPV will be greater than zero. That's good. It means the project is attractive compared to other projects we're considering. If the IRR is equal to r, then the NPV equals zero and that's okay. It means the project is equivalent to other projects we're considering. If the IRR is less than the discount rate r, then NPV is less than zero, which is less attractive. It means this particular project is less attractive financially than others we may be considering. Here's the formula to calculate IRR. It's equal to the NPV formula when instead of the discount rate r, we use IRR, which is what we're trying to find. Now, you can't find this directly. You have to use trial and error. This IRR is the number that makes this statement true. We need to find that number IRR that makes this statement NPV equals zero true. That's not easy to do by hand, certainly difficult. Take a lot of time, but it's not hard to do with Excel function IRR. We'll take a look at that in a little bit. We have either two choices. We can use trial and error, which is tedious or use Excel function or some perhaps a financial calculator to figure out what IRR is. Well, we've covered a lot of ground in this video with a lot of financial calculations. If we had to do these calculations by hand, it would be tedious and time-consuming to say the least. But in this modern world of computers and spreadsheets, it's far easier. Let's take a look at some Excel spreadsheet financial functions that will help us out here. If we want to calculate the present value of an annuity, there is the present value function. If we want to calculate the future value of an annuity, we have the future value Excel function. If we want to calculate the NPV of a stream of cash flows, we have the NPV function, but understand that this function starts in period 1, not period 0. We have to make sure we add in any expenses or costs of that are incurred in period 0. It's a bug, not a feature. Then finally, IRR calculates the internal rate of return for a cash-flow stream. It makes it far easier to find and quick to find than trying to do it by trial and error. In addition, in the resources for this video, there is a summary of all the financial formulas that we've looked at and some additional formulas as well. That's there for your reference as you choose to use it. In summary, we've looked at discounted cash flows, net present value, and internal rate of return. These are important and widely used project financial metrics. Discounted cash flows we've learned, DCF, that's the present value of a cash flow stream. Net present value, or NPV, is the present value of all project cash revenues and cash expenses. Finally, internal rate of return, or IRR, is the effective rate of return or discount rate of a project. For project has a 15 percent or has an IRR of 15 percent, that means we're earning 15 percent annually on the money we have invested. That's a pretty interesting measure. In the next video, we'll be taking a look of how these measures can be applied in more realistic settings. We'll see you there.
