Hi. This is the last video on financial analysis. So far we've learned about discounting and computing the net present value, the NPV of a project. And I've stressed that the NPV is the best way to evaluate a project's financial impact on a company, but there are a few other approaches. And we'll talk about two in this video and do one more practice problem. I hope this gives you enough basic skills so that with some help from your colleagues and your company, probably in the accounting or the finance departments, you can complete a financial analysis for your projects that you can put into your proposal. First, we look at a metric called the ROI or Return on Investment. There's lots of ways to compute an ROI; I'll show you one that makes the most sense for most sustainability investments. It's really pretty simple. You divide the annual cash savings of your change by the amount invested. Now, suppose the cost is $1,400 to replace all the bulbs in your office with new, low-watt LED bulbs. The $1,400 is the investment. Now, over the first year, the energy savings is estimated to be $750. We expect the savings to continue for several years. The ROI for the first year and subsequent years is 750 divided by 1,400 - or 53.6 percent. Now this is an incredibly high return. To give you some perspective, government bonds return three or four percent a year and on average, looking at the last 70 years, the stock market has returned about nine or 10 percent. So 53 percent is enormous. With such a large ROI, it's easy to argue that the investment should be made. If the ROI was lower, but still higher than the return available from other investments, the same argument could be made that this is a good project to pursue. In fact, you can think of returns on other projects or investments, like the 10 percent stock market return, as the hurdle rate that your proposed projects need to exceed to be acceptable. A couple of things to notice about the ROI. It doesn't consider the time value of money. Now maybe for one year that doesn't matter, but for three or four or five years, it does. That's why we like NPV, net present value, better. It recognizes that money has a time value or that there are opportunity costs. The other potential problem with ROI is subtle and usually doesn't affect energy savings investments too much. The issue is that ROI doesn't have any way to include the risk or the variability of the savings in the calculation. If two investments have the same average savings and the same investment, then they have the same ROI. But if one is uncertain and the other is stable, most people prefer the stable or the safe investment. We need to be able to distinguish between safe and risky investments. With net present value, we can increase the discount rate to represent added risk. The mechanics of doing this adjustment are beyond this introduction, but know that NPV does allow for the recognition of risk or uncertainty. Now the other investment criteria you'll see a lot and that you probably need to include in your analysis is the payback period. The payback period is the number of years it takes for the savings to repay the initial investment. Using the numbers from the first example - a $1,400 investment and a $750 annual savings - the payback period would be a little less than two years. And we can be more precise. The first year the savings repays $750 of the $1,400 investment; that leaves $650 to be repaid during the second year. If the savings arrive evenly over the year, then it takes about 87 percent of the year to repay the $650. We find that by dividing the 650 - the amount that still needs to be repaid - by the 750 - the annual savings. So it takes 1.87 years to repay the initial investment. People like quick payback periods like this one. Like ROI, there are some issues with the payback period as a way to decide on investments. First, it ignores any savings after the payback period. Imagine an investment that lasts just two years and then ends. Now imagine a second investment that goes on for five years. If the short-lived project has a shorter payback than the second, the long-lived project, the investment the short-term investment will be chosen even though the second project would have produced more savings or savings for many more years. Payback only looks at a fraction of the total benefits of an investment, which can result in bad choices being made sometimes. The other problem with payback period is there is no good acceptance criteria. Should we invest in projects if the payback is two years or three years? Remember how with net present value we accepted projects if the NPV was positive, because that meant that the investment increased the value of the company. For ROI, if the rate is higher than the rate of return that other opportunities pay, then we accept the proposal. But with payback, there isn't any logical way to identify which projects we should accept and which we should reject. This is a serious problem. But despite this giant flaw, people like to see the payback measure. So put it in your proposal along with the NPV and the ROI and that should give decision-makers plenty of information to think about. Let's do one more practice problem and we'll compute the NPV, the ROI and the payback for a sustainability change. The furnace in our house is 25 years old. When it was new, it was about 85 percent efficient. Now it's closer to 75 percent efficient, probably. New furnaces are 95 percent efficient. If we replace the furnace, the new furnace will cost us about $1,100 after a rebate from our utility company. We estimate annual savings about $180 a year, given low natural gas prices right now. Here's the information about the cost and savings. In the next slide. I've created a table with the data, assuming a 15 year life for the investment. Now we had our other furnace for a lo longer than 15 years, so it's probably an understatement about the life of the new furnace. But if the NPV is positive using 15 years, we know that it will be positive for longer periods of time because we'd be adding more of the savings to the total. If the NPV isn't positive using 15 years, we can look into what a more appropriate life for the furnace is. Now we compute the NPV, the ROI and the payback period. The NPV is $768 using a five percent discount rate. That means this is a good investment. The ROI is 180 divided by 1,100, which is 16.36 percent. This is a pretty high rate compared with other investments, so supports the NPV result. To compute the payback period. I'll divide 1,100 by 180 to see how many years it will take 180 to equal 1,100. We get 6.11 years, or about six years and between one and two months. Now is this a long payback period or a short payback period? Well, it's really hard to know. Maybe the best way to think about payback is relative to the life of the project. The six year payback leaves nine years of additional benefits that we'll receive. That sounds pretty good, but this isn't a rational decision criteria. Since both the NPV and the ROI imply accepting the investment, it looks good. One last thing we need to look at; the environmental benefits of making the change. Now, looking at our gas bill, we pay about 55 cents per hundred cubic feet of natural gas. 100 cubic feet is abbreviated CCF. This includes delivery cost and upstream charges and some other costs. If we save $180 per year, that means we save 322 hundred cubic feet of gas each year. We get that by dividing the 180 by the .5582. According to the EPA, natural gas emits 117.1 pounds of CO2 per thousand cubic feet. That's 1,000 cubic feet. Now, 1,000 cubic feet is abbreviated MCF. And we can convert CCF to MCF by dividing by 10. So 322 CCF is equal to 32.2 MCF. Each MCF, 1,000 cubic feet, emits 117 pounds. So 32.2 MCF emits 3,776 pounds of CO2. Almost two tons of carbon dioxide are avoided every year by upgrading the furnace. The social cost of carbon dioxide is estimated to be about $40 per ton. If a carbon tax were ever implemented, the additional savings from reducing our natural gas use would be about $75, as shown on the slide I'm putting up right now. We've done another NPV problem, but we included a return on investment and payback and then we computed the potential carbon tax savings as well. I hope you're beginning to be comfortable doing these types of analyses. Thanks.