Hi, in this lecture, I want to demonstrate how to do a Net Present Value Analysis. We'll go through an entire process, step by step, so you'll have a clear idea how it works. This would be a great preparation for the final class project. I'm returning to something we did in module four when we discussed baselines. The peer reviewed assignment looked at replacing the current mix of bulbs in an office with LED, those light emitting diode bulbs. The assignment asked you to create a baseline using electricity bills before the installation of the LED bulbs. So you can measure any energy savings from making that change. Now this is important, because you need to provide evidence about how you proposed changes towards sustainability will benefit your company or organization. The story goes like this, as your first sustainability proposal, you'd like to switch out the old light bulbs. There are mix of incandescent and compact fluorescent bulbs for new low energy LED bulbs. You're going to change out 92 light fixtures. Now, that's a lot of light bulbs. Well, actually, someone's going to be hired to do this. Now here's the baseline information from the electricity bills for the twelve months prior to making this change. So for the past 12 months, the electricity bill showed the following information. Total electricity used, 84,780 kilowatt hours, that's Kwh. The total expense, $9,495. That's 11.2 cents per kilowatt hour. Now, this electricity powers the lights, a small kitchen, some computers, and various other small appliances. The light bulbs and the fixtures currently average about 60 watts, so the lighting system accounts for about 25,500 kilowatt hours of the total. And here's the computation I did to get that. 92 bulbs times 60 watts per bulb times 14 hours a day times 330 days a year. And we divide that by 1000 watts to get kilowatts. Now we're going to buy LED bulbs in bulk. So a 100 watt equivalent is the amount of light they give off. So they're about 1,500 lumens. They're about $8.25 each or about $800 after taxes and delivery. And it'll cost about $200 to have them installed. But their longer useful lives will mean avoiding this installation cost in the future. The entire investment will be about $1,000. Now, the bulbs are rated to last around 10,000 hours. But that's for low usage rates, three hours a day or so. But the office uses them fourteen hours a day, so we think 9,000 to 9,300 hours is a better estimate of life. That means the bulbs will last two years before needing to be replaced. Now, we compute the savings from switching to these low energy LED bulbs. First we compute the monthly baseline, it's very important as a starting point. For the electricity usage was 84,780 KwH, so that is 7,065 KwH per month, or about $791.28 cents per month. This is before the LED bulbs are installed. This is the baseline, we need monthly baseline data because we are going to be comparing it to monthly electricity data after the LEDs are installed. Now, we look at the electricity usage after the installation, here's the table on that data. The light blue cells shows the average usage and expense for electricity. The average for the 3 months is 6470 kilowatt hours per month and the average cost is $724.64 both are below the baseline amounts. So we know there is going to be savings. The question is, are the savings large enough to justify making that $1000 investment? So here are the savings, notice what we do we compare the electricity used after the LED are installed to the baseline. This difference, is the savings, the table shows the savings in terms of both the KiloWatt hours and dollars. So, the monthly savings are 595 kilowatt hours, or about 66, almost $67 a month at 11.2 cents per kilowatt hour. This makes the annual savings almost $800, $799.68 is what I computed which is 12 times the monthly savings. The total kilowatt hours saved each year is 7,140. Now, we're going to receive these savings for two years. We'll set up a table, and we'll compute the net present value of this investment. Year 0 is the moment we make the investment. At that time, we pay the thousand dollars for the bulbs and to have them installed. After one year, we've accumulated savings of $799.68 and at the second end of the second year we have another savings of $799.68. We need to turn these savings Into their present value so we can compare them to the initial investment of a $1000. We need everything in today's dollars. Now we're going to use an interest rate of 6% that will be the discount rate for this problem. Now here I've added two columns to the previous table, the first new column gives the present value factors for 6% at one year and at two years. If we multiply the annual amount by the present value factor, we get the present value of that amount. So the present value of $799.68 to be received one year from today Is $754.42. And the present value of that $799.68 to be received in two years is $711.71. Remember what these present values are. They're the amount that we would need to put in a bank today to have our future amount. So if we deposit $711.71 cents into the bank today, in two years at 6% interest, we're going to have exactly 799 dollars and 68 cents. Now, the Net Present Value. Or the MPV is the sum of these present values. The sum of negative 1,000 per outlay, positive 754.42, the benefits from the first year, in present value terms. Plus 711.71, the benefits of the energy savings from the second year In present value terms. Adding all these up the NPV is $466.13, -1000+754+711. Since the NPV is positive this project makes money for the company, how do we know this? Because the sum of the present value of the benefits Is larger than the investment required to do the project, that is the benefits exceed the cost $1,000 is the cost in this case. We can also compute something called the payback period for this project, this is usually done without computing present values. What we need to do is pay back $1,000 that's the blue horizontal line on the graph The first year, the savings are $799.68 or about $800. So, about 80% of the investment has been repaid after one year. After another three months, 25% of the next year, the savings equal $1000 and that’s our payback period. So, it takes about one in a quarter years 1.25 years to repay the $1000 investment, this is very quick payback. For the rest of the second year, the savings are generating a surplus and it's this surplus if we take the present value of this surplus, that produces our positive NPV of $466 13 cells. So, this is a good project with benefit that exceed it's cost. what else can we say about the project? Well E uses less electricity, we know that saves the bulb 575 kilowatts per month, or 7,140 kilowatts hours per year. So, over those two years, We'll use 14,280 kilowatt hours of less electricity than with the other mix of lightbulbs. The table on this slide shows the average carbon dioxide produced to generator kilowatt hour of electricity. Notice that the numbers vary a lot. That's because states have different mixes of generating capacity. States with a lot of coal-fire generation have higher CO2 Emissions, than those with hydro-powers renewables. Here is the bottom half of the table, look at Oregon and Washington, they have very low emission rates, because most of their electricity comes from hydro-electric generations at the Grand Coulee Dam on the Columbia River. Then look at Vermont only 0.007 pounds of CO2 per kilowatt hour, compared to the national average of 1.363 pounds per kilowatt hour. Vermont uses lots of renewables and until 2014 at a nuclear power plant which is considered carbon-free generation. Now, if ee were in an average state in the U.S. The Energy savings would also reduce carbon emissions, by about 19464 pounds is 14280 kilowatt hours And 1.36 pounds per kilowatt hour. That's about 9.7tonnes of CO2. Now we'll talk about this morning in the next class but Aconomous argued that we should be taxing CO2 emissions for around $25 to $40 a tonne So this omissions reduction could add another $200 to $350 to the benefits from switching to LED lights if a carbon tax is imposed. I hope this lesson has given you a good idea of how we do a net present value analysis. Review this video as you do your final project for the class, it's really going to help, thanks.