Hi, welcome to the second video lecture on Financial Analysis. In the first lecture, we developed a general formula for computing the future value from a present value. Here's what that general formula looks like. If we assign today the number zero, then we move forward and give one year from today the number one and two years from today the number two, then the formula says that the future value is the amount that we deposit in the bank today times 1 plus the interest rate to the exponent of the year that the money will be received. So we get the money in 5 years, the exponent is going to be 2. If we get the money in 5 years, the exponent will be 5. What we really need is a formula to compute the present value from some given future value. Now we can use the future value formula to do that, with just a little bit of algebra. I'm going to multiply both sides of the formula by 1 divided by 1 plus the interest rate to the t power. As long as we multiply both sides by the same thing, both sides stay to equal one another. You probably remember that something divided by itself equals one. We use that bit of knowledge to clean things up, then because we read from left to right, we'll flip things around to get our final result and there it is. Now we can find the present value for any future value. We just divide the future value by 1 plus the interest rate to the exponent t, which is the year that the money will be received. Computing this by hand is really, really hard but in a spreadsheet like Excel, it's pretty easy. Here's the Excel formula. The upside down V or the hat is how Excel designates an exponent. Whatever's behind the hat sign is the exponent. Here's an example. We want to find the present value or the amount that we have to put in a bank today of $1,000 to be received in four years at a 5% interest rate. Replace FV with 1000 and the interest rate with 0.05. We always do arithmetic with decimals, not percentages. The exponent is four, because the future value is four years in the future. We put that into Excel and the answer's $822.70. So, depositing $822.70 today will grow into $1000 in four years at a 5% interest rate. We've done a lot of arithmetic and algebra, so let's apply it to something useful. Suppose your company uses hot water for some process. Now the water is heated using natural gas, but there's plenty of sun where the factory is located. You'd like to know about the financial impact of putting solar water heating panels on the roof of the factory. You collect information about solar panels for heating water, the cost of natural gas, how efficient the water heaters are, how much water's heated, and so on. You get some help from friends in the accounting department, you come up with the following set of numbers. The system that's appropriate for your factory would cost about $10,000 installed. Every year for the next 12 years the system would save about $1,800 of natural gas cost. Now here's a spreadsheet that has all these numbers organized by year. The present value of the $1,800 annual savings is computed in the right column, using our 5% interest rate. We add the present value of the future benefits together, and we get $15,953. Next, we subtract the cost of the system, $10,000. The net present value, or the amount that the present value of the benefits exceeds the cost of buying the solar panels, is $5,953. That means that the company gains $5,953 or almost $6,000 of excess value by installing a solar water heating system. This is a really good deal for the company. Making a business case for using solar energy to heat water should be pretty simple. I'll post a spreadsheet so you can see how I got the numbers. Now, I want to change the situation a little bit. Suppose a system costs $15,000 and the annual savings were only $1,500 a year. Now, the net present value, the sum of the present value the future benefits minus the cost of of the system, is negative. Uh-oh. Does that mean you shouldn't pursue this investment? Well, not necessarily. Remember, there are other benefits from making sustainability changes. For example, suppose the price of natural gas when you did the analysis was very low, then the savings wouldn't be very big. But if the price of gas goes up, the savings will get a lot bigger and the project will look better. We could rework the analysis to see at what price of natural gas does a project just break even, have an MBV of zero. There might be regulations of carbon admitting fuels that would raise the cost of using them. If so, the benefits would go up. The company might want to tell shareholders about it's sustainability efforts, so bearing a small cost is acceptable. Just because a project isn't immediately profitable doesn't mean you should forget about it. You just need to work harder to think about how it might provide benefits beyond the direct monetary benefits that the net present value focuses on. When the sustainable business movement started to take off about 25 years ago, many people thought that all companies had to do was find profitable changes that help the environment or help communities. They talked about doing well while doing good. The idea was, the company did well, that is, it made profits while doing good deeds for the environment or for communities. These are also called win-win opportunities. The company wins, the environment wins. But it isn't that simple. We know that some problems are due to market failures like extra knowledge. If a company is using the atmosphere or rivers as a free dumping ground, it's pretty hard to change that behavior profitably. The change probably requires putting expensive equipments on smoke stacks or outlet stacks. But there aren't any income benefits, just the cost of the equipment, so it's all cost. If a company has to start paying for something it was getting for free, it's hard, it's probably impossible, for that to enhance profits. A lot of sustainability initiatives are like this. Your job as a change agent for sustainability is to overcome this mind set for immediate profits from every green initiative and to show how the change produces long-term benefits. Some of those benefits are going to be hard to put into terms of dollars, so you're going to have to be able to articulate the value of a better reputation or happier employees, or better standing in the community or reduced risk. Making the business case for sustainability can be tricky, but we're going to give you a lot of tools that you can use to put the best case together that you can. Quite honestly, these changes aren't easy. If they were, somebody would have already done them. We hope that with the tools from this class and your energy and your passion, you can make some of these difficult changes and make the world a better place. Thanks.