Hi. This week I want to introduce you to the basics of financial analysis. To make the business case for sustainability, we need to show decision makers how the change affects profits. Ideally your proposed change will earn profits for the company. As I'll explain in a minute, that isn't guaranteed. Now, if a proposal doesn't make money for the company, does that mean it won't be implemented? No, not at all. It just means you have more work to do. You'll have to go back to our list of reasons companies should become sustainable and look for other benefits that'll supplement profitability. Now before I get into the details, I want to explain why I think you should have an understanding of these details. And I also want to say that your company, you'd almost certainly have people from various departments helping you to do an analysis because there's lots of company specific information like tax rates and accounting details that you can't be expected to know. So why know these details? If you're making the proposal, you need to understand how the business case is built. So knowing some details is important. If your asked questions, you want to be able to respond to as many of them as you can. Some very specific questions will require finding an expert in the company. But you want decision makers to be confident, that you know what you're proposing so they have some confidence in your analysis. Finally, for the purpose of this class, you need to be able to do the financial part to make a complete proposal. Now don't let the arithmetic worry you. We'll work through it at a comfortable pace and you might even find it interesting. The standard way that analysis like these are done is computing something called a net present value, or NPV. The basic idea is that we're going to compute the monetary benefits of the change over time. These could be savings from lower electricity bills because you've changed lighting systems, of you've added insulation to buildings so they use less energy. The savings could come from finding ways to reuse waste materials, so purchases of raw materials do down, or maybe personnel policies have changed, such as benefits. Reduce employee turnover and the cost of hiring a new employee, which are usually several thousand dollars are avoided. Typically these benefits or savings occur over a long period of time, maybe five years or ten years. But the cost of making the investment for instance, paying for a new lighting system or insulating a building or paying for new benefits, occurs before any of the benefits are received. You have to make and investment to get the benefits. So the benefits are in the future, but the outlay is made today. When we do these analysis, we assume that they start at the moment the Investment is made. That becomes the starting point, or time zero, or today. We need to be able to compare the benefits to the outlay. We need to make the future benefits, so the green arrows in the diagram I just showed you, comparable to the initial investment. The way we do this is to adjust the benefits that will be received in the future to their equivalent value today. Let me repeat that. We need to adjust the future benefits to their equivalent value today or at the time the investment is made. Once we have everything at one point in time, then it's easy to compare them. This is called computing the present value of future benefit. Here's how I like to think about the present value of a future benefit, or a future cash flow. The present value is the amount that we have to put in the bank today so that as it earns interest, it will exactly equal the amount of the future benefit at the point in time when that benefit will be received. So, we put the green arrow into the bank. And it grows into the tall blue arrow in the future. In terms of financial analysis, these arrows are equivalent. The green arrow is a present value of the blue arrow. Or the blue arrow is the future value of the green arrow. Let's do an example with some numbers. We deposited $100 in the bank today. The bank pays interest of 5% per year. So, after one year, we have $105 in our bank account. We have the original $100 that we deposited, plus $5 of interest. We compute the interest by multiplying the original deposit, the $100 by the interest rate, the 5%. So, 5% of $100 is $5. So, the interest we earned is $5. The Future Value, which I'm going to call, FV is the present value which we call PV plus the interest earned. We know that the interest earned in one year is the interest rate times the present value, the original deposit. Now let's do our earlier example but with these symbols and then with numbers. Now let's go out another year or two. We're using something called compound interest which means interest is computed on interest earned in earlier years. This is also called exponential growth. You'll see why in just a second. We know the calculation for year one. $100 grows to $105 at our 5% rate of interest. In year two we repeat the procedure, but now our starting point is $105 instead of just $100. So during the second year, the interest will be 5% of $105 which is $5.25 is just a little more than the interest that you earned in the first year. The extra $0.25 is the interest on the first year's interest so 5% of $5. So, at the end of year to we have $110.25 in the bank. In year three we earn 5% of $110.25 or $5.51. Now our bank balance is worth $115.76. If we kept going the balance at the end of the fourth year would be $121.55 then $127.63. And at the end of year six It'd be about $134. Each of these numbers, 134 at the end of year six, 120, 155 at the end of year four, is equivalent to the present value of $100, or $100 deposited in the bank today. Now I want to do one more thing and then we'll take a little break. Let's look at the future value calculation for year three in more detail. We know that to go from year to year, we multiply the previous result by 1.05. In the year 3 future value formula, instead of FV2, let's put in FV1 times 1.05. Okay, now we're going to replace FV1, with 100 times 1.05. Now we have our deposit times 1.05 times 1.05 times 1.05. But we know, that 1.05 times 1.05 times 1.05 can be condensed into 1.05 to the third power. Aha. FV3, future value in year three, Is the original deposit times 1.05 to the power of 3. The exponent 3, therefore exponential growth. Now we can generalize and say that for the future value in year t, it will always be the present value times one plus the interest rate to the t power. This is exponential growth because the exponent is the number of years that the amount grows. So what we've done is we've derived a general formula for computing a future value at any point in time. But what we really need to do Is compute the present value. So we'll do that in the next video, thanks.