Here, let's spend some time on the Excel tabs. These tabs are set up to help you with the investment techniques that we have discussed. Each one of these tabs can be manipulated so that it can be more useful in your industrial setting. I will show you how to manipulate them to enter and change cells so that you can use these tabs and the investment decision techniques that we've discussed so that you can make better decisions. Here we have a tab called the NPV rule. Now this tab is set up so that we can add a cash flow positive or negative in the top line, in this case it's row 13. We have a present value row 14 which is a function of the interest rate that we put in, in B9. What we do is we get a present value of our cash flow, our cumulative cash flow, cumulative present value, and we can set up our target cell. Here's how we manipulate this. Let's say that we have a scenario, we're going to spend $1 million on a new strip mall and the strip mall is going to return rents over the next, let's say, ten years. So negative $1 million is going to be put into the first cell B13. Then let's suppose that I have positive cash flows going forward. So I have, $130,000 year 1, I have $200,000 year 2, I have $230,000 year 3, another $230,000 year 4, it goes down to $175,000 year 5. It goes back up to $250,000 year 6, another $200,000 in year 7, another $175,000 in year 8, $190,000 in year nine, another $200,000 in year 10. I've got no cash flows in years 11 and 12. This says that an interest rate of 7% with a $1 million cash outlay to buy the strip mall and cash flows of 130,000, 200,000, 230, 230, 175, 250, 200, 175, 190, and 200. This would give me a positive net present value of $382,174. If I had a different investment that I could compare it to this, and choose the investment with the highest NPV. If it turns out that my opportunity cost, the cost in my capital isn't 7%, it's more like 10%, I could throw that in there, change this to 10% and I would change my NPV. It's not 10%, more like 15%. There you go. At 15%, this cash flow is negative, it's worth negative $22,000. That's not very attractive to me. At 8%, it's positive $319,000. The tricks where people get caught up is in this initial cell B13. This is your cash outlay and so you have to make sure you putting a negative number in here. If you put a positive number in here, you will mess up your calculations, so a negative goes in here. Up here, you don't have to put in 0.08 for 8%, just type in 8%. You have 8.23%, 8.23, right there. You can just put it in, in terms of its percentages, you do not have to put it in as 0.0823 or 0.08, or 0.10. Those are the trouble spots. This can also be manipulated to add additional periods. Let's suppose that we want to calculate this out and we've got a project the lasts 15 or so years. What can I do is, I can highlight this area right here. I'm going to highlights all of these right here. What I'm want to do is I'm going to copy this out for another couple of years. Let me show you how I'm doing this again. Let me a highlight a couple of years here, I'm going to copy this out until I get to 15. What happens is I'm highlighting this out. Now, this is going to just copy a set of numbers, they may or may not be appropriate for my cash flows. Let's suppose that after the year 10, I have cash flows that are $210,000 each year. What I have to do then is also make sure that my target cell, my NPV is equal to this guy, right there. Now if I had spent $1 million and my interest rate was 8.23%, and I had cash flows, this, 130, 200, 230, 230, 175, 250, 200, 175, etc, my NPV, my net present value, would be $683,000. This says that with a cash flow of negative $1 million, I spend $1 million to buy this strip mall, at any 8.23%, that's my discount rate. This is the stream of cash that I have coming in, 130, 200,000, etc, my NPV of this stream right here is $683,048. Very easy to use, you can manipulate it, change values, you can copy and paste, you can compare multiple transactions of different language of time, and identify which investment is better. Let's talk about the internal rate of return. I'm going to start by using the same tab that we've been using, NPV. I want to show you something. Remember, the internal rate of return identifies the discount rate such that your NPV is zero. Here is a stream of cash, I'm going to spend $1 million on the strip mall and I'm going to get a stream of cash that's equivalent to what we see right here. Now at 8.23%, I've got a positive NPV of $683,000. I'm going to keep adjusting this upwards until my NPV gets really close to zero. Let's put in 10%. Nope, 10% is still going to be positive, 12%, still positive, 14%, still positive, 15%, 18%, 18% has gone from positive to negative between 15 and 18%. I wonder what 17% looks like, ooh, 17% is positive. I wonder what 17.5% looks like, ooh, 17.7, 17.8, 17.9, 17.95. Aha, 17.95 gives me negative 308, 17.92. A thousand, 17.93, that's $600. So, the internal rate return on this particular investment is just about 18%, 17.93%. I keep adjusting my interest rate until my NPV gets really close to zero as it does right here. Then, what I can do is I can compare two different investments and identify which one has the highest NPV. Let's suppose that I copy this whole thing over here and I'm going to change up my scenario of my different cash flows. I'm going to put this back at 10%. Let's suppose my cash flow over here was 250. Let's suppose this cash flow was 100. Let's suppose this cash flow was 225. And this cash flow over here was 189. I've got slightly different sets of cash flows. What I want to do is, I know that the internal rate of return of this first one is 17.93. I'm going to change the interest rate on this second set of cash flows until it is also close to zero, maybe 12%? I've copied down my formulas and I've redone some cash flows here. What I'm also going to do is I'm going to show you how to make this change right here. You want the interest rate. Instead of being B9, down here, you want the interest rate to be B22. Right here, you just backspace and type in 22 where it says B9 and then you're going to copy that over, just this, just copy it straight over here. Now, what we're going to do is, we're going to change the interest rate here, so that this thing gets close to zero. So 15, 17, 18, 19, 18.5, 18.2, 18.1, 17.99. So 18.05, look at this. So investment one has an internal interest rate of 17.93. The cash flows are such that at an internal rate of return of 17.93, the NPV is zero. This second investment has an internal rate of return of 18.05. I would choose investment structure two over investment structure one. If I had a choice of cash flows, I would choose cash flow two to cash flow one. They're very comparable but it has a higher internal rate of return. You can change these around, you can copy them. When you do, you have to make sure that your discount factor, your present value factor is referring to your new interest rate, rather than your old interest rate. Other than that, you can manipulate them, change them, look at one versus the other, it gives you some really powerful finance.