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Alan Cring Productions in association with Emergent Light Studio presents

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the Illinois State Collegiate Compendium Academic Lectures in Business and Economics.

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This is Business Finance, FIL 341 for Autumn Semester 2024.

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Today, problems in capital budgeting. The basic outline is pretty much anything that you would

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need to do is in the spreadsheet that I am providing for you. Although I do want to make

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some comments on proceeding forward with the capital budgeting, how you use some of the back

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sheets to answer a few questions. And this is just some stupid Excel pet tricks. As a matter of fact,

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I came in a few minutes late because I just realized that I could actually write a worksheet

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in there to calculate payback period. So that's in your portfolio now too. But before we go any

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further here, just a quick look at the numbers to see how the markets are doing. And you have a

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day a slide day here. Well that's not very helpful. Wait, let me see something here. Let's try that

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again. Oh there we go. Okay, well, huh, that's odd. Okay, well anyway, one way or the other.

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As you can see, it's a sour day on the street. It's nothing major, but there is a, the Dow

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is down the most today. And a lot of that's probably price correction from the heady days

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of the last of this past week. The markets surged upward and now they, the profit takers are coming

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in and peeling off some of their equity holdings just to get some money out of them before something

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else happens. The thing that kind of creeps me out is there's this pervasive rumor and I've never

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heard, there's always doomsayers, you know, the end of the world is coming and all that, that's

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through time and history. And I've heard it on from traders all the time you hear one,

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well the market's about to crash, markets are ready for a big fall. I'm hearing it a lot more.

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The last few weeks there was kind of a pickup in it, but just this last couple of days it's there,

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it's almost like noise of the sense that any time now the markets, the bottom is just going to drop

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out from the market. And I don't, how much do you believe it? Well, I don't, but at the same time

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it's just almost like, it's assumed now that it's coming. But of course you don't see anyone

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panicking yet and you certainly don't see the gold markets responding too much, but it's just like an

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underlying hum that there's a black swan coming very soon. So well, does that mean you sell out

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today and go live in the woods? Certainly not. And it probably amounts to nothing. Like I said,

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you hear these rumors all the time. It's just that the noise of it is getting kind of annoying right

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now. Now as you can see crude is really in a trading band. You see that bouncing there, but

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that's not even a dollar of bounce up and down right now. And so it's a good time and you are

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beginning to see gasoline prices, more of them, just under three dollars a gallon. That's good

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news. So that's helpful going into the Christmas season. And right now we're all holding our breath.

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The preliminary numbers pre-black sale are weak and we're hoping that that just means that everyone's

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waiting for Black Friday and they're all going to buy their brains out. But we're just going to have

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to see if black, as I said in the last class, if Black Friday comes in weak, in other words not as

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good as last year, we're probably going to have a bad Christmas season and that's going to be bad

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for the economy. That's a bad message going into the new year. In other words, the Christmas season

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is a leading indicator of business activity for the year following. And so we want to keep an eye

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on that to see if it's going to be a good strong Black Friday or a bad Black Friday. The numbers

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should start coming in Saturday night, Sunday. We should start seeing what happened on Black Friday.

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So we keep an eye on that as finance people, those kinds of numbers. Now looking here at gold, as I

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said, gold is showing no apocalyptic behavior. If you start to see the gold price surge upward,

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especially if it crosses, even comes close to three thousand dollars an ounce, that is a warning sign,

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that's a real warning sign. Right now it's just sitting there looking stupid, $2,700, $2,600 an

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ounce, not moving much. So we're in good shape there. Coming over here, silver is behaving

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differently than from what gold is right now. That's not terrible, but it does indicate

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that the gold bugs are not in play right now. They're staying off the sidelines. But the

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10-year bond, now this is getting to be a little ridiculous here. The yield on the 10-year bond

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keeps going up, and that is going to stifle a recovery if it doesn't quit it. Because that

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10-year bond, if it gets back up, I mean, the concern, the first neckline that would really

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worry us is if it crosses back above 4.5 percent. Right now it's at 4.43 percent, and it's up about 12 basis points down.

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I probably haven't said this before. If you go one, two, even five basis, four basis points movement, either way,

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that's nothing. But once you get above four or five, about five, then that concerns us. And now we've got today,

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it's up a whopping 12 basis points, and that's not good at all. It's, unfortunately, as you can see,

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it's leveled off. We're coming to the end of the cycle, about four hours left on bonds today.

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And right now the sell-off has ended. You see that sell-off there? That's price going down,

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yield going up, the sell-off of the bonds. And interestingly enough, as you see over here,

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just having a quick look back over here at the equities, that sell-off in bonds was generating

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funds. Those funds are not going into equities. So that, and it's not going into gold either,

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so that's clearly going into liquidity. But remember when I said that a lot of this money

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isn't going into quick, high liquidity money markets, it's going into lower liquidity

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CDs, certificates of deposit, one to three year CDs. And so that's concerning. In other words,

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stashing money so that you can get to it if you have to, but it's stashed away for more than a day,

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10 days, and all that. So there's no plan, it doesn't look like the investors have a plan

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to bring those funds, those liquid funds, back onto the playground of equities in the near future.

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And that just keeps happening and more and more every day more CD activity is going on. Now the

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whole world of CDs sounds boring, but it's actually not that boring. I covered in 340, FIL 340, that

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there is an active certificates of deposit primary market, but also there's a secondary market for

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certificates of deposit. In other words, in this world, if you bought a CD from me, a substantial

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interest penalty for early withdrawal, so you're stuck with it for three years, right? You're not,

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because there's a secondary market. Someone else might want to buy your CD and there's a secondary

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market. So that whole interest penalty for early withdrawal really isn't all that meaningful

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anymore because of this highly active market. And there are brokers and there are also dealers in

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CDs on the secondary market side. In other words, a broker takes an order, finds a match for it over

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here. A dealer actually keeps an inventory of whatever security it is you're talking about.

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So there are brokers and dealers and it's a thick market and there's more participants every day.

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Traditional securities brokers are stepping into the world of CDs because there is a market for,

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there is an active secondary market. So there's money to be made, so they're jumping into this

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market. And so that's of some concern to us right now, that these CDs, first of all, they're gathered,

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the number of CDs is growing. That's primary market. And the activity of trading in the CDs,

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that's a secondary market, is picking up enough that you're having new players that used to do

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only traditional kinds of deals in stocks and bonds. Now they're jumping into this too. And so yeah.

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So like people going into the CDs, are they expecting the hailed savings accounts to be going down?

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Yeah, yeah. Very good. That's exactly right. Yeah, that's the idea. And that's the major one. There

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are other reasons, but that's a big one right there. Good point. And what this means is that

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there are a lot of flashes of danger ahead. And whether or not those are just some storm off in

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the distance or if it's coming at us, we can't say yet. But it isn't certainly a time of a lot of

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excitement. It is a time of a lot of excitement. The heading belief that what was the election was

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going to be the golden age of trading and finance, that's going away pretty quickly,

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because especially because of the concern about a global tariff war, which would put us back to 1929

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and what happened after that. That's a concern and it's beginning to build on Wall Street.

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But it's not a reason for trading out and getting out right now. It's certainly not at all.

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I don't want to give that an impression. Now the one thing though is that we do see the dollar

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sliding against other currencies. It's beginning to weaken and that's just how it is. You see

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just as a quick mention and if you want to get more, if you're interested in international finance,

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I teach it and we also have, Stella teaches it, and it's really interesting stuff. And the math

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isn't so bad. It's just you have to keep straight on what makes what happen. But the dollar is

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sliding against the euro, which is because of a belief that the strength of the American economy

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is not as great as it is against Europe. Now if you look over here and you check on the pound

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sterling, it's plummeting against the British pound. And the Japanese, it looks like it's going up,

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it's not. Their quotes are backwards because yen are of such small value compared to the dollar,

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they have to quote it backwards. So what you see going up, the dollar appreciating, is actually

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the dollar depreciating against the yen. If you look here, the yen is USD to yen. Over here,

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that's euro to USD and it's also Great Britain pound to USD. So this one's a backward quote.

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This is that one, the USD to Japanese yen is a direct quote because it's one dollar

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and the others are indirect. More likely you see indirect quotes for everything and you want to

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keep that it that way, but they have to quote it as a direct quote for the Japanese yen because

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it's worth so little. Look at this, 154.75, one dollar will buy you 154.75 yen. So if you turn

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that around, that would be in tiny decimal places if you turned it into an indirect quote.

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But anyway, that's that one going on. Now a few on the horizon. This is a cautionary tale. Let

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me show you just a couple of stocks and what it means of beta and its relationship to risk. One

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that I'll show you right now is Micron. Micron swings badly. It's not an amateur's kind of game.

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It's got a beta of 1.18. It's highly overvalued and if you want to look at this one for a one year,

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that is risk-rich-large. Look at that. It surges and falls and surges and falls. Now if you have the,

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if you do cardio and you have your heart doctor's permission, this is a stock that you might want to

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go with, but it's certainly not something that you are going to say, well I'm rich, now I can live the

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great life because tomorrow you might not be rich and you'll be living in a dumpster. And that's a

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good example of that. Another one which had a boost because of the belief that the owner's new

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government position will make him have more ability to leverage that on his company is Tesla. On one

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day it surges and the next day it just crashes. Going back here again, look at one year, and you

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will see the ups and downs and the spike and now correcting off the spike again. And of course the

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Tesla beta is insanely high and so if you're going to buy something like this, it's not one of those

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buy it and hold it for a week and make a fortune and then get out. If you're going to do a stock

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like this, this is just something you have to put in a drawer and walk away from and in 10 years you

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see where you are. That's one of the things about highly volatile stocks. Unless you think you're a

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genius at timing, they are not quickie investments at all. And I just want to bring those up to you

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as one of those last things that I can impart to you before you leave me and I never see you again

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because you all go to Wall Street and make a fortune and then forget about your old professor

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here. But anyway, enough of that. Let me get down to the lecture here. Now I've uploaded another new

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version of that worksheet. This is capital budgeting. Figure out whether saw courses, whether

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project or go or no go. Now let me go over here to view student and just to remind you of where you

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want to be in this is pretty straightforward. Files, go to your spreadsheets. I said go to your

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spreadsheets and you use the NPV and IRR spreadsheet. This should solve all of your... yes please.

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I had an example on here I forgot to get it. But this is good enough that it should get you through

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almost... oh I did not want that. Please don't, please don't. No, no, no. I want to download

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NPV and IRR. I thought I did and it didn't show up. Oh it is up. Okay. Oh okay. Good.

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This should get you through about any problem that you would need. Now I'm going to assume you already

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know NPV IRR, at least what it is. This is our go no go for finding project whether we're going

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to take on projects or not. And it all boils down to free cash flow. We project the free cash flow

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and I've shown you some of that in chapter 11, went through some of it. And we just lay out the

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free cash flows for a company and then from there we get a couple of metrics. Now I'm repeating some

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of what I've done before here but let me do it again. The three methods, and I'm just repeating

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myself here, are the payback period method. It's old, it's bad, you shouldn't use it, but it's still

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out there. And then you have the two biggies, the net present value method and the other one,

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the internal rate of return method. The most popular of these is the internal rate of return method.

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It is the one that's also the weakest of all of them, of the two I should say. The net present

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value method and the internal rate of return method are mathematically and scientifically

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sound. They essentially assess where a project, the present value of a project gets below the

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point where it can't pay for the initial investment in it. Now the two different methods, and again I

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just want to make sure that you have this down, when you get a question on a quiz or an exam,

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just put the stupid numbers in. Don't think about what you're doing too much. That's all I ask of

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you is that we have Excel, we use Excel in our day and age, so we don't have to do manual calculations.

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In fact, what Excel is doing, and this spreadsheet right now, the first thing that it is doing is it

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is taking each of the free cash flows and finding its present value and then adding them up and then

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subtracting the initial investment. That's all it's doing, but the whole key is the discount rate

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that you use to do that. And like I said, valid, well what most companies use, they use their weighted

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average cost of capital. That's what they use. That's not a good idea because the weighted average

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cost of capital is essentially the measure of the risk of the entire company as an interest rate.

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Whereas a project itself might not be the same risk as the company as a whole. So you're sort of

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forcing every project to live to the expectations that the company overall has, and that might not

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be valid. A better method would be to use the capital asset pricing model. That's another method

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that you can use, but there are other methods out there too, and I won't emphasize them too much.

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I'm just going to give you a discount rate and use it, which is how it's going to be for you in your

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work, especially in the first years. If you're in corporate and you are analyzing projects, you will

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be given a discount rate. Thou shalt use this discount rate, and that's all there will be to it.

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Now the NPV, now again I emphasize, this is not, you don't bother with this. You leave it alone.

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Leave it TF alone. It is merely there to show you a comparative. Okay, I'm going to try 7% and see

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what my NPV is. That's that point on that line. Let me back this off just a little bit. That's

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that point on the line. 7% and it has an NPV of about $2,500. And then this one is just a comparison.

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What is the NPV at 12%? Well, it's negative 42, 4,300. That's that point there, and then this is the

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NPV profile line. That's, and as you can see, if I were to adjust to let's say 8%, it would plot a

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different line. That's all that's doing. So that just gives you a visuality to the exercise. Good

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news. Okay, the next thing is that the point where they crop, where the profile line crosses the

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discount rate axis, the horizontal axis, that is the internal rate of return. That's the holy grail,

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as it were, of a lot of company decision-making. It has the flaw that if the sign of the cash,

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free cash flow switches more than once, there will be multiple internal rates of return. It's

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actually, if it crosses twice, the internal rate of return, the profile line is a parabola. If it

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crosses three times, the NPV profile line is a cubic. The polynomial, the degree of the polynomial,

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the highest part of which X occurs, is the shape of the NPV profile line. You see that it crosses

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once here? So that's a linear equation. X to the first power is the highest power of X. So that's

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why that happens. That is not always how the real world works though. There are several different

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scenarios where you could get into free cash flow. For example, one classic is where you start out

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with an initial investment. You cruise along over the life of the project, but in the last year,

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you get your residual, last sell, last inventory, but your salvage value is negative because it

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costs to close it down and you're paying more to close it down than you get from the last year of

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sales. So you could have negative, then a string of positives, that's one switch, and then at the

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last year, it switches back to negative. So it's got two sign switches, which would mean that the

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NPV profile line would actually be a parabola, and that means that there are two internal rates

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of return, neither of which means anything whatsoever. They are what we call spurious

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solutions. They're spurious. So that makes the traditional internal rate of return not really

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the best way to use every time you need an internal rate of return. But let me hold that off for a

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minute. We have a way to fix it. It's not actually the best way in the world, but it's a way to fix

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it. And Excel fortunately can do that because if you have to do that by hand, it is a pain in the

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butt. It's called the modified internal rate of return. But let me go through something here. This,

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okay, this one, positive, accept, negative, reject, that's all there is to it. Its challenge is finding

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a discount rate. How do most companies do it? They cop out and say whack. They just say 7% or

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whatever their whack is. They don't use the cap M. They don't use bond plus equity premium. They

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don't do any of that. They just say whack. So it is, even at that, it's still, it is straightforward.

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Negative, if the project NPV is negative, well, you say reject. If it's positive, you say accept.

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But the internal rate of return has another way that it is used. The internal rate of return in

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a way is called the breakeven, I've even heard this term, the breakeven ROI. So for example,

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suppose that a project, well, let me show you this one here. Suppose that I say, okay, the internal

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rate of return of this project is 8.75%. See, it calculates it for you. But what if I say that we

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have a project that has an internal rate of return of, let's say, 8%. Well, 8% would be down here.

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That's a negative. So if we have an internal rate of return of a project that is unacceptable,

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we would reject it. Now here's how they use it in business. They usually use a term, and there are

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other terms for it, but they use a term called hurdle rate. This is essentially the internal

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rate of return that we will use for evaluating projects. So suppose that a company, so in other

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words, let's say that the hurdle rate is 10%. So in other words, out here at 10%, that's our

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threshold. So suppose that we do an NPV IRR and we have a project that comes in with a,

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project A has an internal rate of return of 8, let's say 8.5%. Whatever else we know or don't

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know, we know that this project A crosses the discount rate axis at 8.5%. That means that we

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would reject this project because at our hurdle rate of 10%, this is a negative NPV project. So

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the decision criterion works like this. Set your hurdle rate. Then any project that has an internal

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rate of return, project internal rate of return less than the hurdle rate, we reject because it

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doesn't meet our threshold. Any project above that hurdle rate, internal rate of return, we accept.

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That's how you do it. It's a very simple method. All you have to do is crank out the IRR of the

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project. Notice that, by the way, let me warn you of something. When you're calculating an

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internal rate of return, you don't need a discount rate. I may be repeating what I said in the last

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lecture, but I have to emphasize this. I'll give you two problems on the final exam, let's say.

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One will be find the NPV. I'll give you a free cash flow, find the NPV. Well, in order to find

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the NPV, you need the free cash flow, you need a discount rate. But then I'll give you one where

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I'll give you the free cash flow and I'll say find the internal rate of return. Don't come up and ask

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me, well, what's the discount rate? You don't need a discount rate. There's no use for it. The

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internal rate of return is the discount rate. So you don't need a discount rate if all you're

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finding is an internal rate of return. You see the temptation in this, though, is because you

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can just crank out free cash flow analysis every day and all you need to do is run internal rate

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of return. You don't need to worry about, God, what's discount rate? Just run the internal rate

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of return and compare it to your corporate policy hurdle rate. And every company that uses internal

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rate of return that I've run into has a hurdle rate. And the problem with that is kind of simple.

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Where are you getting this hurdle rate? It would have to be purely subjective. You pull it out of

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your ass. And I had, when I was consulting, I had several companies that were, you know, they were

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using internal rates of return. So they were very modern, very hip and with it. I said, well, where

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did you get this hurdle rate? I had one that had a hurdle rate on projects of 12.5%. And I said,

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well, where did that come from? And they were actually, only one person offered us an answer.

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He said, well, I know that it was, some years back, it was 12.5% when I first came here and we just

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never changed it. That's the way we always do it. But you see, that's, it doesn't take into account

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varying interest rates over time in the macro economy, the growth of the corporation, what its

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risk profile changing through time. 12.5% is actually a pretty steep, especially back in that

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time when I was doing this. That was a pretty steep, in other words, a project would really have to pay

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off big to get an internal rate of return above a 12.5% hurdle rate. In other words, the company was

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essentially biasing itself away from safe projects. See, if you had a project that came in with an

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internal rate of return of 6%, they say reject it. Well, that might be a good project. It's just a

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very safe project. Doesn't return a lot of money, but it's a very safe project. But if you find one

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that has a 20% internal rate of return, well, that's, yeah, we'll take that one any day. But

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you're also taking on a frickin boatload of risk with a project. So in other words, it was constantly

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making itself a riskier corporation because it would take only projects that were at least as

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good as 12.5%. And if the higher it was above the hurdle rate, the better they loved it. And so that

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just constantly increased the risk of the corporation because it was taking on risky projects and it was

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rejecting safe projects. Even though they would have been perfectly okay, they didn't want them

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because they did not meet that hurdle rate that the company had set. And ask the company, well,

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why did you use that hurdle rate? They couldn't tell me. They just said, that's what we do. And

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then they kind of sometimes say, well, we got this guy, he does some pretty fancy math, and this is

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what he figured out. Oh, you probably got some guy named Earl down at Earl's Bar and Grill, and he

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does financial consulting on the side. Yeah, yeah, that probably was about it. Okay, so in other words,

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this is a popular method. Internal rate of return, set the hurdle rate, reject any project that has

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an IRR below the hurdle rate, accept any project that has an IRR above the hurdle rate. Okay, so we're

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all good and dandy now, except for the fact that internal rate of return does not work if there's

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more than one flip in the sign of the cash flow. Matter of fact, you could put in a, let me show

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you something here. You could put in the numbers for a free cash flow with a negative value in one

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of them, and you know what would happen? Excel, a financial calculator, will give you an internal

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rate of return. But what it did was, okay, let me show you. Here would be a possible NPV profile

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line if you had two sign switches. It would be a parabola, degree two polynomial, two roots, in other

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words, two IRRs. Well, what Excel and a financial calculator do is they just start somewhere and

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they start searching. And let's say it starts at a low rate. Now it's doing this at the speed of

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light so you don't see how much it's doing here. But it's a, okay, we've got a negative NPV. That

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means that we are already on the wrong side. So it's going to go down and it's just going to get

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more negative. So it starts running this way and it says, bing, bing, oh, we've got a positive NPV.

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So the internal rate of return must be between here and here. And it'll just zero in on that. Like

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I said, at the speed of light, you're not seeing this happen. And then it says, here's your internal

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rate of return. If it had started somewhere like up here, it would have seen that the NPVs were

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falling and then it would have gone over here and it would have worked its way back and forth. Which

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one it would find is purely where it would start. And it would mean anything. Neither of them really

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means one damn thing. Now some books, I don't know if this one, there was a previous edition that tried

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to give some kind of a weird ass explanation. Well, this one means this. Don't, just don't. There is a

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way to modify the internal rate of return to make it so that it gives, it has only one sign switch.

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It's called the modified internal rate of return, the MIRR. And thank God we have that. Because let

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me show you, I've got an MIRR here. MIRR, okay. See this one, it's got a sign switch here, that's one.

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Then it switches, that's two. And then it switches, that's three. So in other words, this would, the NPV

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profile line would actually be a cubic equations graph. This son of a bitch would look like,

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excuse me, would look like that. Three internal rates of return. Well we can't have two, so we sure as

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heck can't have three. So you've got to figure out a way, is there a way to straighten this up? In

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other words, to go, like that. And there is. It's stupid, but it actually works in a pig's eye. It

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works on, you have to think about this. So if, see how they're at year zero and then at year three,

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you have to throw money into the project. Now obviously there would be some cost of that capital

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to do that. So we call that the financing rate. I put six percent here, you could put other things.

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But you see, on the other hand, see these years when it's making money, 15,000, 50,000, 70,000,

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10,000. That's when it's got money coming out into retained earnings that it could use for

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reinvestments, investments in other things. So in other words, in this problem there are really two

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different interest rates, discount rates as it were, or compounding rates. There is a six percent

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cost of financing. That would be a discount rate. And then there is also an interest rate, what we

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make off extra that we make in a project. Okay, we made 15 grand in the first year. Well, we can do

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something with that. So that would be a reinvestment rate of the company, whatever it can put money

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into inside the company or invest in other companies, whatever. But there will be two different

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rates. Now, here's the pain in the butt part of it if you do it by hand. First of all, you take

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anything that's negative and discount it back at the finance rate to the beginning and add it to

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the initial investment. And then you take any time that the project spits out money and you throw it

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forward as a future value to the end of the project, compounding at the investment rate. So in other

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words, what you're doing basically in this project, in this right here, is if I do these as one, two,

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three, four, five, was this a five year project? Yeah. Okay. Oh, I got to do a zero here. So there in

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year zero, there's a negative. And then there's a positive and a positive. And then a negative and

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then a positive and a positive. So what you're doing is you are discounting any negatives back

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to the present, taking a present value of them, adding them up. And it's taking any positives and

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you're finding the future value. So this one is present value at the discount rate. And all these

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that are positives, you're taking forward as future values and clustering them all up. And then you

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just zero all the numbers in between because you've done something with them. So in other words,

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what Excel is doing, what we used to do by hand, and I don't want to see, I want you to live better

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lives than I did. What we're doing, what Excel is doing is it's actually taking the present value of

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12,000, negative 12,000 and adding it to 120,000. And then it makes that 12,000 a zero. And then it's

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taking the future value at that compounding rate, the reinvestment rate, and it's taking all of

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those forward to your five. And then it's making those zeros because you've done something with

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them. And then it finds the internal rate of return of that number there at the beginning,

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a zero, a zero, a zero, a zero, and the last year right there. And it's finding the internal rate

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of return of basically a negative number at the beginning and a positive number at the end. And

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that's finding the internal rate of return of that mess. That's called a modified internal rate of

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return, MIRR. And you can do this. Let me do a, I'll do a couple of other projects. But before I

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show you that, notice that the modified internal rate of return of this project is 5.37%. Do you

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see that the financing rate is 6%? This is a project you shouldn't take because the project

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overall has a return that is less than it costs you to finance it. Let me say that again. This

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project is coming out with an overall return of 5.37%. But the capital that I needed to make this

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project happen costs me 6%. Well, that sucks. Here's a rule. It should not cost more than you

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make. That's just, it's just basically at its heart, it's just a pretty simple, stupid ass rule.

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That's all it is. So that's worth your attention. But MIRR is, is if there's more than one sign

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switch in the free cash flow, then just use MIRR. Now on a quiz or an exam, well, that's all you do

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is just put in the numbers and look at the result. Now, there are some simple problems. I think the

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book has one where the financing rate and the reinvestment rate are the same. That's kind of

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unrealistic. But you know, put, just put in whatever they say the financing rate is and what the

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reinvestment rate is and just put in the free cash flows, whatever I tell you they are, and there's

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your answer. That's all there is to it. And let me tell you again, I can't emphasize enough, that it

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is a lot easier to do it with Excel. The book uses a financial calculator, a cheapo BA2, and says,

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well, you key this here and you key that there and then you swing around a cat and you offer your

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firstborn. Just use Excel to do this. It's a lot faster. These templates, I mean, they aren't

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sophisticated at all, but it certainly is easier than doing it with financial calculators, basic

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financial calculators, and it sure is heck a lot easier than doing it manually. That's that one.

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Now let me take you over here. I forgot, I did put in, and I didn't have this in the one, so you'll

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want to download this again. Payback period method. If you want to get down to the fraction of the

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year in which you cover your initial investment, I've written a small sheet right here and you can

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extend this if you want out further. But in this project right here, you start out with an

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investment of $100 and then you make $10 in your first year, 60 in your second year, and 80 in your

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third year, maybe some more. But as you can see, if the year of crossing, it was some time before

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year three. Now you could just say simply, okay, whatever our, let's say that we have a required

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payback period of four years. Okay, we take the project because it clearly pays for itself after

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three years. Now if they want to say just exactly how much of three years, well then you have to

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work a little harder. I've got a formula here that will tell you exactly the number of years to cross

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into the payback period. In this case, the payback period, you can say three years, but if you want

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to be exact about it, it's 2.38 years. And I've got a formula right here that cranks it out for you.

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If you want to suffer, you can see that nested if statement that I wrote to do that, but there it is,

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if you need the actual exact number of years. And like I said, you can extend this, just drag the

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formula down and you can get, if it's like it doesn't pay off until year five, it'll do that

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for you too. So there you go, that's all there is to that one. So that's your payback period method.

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Now I won't get into this, I'm not going to ask you this on a quiz or a test, but when you have

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mutually exclusive projects, that can be difficult. I encountered, now technically there's an argument

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among finance people that you should never have mutually exclusive projects. There's always

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a way that you could run, if it's two good projects, you should be able to do both of them,

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if they both have strong NPVs. But there are, and I did encounter it, where at least in the

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time period in which the decision had to be made, there were two projects that were mutually

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exclusive. And I had to dig through some ancient notes of mine, because I keep forgetting how it

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worked, but this company had a very large piece of land, well it wasn't very large, it was about

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five acres of land, and there were two possible ways that they could take that land. One was for

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an industrial park, they were a business park for companies, it wasn't really high tech back in that

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time, that was in the early 90s, but they had more or less, they could put up all these office

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buildings, two floors, and they could run it that way. And then they had another possibility on their

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table, where they could take that land and they could turn it into something that was very popular

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back at the time. Now my original, I had had a memory that it was like an entertainment center,

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but it was actually, when I look back, it was a kind of mall, partly outdoor mall, but it was a

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special kind, and I've just noticed that it's kind of coming back into vogue very recently, whether

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it's going to come back full-blown, it was one of those where you have the lower level is all these

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shops and restaurants, entertainment everywhere, and then on the second and third floor it was

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upscale, what we called yuppie in the time, young upwardly mobile people, apartments with balconies

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and they could sit out there like, sort of like an Italian villa type of environment. They had a,

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they planned, you know, some restaurants and some shopping and there was even a plan for a daycare

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center in there and all this, but they could not do both with the same piece of land, so they were

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mutually exclusive projects, and that was where the question, well, which one do we use? Well the

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funniest thing was, let me show you the two NPV profile lines of these. One of them had an NPV

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profile line that looked something like this. The other one had an NPV profile line that, well,

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that's a little too steep, but it had a much steeper NPV profile line, like that. See, the

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problem was that they had different internal rates of return. This was project A and this was project

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B. Project B had a lower internal rate of return than project A, but at low discount rates it had a

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higher NPV. See how project B had discount rates down in here, it had that NPV, whereas project A

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had that NPV. So at low discount rates for fighting the NPV, you'd say accept project B, but at high

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discount rates, like up in here, this one would actually have a negative NPV. B would have a

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negative NPV. So the whole question was, it came down to, well, we've got to choose a discount rate.

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Now, the trick here is to find the crossover rate, because it's a crossover rate. Any discount rate

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you would use below the crossover rate, you'd take B. Any discount rate above the crossover rate,

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you would take A. And so it would just boil down to, well, what are we going to use for our discount

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rate? And they said, well, why don't we use a hurdle rate? And the problem was that their hurdle

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rate was lower than the IRR of either of them. So with the hurdle rate, you'd take them both,

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but you couldn't take them both. See, if I had a hurdle rate down here somewhere, you'd take both

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of them because they both exceed their internal rates of return, exceed the hurdle rate. And their

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hurdle rate was actually fairly low. And so they said, by the hurdle rate, internal rate of return

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method, we take them both. And so it all boils down to the crossover rate. Now, I will not ask you to

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find a crossover rate. I'm bringing it up here because it does happen from time to time. You have

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two projects and you just can't do both of them because of some constraint on you. Oftentimes,

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that constraint is land. Land you don't have access to. And that was the case with the convention

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center in downtown Bloomington. They had one piece of land and they had to decide what to do with it.

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There were several different things they could have done. For one thing, they could have sold it.

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They could have made this convention center, which is what they did, or they could have made it into

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some kind of a community entertainment center. A lot of different things, some of it's kind of related.

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But they did not even consider mutually exclusive projects. They were hell-bent on one. And if they

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had considered other projects, they probably would have, and also been more realistic in their

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assessments of future expected free cash flows, they probably would have taken something else.

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So it's worth it to say, what else could we do? You don't obsess with it, but you ask, are there

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other possibly profitable things you can do? This mostly happens in real estate, where you can decide,

404
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okay, a residential apartment complex or something commercial. That's a big one for a lot of this

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mutually exclusive decision making. A strip mall versus an indoor mall, things like that.

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That's where this comes in. Now, one last one that I will bring up. It's the simplest one in the world

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to do. And almost any business person who's an entrepreneur is going to do this if he possibly

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can. It's very straightforward. And I do it. And I even have my numbers to show you what it means.

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It's called breakeven. Breakeven is simple. It just works like this. Look, your profit is going to be

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your revenue minus your costs. And you're going to say, I'm in college for a degree and I already

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knew this. What are you getting at? Very simple idea. Now, the costs actually have two parts.

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There are the variable costs and there's a fixed cost. Now, the variable cost moves with your output,

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moves with your sales. My variable costs. So, give you an example. In my business, the average,

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I make and sell art. Photographs, paintings, that kind of stuff. Okay, so I have to get that ready for a show.

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Okay, so at the show, I'm going to have the cost of the frame, the dry mount board, the dust backing,

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the museum glass, the wire, and all that. Put that together, that runs approximately, if I do it with good

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quality stuff, $225 per unit of art. So, in other words, my unit variable cost is that. But I also have fixed cost,

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the cost of the exhibition fee. Sometimes it's not bad, sometimes it's a killer. I also have the fixed cost,

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whether I sell anything or not, these are going to be there. They're fixed. I have the cost of driving to the

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show and driving back. And I have the cost of my infrastructure, my pop-up tent, my wire, my frames,

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and all that kind of stuff. And that fixed cost on a seasonal divided by the number of shows that I do runs

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about $2,000. And that adds in, that's including an estimate of my booth fee, what they call the booth fee,

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the exhibition fee, and all that kind of stuff. So that's a fixed cost. And finally, I have my price of my art,

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unit price. And that I average about $800 per artwork on average. We got all the pieces. So in other words,

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my profit boils down to a simple, the price, unit price times the quantity minus these two, which would be

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$225. Well, let me just put it this way, a little v times the output plus the fixed cost. Doing a little bit of

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rearranging p times q minus little v times q minus fc. And that's my profit. Now, I want to factor out the q on

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the first part. P minus v times q minus fc. First things first, if you look carefully, that is nothing but a

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y equals mx plus b's y. The x, the independent variable, is a q. The y is the profit. P minus v is the slope.

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And negative fc is the y-intercept. It's just the y equals mx plus b line. So in other words, if I were to graph

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this, q here, profit here, it looks like that. The y-intercept is negative fc, and the slope is little v minus p,

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p minus little v. A little side note here. In common business terminology, we call that price minus unit variable

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cost, unit price minus unit variable cost, we call that profit, we call that our margin, our unit margin. It's just

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the way, it's just a term. Technically, margins are supposed to be part of ratio and all, but the common lingo is

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my unit margin is p minus v. So my unit margin here is unit margin, where the hell is 800, $575. That's my unit margin.

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Now, our big question is, okay, where do I break even? Quantity break even. Okay? You follow it? That's all there is to it.

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I need to know that. I really, really care about that. And every business does care about how many it has to sell to make a

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profit. So in other words, we want the zero point of profit, which would be p minus v, the unit margin, times the

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break even quantity minus the fixed cost. That is what we're after. So in this, you rearrange it a little bit, and the

440
01:01:06,600 --> 01:01:19,600
survey says that your quantity break even, adding fc to both sides and dividing by the p minus v, is fixed cost over unit

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01:01:19,600 --> 01:01:32,600
margin. That's all there is to it. It's simple. And as you can see, the worse your fixed costs are, the higher your break even.

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01:01:32,600 --> 01:01:42,600
The better your spread between unit price and unit variable cost, the lower your break even. And this, all you have to do in

443
01:01:42,600 --> 01:01:53,600
this one is put in your numbers. Now, let me do this. Let's say that I have, I'm going to put in my unit price is $800. My unit

444
01:01:53,600 --> 01:02:10,600
variable cost is $225. My unit fixed cost is $2,000. So I have to make, I have to sell six. I have to sell six. Now let me

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point something out. Suppose that I can up my unit price to let's say $875 if it's a show up in Schomburg or some place like

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01:02:20,600 --> 01:02:41,600
that. $875, what, is this B? Oh, I screwed up there, you're right. Let me get that out. I screwed that up. Okay, so I put in, let

447
01:02:41,600 --> 01:03:00,600
me put in my numbers again there. The $875, the unit variable is $225 and my fixed cost is $2,000. I knew that was not going to

448
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be real. 3.08 units. Okay, so if I say how many do I have to sell to break even? Four. Don't say 3.08. I can't break off a piece.

449
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Here's your damn sale. No, it's the first units above the zero point. So whatever fraction there is, you just round it up.

450
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Because if I round it down, I lose. So you round up to say that's break even. So in my case, four to show. And that sounds easy,

451
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that is hard as hell in my business. But yeah, this is how it's done. And it's a very simple, but every good business, especially

452
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if it's small, it has to say this is what we have to do in order to stay in business. Because if we don't do that, then we haven't

453
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covered our business expenses, fixed and variable. It's a very simple and all you have to do is put the numbers in there and

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you're all done. Okay, that's all I have for you today. I thank you.