Alan Cring Productions in association with Emergent Light Studio presents
the Illinois State Collegiate Compendium Academic Lectures in Business and Economics.
This is Business Finance, FIL 341 for Autumn Semester 2024.
Today, problems in capital budgeting. The basic outline is pretty much anything that you would
need to do is in the spreadsheet that I am providing for you. Although I do want to make
some comments on proceeding forward with the capital budgeting, how you use some of the back
sheets to answer a few questions. And this is just some stupid Excel pet tricks. As a matter of fact,
I came in a few minutes late because I just realized that I could actually write a worksheet
in there to calculate payback period. So that's in your portfolio now too. But before we go any
further here, just a quick look at the numbers to see how the markets are doing. And you have a
day a slide day here. Well that's not very helpful. Wait, let me see something here. Let's try that
again. Oh there we go. Okay, well, huh, that's odd. Okay, well anyway, one way or the other.
As you can see, it's a sour day on the street. It's nothing major, but there is a, the Dow
is down the most today. And a lot of that's probably price correction from the heady days
of the last of this past week. The markets surged upward and now they, the profit takers are coming
in and peeling off some of their equity holdings just to get some money out of them before something
else happens. The thing that kind of creeps me out is there's this pervasive rumor and I've never
heard, there's always doomsayers, you know, the end of the world is coming and all that, that's
through time and history. And I've heard it on from traders all the time you hear one,
well the market's about to crash, markets are ready for a big fall. I'm hearing it a lot more.
The last few weeks there was kind of a pickup in it, but just this last couple of days it's there,
it's almost like noise of the sense that any time now the markets, the bottom is just going to drop
out from the market. And I don't, how much do you believe it? Well, I don't, but at the same time
it's just almost like, it's assumed now that it's coming. But of course you don't see anyone
panicking yet and you certainly don't see the gold markets responding too much, but it's just like an
underlying hum that there's a black swan coming very soon. So well, does that mean you sell out
today and go live in the woods? Certainly not. And it probably amounts to nothing. Like I said,
you hear these rumors all the time. It's just that the noise of it is getting kind of annoying right
now. Now as you can see crude is really in a trading band. You see that bouncing there, but
that's not even a dollar of bounce up and down right now. And so it's a good time and you are
beginning to see gasoline prices, more of them, just under three dollars a gallon. That's good
news. So that's helpful going into the Christmas season. And right now we're all holding our breath.
The preliminary numbers pre-black sale are weak and we're hoping that that just means that everyone's
waiting for Black Friday and they're all going to buy their brains out. But we're just going to have
to see if black, as I said in the last class, if Black Friday comes in weak, in other words not as
good as last year, we're probably going to have a bad Christmas season and that's going to be bad
for the economy. That's a bad message going into the new year. In other words, the Christmas season
is a leading indicator of business activity for the year following. And so we want to keep an eye
on that to see if it's going to be a good strong Black Friday or a bad Black Friday. The numbers
should start coming in Saturday night, Sunday. We should start seeing what happened on Black Friday.
So we keep an eye on that as finance people, those kinds of numbers. Now looking here at gold, as I
said, gold is showing no apocalyptic behavior. If you start to see the gold price surge upward,
especially if it crosses, even comes close to three thousand dollars an ounce, that is a warning sign,
that's a real warning sign. Right now it's just sitting there looking stupid, $2,700, $2,600 an
ounce, not moving much. So we're in good shape there. Coming over here, silver is behaving
differently than from what gold is right now. That's not terrible, but it does indicate
that the gold bugs are not in play right now. They're staying off the sidelines. But the
10-year bond, now this is getting to be a little ridiculous here. The yield on the 10-year bond
keeps going up, and that is going to stifle a recovery if it doesn't quit it. Because that
10-year bond, if it gets back up, I mean, the concern, the first neckline that would really
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.
I probably haven't said this before. If you go one, two, even five basis, four basis points movement, either way,
that's nothing. But once you get above four or five, about five, then that concerns us. And now we've got today,
it's up a whopping 12 basis points, and that's not good at all. It's, unfortunately, as you can see,
it's leveled off. We're coming to the end of the cycle, about four hours left on bonds today.
And right now the sell-off has ended. You see that sell-off there? That's price going down,
yield going up, the sell-off of the bonds. And interestingly enough, as you see over here,
just having a quick look back over here at the equities, that sell-off in bonds was generating
funds. Those funds are not going into equities. So that, and it's not going into gold either,
so that's clearly going into liquidity. But remember when I said that a lot of this money
isn't going into quick, high liquidity money markets, it's going into lower liquidity
CDs, certificates of deposit, one to three year CDs. And so that's concerning. In other words,
stashing money so that you can get to it if you have to, but it's stashed away for more than a day,
10 days, and all that. So there's no plan, it doesn't look like the investors have a plan
to bring those funds, those liquid funds, back onto the playground of equities in the near future.
And that just keeps happening and more and more every day more CD activity is going on. Now the
whole world of CDs sounds boring, but it's actually not that boring. I covered in 340, FIL 340, that
there is an active certificates of deposit primary market, but also there's a secondary market for
certificates of deposit. In other words, in this world, if you bought a CD from me, a substantial
interest penalty for early withdrawal, so you're stuck with it for three years, right? You're not,
because there's a secondary market. Someone else might want to buy your CD and there's a secondary
market. So that whole interest penalty for early withdrawal really isn't all that meaningful
anymore because of this highly active market. And there are brokers and there are also dealers in
CDs on the secondary market side. In other words, a broker takes an order, finds a match for it over
here. A dealer actually keeps an inventory of whatever security it is you're talking about.
So there are brokers and dealers and it's a thick market and there's more participants every day.
Traditional securities brokers are stepping into the world of CDs because there is a market for,
there is an active secondary market. So there's money to be made, so they're jumping into this
market. And so that's of some concern to us right now, that these CDs, first of all, they're gathered,
the number of CDs is growing. That's primary market. And the activity of trading in the CDs,
that's a secondary market, is picking up enough that you're having new players that used to do
only traditional kinds of deals in stocks and bonds. Now they're jumping into this too. And so yeah.
So like people going into the CDs, are they expecting the hailed savings accounts to be going down?
Yeah, yeah. Very good. That's exactly right. Yeah, that's the idea. And that's the major one. There
are other reasons, but that's a big one right there. Good point. And what this means is that
there are a lot of flashes of danger ahead. And whether or not those are just some storm off in
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
excitement. It is a time of a lot of excitement. The heading belief that what was the election was
going to be the golden age of trading and finance, that's going away pretty quickly,
because especially because of the concern about a global tariff war, which would put us back to 1929
and what happened after that. That's a concern and it's beginning to build on Wall Street.
But it's not a reason for trading out and getting out right now. It's certainly not at all.
I don't want to give that an impression. Now the one thing though is that we do see the dollar
sliding against other currencies. It's beginning to weaken and that's just how it is. You see
just as a quick mention and if you want to get more, if you're interested in international finance,
I teach it and we also have, Stella teaches it, and it's really interesting stuff. And the math
isn't so bad. It's just you have to keep straight on what makes what happen. But the dollar is
sliding against the euro, which is because of a belief that the strength of the American economy
is not as great as it is against Europe. Now if you look over here and you check on the pound
sterling, it's plummeting against the British pound. And the Japanese, it looks like it's going up,
it's not. Their quotes are backwards because yen are of such small value compared to the dollar,
they have to quote it backwards. So what you see going up, the dollar appreciating, is actually
the dollar depreciating against the yen. If you look here, the yen is USD to yen. Over here,
that's euro to USD and it's also Great Britain pound to USD. So this one's a backward quote.
This is that one, the USD to Japanese yen is a direct quote because it's one dollar
and the others are indirect. More likely you see indirect quotes for everything and you want to
keep that it that way, but they have to quote it as a direct quote for the Japanese yen because
it's worth so little. Look at this, 154.75, one dollar will buy you 154.75 yen. So if you turn
that around, that would be in tiny decimal places if you turned it into an indirect quote.
But anyway, that's that one going on. Now a few on the horizon. This is a cautionary tale. Let
me show you just a couple of stocks and what it means of beta and its relationship to risk. One
that I'll show you right now is Micron. Micron swings badly. It's not an amateur's kind of game.
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,
that is risk-rich-large. Look at that. It surges and falls and surges and falls. Now if you have the,
if you do cardio and you have your heart doctor's permission, this is a stock that you might want to
go with, but it's certainly not something that you are going to say, well I'm rich, now I can live the
great life because tomorrow you might not be rich and you'll be living in a dumpster. And that's a
good example of that. Another one which had a boost because of the belief that the owner's new
government position will make him have more ability to leverage that on his company is Tesla. On one
day it surges and the next day it just crashes. Going back here again, look at one year, and you
will see the ups and downs and the spike and now correcting off the spike again. And of course the
Tesla beta is insanely high and so if you're going to buy something like this, it's not one of those
buy it and hold it for a week and make a fortune and then get out. If you're going to do a stock
like this, this is just something you have to put in a drawer and walk away from and in 10 years you
see where you are. That's one of the things about highly volatile stocks. Unless you think you're a
genius at timing, they are not quickie investments at all. And I just want to bring those up to you
as one of those last things that I can impart to you before you leave me and I never see you again
because you all go to Wall Street and make a fortune and then forget about your old professor
here. But anyway, enough of that. Let me get down to the lecture here. Now I've uploaded another new
version of that worksheet. This is capital budgeting. Figure out whether saw courses, whether
project or go or no go. Now let me go over here to view student and just to remind you of where you
want to be in this is pretty straightforward. Files, go to your spreadsheets. I said go to your
spreadsheets and you use the NPV and IRR spreadsheet. This should solve all of your... yes please.
I had an example on here I forgot to get it. But this is good enough that it should get you through
almost... oh I did not want that. Please don't, please don't. No, no, no. I want to download
NPV and IRR. I thought I did and it didn't show up. Oh it is up. Okay. Oh okay. Good.
This should get you through about any problem that you would need. Now I'm going to assume you already
know NPV IRR, at least what it is. This is our go no go for finding project whether we're going
to take on projects or not. And it all boils down to free cash flow. We project the free cash flow
and I've shown you some of that in chapter 11, went through some of it. And we just lay out the
free cash flows for a company and then from there we get a couple of metrics. Now I'm repeating some
of what I've done before here but let me do it again. The three methods, and I'm just repeating
myself here, are the payback period method. It's old, it's bad, you shouldn't use it, but it's still
out there. And then you have the two biggies, the net present value method and the other one,
the internal rate of return method. The most popular of these is the internal rate of return method.
It is the one that's also the weakest of all of them, of the two I should say. The net present
value method and the internal rate of return method are mathematically and scientifically
sound. They essentially assess where a project, the present value of a project gets below the
point where it can't pay for the initial investment in it. Now the two different methods, and again I
just want to make sure that you have this down, when you get a question on a quiz or an exam,
just put the stupid numbers in. Don't think about what you're doing too much. That's all I ask of
you is that we have Excel, we use Excel in our day and age, so we don't have to do manual calculations.
In fact, what Excel is doing, and this spreadsheet right now, the first thing that it is doing is it
is taking each of the free cash flows and finding its present value and then adding them up and then
subtracting the initial investment. That's all it's doing, but the whole key is the discount rate
that you use to do that. And like I said, valid, well what most companies use, they use their weighted
average cost of capital. That's what they use. That's not a good idea because the weighted average
cost of capital is essentially the measure of the risk of the entire company as an interest rate.
Whereas a project itself might not be the same risk as the company as a whole. So you're sort of
forcing every project to live to the expectations that the company overall has, and that might not
be valid. A better method would be to use the capital asset pricing model. That's another method
that you can use, but there are other methods out there too, and I won't emphasize them too much.
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
work, especially in the first years. If you're in corporate and you are analyzing projects, you will
be given a discount rate. Thou shalt use this discount rate, and that's all there will be to it.
Now the NPV, now again I emphasize, this is not, you don't bother with this. You leave it alone.
Leave it TF alone. It is merely there to show you a comparative. Okay, I'm going to try 7% and see
what my NPV is. That's that point on that line. Let me back this off just a little bit. That's
that point on the line. 7% and it has an NPV of about $2,500. And then this one is just a comparison.
What is the NPV at 12%? Well, it's negative 42, 4,300. That's that point there, and then this is the
NPV profile line. That's, and as you can see, if I were to adjust to let's say 8%, it would plot a
different line. That's all that's doing. So that just gives you a visuality to the exercise. Good
news. Okay, the next thing is that the point where they crop, where the profile line crosses the
discount rate axis, the horizontal axis, that is the internal rate of return. That's the holy grail,
as it were, of a lot of company decision-making. It has the flaw that if the sign of the cash,
free cash flow switches more than once, there will be multiple internal rates of return. It's
actually, if it crosses twice, the internal rate of return, the profile line is a parabola. If it
crosses three times, the NPV profile line is a cubic. The polynomial, the degree of the polynomial,
the highest part of which X occurs, is the shape of the NPV profile line. You see that it crosses
once here? So that's a linear equation. X to the first power is the highest power of X. So that's
why that happens. That is not always how the real world works though. There are several different
scenarios where you could get into free cash flow. For example, one classic is where you start out
with an initial investment. You cruise along over the life of the project, but in the last year,
you get your residual, last sell, last inventory, but your salvage value is negative because it
costs to close it down and you're paying more to close it down than you get from the last year of
sales. So you could have negative, then a string of positives, that's one switch, and then at the
last year, it switches back to negative. So it's got two sign switches, which would mean that the
NPV profile line would actually be a parabola, and that means that there are two internal rates
of return, neither of which means anything whatsoever. They are what we call spurious
solutions. They're spurious. So that makes the traditional internal rate of return not really
the best way to use every time you need an internal rate of return. But let me hold that off for a
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
it. And Excel fortunately can do that because if you have to do that by hand, it is a pain in the
butt. It's called the modified internal rate of return. But let me go through something here. This,
okay, this one, positive, accept, negative, reject, that's all there is to it. Its challenge is finding
a discount rate. How do most companies do it? They cop out and say whack. They just say 7% or
whatever their whack is. They don't use the cap M. They don't use bond plus equity premium. They
don't do any of that. They just say whack. So it is, even at that, it's still, it is straightforward.
Negative, if the project NPV is negative, well, you say reject. If it's positive, you say accept.
But the internal rate of return has another way that it is used. The internal rate of return in
a way is called the breakeven, I've even heard this term, the breakeven ROI. So for example,
suppose that a project, well, let me show you this one here. Suppose that I say, okay, the internal
rate of return of this project is 8.75%. See, it calculates it for you. But what if I say that we
have a project that has an internal rate of return of, let's say, 8%. Well, 8% would be down here.
That's a negative. So if we have an internal rate of return of a project that is unacceptable,
we would reject it. Now here's how they use it in business. They usually use a term, and there are
other terms for it, but they use a term called hurdle rate. This is essentially the internal
rate of return that we will use for evaluating projects. So suppose that a company, so in other
words, let's say that the hurdle rate is 10%. So in other words, out here at 10%, that's our
threshold. So suppose that we do an NPV IRR and we have a project that comes in with a,
project A has an internal rate of return of 8, let's say 8.5%. Whatever else we know or don't
know, we know that this project A crosses the discount rate axis at 8.5%. That means that we
would reject this project because at our hurdle rate of 10%, this is a negative NPV project. So
the decision criterion works like this. Set your hurdle rate. Then any project that has an internal
rate of return, project internal rate of return less than the hurdle rate, we reject because it
doesn't meet our threshold. Any project above that hurdle rate, internal rate of return, we accept.
That's how you do it. It's a very simple method. All you have to do is crank out the IRR of the
project. Notice that, by the way, let me warn you of something. When you're calculating an
internal rate of return, you don't need a discount rate. I may be repeating what I said in the last
lecture, but I have to emphasize this. I'll give you two problems on the final exam, let's say.
One will be find the NPV. I'll give you a free cash flow, find the NPV. Well, in order to find
the NPV, you need the free cash flow, you need a discount rate. But then I'll give you one where
I'll give you the free cash flow and I'll say find the internal rate of return. Don't come up and ask
me, well, what's the discount rate? You don't need a discount rate. There's no use for it. The
internal rate of return is the discount rate. So you don't need a discount rate if all you're
finding is an internal rate of return. You see the temptation in this, though, is because you
can just crank out free cash flow analysis every day and all you need to do is run internal rate
of return. You don't need to worry about, God, what's discount rate? Just run the internal rate
of return and compare it to your corporate policy hurdle rate. And every company that uses internal
rate of return that I've run into has a hurdle rate. And the problem with that is kind of simple.
Where are you getting this hurdle rate? It would have to be purely subjective. You pull it out of
your ass. And I had, when I was consulting, I had several companies that were, you know, they were
using internal rates of return. So they were very modern, very hip and with it. I said, well, where
did you get this hurdle rate? I had one that had a hurdle rate on projects of 12.5%. And I said,
well, where did that come from? And they were actually, only one person offered us an answer.
He said, well, I know that it was, some years back, it was 12.5% when I first came here and we just
never changed it. That's the way we always do it. But you see, that's, it doesn't take into account
varying interest rates over time in the macro economy, the growth of the corporation, what its
risk profile changing through time. 12.5% is actually a pretty steep, especially back in that
time when I was doing this. That was a pretty steep, in other words, a project would really have to pay
off big to get an internal rate of return above a 12.5% hurdle rate. In other words, the company was
essentially biasing itself away from safe projects. See, if you had a project that came in with an
internal rate of return of 6%, they say reject it. Well, that might be a good project. It's just a
very safe project. Doesn't return a lot of money, but it's a very safe project. But if you find one
that has a 20% internal rate of return, well, that's, yeah, we'll take that one any day. But
you're also taking on a frickin boatload of risk with a project. So in other words, it was constantly
making itself a riskier corporation because it would take only projects that were at least as
good as 12.5%. And if the higher it was above the hurdle rate, the better they loved it. And so that
just constantly increased the risk of the corporation because it was taking on risky projects and it was
rejecting safe projects. Even though they would have been perfectly okay, they didn't want them
because they did not meet that hurdle rate that the company had set. And ask the company, well,
why did you use that hurdle rate? They couldn't tell me. They just said, that's what we do. And
then they kind of sometimes say, well, we got this guy, he does some pretty fancy math, and this is
what he figured out. Oh, you probably got some guy named Earl down at Earl's Bar and Grill, and he
does financial consulting on the side. Yeah, yeah, that probably was about it. Okay, so in other words,
this is a popular method. Internal rate of return, set the hurdle rate, reject any project that has
an IRR below the hurdle rate, accept any project that has an IRR above the hurdle rate. Okay, so we're
all good and dandy now, except for the fact that internal rate of return does not work if there's
more than one flip in the sign of the cash flow. Matter of fact, you could put in a, let me show
you something here. You could put in the numbers for a free cash flow with a negative value in one
of them, and you know what would happen? Excel, a financial calculator, will give you an internal
rate of return. But what it did was, okay, let me show you. Here would be a possible NPV profile
line if you had two sign switches. It would be a parabola, degree two polynomial, two roots, in other
words, two IRRs. Well, what Excel and a financial calculator do is they just start somewhere and
they start searching. And let's say it starts at a low rate. Now it's doing this at the speed of
light so you don't see how much it's doing here. But it's a, okay, we've got a negative NPV. That
means that we are already on the wrong side. So it's going to go down and it's just going to get
more negative. So it starts running this way and it says, bing, bing, oh, we've got a positive NPV.
So the internal rate of return must be between here and here. And it'll just zero in on that. Like
I said, at the speed of light, you're not seeing this happen. And then it says, here's your internal
rate of return. If it had started somewhere like up here, it would have seen that the NPVs were
falling and then it would have gone over here and it would have worked its way back and forth. Which
one it would find is purely where it would start. And it would mean anything. Neither of them really
means one damn thing. Now some books, I don't know if this one, there was a previous edition that tried
to give some kind of a weird ass explanation. Well, this one means this. Don't, just don't. There is a
way to modify the internal rate of return to make it so that it gives, it has only one sign switch.
It's called the modified internal rate of return, the MIRR. And thank God we have that. Because let
me show you, I've got an MIRR here. MIRR, okay. See this one, it's got a sign switch here, that's one.
Then it switches, that's two. And then it switches, that's three. So in other words, this would, the NPV
profile line would actually be a cubic equations graph. This son of a bitch would look like,
excuse me, would look like that. Three internal rates of return. Well we can't have two, so we sure as
heck can't have three. So you've got to figure out a way, is there a way to straighten this up? In
other words, to go, like that. And there is. It's stupid, but it actually works in a pig's eye. It
works on, you have to think about this. So if, see how they're at year zero and then at year three,
you have to throw money into the project. Now obviously there would be some cost of that capital
to do that. So we call that the financing rate. I put six percent here, you could put other things.
But you see, on the other hand, see these years when it's making money, 15,000, 50,000, 70,000,
10,000. That's when it's got money coming out into retained earnings that it could use for
reinvestments, investments in other things. So in other words, in this problem there are really two
different interest rates, discount rates as it were, or compounding rates. There is a six percent
cost of financing. That would be a discount rate. And then there is also an interest rate, what we
make off extra that we make in a project. Okay, we made 15 grand in the first year. Well, we can do
something with that. So that would be a reinvestment rate of the company, whatever it can put money
into inside the company or invest in other companies, whatever. But there will be two different
rates. Now, here's the pain in the butt part of it if you do it by hand. First of all, you take
anything that's negative and discount it back at the finance rate to the beginning and add it to
the initial investment. And then you take any time that the project spits out money and you throw it
forward as a future value to the end of the project, compounding at the investment rate. So in other
words, what you're doing basically in this project, in this right here, is if I do these as one, two,
three, four, five, was this a five year project? Yeah. Okay. Oh, I got to do a zero here. So there in
year zero, there's a negative. And then there's a positive and a positive. And then a negative and
then a positive and a positive. So what you're doing is you are discounting any negatives back
to the present, taking a present value of them, adding them up. And it's taking any positives and
you're finding the future value. So this one is present value at the discount rate. And all these
that are positives, you're taking forward as future values and clustering them all up. And then you
just zero all the numbers in between because you've done something with them. So in other words,
what Excel is doing, what we used to do by hand, and I don't want to see, I want you to live better
lives than I did. What we're doing, what Excel is doing is it's actually taking the present value of
12,000, negative 12,000 and adding it to 120,000. And then it makes that 12,000 a zero. And then it's
taking the future value at that compounding rate, the reinvestment rate, and it's taking all of
those forward to your five. And then it's making those zeros because you've done something with
them. And then it finds the internal rate of return of that number there at the beginning,
a zero, a zero, a zero, a zero, and the last year right there. And it's finding the internal rate
of return of basically a negative number at the beginning and a positive number at the end. And
that's finding the internal rate of return of that mess. That's called a modified internal rate of
return, MIRR. And you can do this. Let me do a, I'll do a couple of other projects. But before I
show you that, notice that the modified internal rate of return of this project is 5.37%. Do you
see that the financing rate is 6%? This is a project you shouldn't take because the project
overall has a return that is less than it costs you to finance it. Let me say that again. This
project is coming out with an overall return of 5.37%. But the capital that I needed to make this
project happen costs me 6%. Well, that sucks. Here's a rule. It should not cost more than you
make. That's just, it's just basically at its heart, it's just a pretty simple, stupid ass rule.
That's all it is. So that's worth your attention. But MIRR is, is if there's more than one sign
switch in the free cash flow, then just use MIRR. Now on a quiz or an exam, well, that's all you do
is just put in the numbers and look at the result. Now, there are some simple problems. I think the
book has one where the financing rate and the reinvestment rate are the same. That's kind of
unrealistic. But you know, put, just put in whatever they say the financing rate is and what the
reinvestment rate is and just put in the free cash flows, whatever I tell you they are, and there's
your answer. That's all there is to it. And let me tell you again, I can't emphasize enough, that it
is a lot easier to do it with Excel. The book uses a financial calculator, a cheapo BA2, and says,
well, you key this here and you key that there and then you swing around a cat and you offer your
firstborn. Just use Excel to do this. It's a lot faster. These templates, I mean, they aren't
sophisticated at all, but it certainly is easier than doing it with financial calculators, basic
financial calculators, and it sure is heck a lot easier than doing it manually. That's that one.
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
want to download this again. Payback period method. If you want to get down to the fraction of the
year in which you cover your initial investment, I've written a small sheet right here and you can
extend this if you want out further. But in this project right here, you start out with an
investment of $100 and then you make $10 in your first year, 60 in your second year, and 80 in your
third year, maybe some more. But as you can see, if the year of crossing, it was some time before
year three. Now you could just say simply, okay, whatever our, let's say that we have a required
payback period of four years. Okay, we take the project because it clearly pays for itself after
three years. Now if they want to say just exactly how much of three years, well then you have to
work a little harder. I've got a formula here that will tell you exactly the number of years to cross
into the payback period. In this case, the payback period, you can say three years, but if you want
to be exact about it, it's 2.38 years. And I've got a formula right here that cranks it out for you.
If you want to suffer, you can see that nested if statement that I wrote to do that, but there it is,
if you need the actual exact number of years. And like I said, you can extend this, just drag the
formula down and you can get, if it's like it doesn't pay off until year five, it'll do that
for you too. So there you go, that's all there is to that one. So that's your payback period method.
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
mutually exclusive projects, that can be difficult. I encountered, now technically there's an argument
among finance people that you should never have mutually exclusive projects. There's always
a way that you could run, if it's two good projects, you should be able to do both of them,
if they both have strong NPVs. But there are, and I did encounter it, where at least in the
time period in which the decision had to be made, there were two projects that were mutually
exclusive. And I had to dig through some ancient notes of mine, because I keep forgetting how it
worked, but this company had a very large piece of land, well it wasn't very large, it was about
five acres of land, and there were two possible ways that they could take that land. One was for
an industrial park, they were a business park for companies, it wasn't really high tech back in that
time, that was in the early 90s, but they had more or less, they could put up all these office
buildings, two floors, and they could run it that way. And then they had another possibility on their
table, where they could take that land and they could turn it into something that was very popular
back at the time. Now my original, I had had a memory that it was like an entertainment center,
but it was actually, when I look back, it was a kind of mall, partly outdoor mall, but it was a
special kind, and I've just noticed that it's kind of coming back into vogue very recently, whether
it's going to come back full-blown, it was one of those where you have the lower level is all these
shops and restaurants, entertainment everywhere, and then on the second and third floor it was
upscale, what we called yuppie in the time, young upwardly mobile people, apartments with balconies
and they could sit out there like, sort of like an Italian villa type of environment. They had a,
they planned, you know, some restaurants and some shopping and there was even a plan for a daycare
center in there and all this, but they could not do both with the same piece of land, so they were
mutually exclusive projects, and that was where the question, well, which one do we use? Well the
funniest thing was, let me show you the two NPV profile lines of these. One of them had an NPV
profile line that looked something like this. The other one had an NPV profile line that, well,
that's a little too steep, but it had a much steeper NPV profile line, like that. See, the
problem was that they had different internal rates of return. This was project A and this was project
B. Project B had a lower internal rate of return than project A, but at low discount rates it had a
higher NPV. See how project B had discount rates down in here, it had that NPV, whereas project A
had that NPV. So at low discount rates for fighting the NPV, you'd say accept project B, but at high
discount rates, like up in here, this one would actually have a negative NPV. B would have a
negative NPV. So the whole question was, it came down to, well, we've got to choose a discount rate.
Now, the trick here is to find the crossover rate, because it's a crossover rate. Any discount rate
you would use below the crossover rate, you'd take B. Any discount rate above the crossover rate,
you would take A. And so it would just boil down to, well, what are we going to use for our discount
rate? And they said, well, why don't we use a hurdle rate? And the problem was that their hurdle
rate was lower than the IRR of either of them. So with the hurdle rate, you'd take them both,
but you couldn't take them both. See, if I had a hurdle rate down here somewhere, you'd take both
of them because they both exceed their internal rates of return, exceed the hurdle rate. And their
hurdle rate was actually fairly low. And so they said, by the hurdle rate, internal rate of return
method, we take them both. And so it all boils down to the crossover rate. Now, I will not ask you to
find a crossover rate. I'm bringing it up here because it does happen from time to time. You have
two projects and you just can't do both of them because of some constraint on you. Oftentimes,
that constraint is land. Land you don't have access to. And that was the case with the convention
center in downtown Bloomington. They had one piece of land and they had to decide what to do with it.
There were several different things they could have done. For one thing, they could have sold it.
They could have made this convention center, which is what they did, or they could have made it into
some kind of a community entertainment center. A lot of different things, some of it's kind of related.
But they did not even consider mutually exclusive projects. They were hell-bent on one. And if they
had considered other projects, they probably would have, and also been more realistic in their
assessments of future expected free cash flows, they probably would have taken something else.
So it's worth it to say, what else could we do? You don't obsess with it, but you ask, are there
other possibly profitable things you can do? This mostly happens in real estate, where you can decide,
okay, a residential apartment complex or something commercial. That's a big one for a lot of this
mutually exclusive decision making. A strip mall versus an indoor mall, things like that.
That's where this comes in. Now, one last one that I will bring up. It's the simplest one in the world
to do. And almost any business person who's an entrepreneur is going to do this if he possibly
can. It's very straightforward. And I do it. And I even have my numbers to show you what it means.
It's called breakeven. Breakeven is simple. It just works like this. Look, your profit is going to be
your revenue minus your costs. And you're going to say, I'm in college for a degree and I already
knew this. What are you getting at? Very simple idea. Now, the costs actually have two parts.
There are the variable costs and there's a fixed cost. Now, the variable cost moves with your output,
moves with your sales. My variable costs. So, give you an example. In my business, the average,
I make and sell art. Photographs, paintings, that kind of stuff. Okay, so I have to get that ready for a show.
Okay, so at the show, I'm going to have the cost of the frame, the dry mount board, the dust backing,
the museum glass, the wire, and all that. Put that together, that runs approximately, if I do it with good
quality stuff, $225 per unit of art. So, in other words, my unit variable cost is that. But I also have fixed cost,
the cost of the exhibition fee. Sometimes it's not bad, sometimes it's a killer. I also have the fixed cost,
whether I sell anything or not, these are going to be there. They're fixed. I have the cost of driving to the
show and driving back. And I have the cost of my infrastructure, my pop-up tent, my wire, my frames,
and all that kind of stuff. And that fixed cost on a seasonal divided by the number of shows that I do runs
about $2,000. And that adds in, that's including an estimate of my booth fee, what they call the booth fee,
the exhibition fee, and all that kind of stuff. So that's a fixed cost. And finally, I have my price of my art,
unit price. And that I average about $800 per artwork on average. We got all the pieces. So in other words,
my profit boils down to a simple, the price, unit price times the quantity minus these two, which would be
$225. Well, let me just put it this way, a little v times the output plus the fixed cost. Doing a little bit of
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
the first part. P minus v times q minus fc. First things first, if you look carefully, that is nothing but a
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.
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
this, q here, profit here, it looks like that. The y-intercept is negative fc, and the slope is little v minus p,
p minus little v. A little side note here. In common business terminology, we call that price minus unit variable
cost, unit price minus unit variable cost, we call that profit, we call that our margin, our unit margin. It's just
the way, it's just a term. Technically, margins are supposed to be part of ratio and all, but the common lingo is
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.
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.
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
profit. So in other words, we want the zero point of profit, which would be p minus v, the unit margin, times the
break even quantity minus the fixed cost. That is what we're after. So in this, you rearrange it a little bit, and the
survey says that your quantity break even, adding fc to both sides and dividing by the p minus v, is fixed cost over unit
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.
The better your spread between unit price and unit variable cost, the lower your break even. And this, all you have to do in
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
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
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
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
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
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.
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.
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,
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
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
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
you're all done. Okay, that's all I have for you today. I thank you.