The Illinois State Collegiate Compendium, Academic Lecture in Business and Economics.
This is Business Finance, FIL 240 for Autumn semester 2023.
Today, the weighted average cost of capital and we will go into that in just a little bit here.
A couple of other little pointers as far as class goes.
I'll have a pop quiz on Wednesday of next week, a surprise quiz and as usual I ask that you please be surprised by it.
What else was I thinking? The content today, I've built a template for you, but I'm going to set it up on the whiteboard, at least partially.
I tried to do it completely on the whiteboard in the last class and that was a fiasco of my bad calculations and all that.
So I don't think I'll do it in quite such detail this time around, but that will help a lot with this.
Now, there are a couple of tricks here that I can do to make the spreadsheets move faster for you.
The problem is, as I found out the hard way in the last class, I don't think you can do them on a Mac.
I'm not sure, but every different way that we tried it, it just didn't work.
But the main thing is that the primary worksheet works fine.
The real issue is just getting the numbers into the places so that the calculations part of Excel can take control of it and get you your answers.
But I'll get to that in a little bit here.
First, let's have a look at the numbers and the numbers are just peachy today.
The Dow up two-thirds of a percent, the S&P 500 up more than a percent, and the NASDAQ up almost one and two-thirds percent.
Back to the usual way that the numbers look, comparatively speaking.
Now, another thing here, look at the S&P 500, the volume on it.
It's still well below the 52-week daily average of 3.7 billion shares.
However, you notice if you've been watching these numbers with me every time we hold the class, it's been creeping upward.
Today, it was nearly 2.8 billion.
So the investors are, it looks like they're coming off the sidelines and beginning to put money into the markets.
Now, again, on the markets, we had a good, strong bull day.
And as you know, the bull, you had a bull, explained to you that it's a bull market.
And even when the bears try to bully the bulls, it still works out just fine in the end for the bulls.
One brief mention right here.
The crude oil has broken through its lower resistance at 82, and we're now clear down to 80.91.
$80.91 per barrel on the light sweet Brent benchmark.
That is really good news, obviously, boosts the economy.
However, I don't know that it will actually, we'll see gasoline prices are going to probably ease up over the next week if the oil price stays down.
We may see as low as right around here, $3.19 a gallon.
However, I don't think it'll be going down as much as one might hope, because if you look at the price of diesel right now, it's running at almost $4.20 a gallon.
So that would indicate that there are probably the oil, there will be more production of distillates like diesel just to fill in what appears to be a little bit of a low supply in it right now.
That higher price floor supply produced more of the diesel so you can get it into the pipeline at the expense of producing more gasoline.
So that might put a damper on too much drop in the price of gas for the time being.
Gold finally broke below its $2,000 resistance level.
It got above it, and it chickened out and ran back down.
Good news again, the apocalypse freaks aren't buying gold.
Looking at the euro and the pound and the yen all slid, which is good news, dollar appreciating against these currencies.
But it seems that the euro at least, and the other ones too, are in more or less a trading band around 105 to 106 right now.
So there's that.
Now, 10-year bonds.
Yields are down.
Good news, that means prices are up.
So in other words, investors are buying bonds.
They're buying into the bond market.
That's causing the yields to go the opposite way.
Yields are going down.
That means interest rates are going down.
There was an article, I think it was yesterday, that said that home mortgage rates are starting to slide back again for the first time in quite a whole lot of months.
So that is good news.
Stimulating the economy, lower energy costs, lower mortgage loan rates.
This is all good news for the economy.
We're probably on a roll.
We're still in a kind of a recovery, but we're getting toward an expansion.
That's good news for you, because that means business activity will increase.
That means that more jobs will be available, and you will have a job, an internship or a job, until artificial intelligence takes away all of our jobs and ends us as a species.
So for the time being, they'll celebrate.
Over on the other side of the world, sides of the world, last night, the Nikkei just jumped right at the bell.
It was up.
That meant that before the bell, there was some good news that punched the market up.
But then from there, there was no more news, good or bad, so it just floated for the rest of the day.
And then once the sun had set in Tokyo and it began to rise in Europe and then in London, I don't even know what to say about.
London has been choppy, ups and downs.
You see how that started up, dipped into negatives, did a bull run, and then the bears took over again.
So I'm not sure what's going on over there in Great Britain, but there's considerable volatility in the day-to-day market activity.
Now, let me go on here.
Now, I have a spreadsheet to show you on this, and I'll get to that in a little bit here.
Just some happy news, though, that this mathematically, it's arithmetic and calculator, but it can get tedious as heck.
The subject is calculating the weighted average cost of capital, the WAC.
This thing, as I said on Monday, it's important to businesses.
You may even hear it from time to time in whatever business field you're in in your company.
They'll mention WAC.
For one thing, it is frequently used as a discount rate for projects, for NPVs and all that.
It shouldn't be, but it is.
But even on its own, the weighted average cost of capital has a lot of meaning to it in terms of the cost of financing the company,
financing the company as it is, financing the company as it will be with more projects in it.
So, the weighted average cost of capital is equal to the weight of debt times the after-tax cost of debt plus the weight of equity times the cost of equity.
Nothing complicated there.
Now, the weight of equity has three pieces.
There is the weight of preferred times the cost of preferred stock.
There's the weight of common stock times the cost of common stock, R sub S.
There's another one which I'm not going to push today.
I'll bring it up on Monday just as one last side note.
There's also the weight of new issue common stock times the cost of new issue common stock, R sub N.
For now, we can dispense with that one.
We're just looking for a straight-up, clean weighted average cost of capital.
No new financing, just what we've got, what the company is as it is right now,
not as it would be if it issued more stock for some reason.
Now, all of these, you will recall that I gave you the formulas, the component cost of capital.
So, for example, the cost of preferred is the dividend on preferred divided by the price right now of preferred common stock.
Did you just get the dividend?
Remember, the dividend is the par value of the common stock times the cost of the common stock times the par value.
The dividend times the par value.
Now, the cost of debt, of course, after taxes, is the cost of debt pre-tax times one minus the tax rate.
For right now, until someone changes it, it's 21%.
Even some of the more recent textbooks have it, the top marginal tax bracket is 35% or 39%.
But that massive tax cut in 2017 drove the top marginal tax rate to 21% for companies, for corporate America.
Just a gift that just keeps on giving for the big companies.
So there's that.
Okay.
The pain in the ass is the cost of equity, R sub S.
You will recall that I actually gave you three formulas.
If it's an old company that has constant growth dividends, R sub S would be the D1 over P0, the dividend one period out over the price of the common stock plus G,
where D1 is equal to the current dividend, the dividend just paid time, grown one period, times one plus G.
But I said if it's not an old company with constant growth rate dividends, then you would slide over to the capital asset pricing model.
The expected return to the stock is going to be the risk-free rate plus the beta of the stock times the expected return to the market portfolio minus the risk-free rate.
But then I gave you a third way to do it, where the return to the stock would be the current bond yield plus an equity premium of the industry, the industry equity premium.
So you would have to read the problem to see which one of those you would use.
Like if I gave you the risk-free rate, the dividend, and the growth rate of the dividends, you'd know you'd use the first formula.
If I gave you the beta and the risk-free rate and the expected return to the market, you'd know you'd use the capital asset pricing model.
But if I gave you the bond yield the company was currently experiencing and I gave you the equity premium, then you would probably use the last of those formulas, yield plus equity premium.
So here's what I'll do.
Any problem I give you on a quiz or an exam, it'll use the first way.
You'll use the first one.
In other words, I'll give you the current dividend, the growth rate of the dividends, and the current price.
That way you're not scrambling trying to figure out what the heck you're supposed to use for a problem.
I might ask you about the three different ways in some kind of a question, multiple choice or something like that, but I won't have you do it in a calculation kind of thing.
Now as far as the weights of these, the weights,
the first thing you have to do is get the debt.
You get the market value of the debt.
I'll give you the weight for the preferred stock.
You get the market value of the preferred stock.
For the common stock, you get the market value of the common stock.
If you add those three values, they'll be big numbers.
If you add those up, you get the total market value of the company.
To get the weights, you take each one of these values divided by the total.
The weight of debt would be the market value of debt divided by the total.
To get the weight of the preferred, you take the market value of the preferred
over the total.
And to get the weight of the common stock, you take the market value of the common stock divided by the total.
And then for the WAC, each weight times the cost of the component.
In theory, this is not hard, it's just arithmetic.
In practice, it just can be a pain, all those calculations.
Hence why we invented Excel, it works hard so we don't have to.
The one thing that I should caution here is that this weight of debt,
you're going to need to get the yield to maturity on the debt.
You can't use the coupon, you need to use the yield to maturity.
Now, this template, I will upload it, what I've got here, and I'm going to walk it through with you.
We're going to need costs and we're going to need weights.
We're going to need the component costs and we're going to need the component weights.
And here's how it works.
Now, let's do the debt first.
This is that little mini version of that bond yield calculation template that I gave you earlier.
It's recreated here in the context of calculating weighted average cost of capital.
Now, watch what I'm going to do.
You've got a bond, now in this example that I have here, the bond price on the 100
is 102.40
and it's due in 2031.
With a coupon of 4.25 percent.
That will give us the information to get the yield to maturity.
The 102.40, okay, it has eight years to maturity.
You just figure that out and you put it right there.
The settlement date you don't have to do, nor do you have to do the maturity date.
It will work that out for you.
So I'm going to put those in gray so you know you don't have to fill those in.
You can do one or two payments a year.
It doesn't materially affect the result.
The day's basis is 360.
You don't have to change that either.
And that will give you the 4.39 percent for the cost of debt.
But we're not finished yet.
We need to fill in some information over here.
Let's say that the preferred is 2.00 percent
value $85 per share currently priced at $63 per share.
So I'm at the sell.
Wrap the text.
There you go.
Common stock just paid a $1.80 per share dividend
that is expected to grow at 2 percent per year
and is currently priced at $34 per share.
Wrap that text.
Center it.
Okay, good.
Okay.
Over here, the problem will give you some information.
The par value on the thousand of the company's bonds
outstanding is $12 million.
The number of preferred shares is $120,000.
And the number of common shares is $22 million.
Common share is outstanding, I should say.
Wrap that text.
And again, I'm going to upload this.
These are the pieces of the numbers that you will need
to get your answers, your information.
Wait, let me do this.
Fix some of this formatting. That turned spectacularly bad.
Let me do something here.
I apologize for this, I just want to make sure that...
There we go. That should help a little bit here.
Merge and center.
Let's try that one more time.
Merge and center. Merge and center.
I'm trying here to get that all fitted in, and it's not being too cooperative.
I'll just do it that way. That way nothing is stretched out too much.
This is just making it a little easier for you to see the information.
Okay, you just fill in these numbers.
Now you're not going to touch the tax rate, just leave that at 21%.
The cost of debt will automatically feed to here.
You calculate the cost of debt and it will show up here.
And then the after-tax cost of debt will automatically show up
because it will take this number times this number.
The preferred dividend you put in from the narrative.
The par value you put in from the narrative.
The price of the preferred you put in.
The common dividend, the growth rate.
Oh, that was 1.5%.
Glad I did that. That would have been difficult.
The common stock, the dividend, the price per share.
You fill in these numbers, the ones that aren't shaded.
The 21% is just given.
You calculate from the bond narrative here.
That gives you that number right there.
Give me a second here.
Nope, wrong place for that line.
There you go.
And this box gives you the information.
Insert, illustration, shapes, another arrow.
This box is where you put all that information.
And all this information right here comes from this box right here.
I wish it wouldn't keep taking that away.
Okay.
There you go.
Now let me explain how the machinery of this works.
Okay.
The cost.
You're going to put in all the information to do a bond yield calculation.
That's this information right here just like we did before.
102 on the 100.
Price, par value, you leave alone.
It's 100 on the, it's 100.
It's 1,000, but it's 100 on the 100.
And then the payments per year, you could put in one if you wanted.
Just leave it at two.
And then you put in the term of the bond.
Now since it's in 2031, that's eight years.
You put that in and these two will automatically calculate.
And there's your Uncle Bob, the 4.39%.
That will show up up here.
Your cost will be the bond price, the bond yield times one minus the tax rate.
It will do it automatically for you.
The same will be true for calculating the price, the cost of the preferred stock.
If you put these numbers in correctly here, all these numbers in properly here,
it will give you, it will automatically calculate the dividend divided by the
current price of preferred stock.
The common stock, it will do the same thing.
If you put these numbers in properly here, it will automatically do D1 over R plus G,
D1 over P zero plus G.
It will do it all for you.
Now the market values.
The value of the bonds is $12 million.
This will calculate automatically because each bond is worth,
the price of the bonds was 102.4 on the 100.
So it will take the total value of the bonds times 102 on the 100.
It will do it for you. So you don't have to calculate that.
Number of preferred shares.
You get that from over here. Well, number of preferred shares.
I could put that in there.
I wonder if I could sneak that in there.
Let me do that.
I'm going to insert to make that so you don't have to do that.
Insert.
By the way, I have a reason for doing all of this.
You're actually, the best way to learn something is to see it being done
instead of talking about it.
So you're seeing a bunch of little tricks here.
Shift cells down.
Number of preferred shares.
And put in the 12 million.
Is that how many there were?
12 million, I think.
How many preferred shares did I say there were?
120,000.
So I can make that number.
That's a number.
And then it will get, take care of that for you.
The market value of the preferred shares will be equal to...
Let me fix that.
Equals the price of the preferred times the number of preferred outstanding.
So you don't have to calculate any of these.
Because the market value of the stock will just be the number of shares outstanding.
Let me fix that one for you.
Oh, there it is.
Number of shares outstanding times the price per share, which is already over here.
So this number will calculate automatically.
And then this number will be just adding up these numbers.
So the weights are going to be equal to the market value of the debt divided by the total as an absolute reference.
And then I can just go down the line and calculate each of them.
So you don't have to calculate those.
The weighted average cost of capital will automatically calculate as the sum product of each cost times its weight.
That will be automatically calculated.
So if there's a shaded block, a shaded cell, you don't need to put anything there.
It will do it itself.
And the ones that you do put in, you just include those from the narrative.
I'm formatting it as I go along here.
You just read the narrative and you put the numbers in where they belong.
That should give you your weighted average cost of capital that fast.
Now, if you are using a PC, you can get the weights another way.
If you are using a PC, you don't have to do this calculation.
You just highlight the components and you'll see a little chart icon show up.
If you click on it, you'll get conditional formatting.
Click on totals and go over here to percentage, percent of total.
The little yellow will say that it will put the percentages over in the next column.
And it will do it on its own.
But if you don't have a PC, then you have to go back to the other way of doing it.
Get the same answer.
But conditional formatting can do some amazing things.
And of course, so does some product here.
That's how you calculate a weighted average cost of capital.
This is the Excel way.
It looks a little bit tedious, but I guarantee you that doing all of this by hand
would be a lot like work, doing all those calculations along the way.
This way, all you have to do is put in the stock information that you're given here.
You put those in.
For the bond, you have to put in the term, how many years are left, the coupon rate,
and that's it.
You put in the term, how long it's got left on it, the coupon rate, and the price on the 100.
Over here, you just put in the par value of the bonds, and then it will calculate that on its own
from the information you put in to get the yield.
Now notice that you have to do these in the order that I said.
From the left to the right, you're filling in information.
And then you just fill in the other information along here from that narrative,
and everything will calculate for you.
You want to try it this weekend, I recommend that you give it a stab.
Just throw in some numbers and see what happens.
This will save your bacon on an exam or a quiz.
And believe me, this is a lot easier to do than before we were using Excel.
We did all these calculating the costs one by one, and then the market values one by one.
Along the way, we had to get the yield to maturity on the bond by a calculator or a hand calculation.
I mean, it does look a little bit intense, but trust me when I tell you,
if you just get all the information in from left to right, everything will work just fine for you.
You could even put in another tax rate if they give you one in the homework.
But everything else, it just flows very nicely.
Trust me on that.
So I'm going to save this, and I'm going to upload it to your Canvas files and in the spreadsheets,
and you will be very happy for this to be there.
And the format of a question that I would give you would be right along the lines of the narrative.
I don't throw curveballs at you like that.
So if you can understand how the narrative translates to the numbers
that you fill in in the white cells during business.
Now, the next thing I'm going to talk about is something called the equity breakpoint.
There's a term that I will bring up on Monday called optimal capital structure.
It is the combination of debt and equity that minimizes the weighted average cost of capital.
It's the combination of debt and equity that minimizes the weighted average cost of capital.
So if I were to draw a curve, a weighted average cost of capital curve.
Here's the weighted average cost of capital on the vertical axis,
and here is the percent of debt on the horizontal axis,
where this would be a company that is 100% debt right here,
and this would be a company that's 0% debt.
Put another way, the leftmost tick mark would be a company that's pure equity.
The rightmost 100% would be a company that's pure debt.
In between those, if I have only equity,
then the weighted average cost of capital would just be the cost of common stock.
Weight of debt times the cost after tax cost of debt plus the weight of equity times the cost of equity.
In other words, if the weight of debt is 0, then W sub E is 100% times the cost of debt.
On the other hand, if the company is 100% debt,
then the second term W sub E times R sub S is 0,
so at 100%, that would be the after tax cost of debt.
So what a weighted average cost of capital curve looks like is something like this.
As you increase the amount of debt, debt is cheaper than equity at first,
and your weighted average cost of capital goes down.
You're using more debt, less equity, so the cheaper debt pulls the curve down.
But there's a point where your creditors are going to say,
you're getting awful frisky with debt, and we're going to start charging you more for debt,
and that begins to pull the curve back up.
This bottoming out point is called the optimal capital structure.
It's a combination of debt and equity that minimizes the weighted average cost of capital curve,
the optimal capital structure, and companies spend a lot of time to find out exactly where that is.
And it's not the same for all companies.
Some companies, 20% debt, 80% equity is where it bottoms out.
Some, 40% debt, 60% equity.
Some, 80% debt, 20% equity.
But once they find it, they really try hard to hold that cost, that combination of debt and equity.
So you see up here, if we were to say this company has found its optimal capital structure,
it's 16% debt and then 84% equity.
Really? No, I'm sorry. It's 1.6% debt and 98.4% equity.
We could just, look, companies are probably at any given time period near their optimal.
So when they start to finance new projects, grow their retained earnings,
they have to finance those by the same combination of debt and equity.
So if this company is, let's say, well, let's just do a simple example.
20% debt and 80% equity.
When they take on new money, they would use 20% debt and 80% equity
in order to stay at the same optimal capital structure.
This is called the equity breakpoint.
How much extra money could we raise before we'd have run out of equity?
So the way the formula works is it's the change in retained earnings
divided by the equity percent.
So in a case like this, let's say that the company anticipates change in growing by $30 million.
Then its equity breakpoint would be $30 million over.80.
If I were to work that out, the company's equity breakpoint would be, pull up a calculator,
$30 million divided by.8.
In other words, they could run up projects using $37,500,000 of equity.
They could do that.
But they would also have to use 20% debt, and they could grow,
they could change their retained earnings by a considerable amount of money.
$37,500,000 would be 80% of it, and then the debt would be the rest of it.
Just know the equity breakpoint.
I'll talk more about it in the next lecture on Monday.
But the last thing that I'm going to show you today, and that's just a side note.
Let me save this for you.
What I want to show you here is in reality, this is a huge thing.
Now this data is revised every January by the Stern School of Business at New York University.
And we're all grateful, both in academia and in industries, because they do pretty much
what I just showed you here, down to the Excel spreadsheets.
So they show you by industries.
They will give you the betas of the industries.
They will give you the cost of equity, which they calculate just like I did,
except they do it on an industry level.
So in advertising, they use 58 companies to do it.
They got the average beta of those companies.
They calculated the cost of equity, and then the equity over the debt plus equity,
just like I did here, except I put preferred, I separated out preferred and common.
And then they go, well, they do the standard deviation.
And then they do the cost of debt, cost of debt, just like I did in the spreadsheet.
And then the tax rate for the after-tax cost of debt.
See that?
And notice something.
I got to come back to that.
They don't use 21%.
That is just theoretical.
That's what the law says.
They dig in and they see what these companies really paid.
And it's a hell of a lot less than 21%.
You could look down that list, and the only one I see right off the top is cable TV,
which paid more, and that was because of certain special taxes on cable.
But do you see how virtually every one of those actual effective tax rates
is ridiculously low anymore?
That's the whole problem with these insane debts you guys are going to take on,
and you have to pay it, the national debt, the budget deficits every year.
It's because these rates, when I did this like 10 years ago,
these numbers were in the 20s and 30s.
And now their effective tax rates are down in the single digits
and in the teens.
That's enough bitching about that.
But they take the cost of debt times the actual tax rates, which I don't do.
I just use the statutory 21%.
But then they get the debt over the debt plus equity, which I did,
and then they get the weighted average cost of capital.
They don't even call it the WAC.
There it is.
Now, first of all, notice the numbers.
They are actually, for the most part, very tight, around 9 to 10%.
You've got a few down here, like banks.
Banks, retail versus the money centers, regional versus the money centers.
Good grief, those are low.
Poor bankers may suffer so much.
God.
Okay, but notice for the most part the numbers are very tight between 9 and 10.
There are a few that are up around 11, electrical, and there was one here.
I think software development.
Healthcare is a little higher on the weighted average cost of capital.
And then information services are higher.
And I'm not sure about that one, though.
You've got a few up here, but they are actually fairly tightly packed.
You see some of these are lower, and that's the result of effective tax rates
that are very generous on these.
Here's one, 12.
Huh, retail, building supplies at the retail.
In other words, your Home Depot and stuff like that.
Those industries that produce that stuff are, okay, semiconductors, they take a good hit.
That's one of the highest, semiconductor industry.
And yet we bitch about, we've got to bring all that semiconductor industry back to the U.S.
from China, and then we've got a high weighted average cost of capital for it,
which is a high weighted average cost of capital, I would bet,
because their effective tax rate is high.
Let me look here real quick.
Semiconductors, are you kidding me?
Yeah, it's not that bad.
Here's, that's interesting.
Okay, though, however, the bottom line, though, is this,
that the average weighted average cost of capital is 9.25%.
That was at the beginning of this year.
Now, interest rates went up in the economy over the year, but now they're sliding again,
so I'm not sure what to say about next year.
However, if you want to pull a weighted average cost of capital out for a discount rate,
you probably, 9.25% would be a decent number to use,
just as a stab for doing a discount of finding the present value of future expected cash flows.
You're not going to go wrong if you use about 9.25% for it.
One interesting thing, just to finish up, I talk about beta as if it's something very important.
Well, here we see it.
You're actually seeing, industry by industry, across the economy,
this is about all of it.
Is there something you notice about these betas?
Now, these are industry.
In other words, they're the weighted average betas of all the companies that are polled.
Like, for example, they, for polling for advertising, they took 58 companies,
and they found their average beta, and they took 77 companies for the aerospace defense.
Do you notice something about those betas?
Is there anything that just strikes you just visually from looking at those betas?
Anything you see that looks?
They're all overvalued.
They're all what?
Overvalued.
No, that's the PE ratio, just beta.
I think I know what you're saying, though.
They're above one.
Isn't that interesting?
Across the industries, the average beta is riskier than the market portfolio, the world portfolio.
And that's why you wouldn't want to make a portfolio that was industry-specific,
because you would probably guarantee that it had a beta that was higher than one.
You might like that, but at the same time, by just focusing on an industry,
you are going to get a beta probably above one if it's most of these.
Look at this one.
Auto and truck, the average beta of 51 companies, or how many is that?
31 companies.
The average beta is above 1.5.
So investing only in the auto industry is dooming your portfolio to have a lot of risk.
In fact, if you want to avoid risk, regional banks, they're very low risk, surprisingly.
And one of the reasons for that is because of this.
Banks are required to keep Tier 1 capital, super safe capital, cash and treasury bills.
So by the very nature of what is in the bank, cash and T-bills, a lot of them, the banks are very safe investments.
Yeah, asset management, same thing.
But okay, so anyway, I've uploaded this, by the way, in case you're interested in just kind of having a look at it just for personal investment purposes.
And I've got the website down here where you can go and get the data yourself to refresh it when January comes.
It usually shows up in early February.
They run the numbers using an Excel sheet.
They get these numbers and then you have this data for your own purposes.
Other than that, that's all I have for you today.
I thank you.