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.
Give me a minute here.
The one minor announcement.
I will have a quiz, a pop quiz for you next Wednesday, a week from today.
And that should cover this topic and a little bit of what we did in the previous week.
And this is kind of a math thing, but like I said, I'm going to build a template here with you just so you can get this down more quickly.
It's not all that hard, any given step, but there are a number of steps in it.
And the use of a template sort of clarifies how the steps go.
Of course, it will do the calculations too, but like I said, the calculations themselves aren't that hard.
It's just this doing this thing can wear you out.
But first, I'll look at the numbers, and the numbers are there.
And it was a bold day.
It wasn't a spectacular bold day, but it was a solid bold day.
You had the Dow up about 0.4%, and then the S&P 500 cranked up 0.65% and the NASDAQ, of course.
It's back to the typical kind of day.
NASDAQ up almost a full percent, not quite a full percent.
But I'm just curious about something here real quick.
Oh, well, I'll be darned.
Anyway, so decent day, and a lot of that is being driven by the Fed still holding the line on raising interest rates.
Very reasonably good economic conditions and all that.
Crude has actually punched through its lower resistance level of 82, and it's down there at 80.
Am I looking at that right? $80.67 on the light sweet Brent benchmark.
So, I mean, yeah, we probably will see lower gas prices, but maybe it won't be too much.
Here's the thing is if you look at the gas stations, the ones that sell both gasoline and diesel,
you'll see the diesel prices are almost a dollar more a gallon,
which would indicate that the supply of diesel right now is not that good.
And so obviously in production, you have there's a tradeoff between production of gasoline and production of distillates, distillates like diesel and jet fuel and all that.
So if the price of diesel is that high right now, there might be more allocation of fuel of oil coming in to the production of the diesel, if possible,
whether or not that feasible or not is another thing.
So we might not see gas prices go down that much.
But I would imagine that by this weekend, if these prices hold where they are,
we could see gasoline prices down maybe 3.19 a gallon.
But we'll see how that goes. I have a feeling it will get there.
I'm already seeing some movement on gasoline prices down this morning.
OK, moving over here, the 10 year bond, the yields are sliding, which as you can see, which means the price is going up.
Investors are going to buy.
The yields are easing up because of the reality that the Fed isn't going to raise interest rates.
And so you're beginning to see interest rates in general, not just the yields on the treasuries, but interest rates in general beginning to slide a little bit.
There was a report yesterday that home mortgage loan rates are on the way down, which is great news.
And that's going to stimulate the economy, spur growth.
So we have some good signs for not just now the economy is good, but the economy will be good going into the new year.
Which is good, as I said, good news for you folks looking for jobs.
Now, as far as the euro and the pound, they have, and the yen too, they're all depreciating.
If I, yeah, the yen, they're all depreciating against the dollar.
They were appreciating, but now they're coming back down.
And you see the euro coming down toward the bottom end of its trading, the current trading range.
It's now below $1.05 to the euro.
Strong dollar, strong American economy, strong dollar, all that stuff.
Gold, yeah, it's just kind of, it came back down below $2,000 an ounce.
It probed the resistance at $2,000, and then the traders chickened out and got it back down below, and drove it back down below that.
So that's good news for normal people.
Now, if you look over at Japan, there was a spike at the bell, it just jumped up, and then it stayed there.
So that would mean that before trading began in Japan last night, last night, our time, there was good news.
It got pushed into the prices right away, but there was no more good news.
So the Nikkei 225 just eased along for the rest of the day, their day.
And then come into London, and London had a drop off, and then it had a bull surge, and then a bear surge.
It was all over the place. Kind of hard to tell what that's all about.
I haven't been following their news too much lately, but anyway, on our side of the Pacific, another good day, a bull day.
So when you have a spokesman come in here and tell you that it's a bull market, even if the bears try to stop them, the bull is just going to keep going.
And to quote a famous bull, that's no bull.
Where am I? Oh, okay. Good enough.
Now, down to the subject of the day here. I'm going to write some equations on the board here.
I'm going to find a marker that's going to have some punch to it.
The weighted average cost of capital, the WAC.
Again, very big stuff for use by businesses for a number of purposes.
And we can do it this way.
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.
Now, we can break that down a little more. The weight of equity can be broken down to the weight of preferred stock times the cost of preferred stock plus the weight of common stock,
which I'll put as an S, times the cost of common stock.
I showed you the three components, how you get them.
The cost of debt after taxes is going to be the cost of debt times 1 minus the tax rate, which is uniformly right now 0.21%.
If I'm not mistaken, your book is still using 0.35% or 0.39%, which justifiably we had it there for so long.
And then that massive tax cut on the top income earners in corporate America just changed that 0.39 or 0.35 to 0.21 for everybody.
Now, remember that the cost of debt, you're probably going to want to use the yield to maturity, the YTM, not the coupon.
The coupon is a historical cost, but the market is pricing the debt from day to day, which prices the yield to maturity by the math of it, that bond calculation.
That's going to come into play here, so we're going to have to use that at some point today, unfortunately.
And then the cost of preferred stock is going to be the dividend that's paid on the preferred divided by the current price of the preferred stock.
That was what I did on Monday. Nothing hard there. I mean, it's just push in some silly numbers and you're all done with it.
The one that's a pain in the butt is this one, the cost of common stock. If it's an old company, all you do is you take the dividend one period out divided by the current price of common stock plus the gross.
Plus the growth rate, where the dividend one period out is the current dividend times one plus the growth rate.
Now, you see that these are actually, this is calling for an Excel sheet where you can just put in the raw data and it'll punch out the numbers quite well.
The problem is that if you don't have a constant growth rate of dividends, the next place you go is to the capital asset pricing model.
You take the risk-free rate plus the beta of the stock times expected return to the market portfolio minus the risk-free rate to get it.
Quick, dirty way to have a beta.
Then there was this third way, that's A, that's B, and there was a third way to say that the cost of equity, cost of common stock would be the current bond price, yield to maturity,
the industry bond price, I'll put it as BP, for the industry plus the current yield to maturity, I'm sorry, plus the equity premium of the industry.
You can do it that way.
Now, I'm going to tell you right now that doing this on a test, I wouldn't make it so that you had to figure out which of those three you would use.
What I will do is I will make it so that the first one is the one that you would use.
I mean, it's bad enough when you've got a long word problem and then there's an ambiguity.
You have to figure out, okay, did he give us a constant growth stock or did he give us a beta or did he give us an equity premium?
That makes it even worse and it's not worth the effort to test that at this level.
Now, if you take my next course, yeah, and I'm sure most of you are saying I can't wait to take that next course or not, probably not, it's more like it.
Okay, now, here's what I'm going to do. Let me, actually, here is, I'm going to show you a template real quick and then I'm going to back down from that and rebuild it somewhat.
There's a problem with all of this. How in the hell do we get these weights?
Those would be market weights, the weight of each one. The WD, weight of debt, plus the weight of preferred, plus the weight of the common stock, should equal 1.00.
That's what they should, they should equal 1.00. Okay.
So, the weight of debt would be the market value of debt over total market value.
The weight of the preferred would be the market value of the preferred over the total market value.
And the weight of the common stock would be the market value of the common stock over the total market value.
Now, let me show you what I mean by that.
Oops, sorry. Okay, here. I put the market values in here. And I'm glad the new stock is a little bit complicated here.
I might just pull that out for the time being. But, where would the market value of the debt come from?
Well, the market value of it, you would take your total, the prices of your debt out there in the market times the amount of it.
So, I'll get to that in a minute.
Well, preferred stock, you take the price of the preferred stock times the number of preferred shares outstanding.
For the common stock, you take the number of shares of common stock outstanding times the price per share, which is what we call the market cap.
So, what that tells us, what we're doing here, what it tells us is we've got to get these market values.
Okay, fair enough. I'm tempted to just kind of pull out this market value.
Well, no. Let me do another sheet here and just work it through. I'll do another sheet here in a minute.
Okay. Market value of debt.
In real practice, this can be a total pain in the backside, simply because a company could have different debt out there.
Some seniors, no senior subordinated and all that. You have to take how many of those bonds are out there times their price per bond.
So, let's make it simple. Let's say you have 1,500,000 bonds outstanding.
The price right now on those bonds is, let's say, $987.50.
So, the market value of debt would just be the 1,500,000 of those bonds we have outstanding times the price per bond, per each one of them, $987.50.
If I do that real quick here. Calculator. I take 1,500,000 bonds.
These are the actual bonds themselves times the price of each one of those in the market right now. That would be $1.481 billion.
That would be the market value of its bonds.
You see, if those bonds were selling at par, the market value would be $1.5 billion.
A thousand times 1,500,000 of them. But these bonds are selling at a discount to par.
So, their market value is a little less than $1.5 billion.
That means that the market weight of the debt is a little lower because the bonds are selling at a discount.
Now, if the bonds were selling at a premium, then the market value of the bonds would be above $1.5 billion.
But the bottom line is, you need to know how many of the bonds are out there and what the price of the bonds is.
But that's also one of the, you also need to know the price of the bonds.
That's one of the things to find the yield to maturity on the bonds too. So, it's a double problem there.
You just have to walk your way through the pieces and that's why it's nice to be able to put the problem into a table.
And then get it done. Let me try something here.
Okay, now the preferred stock.
The market value of the preferred.
Getting a little low on this board here.
That would be just the price per share of the preferred times the number of preferred shares outstanding.
That would be the market value of them.
Suppose the company has, let's say, 500,000 shares of preferred stock.
And the price per share of the preferred right now is, let's say, $85.
Well, then the market value, and I am getting low on here. I'll read this to you.
Market value of preferred would be nothing but 500,000 shares times a market price right now of $85 per share.
I'm not even going to try it. I'm just going to do it on the calculator.
500,000 times, what was I thinking here, times $85 per share.
42,500,000.
Let me get over here so I can do this a little easier, a little more easily.
This is truly a pain.
So I've got the market value, the market value of debt, the market value of preferred,
and the market value of the debt was, what was that, 1.48125.
$1,481,000,000.
Market value of the preferred was $42,500,000.
And now the cost of the market value of the common.
Let's say that there are 50 million shares of common stock outstanding.
Let's say that the price per share right now, price of the common stock right now is $120 per share.
So the market value of the common would be 50 million shares of it out there at $120 per share.
And again, I'm not even going to try that. 50 million shares of stock outstanding.
Times $120 per share, $6 billion.
Market value of common.
There you go.
And finally, I'm going to do this on the calculator the first time.
And then we're going to use Excel to do it and automate this pain in the butt.
The total market value of all of its securities would be the $1,481,250,000
plus the $42,500,000 plus the $6 billion.
My ass.
Let's try that again. $1 billion. Thank you.
$1,481,250,000 plus, try it again, $4,500,000 plus $6,000,000.
Did I do it that time? Ha!
And you can see this is where Excel really begins to help you out a lot with this.
$7523,750,000, $7523,750,000.
That is the total.
Now you can see, I hope you see how Excel is going to accelerate this process.
So the weight of debt is the $1,481,250,000 divided by the $7,523,750.
The weight of preferred would be the $42,500,000 divided by the total $7523,750,000.
And the weight of common stock would be $6 billion divided by $7,523,750,000.
I'm almost losing my will to live doing it this way.
Not fun.
Okay, so.
I'm going to do it on the calculator.
I'm going to be a little lazy here.
I'm going to save the total in memory.
So now the first one.
The first one would be $1481,250,000 divided by that monster total, memory recall, $7.5 billion.
So the weight of debt is.1969.
The weight of equity of, I'm sorry, that's the weight of debt, the weight of preferred would be the $42,500,000 divided by that $7.5 billion, memory recall.
And you get.006, the very small part of the capital structure of the company.
.0056.
And then the weight of equity would be $6 billion divided by that $7.5 billion, or would be.7975.
.7975.
And if you add those up, those will come, those weights will come up to exactly one.
Now you're going to get maybe a little tiny bit of rounding error, and obviously I give account for that in looking for the correct answer.
But there is how you get the weights, using a calculator.
But we can do a little bit of that.
So what I'm going to do is I'm going to build another sheet here, over here, make it bigger.
Now the one that I have already prepared includes new common stock, which I haven't shown you yet.
And I'm probably not going to do that, well, let me not be vague.
I will not do that on a test.
So all you'll be doing is the security type, and then the cost, and then the market value.
And then the weight.
Oh, I have to put in the, how did I do it on the other one?
Yeah, the market value, market value, and then I put in the weight.
Yeah, the weight.
Get those in.
I'm going to take a quick side jump here.
You don't have to know this, obviously, it's just something that avoids an annoyance of mine.
Right click on the sheet you're working on, view code.
See that general, do the worksheet.
And I'm going to type in a single line of VBA.
Cells.EntireColumn.
We can't see this.
Really? Oh.
Now?
Yes.
Oh well, that helped a whole hell of a lot.
Will you let me put it here so I can, okay, let me do it again.
I'm just showing you a stupid pet trick.
Cells, it'll make you feel like you're really cool because you can write VBA.
Cells.EntireColumn.
See, it's even offering it to you if you want.
.autofit.
Whoops,.autofit.
.autofit.
Okay, let me just get rid of it.
Now watch what happens when I hit enter.
Did you see what happened?
I don't know why Excel never put this VBA and embedded it, but you'll catch it as I go along.
So we're going to have debt preferred.
Did you see what happened there?
Common.
Now let's just throw in those numbers and throw in a cost.
Okay, so the after-tax cost of debt, let's say, is 4.25%.
Oops.
4.25%.
So the cost of preferred stock is, let's say, 5.80%.
And the cost of common equity is 12.63%.
Now let's put in the market values.
Just the ones that I got there.
What did I have?
1481
81
250
000
The preferred was 42,500,000.
And I wanted to put a dollar sign on that.
The cost of common stock, rather the market value of the common stock was $6 billion.
Okay.
Now
I add those up and I get that $7.5 billion.
Oh.
Yeah, I know, yes.
You wait until I make a fool of myself to tell you, right?
There you go.
And then each of those would be equal to, for example, the market value of debt
divided by the total.
And I'm going to make that an absolute reference so I can just scope it down.
And you get the same numbers I did over there.
I want you to catch up with me because I'm going to show you a faster way to do it.
I think I showed you last time, but I'll show you for sure this time.
So first you get the market values in each one.
You add them up.
Then you take each market value divided by the total.
That's how you get a weight.
Okay.
Are you ready for a stupid pet trick?
Watch this.
I'm going to get rid of that.
If you want to follow with me, I'll stop at each step.
You highlight the three market values.
When you do that, you're going to see a little icon down in the lower left side of the highlight.
Got it?
Click on it.
Choose totals.
And scoot clear over to the end and you'll see a percent total with a yellow column.
That's saying find the percents and put them in the next column.
Did you see it?
It's even flashing it.
And if I click on it, it will make it permanent.
Well, spank me, Jesus.
Look at that.
There's a lot you can do.
If you look at that icon, just play with it.
You can do charts from it.
You can do averages.
A lot of different things.
You can either do them underneath or you can do them as a side column.
And now, ladies and gentlemen, for the end.
Whack.
I want to take cost of debt times the weight of debt plus the cost of preferred times the weight of preferred
plus the cost of common times the weight of common.
And I'm going to do a sum product.
Equals sum product.
Open the parentheses.
You say do this column, cost column, comma, this column, the weight column.
So the weighted average cost of capital for this firm is 10.94%.
Yes?
Yeah.
Is getting that weight percentage the only way by doing that by highlighting market value
or is there another way to get to that?
To the final weighted average cost of capital.
Is the shortcut that you're showing us right now, is us highlighting those three cells
the only way to get to quick analysis or is there another way to get to that?
There's another way I can show you.
Hang on.
I can take.
You don't have that icon that you're showing us.
You don't?
Apple.
Yeah.
I'm sorry, I forgot.
Okay, so I take equals this times this.
You're not understanding my question.
So I don't have the weight 19.69%.
You don't have those?
Because, so I did from dividing.
Oh, you didn't.
It's the same weights, isn't it?
Yeah.
So I'm just going to take this times this plus this times this plus this times this.
Should give me the same number.
Yep.
Is that the same stock product?
Yeah.
That's doing, that's the sum product does that for you.
It works hard so we don't have to.
Sum product does.
It's exactly the same thing.
Now, I've been finding out that sum product does some really weird stuff that's more advanced
too.
So use it cautiously because it's apparently a rather more powerful tool than I normally
use it for.
But the sum product is just really nice.
Especially, imagine if you had like 10 rows, you would be doing this times this plus this
times this.
The sum product is wham.
It does it in one shot.
Yeah.
Can you show the quick way to get the weight down?
Yeah, sure.
Watch.
Just always ask me.
Do it again, fat boy.
Watch.
I don't have the weight percentages on this.
Oh, the weight percentages?
I'm going to click a little pop up on the screen.
Okay.
I just, all I did was I just took, let me clear this.
By all means, always just say stop and go back because, okay, here's what you're going
to do.
You're going to take equals.
Do you know how you highlight it and then there's a little pop up to like the bottom
right?
Oh, yeah.
You want that?
Okay.
Watch.
This one?
I highlight these three.
That one?
Is that what you want?
Okay, watch.
When I highlight them, this, whenever you highlight anything, that always shows up.
And people think why?
It does not on Mac.
Yeah.
Right?
Okay.
That's why.
Yeah.
That's what, I didn't realize that Macs didn't do that trick.
Yet another reason to trade in your Macintosh.
Would command Q do it?
Try, yeah, try command Q.
So I need to try to impose my.
I can't do it on this because it's a PC, but see if command Q will pull that.
Q is quantitative.
At least that's what I thought it meant.
Let me try something here.
Command Q.
Hey, spank me.
Control Q does it on the PC.
No, on Mac it just pulls it down.
Command Q does?
Yeah.
I am so disappointed.
I have such neat tricks here.
Trying to think what else I could do.
Wait, let me try.
Okay, I'm going to do something I usually don't do.
I'm going to try to Google.
Command Q on Mac.
That quits it.
Try one more thing.
I don't want to spend too long on this, but let me try something here.
Okay.
Okay, let's try this.
Let me try this.
Let's do conditional formatting.
On the format sidebar, click the cell tab, and then you should get conditional highlighting.
That's where that is.
So you would highlight the cells and then click on the format sidebar, whatever that is, and click the cell tab.
Does that work?
Hmm.
Did it work?
It did?
Or not?
Okay.
Anyway, let me get these back in here.
Okay.
Let me kind of proceed on here.
I kind of took the wind out of my sails pretty quickly here.
Okay, now, the cost.
Let's add in, and we'll go back over to my existing one here.
On this one, let's put in now, and now I'm going to put in, we're going to get the cost.
Now on this one, what's going to happen is we're going to need a bunch of little information.
We're going to need the tax rate, the cost of debt, the preferred dividend, the par value,
the price of the preferred, common dividend, and all of those other things you need to create the price
and therefore the cost of each one.
Now the first thing we'll need is the yield to maturity on the debt.
There's the yield to maturity.
That's that, calculate the yield from that other spreadsheet that I gave you.
This is the same thing.
It's a mini version of it.
All you have to do is put in the term and the coupon, and remember that you have to do the price on the 100.
And then that 100 won't be, you don't touch that, payments per year, 360-day basis, and there's your yield.
It's the same as the one, the bond calculation that almost all of you got right on the test.
This is just doing it again, and it gives you the yield.
This is just taking this number and multiplying it by your tax rate.
So you're going to leave the tax rate alone.
And if you do, and if you calculate the bond yield to maturity, that number will just appear for you.
The 1.92, that is the cost of preferred stock.
Notice that it's just the formula.
The dividend on the preferred, which you put down here, which is nothing, the dividend on the preferred is nothing but the two,
whatever you give for the dividend, times the par value of the preferred.
In this case, the par value was $85 per share.
I didn't tell you the dividend, but now here we have it.
And the current price of the preferred, I put in a price there.
Now the common stock dividend, I'll give you that.
You just put it in there, and then the growth rate, and that will give you D1.
And that is just the current price, the D1.
The common stock, its cost,
it's just going to be D1, which is D0, times 1 plus the growth rate,
divided by the R minus the return, plus B17.
And this one, don't worry about it.
I'm getting rid of, I'm not going to use it for this one.
I'm going to put in the price of the common stock and the number of shares of the common stock outstanding.
I wonder where I put that, oh.
Oh, there's the rest of the information over there.
And I'm going to shade that.
Because you won't use it for the problems this time.
You get the par value of the bonds, how much they are actually, price of the bonds.
That would be the price of the bonds times, I give you the price.
Number of preferred shares outstanding, number of common shares outstanding.
As long as you can fill in these numbers and get the bond, calculate the yield,
and put these numbers here, these numbers will come out.
Matter of fact, let me remove that row entirely.
And this one won't come out to be that one because the numbers, these numbers I put in are different.
So in the template, all you have to do is put in this number right here.
This number you don't have to calculate because it's done for you by the yield to maturity calculation over here.
The preferred dividend would come from the problem.
You give the preferred dividend, the par value of the preferred, the price of the preferred,
and then the common stock dividend, the growth rate, and the current price.
And I'm going to just get rid of this because we're not going to use it.
And this all should calculate for you.
Play around with it. It'll take a little bit to get used to it.
And I'm going to put this one up as your save as. I'll just put it in documents.
Now I put a macro in there and it's going to bitch at me about that macro I put in there.
So I'm going to just, it won't be in there. It doesn't affect the problem at all.
And then I'm going to upload this to your sheets, to your spreadsheets so that you have it for that.
Now a little bit of background here. One last thing.
Well, as a matter of fact, let me show you this.
When would you need to issue common stock?
Because you can get debt, you can get preferred, you can get common.
When would you need to, if you had new projects, that would change your retained earnings?
If I take the, suppose I'm going to do projects that will total, let's say, $100 million.
$100 million. Divided by the weight of common stock, which was.7975.
We have a need for that. The weight of the common, we're going to grow our retained earnings by $100 million.
Because we're going to take on $100 million in new projects.
We will finance with debt, preferred, and common stock, and our retained earnings.
If I take the $100 million and divide that by.7975,
then I would have to go to start using new common stock when I had reached $125,391,850.
In total changes in retained earnings, which would include income that was brought in.
We have a name for this. This is called the equity break point.
It is when we reach a retained earnings total level of $125,391,850 that we would have to go out and issue more common stock.
That's called the equity break point.
I'll explain a little more on Monday, but I do want to show you something before I finish today.
Let me show you one last thing.
Don't worry too much about that right now. I'll go back through that on Monday.
As a matter of fact, I'll go through some of this again on Monday just to make sure you've got it down well.
I'll extend the deadline to Tuesday night on your homework too, by the way.
I did want to show you one thing before I quit here.
What you're seeing here, this comes from the Stern School of Business at New York University.
Every January they take companies in lots of industries, 90-some industries,
and they show what they calculate, just what I did here.
The cost of equity, the weight of equity, the cost of the after-tax, the cost of the standard deviation.
They do that. The cost of debt, the tax rate, the after-tax cost of debt, and then they do the weight of the debt.
Here's the weight of equity times the cost of equity. Here's the weight of debt, weight of debt times the after-tax cost of debt,
and they calculate the weighted average cost of capital.
Now, this was fresh in January of this year.
Now, by industry, if I shrink this down just a little more, you can see it a little better here.
These are the weighted average cost of capital for all these different industries in the U.S.
You notice something.
First of all, most of the industries have weighted average cost of capital that is less than 10%.
Only a few, like this one, the energy.
Oddly enough, energy has a higher weighted average cost of capital than almost any other industry.
Here's another one.
Electrical equipment. One more.
Health care has a high weighted average cost of capital relative to all industries.
Looking down here, there was one more that was, well, here we have three in a row.
Shoes, software, entertainment software, productivity software.
They all have high weighted average cost of capital.
But the average overall is about 9.25%. Overall is the typical weighted average cost of capital.
Kind of gives you an idea for, if nothing else, if you're just pulling a weighted average cost of capital out of the air,
but you want it to be kind of realistic, you probably would want to use about 9.25 for your typical weighted average cost of capital.
Not sure what that indicates, but keeping an eye on this, interestingly,
2022, the weighted average cost of capital was somewhat lower because interest rates went up through 2022.
Now, it will take a few more months before we will know what they did in 2023.
But just for a general problem, a weighted average cost of capital of 9.25 isn't a bad number to try.
Anyway, that's all I have for you today. I thank you.