0:14

So we had done an exercise where we figured out the value of the firm.

With taxes, and with the real world twist, which is pretty important.

The interest is deductible as well, on debt.

And if you stare at the my beautiful handwriting on top,

I broke it up into two parts.

I first valued the unlevered firm, which we know, very simply is 660 million.

99 million to equity holders divided by a discounted of 15% which

is the return on assets and the return on equity for the unlevered firm.

I know this gets a little bit confusing but

always think of unlevered as being the real assets in some sense, right?

So where financing is not affecting anything.

But now financing starts affecting value.

But value not of the real assets, because that's determined by supply,

demand out there, by markets, but

by the fact that a financial asset has been given to you by the government.

So you pay the government, and the government pays you something back.

It's kind of really weird, but that's the way it is.

So what's the value of the tax shield?

Well, like value of anything, cash flows divided by discount rate.

The cash flows every year, for simplicity, are fixed $500 million is the debt,

interest is 10%, that gives you 50 million.

1:41

And the cash flow that goes to that total of every year.

But then you deduct them from taxes, so

that times 0.34 which is the tax rate is the cash flow.

So 500.1, 0.34 turns out to be $17 million.

So this is the cashflow on the tax here.

2:04

I should publish this, it's a beautiful design.

This is every year.

So if you're getting $17 million every year,

and let's assume the risk of this is the same as the risk debt itself.

We know the discount rate for debt is 10% so

we divide 17 million by 0.1 and we get 170 million.

So the total value of the firm is 830.

Let's keep going.

2:35

As I said, you are thinking with me.

And pause whenever you can.

I will take pauses, but you should pause whenever you can.

This is easy, right?

Because one thing you must remember, is the value of the levered firm is E + D.

And the way I'll solve problems, I'll solve problems using a technique which

I didn't develop, but you should makes a lot of sense.

Like common sense, is that use the information you have to answer

the question, and the beauty about finances, even if the information changes,

the way you address it, changes, but the answer quote unquote is the same.

We know this.

3:49

What is the return on equity of the levered firm?

Second part of the question, what is the relationship between

the return on the equity of the levered and unlevered firm?

Right?

So [LAUGH] this is I'm making you think.

And the beauty of this is the videos are like a textbook, in fact,

better, in my book.

You can go back and forth.

So let's ask the question.

What is the return on equity of the levered firm?

4:21

This is not an easy question.

And this is where you could answer it many different ways.

But I will spend some time on the beauty of finance and

the beauty of the methodology we are using.

So remember,

the value of anything is CF/R.

In this case, what are we looking for?

We are looking for return on equity.

4:54

And this will be equal to value of equity.

And remember the value of equity is denoted by E and

the value of debt is denoted by D.

The value of the whole firm is denoted by V.

Okay, so that's terminology.

And let me ask you, do we know this?

5:26

Using the method that suits the information the most.

Answers we know CFe, right?

Right?

We know CFe.

How much is it?

Then with leverage, remember?

L, it was 66 million.

Because the total cash flows to the firm were 152,

oh, they told us 66 to equity holders.

This implies that Re L is equal

to I beleive 66/330.

Million, million cancels.

This is a ratio and the answer should be 20%.

Let's double check.

20% means that 5 times this is this.

You can plug in 20% and figure out whether it's consistent, and

I think that's the right answer.

So the question is what has happened to the return on equity

compared to the time when there was no debt versus debt.

Without debt return on equity of the un-levered firm was also return on asset.

6:42

Sometimes I get a little bit irritating writing with this.

But there's a lot of stuff that's irritating but life goes on.

It's 15%.

So what has happened?

The return on equity of the levered firm has gone up and

you should remember back now.

Why?

Because you're taking on financial risk as the shareholders on top of

the business risk.

7:34

What is the relation between the returns on equity of the levered firm with and

without tax deductibility of interest.

So, what I'm asking here is a very simple question.

You had a world where there were taxes, but

the taxes didn't go beyond income tax or corporate tax on

the corporate income, didn't distinguish between equity and debt.

So I'm asking you what happens to the return on equity of the leveled firm

if there were tax deductibility of interest, or if there was not?

We know that with tax deductibility, we just calculate it.

Return on equity first, 20% of the levered firm.

8:25

Without tax deductibility.

We did this a while ago, while meaning little bit earlier in the slides.

It was return on equity, was about 30% approximately.

It was higher.

And the reason is, here,

the government gives back the subsidy to the shareholders.

Here, the government keeps most of the money, all of the money, all the taxes.

Let's dig into it a little bit more.

I just want to provoke you so that you think.

Who pays the tax-deductibility of interest on debt?

9:06

Who gains that value?

So, now I'm asking you the following thing, just to think through.

You pay 34% taxes on income as a corporation.

Who owes that tax?

Not debtholders, but equity holders.

You are the owners.

You are the residual claimants.

9:27

Now the government says this,

you know if you take on debt I will give you back some money, but

it's only on the interest deductibility part of the debt, not on equity.

So who pays the tax deductability of interest on debt?

It's the government.

10:24

it means non contracted whatever's left don't you find that beautiful?

Anyway, so the point here is

if the government pays back anything it goes to the residual claimant.

So the tax return, the gain in value goes to equity.

10:55

Okay, so let's do this and then we'll pause for a second.

Remember weighted average cost of capital is a definition of that and

I'm going to write it out for you.

It is Re E/E+D.

If you had only equity, what would be your weighted average cost of capital?

Regardless of taxes because remember you are not debt anymore.

If you had only equity that would be 0, E/E is 1 and

a return on equity is also a weighted average cost of capital.

But I'm asking you about the levered firm.

11:51

Your equity your debt, what has to be true about these two?

They have to add up to 1, which is that the balance should balances so

the weight of equity and the weight of debt Is equal to 1.

In textbooks many times these are called We,

Wd weights, or Xe, Xd, whatever.

So, the question is what goes here.

Clearly Rd goes here.

But think about it, Rd would go here if you paid Rd 10%, in our case.

And didn't get any tax deductibility.

12:47

Why? Because you pay 10% but

then you get it to be deductible from taxes.

So if the tax rate is 34% how much are you paying?

Your interest rate is not 10% it's 6.6%.

Therefore, you try to take advantage of that tax deductibility.

To remind you, if you kept doing that you would have only debt.

And there are firms out there, technology firms, Apple,

Microsoft, name it who don't have any debt.

So they are clearly concerned about some disadvantages of debt

not to take any debt.

And that's a debate we'll have.

Or think about very carefully.

So for the time being we know these numbers so let's calculate them.

14:13

This is in some senses, the easiest and a kind of difficult thing to get.

You can,

I think we talked about this if you read our books, it's not the yield to maturity.

Because yield to maturity is calculated like an IRR and

is always higher than the actual return.

Because you may not get the cash flows.

Okay?

This was how much?

1-Tc is 0.66.

What is the weight on debt?

Weight on debt is

500/830.

Right?

20% time its weight.

10% time its weight.

The weights add up to 1.

You can stare at the numbers and they have to.

But the key here is never forget this in the real world.

Because that's the tax deductibility after tax cost of capital.

15:12

While we are here also think of after inflation value of income.

Your real income.

Similarly think of after tax because that's rare for you.

Okay this will turn out to be 11.93%.

If you do the calculations which I encourage you to do we are going to take

a break in a second.

But before we take the break the question also asks what is the relationship

between WACC and Ra?

Always remember the Ra's associated with which assets real assets and

we know that number is 15%.

What do you see?

16:18

In other words, you remember from past if you didn't have a tax break on the return

on debt, there would be no construct saying that there's a difference.

There's no tax break being given as far as cost of capital is concerned.

Here, you're getting a discount on cost of capital,

on one part of cost of capital, which is debt.

16:39

And therefore, your after tax cost of capital

has to be lower than the return on asset.

And many people therefore say, wow, that's value generation.

Yes it is, because you're able to borrow at a rate after tax cheaper than without

the tax break.

But I would like you to think about it during the break.

Is that a real asset you have created?

Or is that a financial asset given to you by us collectively,

also known as the government?

Let's take a break, and when we come back, we'll put it all together.

See you.