0:14

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

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

Â The interest is deductible as well, on debt.

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

Â I broke it up into two parts.

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

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

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

Â I know this gets a little bit confusing but

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

Â So where financing is not affecting anything.

Â But now financing starts affecting value.

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

Â demand out there, by markets, but

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

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

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

Â So what's the value of the tax shield?

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

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

Â interest is 10%, that gives you 50 million.

Â 1:41

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

Â But then you deduct them from taxes, so

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

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

Â So this is the cashflow on the tax here.

Â 2:04

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

Â This is every year.

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

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

Â We know the discount rate for debt is 10% so

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

Â So the total value of the firm is 830.

Â Let's keep going.

Â 2:35

As I said, you are thinking with me.

Â And pause whenever you can.

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

Â This is easy, right?

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

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

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

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

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

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

Â We know this.

Â 3:49

What is the return on equity of the levered firm?

Â Second part of the question, what is the relationship between

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

Â Right?

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

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

Â better, in my book.

Â You can go back and forth.

Â So let's ask the question.

Â What is the return on equity of the levered firm?

Â 4:21

This is not an easy question.

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

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

Â the beauty of the methodology we are using.

Â So remember,

Â the value of anything is CF/R.

Â In this case, what are we looking for?

Â We are looking for return on equity.

Â 4:54

And this will be equal to value of equity.

Â And remember the value of equity is denoted by E and

Â the value of debt is denoted by D.

Â The value of the whole firm is denoted by V.

Â Okay, so that's terminology.

Â And let me ask you, do we know this?

Â 5:26

Using the method that suits the information the most.

Â Answers we know CFe, right?

Â Right?

Â We know CFe.

Â How much is it?

Â Then with leverage, remember?

Â L, it was 66 million.

Â Because the total cash flows to the firm were 152,

Â oh, they told us 66 to equity holders.

Â This implies that Re L is equal

Â to I beleive 66/330.

Â Million, million cancels.

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

Â Let's double check.

Â 20% means that 5 times this is this.

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

Â I think that's the right answer.

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

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

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

Â 6:42

Sometimes I get a little bit irritating writing with this.

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

Â It's 15%.

Â So what has happened?

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

Â you should remember back now.

Â Why?

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

Â the business risk.

Â 7:34

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

Â without tax deductibility of interest.

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

Â You had a world where there were taxes, but

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

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

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

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

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

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

Â 8:25

Without tax deductibility.

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

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

Â It was higher.

Â And the reason is, here,

Â the government gives back the subsidy to the shareholders.

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

Â Let's dig into it a little bit more.

Â I just want to provoke you so that you think.

Â Who pays the tax-deductibility of interest on debt?

Â 9:06

Who gains that value?

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

Â You pay 34% taxes on income as a corporation.

Â Who owes that tax?

Â Not debtholders, but equity holders.

Â You are the owners.

Â You are the residual claimants.

Â 9:27

Now the government says this,

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

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

Â So who pays the tax deductability of interest on debt?

Â It's the government.

Â 10:24

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

Â Anyway, so the point here is

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

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

Â 10:55

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

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

Â I'm going to write it out for you.

Â It is Re E/E+D.

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

Â Regardless of taxes because remember you are not debt anymore.

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

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

Â But I'm asking you about the levered firm.

Â 11:51

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

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

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

Â In textbooks many times these are called We,

Â Wd weights, or Xe, Xd, whatever.

Â So, the question is what goes here.

Â Clearly Rd goes here.

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

Â And didn't get any tax deductibility.

Â 12:47

Why? Because you pay 10% but

Â then you get it to be deductible from taxes.

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

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

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

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

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

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

Â So they are clearly concerned about some disadvantages of debt

Â not to take any debt.

Â And that's a debate we'll have.

Â Or think about very carefully.

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

Â 14:13

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

Â You can,

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

Â Because yield to maturity is calculated like an IRR and

Â is always higher than the actual return.

Â Because you may not get the cash flows.

Â Okay?

Â This was how much?

Â 1-Tc is 0.66.

Â What is the weight on debt?

Â Weight on debt is

Â 500/830.

Â Right?

Â 20% time its weight.

Â 10% time its weight.

Â The weights add up to 1.

Â You can stare at the numbers and they have to.

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

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

Â 15:12

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

Â Your real income.

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

Â Okay this will turn out to be 11.93%.

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

Â a break in a second.

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

Â between WACC and Ra?

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

Â we know that number is 15%.

Â What do you see?

Â 16:18

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

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

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

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

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

Â 16:39

And therefore, your after tax cost of capital

Â has to be lower than the return on asset.

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

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

Â the tax break.

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

Â Is that a real asset you have created?

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

Â also known as the government?

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

Â See you.

Â