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Welcome back.

What we're going to do now is we're going to talk about

the process of unlevering and why do we do it.

So we want to unlever because ''let me just draw the thing. ''

you want to unlever is because we'll find it very easy I shouldn't say very.

We'll find it easier to figure out some information.

And so we have equity here, we have debt here,

we have value of the real assets here,

we have the value of the tax shield.

We want these returns but the return we really want,

the return we really want is this one.

Why? Because this values the fundamental business I am in.

And who are you looking at right now.

You've done your own cash flows.

I promise I'll do a very detailed example following this,

but you are now advanced students so you first need to

understand the concept. It's not profound.

It's just practical, at this stage it's practical to it.

So you want Ra, because if you don't know Ra

from your comparable you don't know how to discount your cash flow,

and your comparable has to be pure play.

But when you look at the comparable's information there's no way you can figure this out.

So the first thing is,

this is relatively easy to look at and because we

know we can figure this out both are kind of based on market information,

not perfect but market information.

We can go from here to this guy but in doing so we'll adopt two approaches.

So un-levering will have two approaches.

The first approach will assume that Rd is the discount rate for the tax shield.

The second approach will assume Ra will be the discount rate of the tax shield.

And then what we'll do is we'll see scenarios under which,

which assumption is right.

And the reason is this,

if you don't know,

what discount rate is the appropriate one for the tax shield.

You don't know how to go from here to here.

Remember you are trying to tease out Ra.

So if you assume Rd is the discount rate for

the tax shield remember Ra won't be relevant for the tax shield,

and the formulas will change.

So I'm going to get into the formulas and then we'll practice

the formulas later on when we do a detailed example.

Okay. So that's why there's approach one.

So I'll save one here and then two here.

Not in sense of one or two in this graph but how we're going to approach it.

And the fundamental reason of unlevering is: we have to go from here,

and we want to get Ra Okay.

What are the other things you need to worry about?

You need to worry about the relative magnitudes of E and D,

because if you don't know the relative magnitudes of E and D,

you don't know how to weight these guys to be able to go across.

So bear with me for a second and we will get there.

So approach number one: Assume the risk of

the tax shield is the same as the risk of the debt, right?

And let's think about it,

when is this assumption valid.

This may be getting a little bit boring.

It's valid when think like this,

when you feel that it's safe to assume that changes in

the value of the firm won't affect the riskiness of your tax shield.

Right? So if you feel you're going to pay your tax,

you're going to be able to deduct your interest rate,

and you're going to be able to safely use the return on debt, that's fine.

Okay? And we'll talk a little bit more when we get to the light side of it.

So the assumption valid should feel comfortable that

the value of the firm is somehow not affecting the value of the tax shield.

Okay?

Un-levering let's do cash flows again.

So remember in un-levering the cash flows could have been written in this way.

And we're going to use the cash flow equations to derive the return,

because the cash flow equations tell you the rates.

Remember you need to know what the relative values

are of Re and Rd that you need to place.

So you know what is the relative value of Re.

Let's go there. It has to have E multiplied by it,

but in the end it will be weighted somehow by the total value of debt in equity.

And the trick here is to try to figure out those equations that take you from Re to Ra.

Okay? So you kind of can figure out Re from beta E. That's the math.

You then want to go from Re to Ra and this is the nice way,

balance sheet way of thinking about it okay?

So remember ''balance sheet always balances'', okay?

Remember that ''balance sheet always balances''.

I'll give you a second because you're so used

to it already to write down the left hand side.

And I'll talk you through it.

Ra times Vu is the cash flow to the real assets.

Rd times Ts (which is the tax shield) is the cash flow to the tax shield.

(Why Rd because we made an assumption approach number one,

that the discount rate appropriate for the tax shield is same

as Rd) and then Rd times D both sides should balance.

So what are the un-levering equations.

So please one more time see this.

I'm going to write it out.

Balance sheet tells me that Ra times Vu plus

Rd times tax shield has to be equal to Re times E plus Rd times

D. Nothing profound go back one more time.I mean you remember when you go to

dentist this they say ''this or this this

or this''.So I'm doing a little bit of that with you, Okay?

In solving these problems remember you do not

want to use Vu because it doesn't tell you very much,

but remember always what will Vu be?

Vu plus tax shield has to be equal to what E plus D. Remember,

''balance sheet always balances''.And

that trick that the value of the real assets and value of tax shield is,

equal to value of equity and value of debt,

is the trick to solving this problem.

A little bit always right.

So look at this.

I will want to know Ra So what do I do.Just keep Ra on the left hand side very simple.

First step what will the right hand side become?

Re times E plus Rd times D minus Rd times tax shield, fair enough?

Nothing no magic.

I've just taken this guy to the right hand side.

Now I don't know Vu.

There's no E and D in there.

So the goal is to kind of bring E and D in there because you know if you have those,

your formula will become based on observable's.

Remember you can't observe Vu but you can observe E and D in real life.

So let's see what Ra will be.

Let me write it out for you.It will be E plus D minus Ts.

Why?

Because Vu plus Ts equal to E plus D means Vu is equal to what,

E plus D minus Ts.

I'm just pausing and smiling,

I haven't done anything profound here.

Okay? is equal to Re E Plus Rd D minus Rd Ts.

Just taking a pause here for you to have some fun and I hope you enjoy this.

I know it can get tedious and the fun part is this,

I can't believe my handwriting gets better and then you know I can't do

all the videos in one long session,

or even days on because it's it takes a lot of focus and so on.

But what I've noticed is that my handwriting gets better and better so,

as I'm taping, as I'm doing more of it in

a particular sequence then my handwriting gets worse.

Why? Because we never write.

We go back to a laptop and start working on it.

The trick now is what is Ts,

because Ts doesn't tell me anything either.

I can't observe it.

The good news is if Rd is discount rate for

Ts I know what Ts is TCD.

Remember I'm going to not do it and make you do it.

The tax shield the value of tax shield is TCD.

I'll walk you through it,

you know I can't help myself.

So what is the cash flow.

Rd times D is interest times,

TC is the cash flow.

But if the discount rate is also Rd you divide by Rd Rd Rd cancel.

You are left with TCD.

Okay? Substitute Ra E plus D minus TCD,

is equal to Re E plus Rd D,

minus Rd TCD.

So all I have done is substituted.

I'll do quickly now.

Now it's algebra.

Turns out Ra E,

plus D one, minus Tc is the left hand side.

I'm doing this so that it becomes easy for you to understand what I'm doing.

More importantly we are rewriting it so that it matches the books

and how it looks easy to understand Rd.

Now what will I have?

Again Rd multiplied by D one, minus Tc.Why?

Because Rd's here and Rd's here as well, okay?

So Rd D is this one,

and Rd D Tc is this one,

and the negative sign is gone inside.

What this does is beautiful Ra becomes Re E,

over D times one minus Tc,

plus E plus Rd D one minus ''i'll go a little slower''

Tc over D one minus Tc

plus E. Okay, so saying it loud.

I've just taken E plus D one, minus Tc on the right hand side.So the way I

remember this equation is if Rd is the discount

rate.And many people use this approach many times not correctly,

because you want to use it when you're pretty

sure that the value of the firm and the value of the tax shield are not related,

and that is the only thing you're focused on So remember this whenever

you have D in this equation it's multiplied by one minus TC, and that's the math.

That's the way it works out.

Let's keep going with this approach un-levering equations and

so the equation turns out Ra one more time is D one minus Tc,

over D one minus Tc plus E, multiplied by Rd.

I may have switched things but that's not bad.

E D one minus Tc plus E times Re.

This is what I meant every time you see D it's being multiplied by one minus Tc.

That's the way the math books are.The Good news is what can I do?

I can figure this out,

I can figure this out,

I can observe this,

I can observe this, I can observe this.

And therefore I can do what I can go from

observables to Ra and this process called un-levering.

You're going from Re figuring out Rd and going back to Ra.

Which is higher Re or Ra?

Re is always higher.

So one last thing which is kind of interesting is what would be the beta asset equation?

Remember, why can't you figure it out Re?

Because you can figure out beta E and put it in CAPM.

Don't ever forget that.

Yes if you already know Re because I gave it to you or

your somebody has given you that

number.You don't have to backtrack and figure everything out.

It's good, turns out beta whenever beta equation,

it has to mirror return equation.

And what relates the two CAPM.

So let's write it out D one minus Tc,

D one minus Tc, plus E what will you have here?

Beta debt, plus E D one minus, Tc plus E what will you have here?

Beta equity.

So they go hand in hand.

And what connects the two sides are always CAPM.

Of course modified for beta data and so on and so forth.

So I'm going to take a little break

here and when we come back we will go to approach two,

this is approach one.

And what does approach one on un-levering have?

Rd is discount rate of tax shield.

Important thing I want Ra, I want beta asset A, I can't see them.

I can see Re beta E usually beta E first, put in CAPM Re.

But I can see everything else.

I can see value of equity price,

times number of shares of the comparable,

and I can also see value of debt.

But unfortunately, debt doesn't trade.

Many countries it's a contract between the bank and the company.

So there we use book value.

So that's a little bit of a bummer,but you have to deal with

it.So we're catching our nose we want these two,

Ra and beta asset.

But we're going through beta equity.

And then kind of ramping up.

The process is called un-levering.

Let's take a break, do the second approach of un-levering and then we'll kind

of wrap things up conceptually before we go to a mega example.See you soon.