in other words you should know how much equity and debt you’ll use

the other thing to remember is we are thinking long run

and perpetuity is a convenience with the long run

so perpetuity is a really long run but long run is the key word

there right so you're thinking long run and you're thinking the future

so it's very important to know that this is a strategic decision

where keeping equity and debt ratios constant means actively managing

the mix of the

two why because value of the firm will change

either because you're taking new good idea strategically and

they turn out to be good or just life remember you make

valuation decision at point zero and after that life takes over

kind of thing so the value of equity and debt mix will

change and the idea is you are keeping up with it and keeping with it

this is very important the other key element

of the WACC to remember is look at the discount rate built into it

as far as the debt proportion is concerned you are lowering your discount

rate from

Ra to WACC simply too capture all the

tax break so that's the methodology

so let's do it what is the value of the levered firm

using this methodology so this is what it does

so you do EBIT 1 minus

TC these are you after-tax cash flows

you haven't taken financing into account what else will you

add and subtract from this in real life you’ll add back depreciation

you’ll subtract changes in working capital and you’ll subtract

cap ex another item right I'm trying to capture the essence of cash flows and

for convenience we have assumed you will do that you know how to do that

and assuming this is a perpetuity you’ll

discount it by

this is called enterprise value and the enterprise value we know

we can calculate very simply here is what was EBIT

150 million what was

taxes 34 percent so I'm going to

multiply it by .66

okay and I’m going to divide it by how much

.1193

remember I'm not dividing by .15 also remember this number has to be

lower than .15 where .15 is

the return on your essential assets

and the answer to this has to be it 830

why because I'm cheating I already know the value of the firm

right but just do it and the answer will be

.1193 okay we'll come back to this but

I'm not interested in the 830 as I say always all numbers are wrong

because they're about the future all your assumptions make sense but your

numbers are wrong

always iterate always do sensitivity analysis

so we know 830 can’t be the right number but it's the right way of

thinking the

key things to take away from here which I think are very important

are your WACC has a

financial asset which is the tax shield

built into it in other words you're not distinguishing

between the value of the firm coming from your real assets

and the value of the firm coming from the financial asset given to you by the

government I'm calling it that even if

textbooks don’t so you’re pushing them all together and getting

830 what will be the value of debt and equity

in this case we know it 500 million

will be debt therfore 330 million

will be

equity

okay so this is called enterprise value there's

another thing you'll see where value of the firm

L is always equal to value of debt and

equity and what we’ll see many times is which I’ll

talk again and it happens in practice the enterprise value is the value of your

actual assets but there's cash sitting

on your balance sheet as well it happens to technology firms

a lot because they have great ideas and then

they market them they sell the product and then they are waiting for the next

in fact Microsoft my favorite example never paid any dividends because we

wanted it to reinvest it

was just awesome and then it was sitting with

billions of dollars and that was called excess cash

that is cash that is not working for you in an idea

and you’ll have to incorporate that so you'll see that in enterprise valuation

or any valuation

you need to worry about the value of the excess cash and

kind of taking that into account because the value of your whole firm

equity and debt is value of your levered

firm assets tax break included

plus excess cash the second method

is called adjusted present value and I like it

for many reasons and I like it because

it is cleaner and it's more informative

so what does it do we have already done it kind of

so let’s repeat it what it does is it says let me value Vu

separately because those are my real assets

and let’s value TS

separately and the two will be the value of

the firm so what am I doing here I am

saying the reason I like it it's called adjusted present value so what is being

adjusted

this is the value of your real assets

to me that's life I mean that's what

that is the iPods the iPads name it service University of Michigan's courses

are hopefully creating a lot of value but then the government

in the case of debt gives you a tax break obviously to

for-profit companies right so this

part I like to think of it separately because they have very

directly very little to do with the value of your assets

so what does this do adjusted present value takes the present value of

your fundamentals and

adjusts them upwards for the tax break

but it's also important to remember if you do it well

you’ll also adjust it downwards

for the value of bankruptcy costs so think about this

you take the value the firm VU and then you adjust it upwards for any kind of

non real asset related

breaks you're getting and adjust it downwards for any costs you're imposing on

yourself

so bankruptcy costs can be very important when you have high levels of

leverage and you’re close to bankruptcy

okay so you have to build them in tricky

very tricky to do simply because it's easy to think of a tax break because

it's based on cash flows that are simple and the tax rate

bankruptcy is tough to predict and then what are the costs involved are

tough to predict but let's get started on this

how would you do this so what is Vu

Vu is the value of the firm without any

tax break of debt included we know the answer already

but let's go slowly how did I get 660 million

I took 150 million

which was what EBIT 1

minus TC and discounted it at what

Ra and this was

EBIT which is

99 million discounted at 15 percent

remember I'm not discounting at WACC this is clean

I'm just taking the after-tax cash flows and discounting it at the

true cost of capital for my business and it is 660 million

but then I'm saying TS how do you do TS let's go slowly

we did it once you take debt

and you multiply it by the interest rate on debt

and then multiply it by tax

this is the cash flow every year on your tax shield

why let's put it in numbers this is 500 million

this is multiplied by .1 and this is multiplied by .34

and remember this was what 17 million

and then you discount it at a rate that makes sense for the tax shield

let's make the assumption for the time being before getting practical

is that that's the same as Rd which is what

10 percent answer turns out to be

170 million okay

so the total value of the firm is what

830 million clean value of the firm

unlevered and then you add the tax shield turns out the

tax shield formula becomes very simple instead of multiplying it right

through three terms do you see something in common between the

numerator and the denominator

answer is yes in this case all you are looking at is the same Rd so Rd Rd cancels

and this number

turns out to be TcD

what is TC .34

what is this 500

million so about a third of the 500 million

is 170 so valued of the levered firm

is equal to 660 plus 170 million

to 830 so that is called the

adjusted present value there's a third

method and remember they’re multiples but they're based on

basically this kind of thinking so let's do that

the before we do that just very quickly what are the

assumptions underlying adjusted present value the assumptions underlying

adjusted present value is

when we used enterprise value we said we need to know

D over E quick question

what do you need to know for doing the APV method

here you need to know a ratio

here you need to know the level

level of

because think about it what did we do we took the tax break, tax shield

Vu very easy to calculate but then we calculated the tax shield and

to do the tax shield you need to know three things

debt actually four level of debt

multiplied by Rd multiplied by TC

I said three because TC everybody knows right

but you also needed to know what the discount rate was

turns out you could be used two discount rates based on logic

but here we’re using Rd

right so remember if you don't know this

we cannot do it it's the level of debt not the ratio

remember E is not showing up the important point about here is that

D is the same here throughout in perpetuity for convenience

but usually what happens to the level of debt it'll

change over time so the important thing to remember is

AP needs a level of debt this need a ratio

okay let’s go to the last method now

the last method is called equity valuation method

and what the equity valuation method does is it looks at the balance sheet

identity and says look

instead of valuing the assets let’s value the equity

and add back the value of debt

because the value of the levered firm can be written as

value of equity value of debt and add them together

here we already know this is $500 million

so the only thing left to do is value equity

this method is used particularly in certain instances but I put it third

because it's very similar to one of the earlier methods it’s just going

it's going directly to the value of the firm

from the value of the liabilities whereas the earlier two methods are much more

interesting

value comes from your assets so you go to the asset side and value them

the beauty of this method is you can see equity trading and it’s

pretty straightforward to figure out but let's go through the logic of it

in our example so

debt is $500 million

not a problem so what is value of equity

what are the two things I need I need cash flow to equity

and I need return on equity

do I know the return on equity already answer is yes we did it

it was equal to 20 percent and it'll always be

greater than or equal to what return on assets

simply because it’ll be equal to return on assets if

there's no debt as soon as you take debt you make equity riskier

what is the cash flow to equity so let's do it

systematically you have EBIT

of 150 million

do you get this cash flow you just get it directly or do you first

pay somebody else you just first have to pay somebody else and that is called

interest which is 50 million a year

how do I know that my debt is $500 million and my Rd is

10 percent so you have $50 million how much is left over

100 million but somebody else is waiting to

get its money and it's called taxes negative

34 million you’re left with $66 million

so every year in the levered firm

with the tax deductibility of interest please with the taxes you are left with

66 million so what's cash flow 66

million so that's what it does the formula is this

EBIT minus I

1 minus TC remember this is different all of these look similar this is

different from cash flow to the firm

and the difference is coming only because of the fact

that you're paying this guy before paying taxes

you have to do that because you have tax deduction but you also have to do that

because you’ll have to pay

interest first so you pay this and discount it by

Re and the answer turns out to be 66 million

divided by .20 which is

330 million value of the levered firm

is 330 million plus 500 million is equal

to 830 million

okay couple more minutes and we’ll be done

so what are the underlying assumptions of the equity valuation method

pretty much the same as WACC

and equity valuation you need to know

the ratio of D over E

because if you don't know your capital structure and how it looks like

it's tough to figure it out return on equity okay we'll go through

applications of this so many times

that you’ll get tired of it but it's good to know

how to do all three methods

alternative methods of valuation so the wrap-up

to this is are all valuation method substitutes

the real world answer is no

they are different ways of looking at the value of the firm

and based on your assumptions you'll use

methods that apply so the two most used methods are

WACC based enterprise value and

the method of adjusted present value they are substitutes because one requires knowing

the capital structure

ratio the other requires the level of debt should they provide the same valuation

answer is actually a little bit tricky and we'll get the answer in the future

and as you know answers are tougher always to figure out of tougher questions

here we got the same valuation I will leave it at that

and let you think about it just to give you a hint

that's not true always and the question is why what about this situation made you

get the same answers

I can't help myself another hint value

of everything was a perpetuity and it was

without growth so that’s one hint what is excess cash

I’ll come back to that this has been all about valuing

what is called the existing assets of the firm

but the firm many times also sits on cash

because it has ideas for the future

now you may ask why does it do it well maybe it's the case that

cash sitting on your balance sheet or in your company

is easier to access than raising more capital

so that could be one reason there are several reasons why

you would prefer internal cash

as opposed to going out the market over and over again

the point here is not about your financial policy the point here is if your excess cash

sitting

the trick is to figure our that amount and then add it back to the

value of the firm your existing assets

think about it the following way if somebody came to buy your firm

and your firm’s assets were worth 100 million and 20 million you had set aside for

taking future projects or whatever you won’t sell your firm for 100 million

you will sell it for 120 right

that's the logic I hope this has been useful

I'm going to do in my next modular form

most closely related to this method I mean to this topic

it’s called practical aspects of valuation

and it will build on what we just learned and

use a lot of numbers always but more importantly

show you little issues about real life and the primary issue there will be

how do you value a tax shield in the real world

is using the discount rate Rd for your tax shield

the only way to do it and the answer is no

so a lot of detail a lot of real-world

stuff in the next module closely related to

this see you