0:54

right? And I'll repeat things

just because I want you to be very clear and if you're clear you can recreate all

of this on your own

and you are kind of creating your own set of notes for yourself

EBIT is 150 million there is no friction

there are no taxes that's for simplicity so 150 million

no leverage who gets paid

first if you have debt? Interest but interest is

0 so who gets all the

EBIT it's called EBT

goes to whom

no growth company it goes on to equity holders

and it's all so many times called dividend

right here we won't call it a dividend simply to keep things simple

right no taxes nothing everything goes to them

now in order to do the present value of this

to figure out what the value of the ulevered firm is

Vu you know the value of the unlevered firm is also the value

of the equity of which firm the unlevered firm

because there's no debt that's the beauty of a balance sheet it has to balance

so if debt is 0 it’s value has to be 0 right

so let's see what would it be

it would be 150 million divided by

ideally what EBIT is generated what by the equity holders or by the assets of the

company

here it's tempting to use RE directly but it turns out you should

always think of the discount rate of your assets

and when I say asset I mean your real asset your business

your idea has to be the discount rate turns out

in this case it's also equal to

Re by the way if I once in a while complain about things as I'm doing it

it's a small complaint sometimes I can’t

write very clearly which you suffer for but here are the numbers a few

that’s another advantage of simplicity do we know Re

yes we have done all the work we have done cap M we’ve done beta and so on

and turns out to be how much 15 percent

so now you know why I use the numbers I do

because life becomes very simple and how much do you have

thousand million that's the value of the

unlevered company very straightforward and that's how most companies are valued

on the back of the unlevered the assumptions may change but many times you use

especially for the whole firm perpetuities perpetuity with growth

which actually underlie multiples that’s

beauty of it all okay two thousand million

give or take a few dollars now if I want to ask you

what is the price per share what would you go looking for

number of shares but

here's another question as we’re going now so

what will be the price per share go look for number of shares suppose

there were a million shares outstanding

what will be the price per share one buck turns out we are going to

fundamentals to try to value the company

right like an analyst would do or like a person working on wall street would

do or a banker would do but the important thing here to recognize is that in a

marketplace life because very simple

for an existing company how would you value the

with no debt what would you do you’d just take the number of shares

multiplied by price per share and that’s called

market value so market value

used commonly is market value of equity and in this case we have an

unlevered firm so it is a thousand million dollars

okay question number two what is the value of the levered firm

and I could spend and get a Nobel Prize trying to show you that

exactly thousand but let's assume we have done

the course before this or the content before this to know

that in a market without frictions

Vu has to be equal to Vl

we won’t go through the steps but because we know VL is

thousand I'm going to assume that you know how to do this

we'll go through VL when it's much more interesting

which is when there are frictions like in the real world

but when there are no real fictions the Nobel Prize

says the following: debt shouldn't matter equity shouldn't matter

the mix should matter so in this case

the value of the levered firm and unlevered firm have to be the same

and it’s a thousand million dollars right

everybody we just it so the question then becomes what's interesting about

a levered firm

well in a in a world without frictions

the value of the firm can’t change because it comes from my ideas not from financing

because if it came from financing

why the heck we are spending the effort doing this for example

if only money created value and effort in creating ideas or something useful and I

hope this is useful to you

that creates value not the fact that

so I'm doing this exercise and I really hope it's valuable to you

but whether it's financed by University of Michigan or by like a private

company and all that is irrelevant to the

amount it’s value right suddenly I hope you don't find it more valuable just because

some

Gautam used his own money or instead of

Alex is in the room he contributed so this is a very powerful result

actually but so what's unique question number three

so if the value of the company doesn't change does the value of equity in the

levered from

change as opposed to an identical firm

without leverage also has to be yes and the reason is

the value the company's determined by the assets

which are then divided between equity and debt so what was the

amount of equity in the first firm

zero I mean sorry amount of debt in the first

unlevered firm zero so what was the value of equity

value of the firm that's the sequence of thinking

you shouldn’t fall into the trap just because we own the equity

it is ours, the firm no no firm has value

because of ideas and then it splits it up so what's the value of the equity

now here was the balance sheet

and balance sheet says thing should balance

so the unlevered equity what was the value of equity

equity was value of the firm unlevered

or value of thousand million

here value of equity of the levered firm

is equal to value of the levered firm minus the value of

debt I don't need to have an L because debt implies leverage

and do we know this? yes

do you know this? yes

so how much is the value of equity 500 million

so we are using very simple ways

of value things initially but remember the principles behind it

are the same so

even in complicated contexts it's always true

by hook or by crook the value on the asset and liability side

have to match otherwise there’s something wrong okay

let's keep moving question number four what is the return on assets of the

unlevered firm

what is the return on assets of the levered firm

what is the relationship between the two and why

this is pretty straightforward but let me just give you

a way of thinking about it two things

the first is conceptual return on assets

cannot be affected by leverage

simply because we have no frictions

there's another way of thinking about it let's make Vu

equal VL yes

in a world without taxes and so on which is equal to what

EBIT total

right so what has to be common to both

that return on assets has to be common to both otherwise

the equations won’t work so it's almost by design

that if the value of the firm doesn't change the leverage

return on assets can’t change either because they're based on assets

so they shouldn't change or because

if they are different the value of the firm would be different you know because

the earnings at the same

so its kind of tautological that the return assets would be the

same so let's keep moving do we know this number? Yes

we know this number already simply because we knew

the return on equity of an unlevered firm was fifteen percent and therefore

the real assets of the unlevered firm was fifteen percent

what is the WACC of the levered firm what is the WACC

of the unlevered firm what is the relationship between the two

why? Let’s write it out. Weighted average cost of capital

is equal to Re E

over D plus E plus

Rd D over D plus

E I'm going to go fast on this simply because

you know this so very quickly what is E over D plus E

proportion of equity what is D over D plus E

proportion of debt they should add up

what is weighted average cost of capital well it is exactly what its

says that's another thing I like about finance I mean

things mean what they mean you know in reality they're not just

difficult to understand so in the first case what was the WACC

when there was no debt well

simple return on equity you can stare at this why because debt is zero

second term disappears first-term E over D plus E becomes 1

right the more interesting case is

when there is debt and equity which is this equation

right here okay so

weighted average cost of capital in a word without frictions

is very easy to understand because it's

self-explanatory and if there's no debt it’s also equal to return on

equity okay what is the return on equity of the

levered firm what is the relationship within the return on equity of the levered and

unlevered firm? For this let’s write out

WACC

and I'm going to write something in a second

is equal to Ra

in a world without taxes there's no difference between WACC and Ra

weighted average cost of capital is exactly equal to return on assets

simply because there's no friction going on so the left hand side is return on

assets the right hand side is

return on equity and return on debt so this has to be true

14:44

so this answer turns out to be what 20 percent

let me pause here for a second this is the return on equity of

whom of the levered firm

because remember if the firm is not levered what happens to the right hand

side of this equation I’ve put up

right here d is 0 the entire second part of the equation

disappears and return on equity of the unlevered firm

where the L disappears and a U can appear is Ra

one way to think about this is Ra never has a superscript or a subscript

because Ra is your assets and it can’t be affected by debt or equity

that is always fundamentally true regardless of what we do

that has to be true right so that's one of the nice things

question what is the return on equity of the unlevered firm well we know

what it is

because if there's no debt and no return on assets then return on equity will be the

same

and return on equity of the levered firm is

always greater than the return on equity

of an unlevered firm

and the reason is why it's because

leverage increases the risk of the equity holders

what leverage does is effectively

comes with the contract whereas equity is not a contract

right that's the first thing

the second thing is because it's a contract

and it is senior debt gets paid first

so the firm is the same as before but you now take on leverage think of that

as the levered

firm you’re not promising to pay somebody before you get to see the money

it becomes riskier so the return has to

go up I will do this later but while I'm talking write down the beta equations

and they should be identical to the return equations

so everything that I've written here Ra replaced by beta

a Re replaced by by beta e

Rd replaced by beta d

and you will have everything flowing together

okay so I haven't given your betas here because they are

superfluous I’ve assumed I know the Rd and Re

so I don't need to go back to beta but if I had given you betas

I would have to give you some risk premium some risk free numbers and this

will sound familiar to use cap M to go to Re

right so because we're after discount rates and we have all the returns

you do what information you need okay

so return on equity of a levered firm will always be greater than

the return on equity of an unlevered firm

and whenever we say return in finance we are talking

almost 99 percent of the time about

expected return not the actual return

on any particular day anything can happen

we are not interested in

daily events when we think forward we’re thinking on

what's expected remember and we're trying to see what's going to expect

over a long period of time when you

value a company so expected is very very important

okay what is the relationship between beta equity and beta asset of the unlevered

firm answer is they have to be the

same so the beta equity

and beta asset of the unlevered firm

have to be the same this is simple

why because R we can write

return on asset has to be equal to return on equity so

the betas of the two have to be the same for the unlevered

firm right so I'm going to now

ask about the levered firm what is the relationship between beta equity and

beta

asset and I’ve already hinted to you that you should try to do it on your own

so it turns out because balance sheet balances

beta asset of a firm

is a weighted average of the betas of debt and equity

one big caution to you many times a textbook makes strong assumptions but

then we follow those assumptions regardless of real-life

and as I said right now the assumption is frictions are off the table

but to pretend like frictions are always off the table is the wrong thing to do that’s

why I’ll cover frictions in a second

but many textbooks assume the following

for the ease over exposition let us assume that beta debt is equal to 0

which means the debt is risk-free

I think it comes from a simplifying assumption made

in some theory papers including Modigliani-Miller

at times to ease of mechanics and a lot of terms they assume

risk-free debt what happens to beta debt

it’s 0 but then many of us

assume that for all applications of debt

that's not a good idea because recent financial crisis will tell you that debt

can be extremely

risky for a lot of people

and the economy and so on and so forth so

quick this equation is the mirror image of the return equation

and what relates the two cap M

so what will beta equity be

I can rewrite this as beta asset plus debt over equity

beta asset minus beta

debt right

what is this called business

risk business risk

what is this called

financial

I haven't spelled it right there should be another N over here

risk so the

thing to think about is the following the risk of equity of a levered firm

is always greater than the business risk because we consciously

through our managers we being shareholders

through our managers take on debt which increases the riskiness of equity

but it cannot change the riskiness of the business this is

this is the assumption here right so

this is called financial risk this is called business risk so

beta equity of a levered

firm should always be equal to

greater than beta asset

of the levered firm because it's riskier and therefore if you saw

what was the return on equity earlier 20 percent what was the return on asset

15 percent so that's what's going on

so let's take a break here

I'm now entering the universe of taxes

but I'll go through there also slowly I want you to really internalize this stuff

so that you can run with it in complicated spreadsheets

so hang in there take a break think about what you've learned

do whatever you want and see you in a little