straightforward again right you have after-tax

$99 million and the discount rate is how much

15 percent that hasn’t changed

I’ve said nothing about the rates of return

that are different between what was done before and after

I’ll focus just on taxes and you pay taxes on cash flows

and the answer to this have to be 660

million why did I say has to be with such

excitement because I know the answer what it should be right

so imagine what was the value of the firm before one thousand million

and now somebody's come and taken 34 percent of it

what is 34 percent of 1000 340

what are you left with 660 so whether I do it the long way or the short way

finance always make sense

so the taxes are

taking away $51 million every year

and the PV of taxes got 350 million

okay so that's what's going on is

you just have a third party

creating a friction and they're taking away 350 million

from us from the same people if we owned the whole

everything everybody owned what we collectively own

we are just paying us to hopefully do things that are

commonly beneficial to us to give you an example

you know I love Ann Arbor where I stay

and I’ve stayed for many years but we had a very severe winter

this year and believe me driving on the roads

I hope some of those taxes are going to fix them pretty soon

that what taxes are supposed to do is do stuff for the collective

makes sense instead of all of us having to replace our tires every day

that would be a nightmare so why not just spend money collectively and fix the roads

okay so that's what it is the next question is what what's the value of the

equity in the levered firm why now this is a loaded question

why because you have to in order to know the value of the

equity of the levered firm you have to know this first

and I'm going to make a statement

which you can think about in your free time

that the value of the levered firm can’t be any different from the value

of the unlevered firm because the tax imposed on the cash flows of the firm comes

before it has

anything to do with the distribution of the cash flows

there's nothing that I've said about taxes

that relate to the distribution of the cash flows

so the value of the firm has to be 660 million

this is very similar to a world without taxes

because in a world without taxes this was one thousand million

it has gone down to 660 because value of the firm has been taken away

for collective value hopefully but now

you know that you can split it up into what

equity and debt and I'm asking you

simple what would be the value of the equity

always use information you have available to

deal with the issue recognizing the beauty of finance is what

you can answer the question 100 different ways

but the shortest way or the most logical way is one based on the information

we know this is 500 million so what is the value of equity of the

160 million because the two have to add up to the value of the firm

so another way to stare at this and say this is

who has really lost the value imagine

you're taking this approach of firm versus the rest the world

when you stare at this compared to the world without taxes

who has lost money to the government equity holders

and that's one of the lessons to remember because debt is a contract and

we still

owe people $500 million that first goes to

the debt holders by the way we’ve violated this contract

many times because it's easy to

fulfill that contract when the world is doing well but suppose the world was

such that you

owed more than the value of the company company managers and shareholders

have an incentive not to do that and keep the money

and that has happened many times in our recent history

and many times all over the world and to pretend that

it will not happen is not a good idea

that's why you always need markets

but with rules of the game you don't

play football without rules of the game simply markets need sensible rules of the game

okay E equity is 160 million

debt is 500 million both add up to how much

660 let's keep going

the next question is what is the return on assets of the

the unlevered firm what is the return on assets of the levered

firm what is the relationship between the two

why and I'm not going to spend too much time thed answer should be

pretty obvious to you is that value has been taken away

off of the top cash flows but the return on asset

is still fifteen percent it shouldn't be affected

by the taking on of leverage

so they should stay the same

regardless

of I'm actually writing isn’t that cool

by the way you should try to do this sometime

it’s really cool you can write you can erase I mean

it is all going through the internet to you I mean it’s pretty cool stuff

so return on assets doesn't change now

the more interesting part is what happens to the WACC of the levered

firm versus the unlevered firm so let's get the unlevered firm out of the way

WACC of the unlevered firm

is equal to return on equity which is equal to

15 percent we already know that why because there's no debt

so weighted average cost of capital is fully loaded on return on equity by

that I mean the rate on equity is 100 percent

okay now what is WACC

and let me write down the formula WACC

of a levered firm will turn out to be

Re E over

E plus D for Rd

D over D plus E

which will again be 15 percent and the key to

not having to go through everything in this case is remembering

that the tax has nothing to do with leverage

it is off the top if this is true can you figure out Re

Rd and all that yes I'm going to now

ask a question what is the return on equity

of the levered firm what is the relationship between the return on

equity of the levered and

unlevered firm why I think the second part of the question is

pretty obvious and that is that when you take on leverage

risk of equity goes up therefore the return on

equity should also go up but the trick here is

remember that we have lost some value and who's lost the value

debt or equity equities has lost value

so the debt over debt plus equity

is 500

over how much this time the value of the firm has dropped

to 660 because somebody else took away 340 and that's the government

we were talking about and the equity over debt plus equity

has to be 160 over 660

the reasons I'm pointing these out is those are the rates that have

changed as a result of the fact

that the government imposes taxes there's no tax benefit to

the interest rate on debt and taxes

come off the top and you’ve promised your debt holders

$500 million worth of value so

what will Re be Re will be

Ra plus D over

E Ra

minus Rd

very similar equation to what we used before but

as I said the information tells you what to do

and also the numbers change one number that will not change in our

scenario is 15 percent because the return on debt

I mean return on assets this won't change and we are assuming

that the type of date you’ve raised is still

$500 million at an interest rate of

10 percent but what has changed due to the third-party

is market value of the firm

and debt is 500

and equity is now 160

and for the numbers to pan out I believe this is

5 percent multiplied by a factor

greater than 3

so this turns out to be be

30.625%

30.625%

so a factor greater than three by a little bit

why because if it was three times five it would be fifteen

and 15 would be exactly 30% so it’s higher by 30.625

I would encourage you to try to see

if everything adds up so what I would like you to do next step on your own this

is like a homework

exercise return on assets WACC remain the same because

the tax is not discriminating based on debt or equity

it's just taking off value I would use these numbers

to go figure out the WACC and it should be 15 percent

what has changed is the mix of return

on equity and the weight on equity and therefore the weight on debt has also changed

the mix of things have changed but the 15 percent will remain the same

the only reason why I am going through all of the steps

is to make you

understand at a deeper level what exactly is the reason for things to

change

again one last question what is the relationship between beta equity of levered

beta equity unlevered

beta equity of levered firm will always be greater than beta equity of

unlevered firm and the reason is we already talked about it

equity firm leverage always takes on

business risk and in addition to this financial risk

and we did this already so finally

a question related to this which basically is the

in a nutshell the completion of this discussion

in a world with taxes with no implications for leverage

who is the third party sharing in the pie

and who's the party that loses that value

the third-party sharing in the pie is the government

you’ll give up 51 million dollars every year to that party

but in essence in value terms

you give up $340 million out of a thousand million

because a thousand million is the total value of the firm and 34 percent off the top

goes to the

government who loses that

equity holders because debt holders

are contractually obliged to

have a payment system whose present value today

is 500 million dollars that’s why I got debt of 500 million

so what I'm going to do again is I'm going to take a pause

before we go into the home stretch

of trying to understand what's called the real world

with debt and taxes and we’ll

do the same example to show you how things change and this time

things will change even more so and there'll be some subtle changes which

will make you

kind of try to figure things out for yourself and I’ll help you in that process

see you for debt and taxes whenever you have the time