welcome back we are talking about how you go to comparables to figure

out your discount rate but I'm going to connect everything

and then do examples so the first thing you saw was

that we have using perpetuities and for perpetuities the value of the firm the value

of the tax shield the value of the equity in the value of that that

can all be figured out if you know two things about them

one is the cash flows the other is the discount rate

please pay attention to the slide with my beautiful writings on it

and this is the first ingredient cash flows

if you look at the cash flows the value of your assets

come from cash flows which are EBIT 1 minus TC

ignoring below the line items and the tax

shield’s cash flows are I times TC where

I is return on debt multiplied by the level of debt

one little twist which I want to add

even if it adds a little bit of confusion that's okay there should be a

subscript

T-1 here that means the level of debt you pay interest on

at the beginning of the period not at the end of the period

this fundamental you take debt you pay interest for the use of debt for one

year

the reason why T minus 1 doesn't matter here is because we have assumed

everything is in perpetuity the

levels of debt are the same just for simplicity because otherwise it'll keep

changing and you’ll need a spreadsheet

okay so cash flow is EBIT one minus TC to assets

keep staring at that little graph the cash flow to the tax shield is

Rd times DT minus 1 or Rd times D for convenience which is

interest rate on debt times level of debt given that it's a perpetuity

and then TC is the tax rate

that’s the cash flow to the tax shield now go to the other side

equity’s cash flows is EBIT minus I

because you gotta pay the interest first and then you benefit from the tax break

so you calculate taxes after subtracting interest and what goes to the debt

I very important what goes to debt is I

what tax shield you get is a certain fraction of that I

which is TC I so let's go over it one more time

what are the cash flows to the assets of the firm

you write I'll talk EBIT 1 minus

TC what are the cash flows to the tax shield

I times TC where I

is Rd times D times TC

what are the total cash flows to be distributed

this is a really cool thing so let's write it out

and you can write it out many different ways

so EBIT 1 minus TC

minus working capital blah blah blah

right those elements are for the assets

plus you want

I times TC

okay sometimes

I put the times sign sometimes I don't so what is the total cash flow you can

write it out like this

EBIT and I'm going to

cheat a little bit and by that I mean I'm gonna jump ahead a little bit

minus TC EBIT

minus I

you can rearrange

this part and you’ll come up with this part why do I

like this part this is your cash flow

these are your taxes right

so another way of writing the total cash flows is you get

cash flows you're not worried about taxes or anything and then you pay taxes

but in paying taxes it's very important to

realize that you pay taxes after subtracting the interest and if you do

the math

you see EBIT here in EBIT minus

EBIT times TC plus

I times TC take TC out minus out

EBIT because it was a minus here right

and then there was a plus I TC

minus minus becomes plus let's go through

the other side of the balance sheet what is the cash flow to equity

I'm going to again speak it out loud

the cash flow to equity is bracket open EBIT

minus I because you gotta pay the interest bracket closed

multiplied by one minus TC why because you want to pay interest first

but you also get tax deductibility therefore you should subtract it

before calculating your taxes how much cash flow to debt

I how much

total cash flow so think smart your total cash flows to equity

and debt have to match the total cash flows on the asset side

which is the basic value of your real assets plus the cash flows to your

tax shield so let's add them up EBIT

minus

I 1 minus

TC is to whom equity plus

I is to debt rearrange

you will again get EBIT minus TC

EBIT

minus

I this is the total cash flow

and if you notice again it’s split up very nicely

the first piece has nothing to do with taxes

the second piece has just the taxes please play around with this and that

you’ll start

actually enjoying yourself which of all these cash flows come first

so let's go back little bit which of all these cash flows come

first liabilities or assets you have cash flows to the

real assets you have the cash flows to the tax shield and you have the cash flows to equity

and debt

the first is always assets

and which ones the real assets not

the tax shield because the tax shield is based on financing

who pays for below line-items

so remember we did not include

in our cash flows change in working capital

depreciation and cap ex

among other things that come below the EBIT

after-tax we did it for convenience but who is responsible for them

remember whenever you have such a question it's got to be the equity

holders because the debt holders have been promised

money anyways right so they're going to get paid

who benefit from the tax shield though

the people benefiting from

anything also happens to be the equity holders

because the debt is a contract so the tax shield benefits

equity holders who finances the tax shield

remember if you have a firm with hundred million dollars value

essential and then you have a tax rate of 34 percent then you pay 34 percent

taxes

34 million but then government gives you back

some based on the tax shield if you have debt who gets that

debt holders I mean sorry equity holders

the debt holders are paid a fixed amount up front

so who finances the tax shield the government but who’s the government

we in another form you know it's there

who gets paid first in all of this

and I think it's important to recognize that

the government is playing a role here the government gets paid first

then between debt and equity who gets paid first

debt and then equity good to think about this

but we’ve gone to cash flows so we looked at the value

we’ve gone to cash flows now let's come to the

reason why we are at the comparable the reason why we are at the comparable

is looking for returns right but I don't want to just short change

everything and go directly to returns I always like to embed it

within valuation okay so here's a balance sheet

up there it's not a traditional balance sheet anymore

it is a balance sheet where

I've replaced first values with cash flows and now I’ve replaced balance sheet

with

assets returns on

so stare at it for a little while I think the easiest part is this

return on equity is Re for equity

we’ll call Rd return on debt so the two are relatively easy to think about

return on assets fundamental return we are after

to do any kind of valuation is Ra so I want to circle it so that it stays with

you

this is the return on the comparable and relevant to you

if the comparable is rightly chosen a pure-play

in the business in which you are getting into so you cannot

use the discount rate of Walmart for

doing say a company like Apple

unless their risk returned relationship is identical

right now comes the confusion in the real-life

turns out you also have a tax shield which till now we have assumed

just for practical purposes to show you alternative methods of valuation we have used

Rd

but it also could be Ra

so let's go to think about these issues one at a time

what is the corresponding risks

well again one at a time the risk of debt

is called beta D the risks of

equity is called beta e

what is the risk of your real assets beta assets

but there are two possible riskinesses of your tax shield

one is as risky as your debt or as a risky as your

assets and we’ll talk alot about the distinction between

these two types of doing valuation as we get into the concept and in theory

but

the confusion is largely going to be centered around this I'm not saying

the rest is easy but the rest is a little bit cleaner

because there's one to one relationship and there's only one possibility

for return on equity’s Re risk of equity beta

and by the way I’m presuming you know what beta is

beta is the measure of risk of anything okay if it’s equity it’s beta E and so on and

it's based on diversification

the model is called capital asset pricing model we’ll go through it one

more time and through the

steps but it's based on profound thinking

on very simple concepts like people never put all their eggs in one basket

it captures market risk okay

the return on risk of all components are self evident

except ambiguity about tax shield so why

why is there ambiguity and the reason is quite simple

there are circumstances in vhich it is appropriate to use

the level sorry the rate of return on debt

as the discount rate for the tax shield and that is when

you know the levels of your debt and you kind of the

value of your firm

doesn't affect the value of the tax shield so that's

one way to think about it the value of your firm is going to keep changing

if your tax shield’s change in value

the tax shield’s value doesn't change with you believe value of the firm

then it’s appropriate to use Rd and when Modigliani-Miller

designed the theorem both with and without taxes

capital structure they assume not only that Rd would be the

appropriate rate they also assume that the beta of debt is zero

so if beta of debt is zero what is the return on debt

I’m pausing because I'm expecting you to raise your hand and

yell at me the risk-free rate which can be measured by a treasury

security return on a treasury security

okay which equation links risks to return and this is a recap but let's go through

it

it is called CAPM

and CAPM says this and I'm going to write it a little bit painfully

the expected return on anything why am I writing expected

it’s something crucial that we're not talking about real

returns we're talking about on a particular day a return could be anything

you’re looking to the future and we are concerned about what is the rate of

return

on average on anything and it's on average in expectation

very important it says it should be equal to ris-free rate

why because most projects have greater risk than risk-free rate so this is

called a basic

risk plus risk premium

market risk premium

why does RF not have an expected sign simply because we know

you will get RF right this is the whole notion of expected

versus actual right promised return IRR’s

versus the actual rate of return and then you multiply it by beta

so here's the beauty of it it’s simple

this number and this number can be measured actually

not perfectly but can be and so can this

but the key notion about this is the following

if I put equity here I'll get return on

equity if I put beta debt here

I'll get return on debt if I can somehow figure out beta asset

it will give me asset you can put any monkey on the right hand side

it'll be the return on the monkey right so the reason why the simple

model has gotten so much attention

even though it's not perfect no model is about human behavior

is because its applicabile to anything these two numbers

are based on market data and do not change what changes

tell me your risk I’ll tell you your return

so I pretty much covered everything right so the question

left is the tax shield what is the

discount rate you want to use on the tax shield and people use two

alternative ways one is debt one is

assets if your value of the firm is affecting the value of the tax shield you

want to use Ra

if the value the firm is not affecting the value of the tax shield

people use Rd and can get more complicated than that

but we’ll stick with these two alternatives

which of these risk return combinations do you want

for valuing business this is in some ways a silly question or a very profound

one

and that's life you know a lot of questions that sound obvious are actually very

important

so answer is you want all of them right depending on your purpose

but here you are valuing your business

and I always want to go back to which one

beta asset because beta asset

relationship with return on asset equals RF

and remember I'm dropping the expected signs or actually let me retain them for a

little while

plus expected return on market

minus Rf

I want this why because if I don't know Ra I don't know where to begin

if I don't know Ra we’ll see we cannot do the value of the fundamental asset

we cannot figure out WACC

of my firm and we cannot figure out

the Re of my firm so

Ra is the fundamental rate of return

but you have to get it from a comparable therefore every time

I'm emphasizing comparable okay

which of the return risk combinations is easiest to calculate now

the word easy here is a little bit of a misnomer and dangerous

because finance has progressed so much we call it easy

but which of the three let’s choose what are the three

beta asset which we really want but there's beta debt

and beta equity which of these three are easiest to

value fundamentally the most difficult concept is the easiest to

measure why equity is really really profound

why it's paid last you don't know what you're going to get paid and so on

so in some sense one would imagine that this would be tough to measure

but because of markets

this is the easiest to measure and put it in CAPM

and you get expected return on Re

but that's not equal to expected return of Ra

because this is not equal to beta

asset we’ve just done it

right when will the two be the same when there is no

debt so the easiest one to calculate is beta equity

and it's so easy now that you can actually go to Yahoo Finance

and suppose your comparable was Apple the good news about Apple is

or Microsoft or a lot of technology firms there's no beta

debt why not because there's no beta debt there’s no debt so you can’t have beta

debt

so the expected return on assets and equity are the same

but that's not usually true turns out you can go to Yahoo Finance &

beta equity is actually published finance.yahoo.com

do it and you hopefully have done it if you’ve worked with me before

in any of these sessions is that what you learn is you

do key statistics and you could figure it out dangerous

don't do that I would strongly

push for Morningstar

and not because I work for the company or whatever or have to benefit from it

but because they do the best analysis

of data and beta is an estimation it's not a number like price

times

price per share right so please be careful for two reasons one

they do it scientifically yahoo just does if you have 24 observations they

calculate a beta on a regression

so they do the regression adjusting for all kinds of biases

from statistics that’s why you should know statistics

but they also adjust for the fact that beta doesn't I mean sorry CAPM

doesn't work

perfectly so there are some changes made to CAPM

which they adjust for and tell you the beta

equity and beta all the various betas

they do it for you so why

unlever and now

this is the next step which I'm going to take a pause

and there is a whole process of a dealing with data

called levering and unlevering and it’s related to the last point we just made

which was we want to go to beta asset

but we observe better equity

and so think about it what is the concept of unlevering

big hint when we come back we’ll get into the details big hint to think about it

is

if we could directly observe beta asset

that means the

risk of your assets which are real assets you don't trade but equity trades

there wouldn't be the issue of unlevering and textbooks would be beautiful

and very small life would be very easy

so with that in mind let's take a break

think about it why unlever remember leverage is

increasing the risk of whom equity

which makes beta equity larger than beta asset

we somehow have to unlever the beta equity

and you'll see in the next little subsection

that we’ll have to then relever I keep reminding you you're going from the

beta equity to beta assets of what

the comparable but then when you go back

that gives you the return on assets for your business

but depending on which valuation method you want to use

you may use WACC you may use return on equity

for your firm you'll have to again do some

manipulations it’s a little tedious but we’ll get there

see you in a minute