hi welcome

we are talking

about something

that’s dry

but fascinating to me

and hopefully to you we want to go

and get our discount rates from our comparables we have to unlever

because we can observe things on the liability side

we can observe or calculate beta equity and go to return on equity

and we can go from there to return on assets but

it's a little bit tricky because the tax shield

and its risk

determines how you figure out these equations you're looking at your comparable

you can look at the liability side

but you have to make some assumption about the tax shield’s discount rate

so let's just stare again for a second on what we went through

equation wise the Ra equation and beta equation

up for you to look at please write them down

and by the way if I make an error or a mistake

obviously I can when I'm going through but hopefully it's not conceptual that you

can't figure it out for yourself

the way remember this equation is if Rd

is the discount rate for the tax shield and it's a fair assumption to make

then D every time it shows up in the return

on asset equation it's multiplied by 1 minus TC

it’s just the way it is similarly for betas

we can work that out why and so on but after a while the practical

aspect is more important in some situations though intuition is always good

okay let's go to the second approach

and we will then be kind of

a little bit closer to getting finished up with this

second approach of unlevering assumes

that the tax shield is the same risk as the risk of the

business when is this assumption valid

think about it this is assumtion is valid when you

actually think the value of your firm changes in the value of your firm

are related to changes in the value of the tax shield this issue can be viewed as

a kind of a geeky thing to worry about and sometimes it is because the numbers

look very familiar

or similar sorry whichever assumption you make but it's good to know how

you think through things so let's assume that the value of the

tax shield is dependent on the value of the firm which is

likely to happen right so big hint if you are using WACC

as your discount rate

you have to assume a certain capital structure if you assume that capital

structure

and the value the firm will change anyways with new news

you’ll have to change your capital structure if you change your capital structure

turns out maybe it makes sense then

to not use Rd but to use Ra

so big hint so unleveling approach

cash flows again please write this

out you’ve return on assets Ra times Vu

why is Vu there because remember rates are very important to

transferring so we can't assume everything is equal rates because is not

true

so Ra times Vu on the left hand side

but now again Ra times tax shield the difference between this and the

previous version is

it was Rd times tax shield right so here you have

Ra times tax shield that's the key difference conceptually

and on the right hand side you’ve Re times E Rd times D

what can you observe you can observe the right hand side

not the left hand side so you have to go from the right hand side

to the left hand side let's do it unlevering equations

I’m going to write out the equation that the balance sheet

shows me that Vu

times Ra plus Ts times Ra

is equal to Re E

plus Rd D very critical

reminder whose balance sheet am I looking at who am I trying to get the

discount rates from

not myself but my comparable who do I get multiples from

my comparable who do I not worry about cash flows about

my comparable because my cash flows are determined by

my analysis and my product

and you're looking at similar products because they're similar

risks okay that's what an investor will do an investor will never compare investing in

the stock market versus

putting it in the bank that’s the silliest thing you can do

because they are apples and oranges because that's the notion

look how nice this is now you know

that Vu plus TS regardless of what the values are

will always be equal to equity plus

debt you know that right

so let's do it this actually becomes pretty straightforward Ra will be equal

to

Vu plus TS

so always be smart about solving equations

don’t use extra steps

though you can always do it in many ways this will be equal to

Re E plus Rd

D now instead of figuring out what the tax shield value is and so on

trust me it won't be easy but you know how to

make this problem easier for the purpose at hand

take this and substituted so Ra

becomes E plus D

Re E plus Rd

D we're on a roll here therefore Ra becomes what

Re E

D plus E plus

Rd D

D plus E by the way many times I flip these

or I flip these if I flipped these

I mean as long as the logic in the equation is similar

that's all that matters whether I write Re E over D plus first or whatever

doesn't matter doesn't this look cleaner so if

Ra is the discount rate for the tax shield

then the equation is very simple that doesn't mean it's a better or worse

equation

just the way it turns out and the TC doesn't show up here

it's in the background it doesn't show up simply because

Vu plus TS you can just directly substitute

E plus D and you're done so

to just rewrite these

if I wrote Ra as and I'm going to do it in reverse order now

so that you for your comfort level is high