Reading 29,capital structure,page 107
wrong formula: re= r0+ (r0-rd) (1-t) D/E
right formula: re= r0 + (r0-rd (1-t)) D/E
wacc=re*E/(D+E)+rd*(1-t)*D/(D+E) ===> (wacc*E)+(wacc*D)=re*E+rd*(1-t)*D
===> (wacc*D)-(rd*(1-t)*D)=(re*E)-(wacc*E) ===> (wacc-rd*(1-t))*D=(re-wacc)*E
===> (wacc-rd*(1-t))*D/E=re-wacc ===>wacc+(wacc-rd*(1-t))*D/E=re
in capital structure reading we suppose:WACC=r0 so:
re= r0 + (r0-rd*(1-t))*D/E
this is right formula but in this reading we have this formula :re= r0+ (r0-rd) (1-t) D/E
2 of EOC questions is based on this wrong formula!!!
you are wrong when refer WACC=r0
In this topic (Capitap Structure) “ro” refer to WACC for all_equity company
u are right,“ro” refer to wacc for all-euity company but all-euity company is one of many possibilities of wacc that should applied to wacc=re*E/(D+E)+rd*(1-t)*D/(D+E) formula.
re= r0+ (r0-rd) (1-t) D/E and wacc=re*E/(D+E)+rd*(1-t)*D/(D+E) must be equivalent,but they aren’t.
in perivious curriculum of CFA ,re= r0 + (r0-rd (1-t)) D/E formula have been used but in 2012 curriculum this formula changed to re= r0+ (r0-rd) (1-t) D/E.
whats wrong?!!!
that formula you derived
as re = ro + (ro-rd(1-t))D/E is the right one.
This should be an erratum item. If it is not, please report it. This has been corrected in previous years as well, but probably the original author’s reading never gets corrected…
how can I report it to CFA institute?!!!
is there any link or email address for reporting errata!!!
go to their website - and it is there to find out.
or send an email to info@cfainstitute.org and mention Erratum … on the mail subject
with pg #, and details … in the body
thank u for your response cpk123
so this formula is wrong and EOC answer questions that based on this formula are wrong too
I also saw the same formular (Re= Ro + D/E*(1-t)*(R0-Rd)) in the shweser note.
So, is shweser note also wrong?
I think it is not!
You are wronging!
Please renember that, R0 is the cost of all equity company.
WACC is cost of equity and debt firm.
”ro” refer to wacc for all-euity company but all-euity company is one of many possibilities of wacc that should applied to wacc=re*E/(D+E)+rd*(1-t)*D/(D+E) formula
in the case of an all equity company - D=0, E=1
so D/E = 0
So formula reduces to Re = R0
which is right.
If Schweser has the formula in that way, it is definitely incorrect.
R0 = D/D+E* Rd * (1-T) + E/D+E * Re
work back from there to arrive at Re formula
and you will get
Re = R0 + (Ro-Rd(1-T)) * D/E
Suppose Re = 16%, Rd = 5%, Tax = 20% Debt to Asset ratio = 50%
WACC = 0.5 x 5(1-20%) + 0.5 x 16
WACC = 0.5 x 4 + 0.5 x 16
WACC = 2+8
WACC = 10%
Using the formula (incorrect)
Re = Ro + (Ro - Rd)(1-t) D/E
Re = 10 + (10 - 5)(1-20%) x 0.5/0.5
Re = 10 + 5(1-20%) x 1
Re = 10 + 4
Re = 14% (Which is wrong)
Using the correct formula as CPK mentioned
Re = Ro + (Ro - Rd(1-t)) x D/E
Re = 10 + (10 - 5(1-20%))x 0.5/0.5
Re = 10 + (10 - 4) x 1
Re = 10 + (6)
Re = 16% (Which is correct)
be careful may friends,2 EOC Q are based on this wrong formula
Please! I remind that: CFA text book is no wrong!
You should read this link for more detail.
http://en.wikipedia.org/wiki/Modigliani%E2%80%93Miller_theorem
bump
Why’re you bumping this? It is just going to create more confusion for everyone.
for all-equity : wacc=re=r0, Vu=[EBIT(1-t)]/r0
if finance with leverage, Vl=Vu+tD=D+E=[EBIT(1-t)]/rwacc, and rwacc=(D/Vl)rd(1-t)+(E/Vl)re
==> Vl*rwacc=rd*(1-t)*D+re*E
==> EBIT(1-t)=rd*(1-t)*D+re*E
==> Vu*r0=rd*(1-t)*D+re*E
==> r0*(Vl-t*D)=rd*(1-t)*D+re*E
==> r0*(D+E-t*D)=rd*(1-t)*D+re*E
==> ro*(1-t)*D+r0*E=rd*(1-t)*D+re*E
==> re=r0+(r0-rd)*(1-t)*(D/E)
Oh no not again. Aether, are we going to bother?
LOL, exactly my thoughts.
Guys, quit bumping this thread… the formula given in the CFAI text is correct as given. No need for proofs or second-guessing the core material.