Hi guys!
The cost of equity is given as: r(e) = r(o) + [r(o) - r(d)] [D/E]
The above equation is said to be derived from the WACC: r(wacc) = [D/V] r(d) + [E/V] r(e)
I can’t quite get my head on how it is derived. Can someone help I’ve a feeling the derivation has been shown before some place.
Thanks and happy studying to all those preparing for the exams now!
kevndc
May 20, 2016, 7:31pm
#2
r(w) = r(d)*D/V + r(e)*E/V
Multiply through by V/E
r(w)*V/E = r(d)*D/E + r(e)
Rearrange to isolate r(e)
r(e) = r(w)*V/E - r(d)*D/E
Remember that V = D+E
r(e) = r(w)*(D+E)/E - r(d)*D/E
r(e) = r(w)*D/E + r(w)*E/E - r(d)*D/E
r(e) = r(w)*D/E + r(w) - r(d)*D/E
r(e) = r(w) + (D/E)*[r(w) - r(d)]
Hi Kevndc, thanks for the working.
Just to understand how is it that r(w) = r(o)?
If I’m not mistaken r(o) is the unlevered cost of capital while r(w) is then WACC which is the total cost of capital?
Thanks!
kevndc
May 21, 2016, 7:48am
#4
r(WACC) = r(o) for MM Prop I.
Thanks kevndc sorry I couldn’t find that in my textbook.
How is it that r(wacc) can equal r(o) for MM Prop I when clearly there debt and leverage included in WACC and r(o) is defined as the unlevered cost of capital?
Hardj
May 23, 2016, 7:36pm
#6
p.s the LOS doesn’t mention calculating any of these formulas for the MM reading.
Feel like I have come across problems in the TT and in mocks that require you to do the calcs in the MM Props