Suppose the cost of capital of the Gadget Company is 10%. If Gadget has a capital structure that is 50% debt and 50% equity, its before-tax cost of debt is 5%, and its marginal tax rate is 20%, then its cost of equity capital is closest to: A) 10% B) 12% C) 14% D) 16%
WACC = wd * rd*(1 - TR) + we * re 0.10 = 0.50*0.05*(1 - 0.20) + 0.50*re re = 0.16 = 16% = D? Is this really that simple or there’s a hidden surprise which I am not able to see at this late in the night?
Since I don’t think many others will be posting any time soon, I’ll give the sol’n. Hopefully you or someone else could explain it to me. I got the same sol’n as you this is the explanation provided: C is correct. r(e) = r(a) + [r(a) - r(d)]x(D/E) Note: If D/(D + E) = 0.5 then D/E = 1 r(e) = 0.1 + (0.1 - 0.05)(1)(1-0.2) r(e) = 0.1 + [0.05(0.9)] = 0.1 + 0.04 = 0.14 or 14%
Shocking!! Was the question asking us to use the Modiglani Miller postulates? Because this equation is from what they proposed=> re = WACC + [WACC - rd*(1-t)]*(debt/equity)
It only mentioned what I wrote above Would that formula that you provided still not give 16%? = 10 + (10 - (5*0.8))*(1) = 16 ??
They have surely messed up with the calculation. The formula used in their explanation is correct, and then they went on and substituted some weird values, multiplying at the very wrong place and defying all the BODMAS rules to get to 14% I think 16% is a good enough answer, unless someone else could shed some light on reaching to the 14% figure.
I think the schweser answer is wrong- r(e) = 0.1 + (0.1 - 0.05)(1)(1-0.2) they went and multiplied the (1 - .2) by both debt and equity, not just the debt portion. if you take just the 0.05 x .8 in their example, you get the 16%. i can’t imagine that 16% is wrong here. email schweser.
what an unsatisfying way to start Sunday studying 
if this is from the CFAI texts, there is a mis-print in the book - see the errata on CFAI website.
There was a questions very similar to this in the Level I CFA books - for which they had 14% as the answer too, and then later on they retracted and said 16% was right. r(e) = r(a) + [r(a) - r(d)]x(D/E) Note: If D/(D + E) = 0.5 then D/E = 1 r(e) = 0.1 + (0.1 - 0.05)(1)(1-0.2) r(e) = 0.1 + [0.05(0.9)] = 0.1 + 0.04 = 0.14 or 14% For rD they have taken 5% --> the Erratum read it should read as rD’ where rD’ = rD * (1-t) So it should become instead of r(e) = 0.1 + (0.1 - 0.05)(1)(1-0.2) r(e) = 0.1 + (0.1 - 0.05*(1-0.2))(1) = 0.1 + (0.1 - 0.04) = 0.16 So 16% is the right answer CP
patkeenan Wrote: ------------------------------------------------------- > Since I don’t think many others will be posting > any time soon, I’ll give the sol’n. Hopefully you > or someone else could explain it to me. > > I got the same sol’n as you > > this is the explanation provided: > > C is correct. > > r(e) = r(a) + x(D/E) > Note: If D/(D + E) = 0.5 then D/E = 1 > r(e) = 0.1 + (0.1 - 0.05)(1)(1-0.2) > r(e) = 0.1 + [0.05(0.9)] = 0.1 + 0.04 = 0.14 or > 14% This is clearly wrong. D/(D+E)= 0.50/(0.5+0.5)= 0.5 and not 1. So their answer is wrong.
This one fecked me up too. I posted it a few weeks ago. Error.
after-tax cost of debt = 5%*(1-20%) = 4% 10% = WACC = 0.5*4% + 0.5*ke -> ke = 16% -> D