Suppose the cost of capital of the Gadget Company is 10 percent.If Gadget has a capital structure that is 50 percent debt and 50 percent equity,its before - tax cost of debt is 5 percent,and its marginal tax rate is 20 percent,then its cost of equity capital is closest to A 10 percent B 12 percent C 14 percent D 16 percent

D. 50% of cost of equity + 50% of cost of debt (after-tax)=Wt avg cost of capital. equity : 50% of 16% = 8% for Debt : after tax : 5% minus (20% of 5% i.e.1%)=4%; 50% of 4% which is 2%. Add these two : 8% + 2% which is 10% WACC.

Ans is C I did the same thing ,but wrong ( According to the text book ) 0.1+(0.1-0.05)(1)(1-0.2) =0.14

??? That formula doesn’t make sense, does it? After tax debt is 5% * (1 - 0.2) = 4% Since debt is 50% of the total, you have your first 2% right there. Add equity is next… Outcome is 10% so (4% + ?) / 2 = 10% -> ? = 16%. I’d go for D too. I’d be happy to hear where I went wrong.

Which question? Is it in CFAI readings?

D. The After tax cost of debt is 5 X (1-0.2) = 4% The agerage between the cost of debt and the cost of equity (50% each: makes the computation easy) is 10 (x+4)/2=10 => x = 16

vc Wrote: ------------------------------------------------------- > Ans is C > > I did the same thing ,but wrong ( According to the > text book ) > > 0.1+(0.1-0.05)(1)(1-0.2) > > =0.14 What?!?

More Cowbell Wrote: > What?!? My point exactly.

I agree. The Cost of Equity is 16%. I have utterly no clue what this formula is deriving or is derived from, as it conforms to absolutely nothing in any cost of capital formula promulgated by CFAI.

I also suppose ans is D ,so i posted this question here . According to the text book (CFA level 2 v3,p139.Q10) C is correct. cost of equity caital = cost of capital + ( cost of capital - cost of debt )(D/E) anyone has any comment ? the text book is wrong (I hope so ) ?

vc Wrote: ------------------------------------------------------- > cost of equity caital = cost of capital + ( cost > of capital - cost of debt )(D/E) I just looked at this quick but my comment would be: Is this an algebra question? Shouldn’t the the formula read… cost of equity capital = {cost of capital + [cost of capital - (AFTER TAX cost of debt )] (D/E)} and ke = {0.1 + [0.1 - 0.05(1-0.2)] 0.5/0.5} ke = {0.1 + [0.1 - 0.04] 1} = {0.1 + [0.06] 1} So ke = 0.1+ 0.6 = 0.16 >( According to the text book ) > >0.1+(0.1-0.05)(1)(1-0.2) > >=0.14 it seems that the (1-t) is out of place…

I believe the correct answer is D. The formula ( i.e. 0.1+(0.1-0.05)(1)(1-0.2)) in CFAI reading is questionable. My calculation is 0.1+(0.1-0.05*(1-0.2))*(1)=16%

My understanding is that if there are no issuing costs, then the cost of equity capital is just the cost of capital, which is 10% (A). Is the question asking for the Weighted Average Cost of Capital (WACC)? WACC is made up of cost of equity, cost of borrowing (debt) and cost of preferred shares. So I read “cost of equity capital” as cost of equity only, that is, what the market expects as a return on shares, not WACC. I think the rest of the information is trying to trick you. The cost of borrowing is reduced by the tax rate (it would cost 4% to the firm, not the market value of 5%). I haven’t read the CFAI material on this yet so I don’t know if their terminology is the same.

You guys saw this from CFA erratum in prior periods, right? Study Session 9, Reading 38: The derivation of re on p. 205 is incorrect as shown. The correct equation is re = ra + [(ra – rd*)(D/E)], where rd* = rd (1 – t). This formula is used in example 38-9 (p. 207) to calculate the company’s cost of equity with taxes. Using the corrected equation, the solution is re = 13% + [(13% – 6.12%) × (0.5)] = 16.44% instead of 14.36%, which was originally given. Also, at the bottom of page 211 (p. 85 of the Readings), in Panel B of Figure 38-10, the WACC and Cost of Equity labels are reversed.

Thanks for the reference. WACC is covered on page 120 Corporate Finance, under Capital Structure. I guess the Cost of Capital means WACC in this question so my previous assumption was incorrect. Using the standard equation for WACC = %wtEquity x cost of equity (re) + %wtDebt x cost of debt (rd). Since there is a 20% tax rate for the firm, the cost of borrowing is reduced by that amount. So the cost of debt is 4%, not 5%. Plug the formula: 10% = 50% x re + 50% x 4% and solve re. The answer is 16%.