 # Cost of equity

A firm has Zero debt in its capital structure…its overall cost of capital is 9%. the firm is now considering a new capital structure with 40% debt , interest rate on debt is 4% . tax rate is 40% . What is cost of equity with new capital structure ? tks

if they have no debt, it means its 100% equity if they do not give you preferred. so 9% is the current cost of capital, and the cost of equity. New structure: .4(.04)(1-.4) + .6(.09) = .0636 or 6.36%

thanks budfox427 , but the right answer is 11.2% , i used R.Equity = rassets + [D/E ( (rassets – rdebt)] , but i dont get the right answer too , this 9% capital before restructuring i took it as the return on asset coz it was before we had debt in the capital structure

huh. screw me then. all the regular question ninjas like cpk123 are on hiatus. That’s a weird question though. Where is that from (what study program)?

lol … well said … i am not a CFA canditate yet i am taking financial decision making and this course the exam is totaly different then wa they teach … :o-)) … and when i go n tell my teacher that the question u gave they couldnt solve on CFA forum he laughs at my face

I share your suspicion. Under modigliani-miller, absent taxes the d/e mix won’t change wacc. You can confirm this by .4(4) + .6(12.33) = 9% Once you add taxes this can only reduce the wacc to something less than 9% (I get around 8.36). The only way you can get to 11.2% is if you start pricing up debt above 4% – but the problem doesn’t allow you to do that. So I think the answer is wrong.

Here is my 2 cents worth on this question. The 9% is the unlevered cost of capital, since there was no debt initially. And, from what I have learnt in my Corporate Finance Class, Rsl=Rsu+(Rsu-Rd)(1-t)(D/E) Rsl=levered cost of equity (which is whatt you are trying to find in this case) Rd=cost of debt. D/E= debt to equity ratio t=tax rate Thus, the answer I got is: 0.09+(0.09-0.04)(1-0.4)(0.4/0.6) = 0.11 but I can’t get 11.2%. I’d be more than happy to share whatever I know on cpaital structure. HTHs!

I think it should be 6.36%. Would like to know how they got 11.2%. Please let me know

Hmm. For one, my guess is that 11.2% is wrong. But how exactly do you get 6.36%? Judging from what that was written above by budfox who also got 6.36%, and if that was how you got the smae figure, then what you calculated was the WACC and not the cost of equity, as required by the question.Even then, the cost of equity will definitely increase so you cant just plug in 9% to get the WACC.

WACC = 0.6*0.09 + 0.4*0.04*0.6 = 6.36% Ke = 0.6*0.09 = 5.4% Yes I gave the WACC prior, my bad. However, I fail to understand how the cost of equity of a levered company can exceed that of an unlevered company. Almost like saying that it doesn’t benefit the shareholder if a company with no debt took on some debt. Taking on debt is beneficial to the shareholder as long as the cost of debt does not exceed the return on the debt. Debt is tax deductible as well. Hmmm, how does the book solve this one?

sweft Wrote: ------------------------------------------------------- > WACC = 0.6*0.09 + 0.4*0.04*0.6 = 6.36% > Ke = 0.6*0.09 = 5.4% > > Yes I gave the WACC prior, my bad. However, I fail > to understand how the cost of equity of a levered > company can exceed that of an unlevered company. Financial leverage increases the risk (and potential return) to equity investors. Consider that the company has made a commitment to paying a fixed (or floating, or both) payment to the debt investors, who have seniority over the equity investors. Equity investors’ claim on the firm’s assets has become junior to that of debtholders. > Almost like saying that it doesn’t benefit the > shareholder if a company with no debt took on some > debt. I don’t think this is the implication, see my final comment below. Taking on debt is beneficial to the > shareholder as long as the cost of debt does not > exceed the return on the debt. Debt is tax > deductible as well. Hmmm, how does the book solve > this one? My understanding of CFAI’s perspective is that a firm’s target capital structure should consist of debt up to the point at which the marginal benefit of the tax-shelter equals the marginal cost of financial distress. They emphasize that minimization of WACC is the objective (not just Ke), which also results in maximization of firm value. Just my \$0.02.

I agree with budfox. At present the cost of capital of the company is equal to the cost of equity as the company has no debt on its books. Once debt has been introduced then the WACC is : 9(.6) + 4(.6)(.4) = 6.36% Also, when the company increases the level of dept in its capital structure, the overall cost of capital will only decrease. But adding another view to this, If the company plans to not change its WACC then the new cost of equity would be: (WACC - After tax cost of debt)/percentage of equity in the capital structure i.e. [9- 4(.6)(.4)]/.6 = 13.4% so the average cost of equity over the two periods is [9+13.4]/2 = 11.2% Supersunny, i hope you’re not missing out on any important aspect of the question.

What is the justification for taking the average? I thought you should be taking the cost of equity for period 2 as the answer. And, what is the reason behind assuming that the WACC is going to remain constant, and then you use that same WACC to calculate the cost of equity? There does not seem to be any a priori reason to expect that the WACC is going to be constant, i.e. the WACC of a leveraged firm is going to be the same as that of an unleveraged firm. As a matter of fact, gurjeet, Wacc is goign to drop only if your cost of equity remains constant. But, if you get to a point where you take on debt such that your marginal cost of equity is sky high, then your WACC is going to go through the roof too. Cost of equity is expected to go up because of greater bankruptcy risk should the firm ttake on more debt, and thus equity holders demand a greater rate of return. Am not too sure about this, but what I did was just straight out of my book [Intermediate Financial Management by Brigham Daves.] THe issue on optimal capital strucure mentioned by hiredguns was also mentioned in that book…Quite the same. I find that capital structure is the toughest and most confusing topics around…

Hey Hydrogen ! What i meant by doing that is that if the question mentioned was incomplete, the probable answers could be this. Thats the same reason why i asked supersunn yto confirm the question.

supersunny138 Wrote: ------------------------------------------------------- > lol … well said … i am not a CFA canditate yet > i am taking financial decision making and this > course the exam is totaly different then wa they > teach … :o-)) … and when i go n tell my teacher > that the question u gave they couldnt solve on CFA > forum he laughs at my face hmmmm im also thinking somethings missing in the question… either that, or supersunny’s teacher is a loonie

budfox427 Wrote: ------------------------------------------------------- > if they have no debt, it means its 100% equity if > they do not give you preferred. so 9% is the > current cost of capital, and the cost of equity. > > New structure: > > .4(.04)(1-.4) + .6(.09) = .0636 or 6.36% this makes logical sense to me.

gurjeet Wrote: ------------------------------------------------------- > Hey Hydrogen ! > What i meant by doing that is that if the question > mentioned was incomplete, the probable answers > could be this. Thats the same reason why i asked > supersunn yto confirm the question. Ah i see. but for me, in the absence of the other info, i’d do wad i did earlier ( i had the same qquestion for one of my problem sets though the figures wre different and the solution was as per what i gave). yep.