Can anyone educate me as to the theory underlying the following formula for cost of equity? It does not seem to be based on CAPM, and I can't figure out what the rationale for the formula is. Thanks.

It looks quite a bit like MM II with taxes. If 4% was the equity risk premium on the unlevered firm then rf + 4% would be the cost of equity for the unlevered firm. However, MM II uses D/E and your example contains the term D/(E + D*(tc)) so I'm not sure about that part off the top of my head. If you search for Modigliani-Miller Theorem and look at Proposition II with taxes you can see if that helps you. Also, Modigliani and Miller's paper that originally put forth the propositions is entitled "The Cost of Capital, Corporation Finance and the Theory of Investment" so you may benefit from looking that over.

Thanks, gamoon07. That is helpful. I think you are correct -- the formula appears to be an attempt to express cost of equity per MM II. I originally though that it was a horribly botched WACC. Based on your input, I now think that it is actually just a slightly botched MM II. However, this raises another question for me. Assuming the formula was the following, would it provide a useful measure of cost of capital?This is an expression of MM II where represents the unlevered cost of equity. But is it reasonable to calculate a cost of equity based on a constant (i.e. 4%)? Shouldn't any accurate measure of the cost of equity take beta into consideration?

Modigliani and Miller derived this formula to show how the capital structure of a firm could affect the value of the firm (i.e. to show the relationship between the value of the levered firm and the value of the unlevered firm). So in that sense it is useful for answering questions about how the capital structure would affect value and such. For instance, if Company A were going to take over a company they could find the company's unlevered cost of equity then put that number into MM II with their own D/E and tax rate and value that company under their existing capital structure. Beta (unlevered) can be taken into account in a model like this when calculating the unlevered cost of equity. For example, R_U = rf + B_U(rm - rf) = rf + 1.6*(.025) = rf + 4%. As far as using MM II to just compute cost of equity I would agree with you and say no. If I just needed a cost of equity I would use something like FF Three Factor, APT, or CAPM as MM's use would not add any value if you weren't wanting to examine the effects of cap structure.

R_U=b_U(rm - rf)R_L=b_L(rm - rf)=R_U+(b_L-b_U)*(rm-rf)b_L-b_U=?there are several formulas for the relationship between unlevered (asset) and levered (equity) beta, which differ based on the assumptions (constant debt level vs. constant leverage i.e. D/E ratio, whether the "beta" of the debt is assumed to be 0 or not, etc.). Look up Harris-Pringle, Miles-Ezzel, Hamada formulas... here is a good comparison of the different formulas (after page 63)

Thanks for the link. That looks like a good resource to review.Could you be a bit more specific in how your post relates to my question, though? My thought is that the equation I originally provided simply does not take beta into account (though you could argue that it has an implicit beta built-in). Without applying the company's beta to the market premium, it would be difficult to obtain an accurate cost of equity. Provided that 4% equals the company's beta multiplied by the market premium, then the formula provides an accurate cost of equity as of a particular time, but using a constant for that value seems unlikely to produce accurate values in the long-term. Additionally, my main problem with the initially provided formula is that the final term is (rf + 4% - R_D) * D / (D+E), whereas the algebraic manipulation of WACC that is equivalent for all other terms yields (rf + 4% - R_D) * D/E for the final term. I think this latter issue is fatal to the formula. Do you disagree?Thanks.

i think it relates like this:R_D=rf+b_D(rm-rf)on p.67 of pdf I gave you, if you use the relationship due to MM: b_L=b_U+(b_U-b_D)(1-T)D/E, and plug it into what I wrote below then you have:R_L=R_U+(b_L-b_U)*(rm-rf)= R_U+[(b_U-b_D)(1-T)D/E)]*(rm-rf)= R_U+[(b_U-b_D)(rm-rf)]*[(1-T)D/E]= R_U+[(R_U-rf)-(R_D-rf)]*[(1-T)D/E]= R_U+(R_U-R_D)*(1-T)D/Eassuming R_U=rf+4% that agrees with your modified formula. Of course this 4% plug is questionable