Cost of Equity

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pstreat

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Why is the after tax cost of debt not the way to go here? Why do we just add the risk premium to the before tax YTM in order to find the cost of equity? Just curious. Thanks


A 20-year $1,000 fixed-rate non-callable bond with 8% annual coupons currently sells for $1,105.94.
Assuming a 30% marginal tax rate and an additional risk premium for equity relative to debt of 5%,
the cost of equity using the bond-yield-plus-risk-premium approach is closest to:
 
My answer would be 12% (YTM for the Bond of 7% + 5% additional equity risk premium). I think you have to take pre-tax values here because it is asked for the costs of equity and the tax shield would only apply to the cost of debt.
 
Tax does not affect the cost of equity.
the answer should be 12%
 
Isn’t Cost of Debt always put on an aftertax basis though? So we would find the 7% Before tax, put it on a .07*(1-.3) to find the after tax cost of debt of 4.9%.
My question is then, is the reason we add the 5% because of the wording of risk premium? Because it could be taken two different ways. If I were to say “Equity is 5% more than debt” then you’d actually take the 4.9*(1+.05) to find the cost of equity.
Disclaimer: I take the test in December, not June, so I haven’t read about this yet. Just drawing on previous knowledge. Don’t know how CFA treats it.
 
The question asks for the CoE only therefore taxes do not matter here. We add the 5% to the YTM because in the question it states that the CoE are defined as the CoD plus an equity risk premium.
 
I think you are right Oscar. Would make sense that for cost of equity, there wouldn’t be any tax shield factored in. Thanks
 
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