An easy CAPM question
Hey guys,
This is probably obvious but I'm not seeing the answer. In CAPM and I guess you could generalize this to anytime you are using a tax shield, why do you just take the whole value of debt and multiply it by (1-t). I thought principal payments were not tax deductible, so in the CAPM formula they should just be multiplied by just the cost of debt and not (1-t). Is this just a classroom generalization and in banking models they account for this distinction, or is there something I am missing?
Thanks.
First, I think you're referring to WACC, which usually uses CAPM to compute the cost of issuing equity.
So, in WACC, there is the (1-t) you're talking about. The reason it's there is because you're calculating how much your debt is costing you. So you have the portion of you capital from debt times the interest rate, which is your cost of issuing debt, times the (1-t), because this interest is deductable as you mentioned.
Hope this helps.
In effect, you actually only multiply (1-t) by the rate. Even though you also multiply the debt amount, it cancels when you divide by the (debt + equity). This part is only used to find the wieght of debt in the capital structure.
i.e. (debt(1-t)rate)+.../(debt)+...
I agree with the above, but I have a follow-on quesion:
Why do we tax-effect Hamada's equation when unlevering and relevering beta?
More specifically, BL = Bu * (1 + D/E * (1-t))
Why is (1-t) used in this formula when there is no cost of debt to use the tax-shield on?
Might be wrong....but since you are re-levering with new debt levels to find the levered beta, you would want to take the debt tax shield into consideration as this would affect Beta as well (It makes sense...think about it!)
I think Hamada is better written out bL = bU[1+(D/E)(1-T)]
The way you had it is confusing in terms of order of operations. When you unlever beta you're stripping out all of the financial leverage so that you can see the firm's intrinsic risk w/o taking on debt. Never really thought about it before, but just eyeballing it, you know that equity is already taxed at T. So the (1-t) is just leveling the playing field for debt as well -- apples to apples -- so if the tax rate is 0.4 then with Hamada you're really comparing 0.6D/0.6E = D/E. If I'm wrong then feel free to point it out, but I think that's how it goes.
Solidarity,
What you're saying makes sense...equity is already taxed at T...but I'm trying to put it down in terms of formulas and it just doesn't seem to work out.
You're saying that tax is already incorporated into the Cost of Equity.... Re=Rf+B(Rm-Rf) (per CAPM) and Rf,Rm, and Beta are all figures that can be calculated w/o using the tax rate.
Anyone?
Increasing leverage decreases the cost of capital for the Company AS A WHOLE (i.e. WACC) because debt is cheaper than equity. However, as you increase leverage, EQUITY cost of capital increases, since you are making the equity riskier (higher probability of default). That is why you must lever up the asset beta (unlevered beta). Risk is offset somewhat by benefits of tax shield, so levered beta cannot be calculated without tax rate (going to big_dreams question, that in the CAPM, the tax rate is accounted for through beta).
Two separate tax points: 1) Equity beta must be levered to reflect tax adjusted risk of leverage, 2) WACC takes into account the levered (tax adjusted) equity cost of capital and the tax-adjusted cost of debt.
?
Monkenumber7,
Thanks for that response. Anyway...what you're saying makes complete sense to me and I agree with it...especially the following: "as you increase leverage, EQUITY cost of capital increases, since you are making the equity riskier(higher probability of default)".
However, just to clarify on a more basic level of thinking, if I calculated the Beta of a firm by simply regressing it against the market...you are saying that in such a scenario, the tax rate adjustments etc. are already incorporated into this new found Beta behind the scenes?
Yes that's right.
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