MMI Proposition w Taxes?

I understand the impact that taxes have and their place in the evolution of the MM studies. One quick question however, the text says that the effective tax shield is equal to the marginal tax rate times the debt outstanding in the capital structure.

Why is the tax shield based on the total debt (principle) outstanding, and not just the interest expense component, which is the only aspect that is actually tax deductible?

Funny, I was wondering the exact same thing … the only difference between paying interest before and after tax is the tax rate times the interest expense - so I to think the shield is what you described.

As the book doesnt go into much detail, I guess we only need to know that the shield is T x D. I am guessing that if we wanted to value the shield then would have to capitalize the tax savings by the using the interest rate on debt. This is a pure guess though.

MMI is valuing the company as a whole, that’s why they’re using total debt.

How would you value a company by just using interest tax savings?

Good question. But the deductability, and therefore the benefit, is related to interest expense, not total debt. What if the debt was non-interest bearing? The tax related benefit associated with debt financing would be moot. That is, there would be no benefit. I realize that without debt, you have no interest expense. But still, shouldn’t the tax shield be based on interest expense, not total debt??

Dt is the present value of the tax savings, assuming business makes these tax savings each year forever (ie, a perpetuity).

If D x r is the interest paid in one year (where r is the interest rate and D is the value of debt)

Then D x r x t is the tax saving in that year.

Then the present value of the tax saving if we assume the savings occur every year, forever, is

Drt/r = Dt

So its basically the value of the annual savings stream into perpetuity? Makes sense. Thanks