Why is the tax shield tXd where value of d is value of debt and t is the tax rate
I think it should be tXdX(interest rate) since it the interest payment on which the tax payments is exempt.
any clarifications are appreciated.
Here’s an example:
Assume perpetual debt of $100, a cost of debt of 10%, and tax rate of 20%. Assume it’s at par. So, the annual coupon is $10, and annual tax reduction is $2. Then capitalize the tax savings by the 10%. You end up with PV of tax savings of 2/0.10 = 20.
In an equation, it’s 100(0.10)(0.20)/0.10 ==> the cost of debt is in both numerator and denominator, so they cancel, and you’re left with 100(0.20).
Hope that helps.