Doubts

8b - In-class exercise 3c

8b - In-class exercise 3c

by Joshi Benito Schlumberger -
Number of replies: 2
I am struggling to understand the computation of the interest tax shield in this exercise:

according to the lecture slides, the PV of the interest tax shield is computed by multiplying debt with the tax rate:


In exercise 3, however, only the interest payed is considered and also multiplied by 1/3 (which I assume is because the firm only pays interest in one scenario).
Why do we not consider the full debt payment here, i.e. 230 in scenario1 and 85 in scenario2 ?


In reply to Joshi Benito Schlumberger

Re: 8b - In-class exercise 3c

by Alessandro Imbrogno -
I believe that the difference in how the interest tax shield (ITS) is computed depends on whether the firm’s debt is perpetual or temporary. When a company maintains constant debt indefinitely, the annual interest tax shield becomes a perpetuity. In this case, the present value of the tax shield simplifies to 𝐷⋅𝑡, where
D is the amount of debt and t is the corporate tax rate. This formula assumes that interest is paid every year forever and is therefore discounted at the cost of debt 𝑟𝐷, which cancels out algebraically (as shown in the first picture). However, when debt is temporary or scenario-specific, the firm does not benefit from an infinite stream of tax savings. Instead, the tax shield must be computed using the actual expected interest payments, multiplied by the tax rate, and then discounted at the appropriate rate (usually the firm's cost of capital). This approach reflects the realistic timing and probability of the tax shield, rather than assuming it will last forever.

I hope this is clear & correct.
In reply to Alessandro Imbrogno

Re: 8b - In-class exercise 3c

by Julio Crego -
Correct, the PV of the interest tax shield is always:

\(PV(ITS) = t\cdot PV(InterestPayments)\)

In the case of perpetual debt, we use the cost of debt to discount; hence, 

\(PV(ITS) = t\cdot \dfrac{InterestPayment}{r_D} = t\cdot \dfrac{r_D \times D}{r_D} = t\cdot D\)