Your firm currently has 

$ 116$116 

million in debt outstanding with a 

10 %10% 

interest rate. The terms of the loan require the firm to repay 

$ 29$29 

million of the balance each year. Suppose the marginal corporate tax rate is 

30 %30%​, 

and that the interest tax shields have the same risk as the loan. What is the present value of the interest tax shields from this​ debt?

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Part 1

The present value of the interest tax shields is 

​$enter your response here 

million.  ​(Round to two decimal​ places.)

To calculate the present value (PV) of the interest tax shields from the debt, we can use the following formula:

\[
\text{PV of Interest Tax Shield} = \frac{\text{Tax Rate} \times \text{Interest Payment}}{\text{Interest Rate}}
\]

### Step-by-step:

1. **Outstanding Debt** = $116$ million
2. **Interest Rate** = 10% = 0.10
3. **Annual Interest Payment** = $ 116 \times 0.10 = 11.6 $ million
4. **Tax Rate** = 30% = 0.30

The interest tax shield is the tax saving due to the interest expense, calculated as:

\[
\text{Interest Tax Shield} = \text{Tax Rate} \times \text{Interest Payment}
\]
\[
= 0.30 \times 11.6 = 3.48 \text{ million annually}
\]

Since the loan repayment is happening at a constant rate each year, the interest tax shield will decrease as the debt is repaid. However, if we assume the loan has a constant payment structure and the tax shields have the same risk as the loan, the present value of these tax shields can be calculated as a **perpetuity** using the interest rate.

\[
\text{PV of Interest Tax Shields} = \frac{3.48}{0.10} = 34.80 \text{ million}
\]

Thus, the present value of the interest tax shields is **$34.80 million**.

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:
1. What is the formula for calculating the present value of a perpetuity?
2. How does the tax rate affect the interest tax shield?
3. How would changes in the interest rate impact the value of the interest tax shields?
4. What happens to the present value of interest tax shields if the debt decreases over time?
5. How does a loan's risk profile impact the tax shields' discounting?

**Tip:** When calculating tax shields, keep in mind that only the interest portion of debt payments is tax-deductible, and the shield depends on the marginal tax rate.

Your firm currently has $116 million in debt outstanding with a 10% interest rate. The terms of the loan require the firm to repay $29 million of the balance each year. Suppose the marginal corporate tax rate is 30%, and that the interest tax shields have the same risk as the loan. What is the present value of the interest tax shields from this debt? The present value of the interest tax shields is $enter your response here million. (Round to two decimal places.)

This problem demonstrates how to calculate the present value of interest tax shields on a $116 million debt with a 10% interest rate, considering a 30% corporate tax rate. The calculation uses the perpetuity formula to estimate the tax savings due to interest expenses.

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