Math Problem Statement

With its current​ leverage,

ImpiImpi

Corporation will have net income next year of

$ 6.500$6.500

million. If

ImpiImpi​'s

corporate tax rate is

21 %21%

and it pays

7 %7%

interest on its​ debt, how much debt can

ImpiImpi

issue this year and still receive the benefit of the interest tax shield next​ year?

Question content area bottom

Part 1

The debt is

​$enter your response here

million. ** ​(Round to three decimal​ places.)

Solution

To determine how much debt Impi Corporation can issue and still benefit from the interest tax shield, we use the following formula for the interest tax shield:

Interest Tax Shield=Interest Payment×Tax Rate\text{Interest Tax Shield} = \text{Interest Payment} \times \text{Tax Rate}

Where:

  • Interest Payment is calculated as Debt×Interest Rate\text{Debt} \times \text{Interest Rate}.
  • The corporate tax rate is 21%.
  • The interest rate on debt is 7%.

Since Impi Corporation will receive the benefit of the tax shield, we want the interest payment to be deductible, meaning the interest expense should not exceed the amount of net income before taxes.

Let’s break it down step by step:

Step 1: Calculate the net income before taxes

Net income of $6.5 million is after-tax income. To find the income before taxes:

Income Before Taxes=Net Income1Tax Rate=6.5 million10.21=6.50.79\text{Income Before Taxes} = \frac{\text{Net Income}}{1 - \text{Tax Rate}} = \frac{6.5 \text{ million}}{1 - 0.21} = \frac{6.5}{0.79}

Step 2: Calculate the maximum allowable interest payment

Since the interest on debt is deductible, we want the maximum interest payment such that it’s equal to or less than the income before taxes.

Interest Payment=Debt×0.07\text{Interest Payment} = \text{Debt} \times 0.07

Now, we need to calculate the maximum debt based on this condition. I will compute the above values to find the debt amount.The maximum amount of debt that Impi Corporation can issue this year and still receive the benefit of the interest tax shield next year is approximately $117.541 million.

Would you like more details on this, or do you have any other questions?

Here are 5 related questions to expand this topic:

  1. How does the interest tax shield benefit a corporation?
  2. What happens if the interest expense exceeds the pre-tax income?
  3. How would changes in the corporate tax rate affect the maximum debt?
  4. Can a company’s debt level impact its overall cost of capital?
  5. How would a change in interest rates impact Impi's interest tax shield?

Tip: Always compare the benefits of additional debt against the potential risk of financial distress.

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Math Problem Analysis

Mathematical Concepts

Corporate Finance
Tax Shield
Interest Expense

Formulas

Interest Tax Shield = Interest Payment × Tax Rate
Interest Payment = Debt × Interest Rate
Income Before Taxes = Net Income / (1 - Tax Rate)

Theorems

Tax Shield Theorem

Suitable Grade Level

Undergraduate (Corporate Finance or Business Courses)