What is the present value of the debt tax shield if the cost of debt is 10%, value of the debt is $199 million, and corporate tax rate is 32%?

Enter and round your answer to the nearest one-hundredth of a million dollars. Do not include the dollar sign ($).

Question

What is the present value of the debt tax shield if the cost of debt is 10%, value of the debt is $199 million, and corporate tax rate is 32%?

Enter and round your answer to the nearest one-hundredth of a million dollars.  Do not include the dollar sign ($).

BlackTom AI · Accepted Answer

PV of the debt tax shield = corporate tax rate × value of debt when tax shields are perpetual and discounted at the cost of debt.

Step 1 — Key concepts:
- Interest tax shield each year = tax rate (Tc) × interest paid.
- If debt D is permanent and interest rate on debt is rd, annual interest = rd × D.
- Present value of a perpetual annual tax shield discounted at rd is (annual tax shield)/rd. That simplifies to Tc × D.

Step 2 — Compute with given numbers:
- Tc = 32% = 0.32
- D = $199 million
Method A (direct simplification):
- PV = Tc × D = 0.32 × 199

Method B (two-step calculation to show intermediate values):
- Annual interest = rd × D = 0.10 × 199 = 19.9 million
- Annual tax shield = Tc × (annual interest) = 0.32 × 19.9 = 6.368 million
- PV of perpetual tax shield = (annual tax shield)/rd = 6.368 / 0.10 = 63.68 million

Intermediate arithmetic (Method A):
- 0.32 × 199 = 0.32 × (200 − 1) = 64.00 − 0.32 = 63.68

Step 3 — Why this is correct:
- Discounting the perpetual annual tax shield at the debt rate rd cancels rd in numerator and denominator, leaving Tc × D. Both calculation routes yield the same 63.68 million, consistent with the standard formula for perpetually financed debt.

Step 4 — Why alternative misunderstandings are incorrect:
- Using Tc × rd × D as the PV would give the annual tax shield, not its present value.
- Dividing Tc × D by rd again (i.e., Tc × D / rd) would double-count discounting and is incorrect.
- Discounting at a different rate (e.g., WACC) would change the PV; the standard assumption here is discounting at the cost of debt.

Conclusion: The present value of the debt tax shield is 63.68 (million), which matches the provided answer.

What is the present value of the debt tax shield if the cost of debt is 10%, value of the debt is $199 million, and corporate tax rate is 32%? Enter and round your answer to the nearest one-hundredth of a million dollars. Do not include the dollar sign ($).Short answer

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