What is the value of the tax shield if a company's perpetual debt is $400,000, the debt carry's an 8% interest rate, and the company's D/E ratio is 0.40?

Question

What is the value of the tax shield if a company's perpetual debt is $400,000, the debt carry's an 8% interest rate, and the company's D/E ratio is 0.40?

BlackTom AI · Accepted Answer

For a perpetual debt, the tax shield depends on the corporate tax rate; without that rate the tax savings cannot be computed.

1) Relevant knowledge points and concepts
- Annual interest expense = Debt × interest rate.
- Annual tax shield (tax saving) = corporate tax rate (t) × annual interest expense.
- Present value (PV) of a perpetual tax shield, under standard assumptions (constant debt, tax benefits discounted at the debt rate), is PV = t × Debt. All these formulas require the corporate tax rate t.

2) Step-by-step reasoning
- Given debt D = $400,000 and interest rate r_d = 8%:
  - Annual interest = D × r_d = $400,000 × 0.08 = $32,000.
- The tax shield per year would be t × $32,000, where t is the corporate tax rate. The PV of a perpetual tax shield would be t × $400,000.
- The D/E ratio = 0.40 implies D = 0.4 × E. With D known, you can solve for equity E:
  - E = D / 0.4 = $400,000 / 0.4 = $1,000,000.
- However, knowing E or the D/E ratio does not provide the corporate tax rate t, which is essential to compute either the annual tax shield or its present value.

3) Intermediate calculations shown
- Annual interest: $400,000 × 0.08 = $32,000.
- Equity from D/E: E = $400,000 / 0.4 = $1,000,000.
- Tax shield expressions: annual = t × $32,000; PV (perpetual) = t × $400,000.

4) Why the correct answer is correct
- Both the annual tax saving and the PV of the perpetual tax shield are proportional to the tax rate t. Since t is not provided, the numerical tax shield cannot be determined.

5) Why other plausible answers would be incorrect
- Answering $32,000 confuses interest expense with the tax shield (it ignores the tax rate).
- Giving PV = $400,000 (or any fixed dollar) implicitly assumes t = 1, which is unrealistic and not provided.
- Any specific numeric tax shield (e.g., $12,800) assumes a particular tax rate (e.g., 40%) not given in the problem.

6) Conclusion
Because the corporate tax rate is not provided, the tax shield cannot be determined. This confirms the correct answer: "Cannot be determined with the data provided."

What is the value of the tax shield if a company's perpetual debt is $400,000, the debt carry's an 8% interest rate, and the company's D/E ratio is 0.40?单项选择题

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