Part 1Assume that Xanadu Imports has a total market value of $ 304.3$304.3 million and a marginal tax rate of 30 %30%. If it permanently changes its leverage from no debt by taking on new debt in the amount of 12.5 %12.5% of its current market value, what is the present value of the tax shield it will create? Part 1The present value of the tax shield is $[input]enter your response here million. (Round to two decimal places.)

Question

Part 1Assume that Xanadu Imports has a total market value of $ 304.3$304.3 million and a marginal tax rate of 30 %30%. If it permanently changes its leverage from no debt by taking on new debt in the amount of 12.5 %12.5% of its current market​ value, what is the present value of the tax shield it will​ create? Part 1The present value of the tax shield is ​$[input]enter your response here million. ​ (Round to two decimal​ places.)

BlackTom AI · Accepted Answer

The present value of a permanent tax shield equals the corporate tax rate multiplied by the amount of permanent debt: PV(tax shield) = Tc × D.

1) Relevant knowledge points and concepts
- Under the Modigliani–Miller framework with corporate taxes, interest on debt is tax-deductible. For permanent (perpetuity) debt, the value of the tax shield is simply the corporate marginal tax rate (Tc) times the debt amount (D).
- Here the firm currently has no debt and will take on new permanent debt equal to 12.5% of its current market value.

2) Step-by-step reasoning and calculations
- Firm market value V = $304.3 million.
- Debt fraction = 12.5% = 0.125.
- Compute D = 0.125 × V.
  - D = 0.125 × 304.3
  - 0.125 × 304.3 = 38.0375 (million dollars)
- Corporate tax rate Tc = 30% = 0.30.
- PV(tax shield) = Tc × D.
  - PV = 0.30 × 38.0375
  - 0.30 × 38.0375 = 11.41125 (million dollars)

3) Intermediate steps shown above and rounding
- Rounded to two decimal places: 11.41125 → 11.41 million.

4) Why this is correct
- Because the debt is permanent, each year the firm saves Tc × interest. Under the assumption that these tax shields are as certain as debt cash flows and discounted appropriately, the infinite stream of tax savings has present value equal to Tc times the principal (D). Thus Tc × D is the appropriate formula and yields the computed number.

5) Why other approaches would be incorrect
- Multiplying Tc by the entire firm value (Tc × V) would overstate the shield (that would assume debt equals firm value).
- Using a discounting formula with an arbitrary rate or treating debt as non-perpetual would be unnecessary given the permanent-debt assumption.

Conclusion: The present value of the tax shield is $11.41 million, which matches the provided answer.

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