According to MM assuming taxes, what is the present value of the debt tax shield assuming a constant capital structure?

Question

BlackTom AI · Accepted Answer

Under MM with corporate taxes and a constant (perpetual) debt level, the annual tax saving equals Tc × rD × D, and discounting that perpetual saving at the debt rate yields PV = Tc × D.

1) Relevant knowledge points and concepts
- Interest payments are tax-deductible, producing a tax shield equal to the corporate tax rate (Tc) times interest.  
- If debt is constant and perpetual and the tax shield has the same risk as debt, it is appropriate to discount the tax shield at the debt yield rD.  
- MM proposition with taxes implies the value of a leveraged firm equals the value of the unlevered firm plus the present value of tax shields; with constant perpetual debt, PV(tax shield) = Tc × D.

2) Step-by-step reasoning
- Interest each period = rD × D.  
- Tax saving each period = Tc × (interest) = Tc × rD × D.  
- The tax saving is a perpetuity, so PV = sum_{t=1 to ∞} (Tc × rD × D)/(1 + rD)^t.

3) Calculations and intermediate steps
- Sum of geometric series: sum_{t=1}^∞ (1/(1 + rD)^t) = 1/rD.  
- Therefore PV = Tc × rD × D × (1/rD) = Tc × D.

4) Why the correct answer is correct
- Discounting the perpetual interest-related tax savings at the debt rate cancels rD, leaving the simple product of the corporate tax rate and the face value of debt. This is the classic MM result under the stated assumptions.

5) Why other options are incorrect
- "Tc × Cost of Debt × Value of Debt" (Tc × rD × D) is the annual tax saving, not its present value when discounted at rD.  
- "Tc × Cost of Debt" lacks the debt principal D and has incorrect units.  
- "Tc / Cost of Debt" produces an expression without the debt amount and is not the standard MM result.

6) Conclusion
The present value of the debt tax shield under MM with taxes and constant capital structure is Corporate Tax Rate × Value of Debt, matching the provided answer.

According to MM assuming taxes, what is the present value of the debt tax shield assuming a constant capital structure? 单项选择题

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