CFA Level ICorporate IssuersHard
Vantage Corp is currently unlevered and has a firm value of $80 million. The company is considering issuing $50 million in permanent debt and using the proceeds to repurchase equity. The corporate tax rate is 25%, and Modigliani-Miller's proposition with taxes is assumed to hold (no bankruptcy costs). What will be the value of the levered firm after the recapitalization?
- A$92.5 million
- B$100.0 million
- C$80.0 million
- D$105.0 million
Show answer & explanationAnswer & explanation
Correct answer: A. $92.5 million
Under MM Proposition I with taxes: VL = VU + (tax rate × Debt) = $80M + (0.25 × $50M) = $80M + $12.5M = $92.5 million. The value gain reflects the present value of the interest tax shield.
Why the other options are wrong
- B. Overstates the tax shield by using the full debt amount without applying the tax rate.
- C. This ignores the tax shield benefit of adding debt entirely.
- D. Uses an incorrect multiplier for the tax shield calculation.
MM Proposition I with Taxes
States that firm value increases with leverage due to the tax deductibility of interest, with levered value equal to unlevered value plus the present value of the interest tax shield.
- VL = VU + (t × D)
- Assumes perpetual debt and no bankruptcy costs
- Implies 100% debt financing would maximize value in this simplified model
Memory trick: Taxes turn debt into a value-adding shield