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Explanation:
According to Modigliani and Miller's Proposition I with taxes, the value of a levered firm (V_L) is equal to the value of an unlevered firm (V_U) plus the present value of the tax shield from debt:
Formula: V_L = V_U + (Tax Rate × Debt)
Where:
$1.5 billion$0.6 billionCalculation: V_L = V_U + (Tax Rate × Debt) 1.5 = V_U + (0.30 × 0.6) 1.5 = V_U + 0.18 V_U = 1.5 - 0.18 = 1.32 billion
Interpretation:
When the company issues common stock to repay outstanding debt, it becomes unlevered. The value of the unlevered company (V_U) is $1.32 billion, which is closest to $1.3 billion.
Why not the other options:
$0.9 billion): This would be V_L - Debt (1.5 - 0.6 = 0.9), which ignores the tax shield benefit.$1.5 billion): This is the current levered company value, not the unlevered value.Key Concept: In a world with corporate taxes, debt financing creates value through the tax deductibility of interest payments, making levered firms more valuable than unlevered firms.
An analyst gathers the following information about a company:
| Company value ($billions) | 1.5 |
|---|---|
| Value of debt ($billions) | 0.6 |
| Marginal tax rate | 30% |
Based on Modigliani and Miller's Proposition I with taxes, if the company issues common stock to repay outstanding debt, the value of the unlevered company will be closest to:
A
$0.9 billion.
B
$1.3 billion.
C
$1.5 billion.
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