Complete Question:
Modigliani and Miller's world of taxes. Roxy Broadcasting was originally an all-equity firm with a before-tax value of $20,000,000. Roxy now pays taxes at a 30% rate.
A. What is the value of Roxy under the 30/70 debt-to-equity capital structure?
B. Under the 70/30 capital structure?
Answer:
Requirement 1: $15,384,615
Requirement 2: $17,721,519
Explanation:
The value of the firm at zero percent debt is $20,000,000 then this means:
Value of Equity After Tax = Value of Firm * (1 - 30% Tax rate)
Value of Equity After Tax = $20,000,000 * 0.7 = $14,000,000
Now
Value of Levered Firm = Value of Unlevered Firm + (Debt percentage * Value of Levered Firm * Tax rate
Requirement 1: The value of levered company at 30/70 debt to equity ratio would be:
Here
Value of Levered Firm is X
Debt percentage is 30%
Tax rate is 30%
By putting values, we have:
X = $14,000,000 + (30% debt percentage * X * 30% Tax rate)
X = $14,000,000 + (0.3 * X * 0.3)
X = $14,000,000 + (0.09X)
X - 0.09X = $14,000,000
0.91X = $14,000,000
X = $14,000,000 / 0.91 = $15,384,615
Requirement 2: The value of levered company at 70/30 debt to equity ratio would be:
Here
Value of Levered Firm is X
Debt percentage is 70%
Tax rate is 30%
By putting values, we have:
X = $14,000,000 + (70% debt percentage * X * 30% Tax rate)
X = $14,000,000 + (0.7 * X * 0.3)
X = $14,000,000 + (0.21X)
X - 0.21X = $14,000,000
0.79X = $14,000,000
X = $14,000,000 / 0.79 = $17,721,519
