Use the following information to answer questions 21-25. Modigliani Corporation expects it’s EBIT to be $270,000 perpetually and their cost of unlevered equity is 15%. Their tax rate is 30%. They are contemplating borrowing $750,000 at an interest rate of 9% to repurchase shares. 21. What is the value of the unlevered firm? a. $1,240,000 b. $1,260,000 c. $1,280,000 d.$1,300,000 e. $1,320,000
The correct answer and explanation is:
To calculate the value of the unlevered firm, we use the Modigliani-Miller Proposition I with no debt (i.e., unlevered firm value), which assumes: Value of Unlevered Firm(VU)=EBIT×(1−Tax Rate)Cost of Unlevered Equity (rU)\text{Value of Unlevered Firm} (V_U) = \frac{EBIT \times (1 – \text{Tax Rate})}{\text{Cost of Unlevered Equity (r}_U\text{)}}
Given:
- EBIT = $270,000
- Tax rate = 30%
- Cost of unlevered equity (r_U) = 15% or 0.15
Step-by-step Calculation:
First, calculate the after-tax EBIT: EBIT after tax=EBIT×(1−Tax Rate)=270,000×(1−0.30)=270,000×0.70=189,000\text{EBIT after tax} = EBIT \times (1 – \text{Tax Rate}) = 270,000 \times (1 – 0.30) = 270,000 \times 0.70 = 189,000
Now, plug this into the valuation formula: VU=189,0000.15=1,260,000V_U = \frac{189,000}{0.15} = 1,260,000
Answer:
b. $1,260,000
Explanation (300 words):
The value of an unlevered firm is the present value of its future cash flows if the firm is entirely equity-financed (i.e., no debt). According to the Modigliani-Miller (MM) Proposition I with taxes, the value of a firm depends on its earnings and tax shield, but for an unlevered firm, only after-tax operating income and the cost of equity are relevant.
In this scenario, Modigliani Corporation expects perpetual EBIT of $270,000, which means this level of earnings before interest and taxes is expected to continue indefinitely. Since the firm currently has no debt, it pays no interest expense, and the entire EBIT is subject to corporate taxes.
To determine the value of the unlevered firm, we first calculate the net operating profit after taxes (NOPAT), which is the EBIT adjusted for taxes. With a 30% tax rate, the after-tax EBIT is $189,000. This figure represents the net income available to equity holders in the absence of debt.
Next, because the cash flows are perpetual, we use the perpetuity formula to value the firm: Firm Value=NOPATCost of Equity\text{Firm Value} = \frac{\text{NOPAT}}{\text{Cost of Equity}}
With a 15% cost of unlevered equity, the value comes out to: 189,0000.15=1,260,000\frac{189,000}{0.15} = 1,260,000
This valuation reflects the total market value of Modigliani Corporation without any leverage, forming the basis for analyzing how debt would later affect firm value.
✅ Correct answer: b. $1,260,000.