Question

An all-equity firm that pays a 24% corporate income tax has 350,000 shares outstanding, a cost of capital of 13% and generates perpetual annual EBIT of $2.50 Million. According to the M&M theories of capital structure, what is the unlevered firm’s stock price per share? (Note that you may ignore any impact of personal taxes.) Enter your answer rounded to two decimal places. Do not enter $ or comma in the answer box. For example, if your answer is $12,300.456 then enter as 12300.46 in the answer box.

The firm in previous problem plans to borrow $10 Million at 6% annual interest to retire some equity. According to the M&M theories, after the recapitalization, what would be the levered firm’s stock price per share? Enter your answer rounded to two decimal places. Do not enter $ or comma in the answer box. For example, if your answer is $12,300.456 then enter as 12300.46 in the answer box.

Answer 1

Rounded to two decimal places without the currency symbol or comma, the levered firm's stock price per share after recapitalization would be 11109.92.

Step-by-step explanation:

To find the unlevered firm's stock price per share, we can use the following formula based on the Modigliani-Miller (M&M) theory:

Stock Price per Share = EBIT / Cost of Capital

Given:

EBIT = $2.50 million

Cost of Capital = 13%

Substituting these values into the formula:

Stock Price per Share = $2.50 million / 13%

Stock Price per Share = $19.23 million

Since we are asked to provide the answer rounded to two decimal places without the currency symbol or comma, the unleveled firm's stock price per share would be 19230.77.

Now, let's calculate the levered firm's stock price per share after the recapitalization using the same formula. However, we need to consider the impact of the interest expense resulting from the borrowing:

EBIT - Interest Expense = Taxable Income

Taxable Income = (EBIT - Interest Expense) * (1 - Tax Rate)

Given:

EBIT = $2.50 million

Borrowing = $10 million

Interest Rate = 6%

Tax Rate = 24%

Interest Expense = $10 million * 6% = $600,000

Taxable Income = ($2.50 million - $600,000) * (1 - 24%)

Taxable Income = $1.90 million * 0.76

Taxable Income = $1.444 million

Now, we can calculate the stock price per share:

Stock Price per Share = Taxable Income / Cost of Capital

Stock Price per Share = $1.444 million / 13%

Stock Price per Share = $11.109 million