Question

Consider two firms, Firm L and Firm U, that have identical assets that generate identical cash flows. Firm U is an all-equity firm, with 1 million shares outstanding that trade for a price of $26 per share. Firm L has 2 million shares outstanding and $12 million in debt at an interest rate of 5%.

Assume that Modigliani and Miller's (1958) perfect capital markets conditions are met and that you can borrow and lend at the same 5% rate as Firm L. You have $5,000 of your own money to invest and you plan on buying Firm U stock. Using homemade leverage, you borrow enough in your margin account so that the payoff of your margin purchase of Firm U stock will be the same as a $5,000 investment in Firm L stock. The number of shares of Firm U stock you purchased is closest to ________.

Answer 1

Market Value of Firm U = market value of equity = 1 million shares *$26 per share = $26 million

Market value of Firm L = Market Value of Firm U (same assets)

=> 2 million shares * $x per share + $12 million = $26 million

=> x= $7 per share

Firm L has 12/26 = 0.4615 or 46.15% Debt and 53.85% equity

If borrowing is done to replicate Firm L's cashflows, Debt and Equity should be similar

So, $5000 should represent 53.85% of money invested

Total AMount invested = 5000/0.5385 =$9285.71

So, amount to be borrowed = $4285.71

and no . of shares of Firm U to be purchased = $9285.71 / 26 = 357.14

The number of shares of Firm U stock purchased is closest to 357