Question

# Consider two​ firms, With and​ Without, that have identical assets that generate identical cash flows. Without...

Consider two​ firms, With and​ Without, that have identical assets that generate identical cash flows. Without is an

allminus−equity

​firm, with 1 million shares outstanding that trade at a price of​ \$24 per share. With has 2 million shares outstanding and​ \$12 million of debt at an interest rate of​ 5%.

Assume that​ MM's perfect capital markets conditions are met and that you can borrow and lend at the same​ 5% rate as With. You have​ \$5000 of your own money to invest and you plan on buying With stock. Using homemade​ (un)leverage, how much do you need to invest at the

riskminus−free rate so that the payoff of your account will be the same as a​ \$5000 investment in Without​ stock?

Value of the firm without leverage = 1million shares * 24 = \$ 24 million

Value of the firm with leverage = Value of the firm without leverage - Debt = \$24 million - \$12 million = \$12 million

Price per share without stock = \$12 million / \$ 2 million shares = \$6 per share

The leverage ratio is 1:1 i.e. Debt is 50% and equity is 5-%. To match this home made leverage, the portfolio has to be 50% and 50% equity. You already have \$5000 as equity and will require \$5000 which can be met through borrowings.

Total Investment so that the pay off of your account will be same as \$5000 investment without stock is \$10,000 .

No of shares to be bought = \$10,000/ 6 =1,667 shares

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