Question

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?

Answer 1

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