Use the information for the question(s) below.
Consider two firms, With and Without, that have identical assets that generate identical cash flows. Without is an all-equity
firm, with 1 million shares outstanding that trade for a price of $24 per share. With has 2 million shares outstanding and $12
million in debt at an interest rate of 5%.
-Assume that MM's perfect capital markets conditions are met and that you can borrow and lend atthe same 5% rate as With. You have $5000 of your own money to invest and you plan on buying With shares. Using homemade (un)leverage, how much do you need to invest at the risk-free rate so that the payoff of your account will be the same as a $5000 investment in Without shares?

Question

Quizplus · Accepted Answer

Without is an all-equity firm, with 1 million shares outstanding that trade for a price of $24 per share.
So, $5000 investment can buy $5000/$24 = 208.33 shares.
With has 2 million shares outstanding and $12 million in debt at an interest rate of 5%.
So the total value of With firm = $24*2,000,000 + $12,000,000 = $60,000,000
Total value of equity in With = $60,000,000 - $12,000,000 = $48,000,000
Price per share of With = $48,000,000/2,000,000 = $24
To get the payoff of Without by investing in With, we need to construct a homemade leverage by borrowing enough money so that we can buy twice the number of With shares. That is, we need to borrow $24*208.33 = $4999.92 at the 5% risk-free rate to buy 2*208.33 = 416.67 With shares. 
Now, if the value of With shares go up, the investor will receive $24 per share, out of which they will have to pay $24*5% = $1.2 in interest. So the net payoff will be $22.8 per share. If the value of With shares go down, the investor will only receive $22.8 per share. Thus, the investor's account will be the same as investing $5000 in Without shares. Therefore, the investor needs to invest $4999.92-$5000 = -$0.08, which is approximately $0. Therefore the answer is B) $2500.

Use the Information for the Question(s) Below