Question

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 dollars in debt at an interest rate of 5%. a) 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 Without stock. Using homemade leverage, how much do you need to borrow in your margin account so that the payoff of your margined purchase of Without stock will be the same as a $5000 investment in With stock? Plz step by step

Answer 1

Under MM I, the total value of With and Without must be the same.

Value(Without) = 1,000,000 × $24 = $24 million

Value(levered equity) = value(With) - debt = $24 M - $12M = $12 M

Price per share = $12 M / 2M = $6

So, the leverage ratio of with is 50% equity to 50% debt. To duplicate this in homemade leverage we need to have equal proportions in out portfolio, this means we need 50% equity and 50% from a margin loan. So $5000 is our equity we need to match it with $5000 in a margin loan. So the total invested is $10,000/$6 per share = 1667 shares ~1650 shares