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 market 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, you borrow enough 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. The number of shares of Without stock you purchased is closest to:

I got an answer of this problem but I have a question about a solution.

A) 425. B) 1650. C) 2000. D) 825. Answer: B Explanation: 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 = = $6.00 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 our portfolio, this means we need 50% equity and 50% from a margin loan. With $5000 in equity, we need to match it with $5000 from a margin loan. The total invested is $10,000/$6 per share = 1667 share

Why does this solution use $6 per share, not $24 per share which is without firm's share price? In my calculation, the answer is $10,000 / $ 24 = 416.6666667 shares.