Use the information for the question(s) below.
Consider two firms, Firm X and Firm Y, that have identical assets that generate identical cash flows. Firm Y is an all-equity firm, with 1 million shares outstanding that trade for a price of $24 per share. Firm X 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 at the same 5% rate as Firm X. You have $5,000 of your own money to invest and you plan on buying Firm X stock. Using homemade (un)leverage you invest enough at the risk-free rate so that the payoff of your account will be the same as a $5,000 investment in Firm Y stock. The number of shares of Firm X stock you purchased is closest to ________.
A) 100
B) 417
C) 1,650
D) 825

Question

Quizplus · Accepted Answer

B) Under MM I, the total value of Firm X and Firm Y must be the same.
Value(Firm Y) = 1,000,000 × $24 = $24 million
Value(levered equity) = value(Firm X) - debt = $24 million - $12 million = $12 million
Price per share = 11ea84dc_f50a_ab64_9a63_2b93e3d31887_TB1316_11_TB1316_11 = $6.00
So, the leverage ratio of Firm X is 50% equity to 50% debt. To duplicate this in homemade leverage we need to have equal proportions in our portfolio, which means we need 50% equity and 50% in the risk-free asset. So $5,000 is our total portfolio and we need $2,500 in equity (Firm X stock) and $2,500 in the risk-free asset. 11ea84dc_f50a_ab65_9a63_f1980269274c_TB1316_11_TB1316_11 = 417 shares

Use the Information for the Question(s) Below