1. Assume you buy 800 shares of a stock selling for $15 a share, borrowing $4,00

Question

1. Assume you buy 800 shares of a stock selling for $15 a share, borrowing $4,000 at an interest rate of 6% to help finance the purchase. Your account has a maintenance margin of 40%.

A. At what price would you receive a margin call?

B. If, after one year, the price increased to $20 a share, what would be your rate of return?

2. Assume the risk-free rate of return is 6%, the expected rate of return on the market portfolio is 13%, and the beta of Psy Corp. is 1.3. Psy has earnings of $8 per share that are expected to grow 5% a year and pays them all out to stockholders.

A) What is the value of a share of Psy?

B) Assume Psy has an investment opportunity that will yield a return of 20% and decides to reduce the dividend payout ratio to 50% and devote the rest of their earnings to the investment. Calculate the new value of Psy stock.

C) Assume you buy the stock at a price of $70 and expect to sell it in a year. If the stock’s market price is at its intrinsic value in one year, what is your expected holding period return on the stock (using the assumptions in part B)?

Explanation / Answer

A) Maintenance margin = Minimum Equity /Value of shares Equity = (800 x p) - $4000 Value of shares = 800P 40% = (800P - 4000)/800P P = 4000 = (800P - $320P) $8.33 $8.33 or lower will receive margin call B) The stock is purchased for = 800 shares x $15 $12,000.00 Amount Borrowed @ 6% 4000 Equity (12000 - 4000) $8,000.00 Stock Price increased = 800 shares x $20 $16,000.00 Rate of Return = ($16000 - $12000 - (4000 x 6%)/$8000 47.00% A) Cost of Equity = Rf + Beta x (Rm -Rf) = 6%+ 1.3 x (13%-6%) 15.10% Value of share = D0 x (1 + g)/(r-g) = $8 x (1+ 5%)/(17.70% -5%) $83.17 B) Cost of Equity 20.00% Value of share = D0 x (1 + g)/(r-g) = $4 x (1+ 5%)/(20% -5%) $28.00 C) Holding Period Return (loss) = ($28 - $70)/$70 -60.00%

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