Question

Two years ago, you bought 300 shares of Kayleigh Milk Co. for $45 a share with a margin of 70 percent. Currently, the Kayleigh stock is selling for $50 a share. Assume there are no dividends and ignore commissions. Do not round intermediate calculations. Round your answers to two decimal places. a. Assuming that you pay cash for the stock, compute the annualized rate of return on this investment if you had paid cash. b. Assuming that you used the maximum leverage in buying the stock, compute your rate of return with the margin purchase

Answer 1

a) When you pay cash for stock you end up paying entire stock price . Therefore you had paid $45 for each stock 2 years before

Current stock price = $50

or 45*(1+r)^2 = 50

or (1+r)^2 = 50/45

or r = sqrt(50/45) -1

or r = 0.05409255 or r =5.41%

b)When the margin is 70% your broker ends up paying 30 % for you

Price paid by you = 70% *45 = 31.5

Price paid by your broker = 30% * 45 =13.5

Current price of share = 50

Profit made per share = 50-45 =5

So you paid 31.5 and received a profit of 5

Therefore 31.5*(1+r)^2 = 31.5+ 5

or, 31.5 *(1+r)^2 = 36.5

or, r = 0.0764432 = 7.64%