Question

Three years ago, you bought 300 shares of Kayleigh Milk Co. for $45 a share with a margin of 50 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.

Required:
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) Current stock price = $50

45*(1+r)^2 = 50

(1+r)^2 = 50/45

r =
`√(50/45)` -1

r = 0.05409255

r =5.41%

b )When the margin is 50%, 50% is paid by broker

Price paid = 50% *45 = 22.5

Price received from broker = 50% * 45 = 22.5

Current price of share = 50

Profit made per share = 50 - 45

Profit made per share = 5

Therefore 22.5*(1+r)^2 = 22.5 + 5

22.5 *(1+r)^2 = 27.5

(1+r)^2 = 27.5/22.5

1+r =
`√(27.5/22.5)`

r =
`√(27.5/22.5)` - 1

r = 1.1054 - 1

r = 0.1054

r = 10.54%