Suppose that Xtel currently is selling at $$54$ per share. You buy $450$ shares using $$10,000$ of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is $7\%.$

Required:

a$.$What is the percentage increase in the net worth of your brokerage account if the price of Xtel immediately changes to: $($i$)$ $$57\mathrm{.}78$; $($ii$)$ $$54$; $($iii$)$ $$50\mathrm{.}22?$ What is the relationship between your percentage return and the percentage change in the price of Xtel?

b$.$If the maintenance margin is $25\%,$ how low can Xtel$$s price fall before you get a margin call?

c$.$How would your answer to $($b$)$ change if you had financed the initial purchase with only $$12,150$ of your own money?

d$.$What is the rate of return on your margined position $($assuming again that you invest $$10,000$ of your own money$)$ if Xtel is selling after $1$ year at: $($i$)$ $$57\mathrm{.}78$; $($ii$)$ $$54$; $($iii$)$ $$50\mathrm{.}22?$ What is the relationship between your percentage return and the percentage change in the price of Xtel? Assume that Xtel pays no dividends.

e$.$Continue to assume that a year has passed. How low can Xtel$$s price fall before you get a margin call?