a$.$ You are the investment manager for Classic Assets Investment Company$$s mutual fund and you have US$$900,000\mathrm{.}00$ to invest in Blackrock Group Ltd$.,$ a stock selling for US$$70$ per share. The initial margin requirement is $60\%,$ and the maintenance margin is $40\%.$ Show in detail the impact on your rate of return if the stock rises to US$$97$ per share and if it declines to US$$50$ per share assuming

i$)$ You pay cash for the stock

ii$)$ You buy it using maximum leverage

$.$

b$.$ Based on further market analysis you believe that the stock price of another company, Fortune Co$.$ Ltd$,$ may rise shortly and you have US$$760,000$ to open a second margin account to purchase Fortune Co$.$ Ltd$.$s shares at US$$200$ per share. Assuming the initial margin requirement is $55\%$ ;

i$)$ How many shares can you purchase using the maximum allowable margin?

ii$)$ If the maintenance margin is $35\%$ to what price can Fortune Co$.$ Ltd$.$s stock fall before you receive a margin call?

iii$)$ One month later the stock falls to US$$99$ per share and you receive a margin call. You decide to fulfil the margin requirements by adding cash to the account. How much cash should you deposit if you are required to restore the initial margin?

iv$)$ If the stock price fell to US$$99$ and you decide to pay down the loan to satisfy the margin call, by how much should you reduce the loan if you are required to restore the maintenance margin?

Please show workings