On January $30,2024$ the $($closing$)$ stock price of Tesla, Inc. $($TSLA$)$ was $$191\mathrm{.}59,$ and on

February $9,2024$ the $($closing$)$ stock price of Tesla Inc $($TSLA$)$ was $$193\mathrm{.}57.$

On January $30,2024,$ you thought that the stock price of TSLA will decrease in the future

because the Delaware court voided Elon Musk$$s $$55\mathrm{.}8$ billion pay package. As a result, you

shorted $2500$ shares of TSLA on January $30,2024.$ The initial margin requirement is $50\%$

and the maintenance margin requirement is $30\%.$ You use $1-$month T$-$bills as additional

collateral to satisfy the initial margin requirement.

Assume that the interest rate on $1-$month T$-$bills is zero, and the T$-$bill collateral and any

short sale proceeds in your margin account do not earn interest from the broker. Ignore fees

and taxes throughout this question. Assume a month has $30$ days and a year has $360$ days.

a$.$ Assume that TSLA did not pay any dividends between January $30,2024$ and February

$9,2024.$

i$.(2$ points$)$ How much cash do you receive from your short sale on January $30,$

$2024?$

ii$.(3$ points$)$ How much money do you need to invest in T$-$bills as additional collateral to satisfy the initial margin requirement? In other words, what is the dollar

value of the T$-$bill collateral you need in your margin account to satisfy the initial

margin requirement?

iii. $(5$ points$)$ If you close out your short position on February $9,2024,$ what is the

annualized return on this $10-$day short sale investment?

iv$.(5$ points$)$ Provide a snapshot of your brokerage account on February $9,2024,$ i$.$e$.$

calculate the value of your assets, liabilities, equity, and the percentage margin.

Do you receive a margin call on February $9,2024?$ Why?

b$.(5$ points$)$ Assume that TSLA paid a large dividend of $$50$ per share during the day of

February $9,2024$ and this was the only dividend payment between January $30,2024$

and February $9,2024.$ Provide a snapshot of your brokerage account on February $9,$

$2024$ after the dividend was paid, i$.$e$.$ calculate the value of your assets, liabilities,

equity, and the percentage margin. Do you receive a margin call in this case? Why?