Answer:
A) Dee´s Margin = 58.33%; B) Remaining Margin if price drops to $26 is 30.56% C) She won´t receive a margin call (but close...)
D) Rate of Return = - 32.36%
Explanation:
Hi, first let´s find out what the initial margin is, for that we have to use the following formula.
![Margin=\frac{Equity}{ValueStocks}](https://tex.z-dn.net/?f=Margin%3D%5Cfrac%7BEquity%7D%7BValueStocks%7D)
Now, in order to find the equity, we have to find the total value of the stocks and substract the debt from it, since it was 300 shares at $30 per share, the total value of the investment is $7,800, therefore, its equity is $3,300 ($7,800-$4,500).
So everything should look like this
![Margin=\frac{6,300}{10,800} =0.5833](https://tex.z-dn.net/?f=Margin%3D%5Cfrac%7B6%2C300%7D%7B10%2C800%7D%20%3D0.5833)
So the initial margin was 58.33%
If the price drops to $26 by the end of the year, the remaining margin in her account is:
![Margin=\frac{3,300}{10,800} =0.3056](https://tex.z-dn.net/?f=Margin%3D%5Cfrac%7B3%2C300%7D%7B10%2C800%7D%20%3D0.3056)
So the remaining margin one year later, after the stock price dropped to $26 was 30.56%
Now, in order to find the rate of return on her investment, at the end of the year, we have to remember that the money loaned was at 11%, therefore, the best way to find out the return of this investment is to convert this into money, like such.
First (Gross Return of the stock)
![Gross Return=\frac{Final.P-Initial.P}{Initial.P} x100](https://tex.z-dn.net/?f=Gross%20Return%3D%5Cfrac%7BFinal.P-Initial.P%7D%7BInitial.P%7D%20x100)
![Gross Return=\frac{26-36}{36} x100=-0.2778](https://tex.z-dn.net/?f=Gross%20Return%3D%5Cfrac%7B26-36%7D%7B36%7D%20x100%3D-0.2778)
Ok, we have the gross return, which is -$27.78%
The interest expenses are just as follows.
![Interest Expense=4,500*0.11=-495](https://tex.z-dn.net/?f=Interest%20Expense%3D4%2C500%2A0.11%3D-495)
To find the return on the investmen, we need to use the following formula.
![RateReturn=\frac{FinalInvestment-InitialInvestment}{InitialInvesment} x100](https://tex.z-dn.net/?f=RateReturn%3D%5Cfrac%7BFinalInvestment-InitialInvestment%7D%7BInitialInvesment%7D%20x100)
The final investment is: Gross return($)+interest Expenses
![FinalInvest=\frac{300*(-10)+(-4,500*0.11)}{10,800} =-0.3236](https://tex.z-dn.net/?f=FinalInvest%3D%5Cfrac%7B300%2A%28-10%29%2B%28-4%2C500%2A0.11%29%7D%7B10%2C800%7D%20%3D-0.3236)
This means that, by the end of the year, her return on the investment was -32.36%. In money, this is - $3,495.
Best of luck.