Question

Marlene Bellamy purchased 400 shares of Writeline Communications stock at $ 55.36 per share using the prevailing minimum initial margin requirement of 54%. She held the stock for exactly 7 months and sold it without any brokerage costs at the end of that period. During the 7​-month holding​ period, the stock paid $ 1.64 per share in cash dividends. Marlene was charged 7.8 % annual interest on the margin loan. The minimum maintenance margin was 25%.

a. Calculate the initial value of the​ transaction, the debit balance​, and the equity position on​ Marlene's transaction.

b. For each of the following share​ prices, calculate the actual margin​ percentage, and indicate whether​ Marlene's margin account would have excess​ equity, would be​restricted, or would be subject to a margin​ call:

​(1)$44.24​, ​(2)$70.56​, and​ (3)$34.77.

c. Calculate the dollar amount of​ (1) dividends received and​ (2) interest paid on the margin loan during the 7​-month holding period.

d. Use each of the following sale prices at the end of the 7​-month holding period to calculate​ Marlene's annualized rate of return on the Writeline Communications stock​ transaction:

​(1)$50.64​, ​(2)$60.39​, and​ (3)$70.94.

Answer 1

a) The Initial Value of transaction:

Particulars	Amount
No fo Shares Purchased	400
Value of each share	55.36
Total Value of the trade	22144
Initial Margin	54%
Value of Equity	11957.76
Value of Loan	10186.24
Total Value of Trade	22144

b) Margin Call = (1- Initial Margin/ 1- Maintenance Margin )

= 0.46/0.75 * 55.36

= 33.95. The trader will ask the investor to insert equity if the share price falls below $33.95.

Particulars	Share Price
	44.24	70.56	34.77
No of Shares	400	400	400
Total Value of the trade	17696	28224	13908
Value of the Loan	10186.24	10186.24	10186.24
Value of Equity	7509.76	18037.76	3721.76
Status	Restricted	Excess Equity	Restricted

c) Dollar Value of the Dividends and the interest Paid

Particulars	Amount
No of Shares	400
Dividend each share	1.64
Total Value	656
Interest Rate	7.8 p.a
Total value of the loan	10186.24
Interest Amount	463.5

d) Annualized rate of return

Formula: = {(Initial Investment + Gains - Losses)/Initial Investment} ^ 7/12 - 1

Initial Investment + gains - Losses = Total Value of the equity

For share price at 50.64 = (10262.26/11957.76) ^ 7/12 - 1 = -8.533

For share price at 60.39 = (14162.26/11957.76) ^ 7/12 - 1 = 10.37

For Share price at 70.94 = 18382.26/11957.76) ^ 7/12 - 1 = 28.51

Particulars	Share Price
	50.64	60.39	70.94
Dividends received	1.64	1.64	1.64
No of Shares	400	400	400
Total Value	20912	24812	29032
Less Interest paid	463.5	463.5	463.5
Less Principal Paid	10186.24	10186.24	10186.24
Total Value of the Equity	10262.26	14162.26	18382.26
Initial Margin	11957.76	11957.76	11957.76
Annualized return	-8.533	10.37	28.51