Question

6. Sara Sanders purchased 30 shares of Apple stock at $189.29 per share using the prevailing minimum initial margin requirement of 51%. She held the stock for exactly 5 months and sold it without any brokerage costs at the end of that period. During the 5​-month holding​ period, the stock paid $1.37 per share in cash dividends. Sara was charged 4.8% 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​ Sara's transaction.

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

​(1) $174.54​, (2) $207.01​, and​ (3) $122.27.

c. Calculate the dollar amount of​ (1) dividends received and​ (2) interest paid on the margin loan during the 5​-month holding period.

d. Use each of the following sale prices at the end of the 5​-month holding period to calculate​ Sara's annualized rate of return on the Apple stock​ transaction:

​(1) $185.09​, (2) $194.52​, and​ (3) $206.27.

Answer 1

Given that,

· Sara Sanders purchased 30 shares of Apple stock at $189.29 per share

· Initial Margin requirement = 51%

· Holding Period = 5 months

· Cash Dividends received = $1.37 per share

· Annual Interest on Margin Loan = 4.8%

· Minimum Maintenance Margin = 25%

a) Initial Value of the Transaction = 30*$189.29 = $5678.70

Debit Balance = Loan Amount

Let it be L

Equity Position on transaction = Initial Value-Debit Balance

= $5678.70 - $2782.56 = $2896.14

b) 1) Actual Margin % if share price is $174. 54

As actual margin % is greater than minimum maintenance margin % but less than Initial margin %, margin account would be restricted.

2) Actual Margin % if share price is $207.01

As actual margin % is greater than Initial Margin %, margin account is said to have excess equity.

3) Actual Margin % if share price is $122.27

As actual margin % is lower than minimum maintenance margin %, there would be a Margin Call.

c) 1) Total amount of Dividends received = $1.37*30 = $41.1

2) Interest paid on Margin Loan = 2782.56*(4.8%)*(5/12) = $55.65

d) Annualized rate of return if share price is $185.09