Question

Sara Sanders purchased 40 shares of Apple stock at $189.98 per share using the prevailing minimum initial margin requirement of 51 %.

She held the stock for exactly 6 months and sold it without any brokerage costs at the end of that period. During the 6​-month holding​ period, the stock paid $ 1.36 per share in cash dividends. Sara was charged 5.6 % 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) $ 174.24

​(2) $ 206.97

(3) $ 121.09

c. Calculate the dollar amount of​ (1) dividends received and​ (2) interest paid on the margin loan during the 6​-month holding period.

d. Use each of the following sale prices at the end of the 6​-month holding period to calculate​ Sara's annualized rate of return on the Apple stock​ transaction:

​(1) $ 184.42

​(2) $ 194.59

​(3) $ 205.78

Answer 1

(A) Number of shares purchased = 40

Purchase price = 189.98

Total value of transaction = 189.98 * 40 = 7599.20

Margin used = 7599.20 * .51 = 3875.60 (51% initial margin requirement)

Margin loan from broker = 3723.60

(B) 1. Price = 174.24

Account value = 174.24 * 40 = 6969.60

Purchase value = 7599.20

Loss on position = 7599.20 - 6969.60 = 629.60

Current margin percentage will be calculated by subtracting the loss from the margin initially used.  

Current margin percentage = 3875.60 - 629.60 = 3246 / 7599.20 = 0.4272 or 42.72%

The account will be restricted due to the margin going down from the minimum margin requirement.

2. Price = 206.97

Account value = 206.97 * 40 = 8278.80

Purchase value = 7599.20

Profit on the position = 8278.80 - 7599.20 = 676.60

Current margin percentage will be calculated by adding the profit to the margin used initially.

Current margin percentage = 3875.60 + 676.60 = 4552.20 / 7599.20 = 0.5990 or 59.90%

There is excess equity in the account as the margin has gone up because of the profit in the account.

3. Price = 121.09

Account Value = 121.90 * 40 = 4876.00

Purchase value = 7599.20

Loss on the position = 7599.20 - 4876.00 = 2723.20

Current margin percentage will be calculated by subtracting the loss from the margin initially used.  

Current margin percentage = 3875.60 - 2723.20 = 1152.40 / 7599.20 = 0.1516 or 15.16%

The margin in the account has gone below the maintenance margin, there will be a margin call on the account.

(C) Dividend = 1.36 per share

Dollar amount of dividend = 1.36 * 40 = 54.40

Margin loan = 3723.60

Interest rate on margin loan = 5.6% p.a.

Interest paid on margin = 3723.60 * 0.056 * 6 / 12 = 104.26

To calculate interest payment for 6 months the yearly interest payment will be multiplied by 6 / 12.

(D) 1. Price = 184.42

Account value = 184.42 * 40 = 7376.80

Purchase value = 7599.20

Loss on the position = 7599.20 - 7376.80 = 222.40

6 Months return on the trade = Dividend received - loss on the position - Interest on margin loan / Initial investment

Dividend received = 54.40

Interest paid on the position = 104.26

Initial Investment = 3875.60

6 months return = 54.40 - 222.40 - 104.26 / 3875.60 = - 272.26 / 3875.60 = - 0.0702 or - 7.02%

2. Price = 194.59

Account value = 194.59 * 40 = 7783.60

Purchase value = 7599.20

Profit on the position = 7783.60 - 7599.20 = 184.40

6 Months return on the trade = Dividend received + Profit on the position - Interest on margin loan / Initial investment

Dividend received = 54.40

Interest paid on the position = 104.26

Initial Investment = 3875.60

6 months return = 54.40 + 184.40 - 104.26 / 3875.60 = 134.54 / 3875.60 = 0.0347 or 3.47%

3. Price = 205.78

Account value = 205.78 * 40 = 8231.20

Purchase value = 7599.20

Profit on the position = 8231.20 - 7599.20 = 623.00

6 Months return on the trade = Dividend received + Profit on the position - Interest on margin loan / Initial investment

Dividend received = 54.40

Interest paid on the position = 104.26

Initial Investment = 3875.60

6 months return = 54.40 + 623 - 104.26 / 3875.60 = / 3875.60 = 0.1631 or 16.31%