Question

Sara purchased 50 shares of Apple stock at $190.97 per share using the prevailing minimum initial margin requirement of 55%.

She held the stock for exactly 4 months and sold it without any brokerage costs at the end of that period. During the 4​-month holding​ period, the stock paid $1.49 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)$174.81​, (2)$206.54​,and​ (3)$122.35.

c. Calculate the dollar amount of​ (1) dividends received and​ (2) interest paid on the margin loan during the 4​-month holding period.

d. Use each of the following sale prices at the end of the 4​-month holding period to calculate​ Sara's annualized rate of return on the Apple stock​ transaction: (1)$185.83​, (2) $195.99​, and​ (3)$205.89.

Answer 1

(a) Initial Value of transaction = 190.97*50

= 9,548.5

Debit Balance = 55% of 9,548.5

= 5,251.7

Equity Position on Sara's transaction = 9,548.5

(b) Scenario 1 = Stock Price at 174.81

Loan Amount in the transaction is 9,548.5-5,251.7

= 4296.8

Now, total value of stock is 174.81*50

= 8740.5

Value of equity position= 8740.5-4296.8

= 4443.7

Percentage of Equity = 4443.7/8590.5

50.8%, Hence no margin call.

Scenario 2 = Stock Price at 206.54

Loan Amount in the transaction is 9,548.5-5,251.7

= 4296.8

Now, total value of stock is 206.54*50

= 10327

Value of equity position= 10327.0-4296.8

= 6030.2

Percentage of Equity = 6030.2/10327

58.4%, Hence no margin call.

Scenario 3 = Stock Price at 122.35

Loan Amount in the transaction is 9,548.5-5,251.7

= 4296.8

Now, total value of stock is 122.35*50

= 6117.5

Value of equity position= 6117.5-4296.8

= 1820.7

Percentage of Equity = 1820.7/6117.5

29.8%, Hence no margin call. Although the value of equity has fallen significantly but the maintenance margin requirement is 25.0% and we are still above that.

(c) Dollar amount of dividends received is $1.49*50

= 74.5

Interest paid is 4.8%*4296.8*4/12

= 68.75

4296.8 is the loan amount at the beginning and 4.8% is the annual interest on loan and our holding period is 4 months.

(d) To calculate Sara's annual rate of return, we would first compute the holding period return on the 3 scenarios provided

Holding Period Return (HPR) = (Capital Gain or Loss+Dividends - Interest Paid)/ Initial equity investment made by Sara

HPR% = HPR/Initial Investment by Sara

Annualized Return = HPR%*12/4

Scenario 1 = 185.83

Value of Equity Investment = 185.83*50 - 4296.8

= 4994.7

Capital Gain = 4994.7 - 5251.7

-257

HPR = -251.2

HPR% = -4.78%

Annualized = -14.35%

Scenario 2 = 195.99

Value of Equity Investment = 195.99*50 - 4296.8

= 5502.7

Capital Gain = 5502.7 - 5251.7

251.0

HPR = 256.8

HPR% = 4.89%

Annualized = 14.67%

Scenario 3 = 205.89

Value of Equity Investment = 195.99*50 - 4296.8

= 5997.7

Capital Gain = 5997.7 - 5251.7

746.0

HPR = 751.8

HPR% = 14.31%

Annualized = 42.94%