Question

Sara Sanders purchased 30 shares of Apple stock at $189.15 per share using the prevailing minimum initial margin requirement of 59%. 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 $1.41 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)$175.34​, (2) $207.57​, and​ (3) $122.96.

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) $185.89​, ​(2) $195.49​, and​ (3) $205.04.

Answer 1

No. of Shares = 30, Purchase Price = 189.15, initial margin 59%, Holding 4months, Dividend= 1.41 per share, maintainanc margin 25%

a) Inital Value of Transactions =30 x 189.15 = 5674.5

Initial Margin = 5674.5 * 59% = 3348

Debit balance = 5674.5-3348 = 2326.5

Equity position i.e Long position i.e. +30 share of Apple

b) (i) at Price 175.34, Position value decrease by 30 x (189.15-175.34) = 412.5

So 7.27 % drop in margin, make it 51.73% Actual margin. At this no call required as margin is above maintainance margin.

(ii) at Price 207.57, Increase in Position value by 30 x (207.57-189.15) = 552.6

so 9.74% increase in margin which make it total 68.74% actual margin. So no margin call required in this situation.

(iii) at Price 122.96, Decrease in Psoition value by 30 x ( 189.15-122.96) = 1985.7

so 34.99% decrease in margin which make it total 24.01% which is below 25% limit of maintanance level. So subject to margin call.

c) i) Amount of dividend received = 30 x 1.41 = 42.3

ii) Interest on margin loan= Debit balance= 2326.5* 5.6% * 4/12 = 43.43

d) Annualized Return i) at 185.89

First we will calculate Holding period return = (Dividend+capital gain)/ Price at start

1.41+(185.89-189.15)/ 189.15 = -1.85% for 4 month return So annualized return = -5.65%

ii) At price 195.49

1.41+(195.49-189.15)/189.15 = 4.097% and annual return will be 12.80%

iii) At price 205.04

1.41+(205.04-189.15)/189.15 = 9.15% and annual return will be 31.29%

Formula for calculating annualized return is asame as calculate Equalized annual return