Question

Shares of Coopers Ltd are selling for ¢45 per share. Brokerage commissions are 2% for purchases and 2% for sales. The interest rate on margin debt is 5% per year. Your broker demands an initial margin deposit of 60%. The maintenance margin is 30%. You buy 1,000 shares of Coopers Ltd and the company paid dividends of ¢0.85 per share during the year. a. Assuming that you paid the full cost of the purchase, what is your rate of return if at the end of the year you sell your shares for: i. ¢55 per share? ii. ¢35 per share? b. Now, assume that you bought the 1,000 shares on a margin account. What is your rate of return if at the end of the year you sell your shares for: i. ¢55 per share? ii. ¢35 per share? c. If you purchase 1,000 shares at ¢45 each by making a margin deposit of 60%, at what price would you receive a margin call from the broker?

Answer 1

a) Purchase price = 45*1000 = 45000

Commision on purchase = 45000 * 2% = 900

i) Selling price = 55*1000 = 55000

Dividends = 1000*0.85 = 850

Commission on selling = 55000*2 % = 1100

So, Investment = 45000

Net realisation = 55000+850-900-1100= 53850

Rate of Return= (53850 -45000)/45000 = 0.19667 or 19.67%

ii)

Selling price = 35*1000 = 35000

Dividends = 1000*0.85 = 850

Commission on selling = 35000*2 % = 700

So, Investment = 45000

Net realisation = 35000+850-900-700= 34250

Rate of Return= (34250 -45000)/45000 = -0.23889 or -23.89%

b)

i) Margin money required = 60%*1000*45 = 27000

Amount financed by broker = 40%*45*1000= 18000

Interest on Margin = 5%*18000 = 900 (There will be no margin call as there is the shares are sold at a profit)

Commision on purchase = 45000 * 2% = 900

Selling price = 55*1000 = 55000

Dividends = 1000*0.85 = 850

Commission on selling = 55000*2 % = 1100

So, Investment = 27000

Net realisation = 55000+850-900-1100-18000-900= 34950

Rate of Return= (34950 -27000)/27000 = 0.2944 or 29.44%

ii)

Margin money required = 60%*1000*45 = 27000

Amount financed by broker = 40%*45*1000= 18000

Interest on Margin = 5%*18000 = 900

(There will be no margin call as margin balance = 27000- (45-35)*1000 = 17000 > 30% of (35*1000))

Commision on purchase = 45000 * 2% = 900

Selling price = 35*1000 = 35000

Dividends = 1000*0.85 = 850

Commission on selling = 35000*2 % = 700

So, Investment = 27000

Net realisation = 35000+850-900-700-18000-900= 15350

Rate of Return= (15350 -27000)/27000 = -0.43148 or -43.15%

c) Let price be P when the margin call is received (P has to fall below 45 to receive a margin call)

i.e.margin balance at this price = 30% of contract value

=> 27000 - (45-P)*1000 = 30%* P*1000

=> -18000 + 1000*P = 300*P

=> P = 18000/700 = 25.7142 or 25.71 per share

The price has to fall to 25.71 per share to receive a margin call