Question

The shares of Salford Ltd are selling for ¢55 per share. Ruth is considering buying 1,000 shares of Salford Ltd. Her broker demands brokerage commissions of 2% for purchases and 2% for sales; initial margin deposit of 60% and a maintenance margin of 25%. The interest rate on margin debt is 4% per year. a. Assuming that Ruth paid the full cost of the purchase and the company paid dividends of ¢0.80 per share during the year, what is her rate of return if at the end of the year she sells the shares for: i. ¢60 per share? ii. ¢50 per share? b. Now, assume that Ruth bought the 1,000 shares on a margin account and the company paid dividends of ¢0.80 per share during the year. What is her rate of return if at the end of the year she sells the shares for: i. ¢60 per share? ii. ¢50 per share? c. If Ruth purchases the 1,000 shares on a margin account, making the initial margin deposit of 60%, at what share price would she receive a margin call from the broker? d. Now, instead of buying the shares John decided to short sell 1,000 shares of Salford Ltd. Brokerage commissions and margin requirements on short-sales are the same as above but the interest on margin debt for short sales is 6% per annum. While John is short, Salford Ltd paid dividends of ¢0.80 per share. What is John’s rate of return if at the end of one year he buys Salford Ltd shares to cover his short sale at: i. ¢60 per share? ii. ¢50 per share? e. Differentiate between “buying a security on a margin” and “selling a security short”. When would an investor consider using each of these strategies?

Answer 1

You have asked a question with multiple parts. As if the pain was less, some of your parts have two sub parts. I have addressed the first four parts. Please post the balance parts separately.

Please see the table below. Please be guided by the second column titled “Linkage” to understand the mathematics. The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in ¢.

Part (a)

Part(a)	Linkage	Case (i)	Case (ii)
Number of shares	A	1,000	1,000
Purchase price	B	55	55
Sale price	C	60	50
Brokerage commission for sale	D	2%	2%
Brokerage commission for purchase	E	2%	2%
Initial margin	F	60%	60%
Maintenance margin	G	25%	25%
Interest rate	H	4%	4%
Dividend per share	I	0.80	0.80
Proceeds from sale	J = A x C	60,000	50,000
Brokerage on sale	K = -D x J	(1,200)	(1,000)
Dividends	L = I x A	800	800
Cost to buy	M = -B x A	(55,000)	(55,000)
Brokerage on purchase	N = M x E	(1,100)	(1,100)
Dollar Gain	O = J + K + L + M + N	3,500	(6,300)
Rate of return	O / (-M)	6.36%	-11.45%

Part (b)

Part(b)	Linkage	Case (i)	Case (ii)
Number of shares	A	1,000	1,000
Purchase price	B	55	55
Sale price	C	60	50
Brokerage commission for sale	D	2%	2%
Brokerage commission for purchase	E	2%	2%
Initial margin	F	60%	60%
Maintenance margin	G	25%	25%
Interest rate	H	4%	4%
Dividend per share	I	0.80	0.80
Equity Portion	X = A x B x F	33,000	33,000
Loan Portion	Y = A x B - X	22,000	22,000
Proceeds from sale	J = A x C	60,000	50,000
Brokerage on sale	K = -D x J	(1,200)	(1,000)
Dividends	L = I x A	800	800
Cost to buy	M = -B x A	(55,000)	(55,000)
Brokerage on purchase	N = M x E	(1,100)	(1,100)
Interest cost	O = -Y x H	(880)	(880)
Dollar Gain	P = J + K + L + M + N + O	2,620	(7,180)
Rate of return	P / X	7.94%	-21.76%

Part (c)

Hence, the share price at which she would receive a margin call from the broker = 55 x (1 - 60%) / (1 - 25%) =  29.33

part (d)

Part(d)	Linkage	Case (i)	Case (ii)
Number of shares	A	1,000	1,000
Purchase price	B	60	50
Short Sale price	C	55	55
Brokerage commission for sale	D	2%	2%
Brokerage commission for purchase	E	2%	2%
Initial margin	F	60%	60%
Maintenance margin	G	25%	25%
Interest rate	H	6%	6%
Dividend per share	I	0.80	0.80
Equity Portion	X = A x C x F	33,000	33,000
Loan Portion	Y = A x C - X	22,000	22,000
Proceeds from sale	J = A x C	55,000	55,000
Brokerage on sale	K = -D x J	(1,100)	(1,100)
Dividends lost	L = I x A	(800)	(800)
Cost to buy	M = -B x A	(60,000)	(50,000)
Brokerage on purchase	N = M x E	(1,200)	(1,000)
Interest cost	O = -Y x H	(1,320)	(1,320)
Dollar Gain	P = J + K + L + M + N + O	(9,420)	780
Rate of return	P / X	-28.55%	2.36%