Question

You decide to sell 100 shares of Mason Enterprises short when it is selling at its yearly high of ¢42.25. Your broker tells you that your margin requirement is 60 percent and that the commission on the sale is ¢20 and a 6% interest rate on margin debt. While you are short, Mason Enterprises pays a ¢0.85 per share dividend. a. If at the end of one year you buy your Mason Enterprises shares to cover your short sale at ¢35 and are charged a commission of ¢25, what is your rate of return on the investment? b. If at the end of one year you buy your Mason Enterprises shares to cover your short sale at ¢80 and are charged a commission of ¢20, what is your rate of return on the investment? c. At what price would you receive a margin call from the broker if the maintenance margin is 30%?

Answer 1

Part (a)

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 $.

Parameter	Linkage	Value
Number of shares (Nos.)	N	100.00
Short sale price	S	42.25
Margin requirement	M	60%
Equity contribution (=Investment)	E = N x S x M	2,535.00
Loan amount	D = N x S - E	1,690.00
Repurchase price	C	35.00
Sell Value	A = N x S	4,225.00
Sell commission	B	(20.00)
Purchase value	C = - N x C	(3,500.00)
Purchase commission	D	(25.00)
Dividend lost	E = 0.85 x N	(85.00)
Interest on loan	F = 6% x D	(101.40)
Dollar gain	G = A + B + C + D + E + F	493.60
Rate of return on the investment	G / E	19.47%

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Part (b)

The same table as above with two changes in inputs highlighted:

Parameter	Linkage	Value
Number of shares (Nos.)	N	100.00
Short sale price	S	42.25
Margin requirement	M	60%
Equity contribution (=Investment)	E = N x S x M	2,535.00
Loan amount	D = N x S - E	1,690.00
Repurchase price	C	80.00
Sell Value	A = N x S	4,225.00
Sell commission	B	(20.00)
Purchase value	C = - N x C	(8,000.00)
Purchase commission	D	(20.00)
Dividend lost	E = 0.85 x N	(85.00)
Interest on loan	F = 6% x D	(101.40)
Dollar gain	G = A + B + C + D + E + F	(4,001.40)
Rate of return on the investment	G / E	-157.85%

Part (c)

Hence, the price at which you would receive a margin call from the broker if the maintenance margin is 30% = 42.25 x (1 - 60%) / (1 - 30%) = $  24.14