Question

Suppose you buy a round lot of Francesca Industries stock (100 shares) on 60 percent margin when the stock is selling at $30 a share. The broker charges a 8 percent annual interest rate, and commissions are 4 percent of the stock value on the purchase and sale. A year later you receive a $0.70 per share dividend and sell the stock for $40 a share. What is your rate of return on Francesca Industries? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

1).Profit = Ending Value - Beginning Value + Dividends - Transaction Costs - Interest

Beginning Value of Investment = $30 x 100 shares = $3,000

Your Investment = margin requirement + commission.

= (.60 x $3,000) + (.04 x $3,000) = $1,800 + $120 = $1,920

Ending Value of Investment = $40 x 100 shares = $4,000

Dividends = $0.70 x 100 shares = $70.00

Transaction Costs = (.04 x $3,000) + (.04 x $4,000) = $120 + $160 = $280

Interest = .08 x (.40 x $3,000) = $96.00

Therefore:

Profit = $4,000 - $3,000 + $70 - $280 - $96 = $694

The rate of return on your investment of $1,920 is:

$694/$1,920 = 36.15%

2). Profit on a short sale = Begin Value - Ending Value - Dividends - Transaction Costs - Interest

Beginning Value of Investment = $56 * 100 = $5,600 (Sold under a short sale arrangement)

Ending Value of Investment = $43 * 100 = $4,300

Transaction Costs = Commission on Sale + Commission on Purchase = $150 + $135 = $285

Dividends = $2.15 * 100 = $215

Profit = $5,600 - $4,300 - $215 - $285 = $800

Your Investment = Margin Requirement + Commission

= (0.50 * $5,600) + $150 = $2,800 + $150 = $2,950

Return on investment of $2,950 = Profit / Your Investment = $800 / $2,950 = 0.2712, or 27.12%