Question

Investor A makes a cash purchase of 200 shares of AB&C common stock for $60 a share. Investor B also buys 200 shares of AB&C but uses margin. Each holds the stock for one year, during which dividends of $6 a share are distributed. Commissions are 3 percent of the value of a purchase or sale; the margin requirement is 60 percent, and the interest rate is 10 percent annually on borrowed funds.

A.

What is the percentage earned by investor A if he or she sells the stock after one year for $45? Round your answer to one decimal places.
%

What is the percentage earned by investor B if he or she sells the stock after one year for $45? Round your answer to one decimal places.
%

B.

What is the percentage earned by investor A if he or she sells the stock after one year for $60? Round your answer to one decimal places.
%

What is the percentage earned by investor B if he or she sells the stock after one year for $60? Round your answer to one decimal places.
%

C.

What is the percentage earned by investor A if he or she sells the stock after one year for $65? Round your answer to one decimal places.
%

What is the percentage earned by investor B if he or she sells the stock after one year for $65? Round your answer to one decimal places.
%

D.

What is the percentage earned by investor A if he or she sells the stock after one year for $75? Round your answer to one decimal places.
%

What is the percentage earned by investor B if he or she sells the stock after one year for $75? Round your answer to one decimal places.
%

Now the question changes

If the margin requirement had been 40 percent, what would have been the annual percentage returns?

A.

What is the percentage earned by investor A if he or she sells the stock after one year for $45? Round your answer to one decimal places.
%

What is the percentage earned by investor B if he or she sells the stock after one year for $45? Round your answer to one decimal places.
%

B.

What is the percentage earned by investor A if he or she sells the stock after one year for $60? Round your answer to one decimal places.
%

What is the percentage earned by investor B if he or she sells the stock after one year for $60? Round your answer to one decimal places.
%

C.

What is the percentage earned by investor A if he or she sells the stock after one year for $65? Round your answer to one decimal places.
%

What is the percentage earned by investor B if he or she sells the stock after one year for $65? Round your answer to one decimal places.
15% (I got this one right I am not sure how)

D.

What is the percentage earned by investor A if he or she sells the stock after one year for $75? Round your answer to one decimal places.
%

What is the percentage earned by investor B if he or she sells the stock after one year for $75? Round your answer to one decimal places.
%

Please show your work I want to learn this. Honestly if you just show me how to do the first few of both sections (part 1 &2) it would be greatly appreciated and help me learn this for my test later in the semester. Thanks.

Answer 1

A) Amount Invested = No. of shares x Price x (1 + commission) = 200 x 60 x (1 + 3%) = 12,360

Dividends Received = 200 x 6 = 1,200

When Stock Price = 45, Investment Value at year end = 200 x 45 x (1 - 3%) = 8,730

% Returns for A = (8,730 + 1,200) / 12,360 - 1 = -19.66%

For investor B, Initial Investment = 60% x 12,360 = 7,416, Loan = 40% x 12,360 = 4,944

Loan repayment at year end = Principal x (1 + interest rate) = 4,944 x (1 + 10%) = 5,438.40

Value of equity at year end = Total Value - Loan = (8,730 - 5,438.40) = 3,291.60

% Returns for B = (3,291.60 + 1,200) / 7,416 - 1 = -39.43%

B) If Stock Price = 60,

% Returns for A = (200 x 60 x (1 - 3%) + 1,200) / 12,360 - 1 = 3.88%

% Returns for B = (200 x 60 x 0.97 + 1,200 - 5,438.40) / 7,416 - 1 = -0.19%

C) If Stock Price = 75,

% Returns for A = (200 x 75 x 0.97 + 1,200) / 12,360 - 1 = 27.43%

% Returns for B = (200 x 75 x 0.97 + 1,200 - 5,438.40) / 7416 - 1 = 39.05%