Question

Suppose that ZX Inc. is currently selling at $50 per share. You buy 200 shares, using $5,000 of your own money and borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 5%.

1. What is the profit or loss $ in the net worth of your brokerage account if the price of ZX Inc. changes to $46?

2. What is the profit or loss $ in the net worth of your brokerage account if the price of ZX Inc. changes to $50?

3. What is the profit or loss $ in the net worth of your brokerage account if the price of ZX Inc. changes to $54?

4. What is the rate of return on your margined position (assuming again that you invest $5,000 of your own money) if ZX Inc. is selling after one year at $46 (use whole number percentage with two decimals rounded up/down - i.e. 0.3245 input 32.45)?

5. What is the rate of return on your margined position (assuming again that you invest $5,000 of your own money) if ZX Inc. is selling after one year at $50 (use whole number percentage with two decimals rounded up/down - i.e. 0.3245 input 32.45)?

6. What is the rate of return on your margined position (assuming again that you invest $5,000 of your own money) if ZX Inc. is selling after one year at $54 (use whole number percentage with two decimals rounded up/down - i.e. 0.3245 input 32.45)?

Answer 1

Given,

Number of shares purchased = 200

Price at which number of shared purchased= 50

total invested value= 200*50=10000

Own equity contributed= 5000

therefore loan taken from broker account = 10000-5000= 5000

Interest on loan after 1 year = 5000*5%=250

1) Payoff on shares is given as = (price after 1 year- Purchase price)*number of shared purchased

=(46-50)*200

=-800

Value of equity = Inital equity value + pay off =5000-800=4200

(Note: if the share price is given after 1 year then interest shall also be deducted from the equity. hence the value of equity = 4200-250= 3950)

2) Payoff on shares is given as = (price after 1 year- Purchase price)*number of shared purchased

=(50-50)*200

=0

Value of equity = Inital equity value + pay off =5000+0=5000

(Note: if the share price is given after 1 year then interest shall also be deducted from the equity. hence the value of equity = 5000-250= 4750)

3) Payoff on shares is given as = (price after 1 year- Purchase price)*number of shared purchased

=(54-50)*200

=800

Value of equity = Inital equity value + pay off =5000+800=5800

(Note: if the share price is given after 1 year then interest shall also be deducted from the equity. hence the value of equity = 5800-250= 5550)

4) rate of return on the margined posistion after 1 year =(Pay off-interest)/Equity value invested*100

at price 46, pay off = -800(Computed above)

Interest =250 (Computed above)

Hence rate of return= (-800-250)/5000*100=-1050/5000*100= -21%

5) rate of return on the margined posistion after 1 year =(Pay off-interest)/Equity value invested*100

at price 50, pay off = 0(Computed above)

Interest =250 (Computed above)

Hence rate of return= (0-250)/5000*100= -250/5000*100= -5%

6) rate of return on the margined posistion after 1 year =(Pay off-interest)/Equity value invested*100

at price 54, pay off = 800(Computed above)

Interest =250 (Computed above)

Hence rate of return= (800-250)/5000*100= 550/5000*100= 11%