Question

You have just borrowed $67,500 on margin to buy shares in ABC, which is currently quoting as the bid price of $29.99 bid and the ask price of $30.00 ask per share. The minimum margin is 35%, and your initial margin requirement is 55%. Assume that ABC will pay no dividends before you return the loan and that that you pay no interest on your loan.

- If you buy ABC in margin, what is the maximum number of shares you can buy?
- Suppose you bought the maximum number of shares of ABC as in
(1).
- Assume that immediately after your purchase, ABC’s share price drops to $26.00 per share. Calculate your new margin. Will you receive a margin call?
- What is the maximum price at which you will receive a margin call?
- If the stock price falls to $20, you would get a margin call. If that happens, how much in additional funds would you need to add to your account to respond to the margin cal

Hints:

- New fund needed = Original loan – Maximum Loan given market value
- Maximum loan = (1 – minimum margin) (Market value of shares
- When margin call occurs, the margin balance is bumped up to the minimum (maintenance) margin.

Answer #1

Maximum number of shares of ABC that can be purchased = 67500/(55%*30) = | 4091 | |

a) | New margin = 4091*26*35% = | $37228 |

Balance in margin account = 67500-(30-26)*4091 = | $51136 | |

As the balance in the margin account is more than the new | ||

margin required, no margin call will be received. | ||

b) | Maximum price for which no margin call will be required = | |

67500-(30-p)*4091 = 4091*35%*p, where p is the new price | ||

Solving for p | ||

67500-122730+4091*p = 1431.85*p | ||

55230 = 2659.15*p | ||

p = 55230/2659.15 = $20.77 | ||

c) | New margin required = 4091*20*35% = | $28637 |

Balance in margin account = 67500-(30-20)*4091 = | $26590 | |

Additional funds required | $2047 |

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