Question

Miss Good wants to buy BAD stock, which is selling for $5 per share. She can buy on margin. The initial margin requirement is 40%, and the maintenance margin is 30%.

(a) Miss Good has $2,000 in hand. If she decides NOT to buy on margin; that is, she wants to buy using only her own funds. Then what is the total shares she can buy? If the price increases to $6 per share, what’s the rate of return? If the price decreases to $4 per share, what’s the rate of return?

(b) If Miss Good decides to buy on margin, and she want to buy 500 shares. Then how much she needs to deposit to her margin account?

(c) Miss Good buys 500 shares, and the funds in her margin account just meet the initial margin requirement. The price decreases to $4. What’s the rate of return? Will she receive a margin call?

(d) If the price decreases to $3.5, will Miss Good receive a margin call? If she does receive a margin call, but she does nothing (because she is traveling to the Moon). Then how many shares should the broker sell to keep the margin above the maintenance margin?

Answer 1

Initial margin means the percent of purchase price which is required to be paid to broker for using margin account.

Maintenance margin means the minimum balance that must be maintained in margin account. If amount in margin account goes below the maintenance margin broker will ask for margin call, equal to amount which will again increase the balance in margin account to the initial margin amount.

Here in the given question, share price = $5

Initial margin = 40% i.e $5*40% = $2 per share

Maintenance margin = 30% i.e $5*30% = $1.5 per share

(a.) If she does not use margin account and wants to buy shares out of her own funds only, then she will be able to buy 400 shares($2,000/$5) i.e (Total own fund/price per share)

  => If price increases to $6,

Gain per share = Current price - Purchase price

Gain per share = $6-$5 = $1

Total gain = gain per share * number of shares

Total gain = $1*400 = $400

Rate of return = {(Inflow at end - outflow at beginning)/outflow at beginning}*100 ''or'' (Gain or loss/outflow at beginning)*100

Rate of return = ($400/$2000)*100 = 20%

=> If price decreases to $4,

Loss per share = Current price - Purchase price

Loss per share = $4-$5 = -$1

Total loss = loss per share * number of shares

Total loss = -$1*400 = -$400

Rate of return = {(Inflow at end - outflow at beginning)/outflow at beginning}*100 ''or'' (Gain or loss/outflow at beginning)*100

Rate of return = (-$400/$2000)*100 = -20%

(b.) If she decides to buy on margin and wants to buy 500 shares, then intial margin she needs to pay will be

Initial margin = Initial margin per share * number of shares

  Initial margin = $2(calculated above)*500 = $1,000

(c.)  => If price decreases to $4,

Loss per share = Current price - Purchase price

Loss per share = $4-$5 = -$1

Total loss = loss per share * number of shares

Total loss = -$1*500 = -$500

Rate of return = {(Inflow at end - outflow at beginning)/outflow at beginning}*100 ''or'' (Gain or loss/outflow at beginning)*100

Rate of return = (-$500/$1000)*100 = -50%

=> Maintenance margin = maintenance margin per share* number of shares

  Maintenance margin = $1.5(calculated above)*500 = $750

Balance in margin account if price decreases to $4,

margin balance = Initial margin at begining - loss due to change in price

  margin balance = $1000-$500 = $500

Since margin balance is less than maintenance margin, she will receive a margin call

=> Margin call = Initial margin at beginning - Current margin balance

Margin call = $1,000-$500 =$500

(d.) If price decreases to $3.5

Loss per share = Current price - Purchase price

Loss per share = $3.5-$5 = -$1.5

Total loss = loss per share * number of shares

Total loss = -$1.5*500 = -$750

=> Maintenance margin = maintenance margin per share* number of shares

  Maintenance margin = $1.5(calculated above)*500 = $750

Balance in margin account if price decreases to $3.5,

margin balance = Initial margin at begining - loss due to change in price

  margin balance = $1000-$750 = $250

Since margin balance is less than maintenance margin, she will receive a margin call

=> Margin call = Initial margin at beginning - Current margin balance

Margin call = $1,000-$250 =$750,

Now since she does nothing therefore broker will sell shares of value equal to difference between maintenance margin and current margin balance(as question has asked to maintain amount above maintenance margin)

Number of shares to be sold = Difference between maintenance margin and current margin account balance/ current share price

Number of shares to be sold = ($750-$250)/$3.5 = 142.86 (rounded off to two decimals)

Number of shares to be sold = 143 (rounded off)