Question

Maddie buys 83 shares of American Express corp at $91. She borrowed $4,380.74 from a broker with a margin loan charging 5% simple interest. The rest is paid for by Maddie. What is Maddie's rate of return after one period if the stock price falls to $82?

Answer 1

We can calculate Maddie's rate of return after one period by applying following steps:

Step 1: At present :

Total money she required to buy 83 shares of American Express corp = 83 * $91 = $7553

Out of $7553, she borrowed $ 4,380.74 from a broker at 5% simple interest. Therefore the money paid by maddie herself = $7553 - $ 4,380.74 = 3172.26 $

Maddie needs to pay interest @ 5% only on $ 4,380.74

Step 2 : After one period :

Now after one period price of American Express corp falls from $91 to $82

Therefore value of Maddie's investment after one period = 83 * $82 = $6806

Fall in value of investment (Loss) after one period = $7553 - $ 6806 = $ 747

Also Maddie needs to pay interest on capital borrowed which is calculated as follows:

$4380.74 * 5% = $ 219.037

Calculation of total loss to maddie after one period :

Fall in the value of investment + Interest paid on borrowed capital

= $747 + $ 219.037

= 966.037

Step 3 : Calculation of Rate of Return after One Period:

Rate of Return after one period = Return on investment for the period / Initial Investment

= $ -966.037 / $ 7553 ( Maddie lost $966.037 that is why it is taken in negative )

= - 0.1274

= - 12.74 %

Therefore Maddie's rate of return after one period is Negative 12.74 %

Thank You.