Question

Suppose you buy 100 shares of stock initially selling for $50, borrowing 25% of the necessary funds from your broker; that is, the initial margin on your purchase is 25%. You pay an interest rate of 8% on margin loans. a. How much of your own money do you invest? How much do you borrow from your broker? b. What will be your rate of return for the following stock prices at the end of a one-year holding period? (i) $40, (ii) $50, (iii) $60.

Answer 1

When purchasing the stock, you are investing $3,750 of your own money and borrowing $1,250 from your broker. The rate of return at the end of a one-year holding period for stock prices of $40, $50, and $60 would be 6.67%, 33.33%, and 60% respectively.

Step-by-step explanation:

In this scenario, you are purchasing 100 shares of stock at an initial price of $50 per share. The initial margin is 25%, which means you are borrowing 25% of the necessary funds from your broker. To calculate how much of your own money you invest, you need to determine the total value of the stock and the borrowed amount.

The total value of the stock is calculated by multiplying the number of shares (100) by the initial price per share ($50), which results in $5,000. To find out how much you borrow from your broker, you can multiply the total value of the stock by the initial margin (25%), which gives you $1,250. This means that you are investing $3,750 of your own money ($5,000 - $1,250) and borrowing $1,250 from your broker.

For part b, to calculate the rate of return at the end of a one-year holding period, you need to determine the profit or loss from each stock price.

If the stock price at the end of one year is $40, the total value of your stock would be $4,000 (100 shares x $40). Since you initially invested $3,750, your rate of return would be the profit divided by the initial investment, which is ($4,000 - $3,750) / $3,750 = 6.67%.

If the stock price remains the same at $50, the total value of your stock would still be $5,000. With the initial investment of $3,750, the rate of return would be ($5,000 - $3,750) / $3,750 = 33.33%.

If the stock price increases to $60, the total value of your stock would be $6,000. This results in a rate of return of ($6,000 - $3,750) / $3,750 = 60%.

Answer 2

money invest is $3750

amount of loan owned to broker = $1350

when selling price is $40 rate of return = - 29.33%

when selling price is $50 rate of return = - 2.67%

when selling price is $60 rate of return = 24%

Step-by-step explanation:

given data

No of share = 100

initial selling = $50

borrow = 25%

initial margin purchase = 25%

interest rate = 8%

to find out

How much money invest and How much borrow from broker and rate of return at end of 1 year at (i) $40, (ii) $50, (iii) $60

solution

we know total investment is here

total investment = No of share × initial selling per share

total investment = 100 × 50

total investment = $5000

so

borrow fund is = 0.25 × 5000 = $1250

and Equity invest = total investment - borrow fund

equity invest = 5000 - 1250 = $3750

and

amount of loan own to broker at the end of year is

amount of loan = borrow fund × ( 1 + rate )

amount of loan = 1250 ( 1 + 0.08)

amount of loan owned to broker = $1350

and

selling price here after 1 year is $40

so rate of return is =
`((no of share * selling price) -loan amount - equity invested)/(equity invested)` ........................1

rate of return is =
`((100 * 40) - 1350 - 3750)/(3750)`

rate of return = - 29.33%

and

selling price here after 1 year is $50

put here value

rate of return is =
`((100 * 50) - 1350 - 3750)/(3750)`

rate of return = - 2.67%

and

selling price here after 1 year is $60 so from equation 1

put the value

rate of return is =
`((100 * 60) - 1350 - 3750)/(3750)`

rate of return = 24%