Question

Suppose you buy 100 shares of stock initially selling for $50, borrowing 25% of the necessary funds from your broker; that is, t he 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

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%

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 =      ........................1

rate of return is = 

rate of return = - 29.33%

and

selling price here after 1 year is $50

put here value

rate of return is = 

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 = 

rate of return = 24%

rate of return = 24%