Question

An investor buys $16,000 worth of a stock priced at $20 per share using 60% initial margin. The broker charges 8% on the margin loan and requires a 35% maintenance margin. The stock pays a $.50-per-share dividend in 1 year, and then the stock is sold at $23 per share. What was the investor's rate of return?

1. 17.5%

2. 19.67%

3. 23.83%

D. 25.75%

Answer 1

Stock sale price= 23

Stock buying price= 20

Dividend per share= 0.5

Balance after initial margin =40%(100%-40%)

Intial margin= 60%

Broker charge=8%

Investors rate of return= stock sale price -stock buying price + dividend per share -(balance after initial margin × stock buying price × broker charge) /initial margin × stock buying price

Investors rate of return= 23-20+0.5 -( 0.4 × 20× 0.08)/ 0.6 × 20

Investors rate of return= 3.5 -0.64/12= 2.86/12

investors rate of return= 23.83%

Or

Number of share = total stock worth/ stock price per share

Number of share= 16000/20=800

Total worth of stock = number of shares × stock sale price = 800×23

Total worth of stock = 18400

Dividend received= number of shares× dividend per share

Dividend received = 800×0.5=400

Interest due =investors share buying value× balance after intial margin × brokers charge

Interest due= 16000× 40%×8%= 512

Loan payoff = investors share buying value× balance after initial margin= 16000×40%= =6400

Final Account balance= total worth of share - interest due - loan payoff + dividend received

Final Account balance= 18400- 512-6400+400= 11888

Intial margin= investors share buying value× 60% initial margin

Intial margin = 16000×60%= 9600

Investors rate of return= final Account balance / initial margin -1

Investors rate of return= 11888/9600 -1=23.83%