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  SCHOOL OF MATHEMATICAL SCIENCES                            Question 1   A common stock pays annual dividends at the end of each year

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SCHOOL OF MATHEMATICAL SCIENCES                     

 

 

 

Question 1

 

A common stock pays annual dividends at the end of each year. The earnings per share for the most recent year were RM8 and are assumed to grow at a rate of 8% per year, forever. The dividend will be 0% of earnings for each of the next 10 years, and 50% of earnings thereafter. What is the theoretical price of the stock to yield 10%?

Question 2

 

A common stock is currently earning RM6 per share and will pay RM3 per share in dividends at the end of the current year. Assume that the earnings of the corporation increase at the rate of 4% for the first five years, 2% for the second five years and 0% thereafter. Assume that the corporation plans to continue to pay 50% of its earnings as dividends, find the theoretical price to earn an investor an annual effective yield rate of 10%.

Question 3

 

A common stock is currently earning RM8 per share and will pay RM4 per share in dividends at the end of the current year. Assume that the earnings of the corporation increase at the rate of 6% for the first ten years, 3% for the second ten years and 0% thereafter. Assume that the corporation plans to continue to pay 50% of its earnings as dividends, find the theoretical price to earn an investor an annual effective yield rate of 12%.

Question 4

 

A common stock is currently earning RM4 per share and will pay RM2 per share in dividends at the end of the current year. Assume that the earnings of the corporation increase 5% per year indefinitely and that the corporation plans to continue to pay 50% of its earnings as dividends, find the theoretical price to earn an investor an annual effective yield rate of (a) 10%, (b) 8%, and (c) 6% 

Question 5

 

The dividends of a common stock are expected to be 1 at the end of each of the next 5 years and 2 for each of the following 5 years. The dividends are expected to grow at a fixed rate of 2% per year thereafter. Assume an annual effective rate of interest of 6%. Calculate the price of this stock using the dividend discount model.

Question 6

 

MBF stock has a bid price of RM12.65 and an ask price of RM13.00. Assume there is a 0.1% brokerage commission on the bid or ask price.

 

1. What amount will you pay to buy 50 shares?
2. What amount will you receive for selling 50 shares?
3. Suppose you buy 50 shares, then immediately sell them with the bid and ask price being the same as above. What is your round-trip transaction cost?

   Question 7

   Shaun wants to purchase 100 stocks of XYZ. The current price of a stock is RM100. He has RM4,000 on hand, so he decides to borrow RM6,000. The maintenance margin is set to be 30%.

    

4. What is Shaun’s liability and equity?
5. Suppose the stock falls to RM90. What is the actual margin? Would a margin call be in order?
6. How far can the stock price fall before a margin call?

   Question 8

   John wants to purchase 100 stocks of XYZ. The current price of a stock is RM100. He has RM4,000 on hand, so he decides to borrow RM6,000. The broker charges an annual effective rate of interest of 10%. Suppose the stock goes up by 20% in one-year period.

    

   (a) What is the end-year-value of the shares? (b) Find the total of loan repayment and interest. (c) What is the rate of return? (d) What is the rate of return if not buying on margin?