## FIN 435 – Problem set (Mid 1)

**Chapter 2**

1. You are given the following information regarding prices for stocks of the following firms:

Price

Stock

Number of shares

T

T+1

Beximco

1,000,000

60

80

BATBC

10,000,000

20

35

Bank Asia

30,000,000

18

25

a. Construct a *price-weighted* index for these three stocks, and compute the percentage change in the series for the period from *T *to *T *+ 1. Assume a starting index value of 10,000 points.

b. Construct a *value-weighted* index for these three stocks, and compute the percentage change in the series for the period from *T *to *T *+ 1. Assume a starting index value of 10,000 points.

c. Briefly discuss the difference in the results for the two stock indexes.

2. Based on the following stock price and shares outstanding information, compute the beginning and ending values for a price-weighted index and a market-value-weighted index. Assume that the value-weighted index had a base value of 100 points.

December 31, 2016

December 31, 2017

Stock

Price

Shares outstanding

Price

Shares outstanding

Beximco

20

100,000,000

32

100,000,000

BATBC

80

2,000,000

45

4,000,000

Bank Asia

40

25,000,000

42

25,000,000

a. Compute the percentage change in the value of each index.

b. Explain the difference in results between the two indexes.

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**Use the following table for questions 3 to 12.**

Jan. 13, 2017

**Stock** **Price** **X** **Y** **Z**

20 40 30

**# Shares**

**X** **Y** **Z**

1000 2000 1000*

Jan. 14, 2017

25

42

18

1000

2000

2000

Jan. 15, 2017

27

45

8

1000**

2000

2000

Jan. 16, 2017

20

40

10

3000

2000

2000

*2:1 Split on Stock Z after Close on Jan. 13, 2017

**3:1 Split on Stock X after Close on Jan. 15, 2017

The base date for index calculations is January 13, 2017

3. Calculate a price weighted average for January 13th. A. 32 B. 30

C. 36.13 D. 34

4. What is the divisor at the beginning of January 14th? A. 3.0 B. 2.5

C. 2.2734 D. 1.9375

5. Calculate a price weighted average for January 14th. A. 32 B. 30

C. 36.13 D. 34

6. Calculate a price weighed average for January 15th.

A. 30 B. 36.13

C. 32 D. 34

7. What is the divisor at the beginning of January 16th? A. 1.9375 B. 3.0

C. 2.5 D. 2.2734

8. Calculate a price weighted average for January 16th. A. 30 B. 32

C. 34 D. 36.13

9. Calculate a value weighted index for Jan. 13th if the initial index value is 100. A. 111.54 B. 100

C. 102.31 D. 123.07

10. Calculate a value weighted index for Jan. 14th if the initial index value is 100. A. 100 B. 102.31

C. 123.07 D. 111.54

11. Calculate a value weighted index for January 15th if the initial index value is 100. A. 102.31 B. 100

C. 123.07 D. 111.54

12. Calculate a value weighted index for January 16th if the initial index value is 100. A. 123.07 B. 100.00

C. 102.31 D. 111.54

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## Chapter 3

1. Assume you purchased 200 shares of ENVOYTEX common stock on margin at BDT 70 per share from your broker. If the initial margin is 55%, how much did you borrow from the broker?

2. You want to purchase OLYMPIC stock at BDT 40 from your broker using as little of your own money as possible. If initial margin is 50% and you have BDT 4000 to invest, how many shares can you buy?

3. Assume you sell short 100 shares of common stock at BDT 45 per share, with initial margin at 50%. The stock paid no dividends during the period, and you did not remove any money from the account before making the offsetting transaction. What would be your rate of return if you covered the short sale at BDT 40/share?

4. You purchased 100 shares of GLAXOSMITH common stock on margin at BDT 70 per share. Assume the initial margin is 50% and the maintenance margin is 30%. Assume the stock pays no dividend; ignore interest on margin. Below what stock price level would you get a margin call?

5. You sold short 100 shares of common stock at BDT 45 per share. The initial margin is 50%. At what stock price would you receive a margin call if the maintenance margin is 35%?

6. Mofiz opens a brokerage account and purchases 300 shares of Hafiz Corporation at BDT 40 per share. He borrows BDT 4,000 from his broker to help pay for the purchase. The interest rate on the loan is 8%.

a. If the share price falls to BDT 30 per share by the end of the year, what is the remaining margin in his account? If the maintenance margin requirement is 30%, will he receive a margin call?

b. What is the rate of return on his investment?

7. You are bullish on ABC stock. The current market price is BDT 50 per share, and you have BDT 5,000 of your own to invest. You borrow an additional BDT 5,000 from your broker at an interest rate of 8% per year and invest BDT 10,000 in the stock.

a. What will be your rate of return if the price of ABC stock goes up by 10% during the next year? The stock currently pays no dividends.

b. How far does the price of ABC stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately.

8. Sabrina has a margin account with a balance of BDT 150,000. If the initial margin deposit is 60 percent and Apex Industries is currently selling at BDT 50 per share.

a. How many shares of Apex can Sabrina purchase?

b. What is Sabrina’s profit/loss if Apex’s price after one year is BDT 40?

c. If the maintenance margin is 25 percent, to what price can Apex Industries fall before Sabrina receives a margin call?

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9. Hiya has a margin account with a balance of BDT 50,000. If the initial margin deposit is 50 percent, and Reliance Industries is currently selling at BDT 50 per share.

a. How many shares of Reliance can Hiya buy?

b. What is Hiya’s profit if Reliance’s price rises to BDT 80?

c. If the maintenance margin is 25 percent, to what price can Reliance Industries stock price fall before Hiya receives a margin call?

10. Sarah has a margin account with a balance of BDT 60,000. If initial margin requirements are 80 percent, and BD Lamps is currently selling at BDT 40 per share.

a. How many shares of BD Lamps can Sarah buy?

b. What is Sarah’s profit if BD Lamp’s price rises to BDT 50?

c. If the maintenance margin is 25 percent, to what price can BD Lamps fall before Sarah receives a margin call?

11. You decide to sell 100 shares of Beximco Industries short when it is selling at its yearly high of BDT 35. Your broker tells you that your margin requirement is 55 percent and that the commission on the sale is BDT 15. While you are short, Beximco pays a BDT 0.75 per share dividend. At the end of one year you buy your Beximco shares (cover your short sale) at BDT 30 and are charged a commission of BDT 15 and a 6 percent interest rate.

a. What is your dollar return on the investment?

b. What is your rate of return on the investment?

12. You decide to sell 100 shares of Tareq Enterprises Inc. short when it is selling at its yearly high of BDT 42.25. Your broker tells you that your margin requirement is 60 percent and that the commission on the sale is BDT 20. While you are short, Tareq pays a BDT 0.85 per share dividend. At the end of one year you buy your Tareq shares (cover your short sale) at BDT 44 and are charged a commission of BDT 20 and a 5 percent interest rate.

a. What is your dollar return on the investment?

b. What is your rate of return on the investment?

13. Suppose you buy a round lot of DS Solutions stock on 60% margin when it is selling at BDT 55 a share. The broker charges a 10 percent annual interest rate and commissions are 3 percent of the total stock value on both the purchase and the sale. If at year end you receive a BDT 1.10 per share dividend and sell the stock for 55 5/8, what is your rate of return on the investment?

14. Suppose you buy a round lot of GD Inc. stock on 55% margin when it is selling at BDT 40 a share. The broker charges a 10 percent annual interest rate and commissions are 4 percent of the total stock value on both the purchase and the sale. If at year end you receive a BDT 0.90 per share dividend and sell the stock for 35 5/8, what is your rate of return on the investment?

15. Suppose you buy a round lot of Altaf Industries stock on 50% margin when it is selling at BDT 35 a share. The broker charges a 10 percent annual interest rate and commissions are 5 percent of the total stock value on both the purchase and the sale. If at year end you receive a BDT 1.00 per share dividend and sell the stock for BDT 42.63, what is your rate of return on the investment?

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16. You decide to sell short 200 shares of Prime Bank stock at a price of BDT 75. Your margin deposit is 65 percent. Commission on the sale is 1.25%. While you are short, the stock pays a BDT 1.75 per share dividend. Interest on margin debt is 5.25% per year.

a. At the end of one year you close out your short position by purchasing share of Prime Bank at BDT 45 per share. The commission is 1.25%. What is your rate of return on the investment?

b. Suppose at the end of one year Prime Bank is selling at BDT 90 per share and you cover your short position at this price. What is your rate of return on the investment? (Assume a 1.25% commission on the purchase)

17. Shares of Square stock are selling for BDT 45 per share. Brokerage commissions are 2% for purchases and 2% for sales. The interest rate on margin debt is 6.25% per year. The maintenance margin is 30%.

a. At the end of one year shares of Square stock are selling for BDT 55 per share and the company paid dividends of BDT 0.85 per share. Assuming that you paid the full cost of the purchase, what is your rate of return if you sell Square stock?

b. At the end of one year shares of Square stock are selling for BDT 35 per share and the company paid dividends of BDT 0.85 per share. Assuming that you paid the full cost of the purchase, what is your rate of return if you sell Square stock?

c. At the end of one year shares of Square stock are selling for BDT 55 per share and the company paid dividends of BDT 0.85 per share. Assuming that you borrowed 25% of cost of the purchase, what is your rate of return?

d. At the end of one year shares of Square stock are selling for BDT 35 per share and the company paid dividends of BDT 0.85 per share. Assuming that you borrowed 25% of cost of the purchase, what is your rate of return?

e. Assume that you purchase 150 shares of Square stock at BDT 45 each by making a margin deposit of 55%. At what price would you receive a margin call?

18. The stock of the Prime Bank is selling for BDT 28 a share. You put in a limit buy order at BDT 24 for one month. During the month, the stock price declines to BDT 20, then jumps to BDT 36. Ignoring commissions, what would have been your rate of return on this investment? What would be your rate of return if you had put in a market order? What if your limit order was at BDT 18?

19. You decide to sell short 100 shares of Square Pharma when it is selling at its yearly high of 56. Your broker tells you that your margin requirement is 45 percent and that the commission on the purchase is BDT 155. While you are short the stock, Charlotte pays a BDT 2.50 per share dividend. At the end of one year, you buy 100 shares of Square Pharma at 45 to close out your position and are charged a commission of BDT 145 and 8 percent interest on the money borrowed. What is your rate of return on the investment?

20. Suppose you buy a round lot of Zodiac Industries stock on 55 percent margin when the stock is selling at BDT 20 a share. The broker charges a 10 percent annual interest rate, and commissions are 3 percent of the total stock value on both the purchase and sale. A year later, you receive a BDT 0.50 per share dividend and sell the stock for 27. What is your rate of return on the investment?

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## Chapter 5

1. You purchased a share of stock for BDT 20. One year later you received BDT 1 as a dividend and sold the share for BDT 29. What was your holding-period return?

2. You have been given this probability distribution for the holding-period return for ABC stock.

State of the economy

Probability

HPR

Boom

0.30

18%

Normal growth

0.50

12%

Recession

0.20

-5%

a) What is the expected holding-period return for ABC stock?

b) What is the expected standard deviation for ABC stock?

c) What is the expected variance for ABC stock?

3. If a portfolio had a return of 12%, the risk free asset return was 4%, and the standard deviation of the portfolio’s excess returns was 25%, what would be the risk premium?

4. You purchase a share of ACI stock for BDT 90. One year later, after receiving a dividend of BDT 3, you sell the stock for BDT 92. What was your holding-period return?

5. If a portfolio had a return of 15%, the risk free asset return was 5%, and the standard deviation of the portfolio’s excess returns was 30%, what would be the Sharpe ratio?

6. You purchased a share of stock for BDT 30. One year later you received BDT 1.50 as a dividend and sold the share for BDT 32.25. What was your holding-period return?

7. BATBC stock has the following probability distribution of expected prices one year from now:

State of the economy

Probability

Price

1

25%

BDT 50

2

40%

BDT 60

3

35%

BDT 70

If you buy BATBC today for BDT 55 and it will pay a dividend during the year of BDT 4 per share, what is your expected holding-period return on BATBC?