Chapter 1 – Introduction

1. Use the tax table to calculate:
1. The tax bill for an individual who earns $125,000.00.
2. What is the individual’s marginal tax rate?
3. What is the individual’s average tax rate?
4. If the individual receives an additional $1,000 of interest income, what is the additional tax on this investment income?
5. If the individual sells shares of stock that result is $3,000 of capital gains, what is the additional tax on this income? 
6. If the individual receives $500 of dividend income, what is the additional tax on this income?

Chapter 2 – Overview of Securities

1. Calculate the prices of the following T-bonds:
1. $10,000 face value, 8% coupon, quote = 97:25
2. $1,000 face value, 6 % coupon, quote = 101:07
3. $5,000 face value, 12% coupon, quote = 103:20 
2. Identify the cash flows of the following bonds:
1. $1,000 face value, 4 year maturity, 10% coupon
2. $10,000 face value, 2 year maturity, 6% coupon
3. $1,000 face value, 6-year maturity, 8% annual coupon
4. $6,000 face value, 10-year maturity, 4% quarterly coupon 
3. Suppose a municipal bond has a yield of 6.5% and a corporate bond has a yield of 9%.
1. If your marginal tax rate is 20%, what is the equivalent tax-exempt yield of the corporate bond?  Which bond would you prefer if all other features were similar (e.g., default risk)?
2. If your marginal tax rate is 45%, what is the equivalent tax-exempt yield of the corporate bond?  Which bond would you prefer if all other features were similar (e.g., default risk)?

Chapter 4 – Individual security risk and return

1. An investor buys a stock for $47 and gets an annual cash dividend of $2.25. Will he experience a capital gain or a capital loss if he sells the stock for $51.75 one year later? What is the investor’s dollar and percentage return?
2. Another investor purchases a stock for $29.80 and gets an annual cash dividend of $1.60. This investor sells the stock three years later for $26.40 Will he experience a capital gain or a capital loss? What is this investor’s dollar and percentage return?
3. Suppose you buy 400 shares of stock at the beginning of the year for $23/share and sell it in 6 months for $26/share. While you held the stock you received quarterly dividends of $0.25/share.
1. Calculate your income and capital gains over the six months you held the stock. What is your total (dollar) return?
2. Calculate your holding period return.
3. What is your dividend yield and your capital gains yield over the six month period?
4. Annualized your HPR using APR and EAR.
4. Find the EAR for the following periodic returns.
1. HPR =1% over 1 month.
2. HPR=2.5% over 3 months.
3. HPR=3% over 6 months.
4. HPR=0.04% over one day.
5. Imagine you buy a bond for $17,000, which pays $200 interest every 3 months. What are the total income, the amount of capital gain/loss, and the total dollar return you experience if you sell the bond for $15,500 nine months later? What is the HPR?
6. For the following problems, determine (1) the current income, (2) the capital gain or loss, and (3) the total return in both dollars and as a percentage of the initial investment.
1. An investor purchased a stock for $75 one year ago and received four dividend payments totaling $3.80. Today, the investor sells the share for $90.
2. An investor sells his stock for $121. He bought the stock 18 months ago for $137 and received dividend payments of $8.10 every 6 months.
3. An investor purchased a bond for $9,100 15 months ago. The bond paid $90 interest every 3 months and is now sold for $8,700.
7. Bob is interested in a stock that is currently trading at $32 per share and that pays monthly dividends of $0.80 per share. His expectation is to sell the stock in four months for $35. Steve is interested in a different stock that is trading at $34 per share and that pays quarterly dividends of $0.95 per share. He expects to sell the stock in six months for $38. Which stock is more lucrative in terms of the annualized holding period return?
8. You are buying a stock for $81 per share and are expecting to sell it in one year for $89. The Stock pays $1.27 per share in quarterly dividends. At the same time, your friend purchases a share of stock for $69. This stock is paying quarterly dividends of $1.09 per share and your friend is expecting to sell it in 3 months for $71. Will you or your friend have a better annualized holding period return?
9. Imagine that an investment of $3,500 today is likely to return $6,000 in 8 years. Calculate the IRR on this investment. Decide whether it is worth doing this investment if a minimum rate of return of 6% is required. What is your decision if the required minimum rate of return is 8%?
10. Another investment of $7,500 promises a return of $9,600 in 5 years. Estimate the IRR on this investment. Can you recommend this investment if a minimum rate of return of 6% is required? What if the required minimum rate of return is 7%?
11. Imagine you purchased 250 shares of the investment described in the table at the beginning of 2000.
1. Calculate the yearly total return in dollars.
2. What is the aggregate (7-year) return in dollars and as a percentage of the initial investment if you sell the shares at the end of 2006?
3. Calculate the IRR if income is received at the end of the year.
   

Year	Income	Market Value Beginning	Market Value Ending
2000	$2.00	$45.00	$48.00
2001	2.15	48.00	51.50
2002	2.30	51.50	58.00
2003	2.50	58.00	55.50
2004	2.75	55.50	54.00
2005	2.95	54.00	60.00
2006	3.20	60.00	65.00



12.  Assume an investor purchases shares of stock for $4.500 today and will sell them for $5,300 in 5 years. During those 5 years he receives $38, $40, $43, $39, and $41 in dividends. Calculate the internal rate of return on this investment.
13. You invest $11,000 in a stock that pays $98, $105, $102, and $105 in dividends over the next 4 years. After the 4 years, you decide to sell the stock for $ $12,300. Determine the internal rate of return on your investment.
14. Determine the IRR for the investments described in the following situations.
    

Situation	Initial investment	Future value	End of year
1	$3,000	$7,000	8
2	900	4,000	25
3	6,000	6,500	4



15. The returns for two different investments are shown in the following table.
1. Calculate the arithmetic and geometric average returns for each investment.
2. Which of the two investments seems to be more risky? Explain why.
3. What are the standard deviation of returns of each investment?
   

Year	Return on A	Return on B
2002	5%	10%
2003	16	14
2004	11	8
2005	1	13
2006	9	9
2007	24	12

16. The table below shows the returns for three alternative investments.
1. Calculate the arithmetic and geometric average returns for each investment.
   
2. What is the (average) risk premium of each investment?
   
3. Determine which of the three investments seems to be most risky. Which appears to be the safest investment? 
4. What are the standard deviations of returns of each investment?
   

Year	Return on A	Return on B	Return on C
2003	8	16	24
2004	8	5	16
2005	8	9	10
2006	8	14	3
2007	8	1	7

17. Consider the three stocks in the following table. P(t) Represents the price of each stock on day t and Q(t) represents the number of shares outstanding. Stock C splits two for one in the last period.
1. Calculate the rate of return on a price weighted index of the three stocks for the first period (day 0 to day 1). Assume the original divisor is 3.0.
2. Calculate the new divisor on day 2.
3. Calculate the rate of return of the price-weighted index for the second period (day 1 to day 2).
   

Stock	P(0)	Q(0)	P(1)	Q(1)	P(2)	Q(2)
A	90	100	95	100	96	100
B	50	200	45	200	45	200
C	100	200	110	200	59	400

18. Use the data from the previous problem to calculate the rate of return in the first period for a market value weighted index.
19. Use the following data to answer the questions below. 
1. Assume the day 0 value of the index is 100. Find the day 1 value of a market value weighted index and find the rate of return on the index. 
2. Assume the day 0 value of the index is 161.56. Find the day 1 value of a market value weighted index and find the rate of return on the index.
   

Stock	P(0)	Q(0)	P(1)	Q(1)
X	50	300	52	300
Y	65	100	67	100
Z	90	200	44	400

20. Use the following data to answer the following questions.
1. If the divisor for the price-weighted index is 0.9, what is the index value?
2. Suppose the market value of these three stocks was $10 million when a market value weighted index was created. When the index was created the base value of the index was 100. What is the current value of a market value weighted index?
   

Stock	P(0)	Q(0)
M	24	300,000
N	49	125,000
O	17	550,000



21. An investor purchases 150 shares of a certain stock at the following prices and margins. Calculate the loan for each transaction as well as the equity necessary to make these margin transactions.

Transaction	Price/Share	Margin	Loan	Equity
a	45	60%
b	128	45%
c	22	73%
d	10	66%
e	84	57%
f	38	62%



22. Use the information from the previous question. Ignore any interest paid on loans.
1. What is the investor’s new margin position if the stock price increases by $10 per share?
2. What is the margin position if the share price decreases by $10?
23. Bob purchased 150 shares of stock for $120 per share. The initial margin was 70% and the maintenance margin was 40%. At what price will Bob face a margin call?
24. Kelly decides to buy 100 shares of a stock at a price of $62/share, using an initial margin of 60% and the maintenance margin being 30%. How far does the stock have to drop before Kelly faces a margin call?
25. McDonald’s stock is currently selling at $48 per share. An investor purchases 100 shares of this stock using a margin of 70%. The annual dividends are $2 per share and the investor can obtain a margin loan at an annual interest cost of 6%. What is the return on invested capital that the investor can get if the stock price increases to $55 in 12 months?
26. Steve bought 200 shares of UFO stock 12 months ago. The share price was $38 per share and the initial margin requirement used was 60%. Today, Steve decides to sell the shares. During the last 12 months, the stock paid $2 per share in cash dividends and the annual interest on the margin loan charged was 7%. There was a minimum maintenance margin of 35%.
1. What is the initial value of the transaction? Determine the loan amount and the equity position on Steve’s transaction.
2. Imagine the share price is i) $50, ii) $28, iii) $16, and iv) $45. What is the actual margin percentage for each situation? When would Steve be subject to a margin call?
3. Imagine that after the 12-month holding period the sales prices are the following: i) $30, ii) $35, iii) $40, iv) $45, and v) $50. What is the rate of return for each situation?
27. An investor has borrowed 300 shares of a stock from a broker. He decides to short sell them for $25 a share with the initial margin being 60%.
1. Calculate the amount of money that will be in the investor’s account after the transaction.
2. What is the margin if the stock falls to 22/share?
3. What is the holding period return if the stock falls to $22 per share?
4. If the maintenance margin is 35%, when will the investor receive a margin call? 
28. An investor has borrowed 150 shares of stock from a broker. He decides to short sell them for $30 per share with an initial margin of 40% and the maintenance margin being 20%. Calculate the margin and indicate if there will be a margin call for each of the following situations.
1. The stock price falls to $18 per share.
2. The stock price falls to $25 per share.
3. The stock price rises to $37 per share.
4. The stock price rises to $42 per share. 
29. Jimmy makes a cash purchase of 100 shares of a stock for $40 per share.  Louie buys the same stock but uses 50% margin and the loan has an 8% interest rate.  Each investor holds the stock for a year, receiving a $2 dividend.  Suppose they close their positions at the end of the year and all trades are charged a commission of $20.
1. What is the return for each investor if the stock price is $50 per share at the end of the year?
2. What is the return for each investor if the stock price is $30 per share at the end of the year?