. Suppose the term structure of risk-free interest rates

Question 29. Suppose the term structure of risk-free interest rates is as shown below:

1 year	2 years	3 years	5 years	7 years	10 years	20 years
Rate (EAR, %)	1.99	2.41	2.74	3.32	3.76	4.13	4.93

a. Calculate the present value of an investment that pays $1000 in two years and $2000 in five years for certain.

b. Calculate the present value of receiving $500 per year, with certainty, at the end of the next five years. To find the rates for the missing years in the table, linearly interpolate between the years for which you do know the rates. (For example, the rate in year 4 would be the average of the rate in year 3 and year 5.)

c. Calculate the present value of receiving $2300 per year, with certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. (Hint: Use a spreadsheet.)

Question 31: What is the shape of the yield curve given the term structure in Problem 29? What expectations are investors likely to have about future interest rates?

Answer:

Question 2: Assume that a bond will make payments every six months as shown on the following timeline (using six-month periods):

a. What is the maturity of the bond (in years)?

b. What is the coupon rate (in percent)?

c. What is the face value?

Question 6: Suppose a 10-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading for a price of $1034.74.

a. What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)?

b. If the bond’s yield to maturity changes to 9% APR, what will the bond’s price be?

Question 7. Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield to maturity of 6%. What is the bond’s coupon rate?

Question 10. Suppose a seven-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading with a yield to maturity of 6.75%.

a. Is this bond currently trading at a discount, at par, or at a premium? Explain.

b. If the yield to maturity of the bond rises to 7% (APR with semiannual compounding), what price will the bond trade for?

Question28. The following table summarizes the yields to maturity on several one-year, zero-coupon securities:

Security	Yield (%)
Treasury	3.1
AAA corporate	3.2
BBB corporate	4.2
B corporate	4.9

a. What is the price (expressed as a percentage of the face value) of a one-year, zero-coupon corporate bond with a AAA rating?

b. What is the credit spread on AAA-rated corporate bonds?

c. What is the credit spread on B-rated corporate bonds?

d. How does the credit spread change with the bond rating? Why?

Question 30. HMK Enterprises would like to raise $10 million to invest in capital expenditures. The company plans to issue five-year bonds with a face value of $1000 and a coupon rate of 6.5% (annual payments). The following table summarizes the yield to maturity for five-year (annual-pay) coupon corporate bonds of various ratings:

Rating	AAA	AA	A	BBB	BB
YTM	6.20%	6.30%	6.50%	6.90%	7.50%

a. Assuming the bonds will be rated AA, what will the price of the bonds be?

b. How much total principal amount of these bonds must HMK issue to raise $10 million today, assuming the bonds are AA rated? (Because HMK cannot issue a fraction of a bond, assume that all fractions are rounded to the nearest whole number.)

c. What must the rating of the bonds be for them to sell at par?

d. Suppose that when the bonds are issued, the price of each bond is $959.54. What is the likely rating of the bonds? Are they junk bonds?

Question 1. The figure below shows the one-year return distribution for RCS stock.

Calculate:

a. The expected return.

b. The standard deviation of the return.

Question 30. What does the beta of a stock measure?

Question 35. Suppose the market risk premium is 5% and the risk-free interest rate is 4%. Using the data in Table 10.6, calculate the expected return of investing in

TABLE 10.6 Betas with Respect to the S&P 500 for Individual Stocks (based on monthly data for 2007–2012)

Company	Ticker	Industry	Equity Beta
General Mills	GIS	Packaged Foods	0.20
Consolidated Edison	ED	Utilities	0.28
The Hershey Company	HSY	Packaged Foods	0.28
Abbott Laboratories	ABT	Pharmaceuticals	0.31
Newmont Mining	NEM	Gold	0.32
Wal-Mart Stores	WMT	Superstores	0.35
Clorox	CLX	Household Products	0.39
Kroger	KR	Food Retail	0.42
Altria Group	MO	Tobacco	0.43
Amgen	AMGN	Biotechnology	0.44
McDonald’s			MCD
Procter & Gamble	PG	Household Products	0.47
Pepsico	PEP	Soft Drinks	0.51
Coca-Cola	KO	Soft Drinks	0.54
Johnson & Johnson	JNJ	Pharmaceuticals	0.59
PetSmart	PETM	Specialty Stores	0.75
Molson Coors Brewing	TAP	Brewers	0.78
Nike	NKE	Footwear	0.91
Microsoft	MSFT	Systems Software	1.01
Southwest Airlines	LUV	Airlines	1.09
Intel	INTC	Semiconductors	1.09
Whole Foods Market	WFM	Food Retail	1.10
Foot Locker	FL	Apparel Retail	1.11
Oracle	ORCL	Systems Software	1.12
Amazon.com	AMZN	Internet Retail	1.13
Google	GOOG	Internet Software and Services	1.14
Starbucks	SBUX	Restaurants	1.20
Walt Disney	DIS	Movies and Entertainment	1.21
Cisco Systems	CSCO	Communications Equipment	1.23
Apple	AAPL	Computer Hardware	1.26
PulteGroup	PHM	Homebuilding	1.28
Dell	DELL	Computer Hardware	1.41
salesforce.com	CRM	Application Software	1.47
Marriott International	MAR	Hotels and Resorts	1.48
eBay	EBAY	Internet Software and Services	1.48
Coach	COH	Apparel and Luxury Goods	1.60
Macy’s			M
Juniper Networks	JNPR	Communications Equipment	1.71
Williams-Sonoma	WSM	Home Furnishing Retail	1.72
Tiffany & Co.	TIF	Apparel and Luxury Goods	1.80
Caterpillar	CAT	Construction Machinery	1.85
Ethan Allen Interiors	ETH	Home Furnishings	1.95
Autodesk	ADSK	Application Software	2.14
Harley-Davidson	HOG	Motorcycle Manufacturers	2.23
Advanced Micro Devices	AMD	Semiconductors	2.24
Ford Motor	F	Automobile Manufacturers	2.38
Sotheby’s	BID	Auction Services	2.39
Wynn Resorts Ltd.	WYNN	Casinos and Gaming	2.41
United States Steel	X	Steel	2.52
Saks	SKS	Department Stores	2.57

Source: CapitalIQ

a. Starbucks’ stock.

b. Hershey’s stock.

c. Autodesk’s stock.

Question 37. Suppose the market risk premium is 6.5% and the risk-free interest rate is 5%. Calculate the cost of capital of investing in a project with a beta of 1.2.

Question 2. You own three stocks: 600 shares of Apple Computer, 10,000 shares of Cisco Systems, and 5000 shares of Colgate-Palmolive. The current share prices and expected returns of Apple, Cisco, and Colgate-Palmolive are, respectively, $500, $20, $100 and 12%, 10%, 8%.

Answer:

a. What are the portfolio weights of the three stocks in your portfolio?

b. What is the expected return of your portfolio?

c. Suppose the price of Apple stock goes up by $25, Cisco rises by $5, and Colgate-Palmolive falls by $13. What are the new portfolio weights?

d. Assuming the stocks’ expected returns remain the same, what is the expected return of the portfolio at the new prices?