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.Â Calculate the present value of an investment that pays $1000 in two years and $2000 in five years for certain.
b.Â 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.Â 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:Â Assume that a bond will make payments every six months as shown on the following timeline (using six-month periods):
a.Â What is the maturity of the bond (in years)?
b.Â What is the coupon rate (in percent)?
c.Â What is the face value?
Question 6:Â Suppose a 10-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading for a price of $1034.74.
a.Â What is the bondâ€™s yield to maturity (expressed as an APR with semiannual compounding)?
b.Â If the bondâ€™s yield to maturity changes to 9% APR, what will the bondâ€™s price be?
Question 7.Â Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield to maturity of 6%. What is the bondâ€™s coupon rate?
Question 10.Â 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.Â Is this bond currently trading at a discount, at par, or at a premium? Explain.
b.Â If the yield to maturity of the bond rises to 7% (APR with semiannual compounding), what price will the bond trade for?
Question28.Â 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.Â 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.Â What is the credit spread on AAA-rated corporate bonds?
c.Â What is the credit spread on B-rated corporate bonds?
d.Â 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.Â Assuming the bonds will be rated AA, what will the price of the bonds be?
b.Â 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.Â What must the rating of the bonds be for them to sell at par?
d.Â 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.Â The expected return.
b.Â The standard deviation of the return.
Question 30.Â What does the beta of a stock measure?
Question 35.Â 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 2007â€“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 |
McDonaldâ€™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 |
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 |
Macyâ€™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 |
Sothebyâ€™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:Â CapitalIQ
a.Â Starbucksâ€™ stock.
b.Â Hersheyâ€™s stock.
c.Â Autodeskâ€™s stock.
Question 37.Â 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.Â 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.Â What are the portfolio weights of the three stocks in your portfolio?
b.Â What is the expected return of your portfolio?
c.Â 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.Â Assuming the stocksâ€™ expected returns remain the same, what is the expected return of the portfolio at the new prices?