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

Term | 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.)

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?

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?

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?

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?

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?
**28.**- 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?

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:

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

- a. The expected return.
- b. The standard deviation of the return.

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What does the beta of a stock measure?

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

- a. Starbucks’ stock.
- b. Hershey’s stock.
- c. Autodesk’s stock.

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.

**11-2.**

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%.

- 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?