# Fin 571- Week Two Problems

CHAPTER 5

A1. (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this bond?

“The value of a bond, its fair price, is the present value of its promised future payments for coupon and principal.” So we are solving for PV

FV= $1,000

N= 10

I= 9%

Pmt = 7.4% of $1,000 = $74

|Future Value |$1,000|

|Years |10 |

|Rate |9% |

|PMT |$74|

|Present Value |($897.32)| INCORRECT Correct answer PV = -$895.94

A10. (Dividend discount model) Assume RHM is expected to pay a total cash dividend of $5.60 next year and its dividends are expected to grow at a rate of 6% per year forever. Assuming annual dividend payments, what is the current market value of a share of RHM stock if the required return on RHM common stock is 10%?

Fair price = starting dividend/ (required return - growth rate)

Fair price = $5.60/(10%-6%) = $5.60/4% = $5.60/0.04 = $140

A12. (Required return for a preferred stock) James River $3.38 preferred is selling for $45.25. The preferred dividend is non-growing. What is the required return on James River preferred stock?

Value of stock = dividend / return rate

Value of stock * return rate = dividend

Return rate = dividend / value of stock = $3.38/$45.25= 0.075 = 7.5%

B16. (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock Exchange. Suppose PhilEl’s bonds have identical coupon rates of 9.125% but that one issue matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment was made yesterday.

a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?

|Future Value |$1,000 |$1,000 |$1,000 |

|Years |1 |7 |15 |

|Rate |8% |8% |8% |

|PMT |$91.25 |$91.25 |$91.25 |

|Present Value |($1,010.42) |($1,058.57) |($1,096.29) |

b. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%.

What is the fair price of each bond now?

|Future Value |$1,000 |$1,000 |$1,000 |

|Years |1 |7 |15 |

|Rate |7% |7% |7% |

|PMT |$91.25 |$91.25 |$91.25 |

|Present Value |($1,019.86) |($1,114.52) |($1,193.54) |

c. Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price of each bond?

|Future Value |$1,000 |$1,000 |$1,000 |

|Years |1 |7 |15 |

|Rate |9% |9% |9% |

|PMT |$91.25 |$91.25 |$91.25 |

|Present Value |($1,001.15) |($1,006.29) |($1,010.08) |

d. Based on the fair prices at the various yields to maturity, is interest-rate risk the same, higher, or lower for longer- versus shorter-maturity bonds?

Interest rate risk is higher for longer term bonds, simply because the risk exposure is longer.

B20. (Constant growth model) Medtrans is a profitable firm that is not paying a dividend on its common stock. James...

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