THE VALUATION AND CHARACTERISTICS OF BONDS

PROBLEMS

Assume all bonds pay interest semiannually.

Finding the Price of a Bond – Example 7.1 (page 306)

1. The Altoona Company issued a 25-year bond 5 years ago with a face value of $1,000. The bond pays interest semiannually at a 10% annual rate. a. What is the bond's price today if the interest rate on comparable new issues is 12%? b. What is the price today if the interest rate is 8%? c. Explain the results of parts a and b in terms of opportunities available to investors. d. What is the price today if the interest rate is 10%? e. Comment on the answer to part d.

SOLUTION: PB = PMT [PVFAk,n] + FV [PVFk,n] a. n = 20 ( 2 = 40

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7. Longly Trucking is issuing a 20-year bond with a $2,000 face value tomorrow. The issue is to pay an 8% coupon rate, because that was the interest rate while it was being planned. However rates have increased suddenly and are expected to be 9% when the bond is marketed. What will Longly receive for each bond tomorrow?

SOLUTION: PB = PMT [PVFAk,n] + FV [PVFk,n]

PB = $80 [PVFA4.5,40] + $2,000 [PVF4.5,40] = $80 (18.4016) + $2,000 (.1719) = $1,815.93

8. Daubert, Inc. planned to issue and sell at par 10-year, $1,000 face value bonds totaling $400 million next month. The bonds have been printed with a 6% coupon rate. Since that printing, however, Moody’s downgraded Daubert’s bond rating from Aaa to Aa. This means the bonds will have to be offered to yield buyers 7%. How much less than it expected will Daubert collect when the bonds are issued. Ignore administrative costs and commissions.

SOLUTION: The bonds will sell for PB = PMT[PVFAk,n] + FV[PVFk,n] k = 3.5 n = 20 PB = $30[14.2124] + $1,000[.5026] = $928.97

Daubert planned to sell $400,000,000 / $1,000 = 400,000 bonds. Hence selling the same number will bring 400,000 x $928.97 = $371,588,000 which is $28,412,000 less than the $400 million originally expected.

Calculator Solution: n =