1. Callaghan Motors’ bonds have 10 years remaining to maturity. Interest is paid annually, they have a $1,000 par value, the coupon interest rate is 8%, and the yield to maturity is 9%. What is the bond’s current market price?
PV factor of sum = (1+i)^-n
PV factor of annuity = 1 - (1+i)^-n / i
= 1 - (1+9%)^-10 / 9%
= 1 - 0.4224 / 9%
= 0.5775 / 9%
= PV factor of Sum * Par Value + PV factor of annuity * coupon payment
= 0.4224 * 1,000 + 6.417 * 80
= 422.4 + 513.3
2. An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year. a. What will the value of each bond be if the going interest rate is 5%, 8%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L. b. Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?
3. Heymann Company bonds have 4 years left to maturity. Interest is paid annually, and the bonds have a $1,000 par value and a coupon rate of 9%. a. What is the yield to maturity at a current market price of (1) $829 and (2) $1,104? b. Would you pay $829 for each bond if you thought that a “fair” market interest rate for such bonds was 12%—that is, if rd ¼ 12%? Explain your answer. VB =
M = $1,000. PMT = 0.09($1,000) = $90.
VB = $829: Input N = 4, PV = -829, PMT = 90, FV = 1000, YTM = I/YR = ? I/YR = 14.99%.
VB = $1,104: Change PV = -1104, YTM = I/YR = ? I/YR = 6.00%.
Yes. At a price of $829, the yield to maturity, 15%, is greater than your required rate of return of 12%. If your required rate of return were 12%, you should be willing to buy the bond at any price below $908.88.
4. Robert Black and Carol Alvarez are vice presidents of Western Money Management and...
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