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American Airlines is currently considering the issuance of a series of $1,000 par bonds. The coupon...

American Airlines is currently considering the issuance of a series of $1,000 par bonds. The coupon rate offered, based on current market interest rates and the Standard & Poor's based AMR bond rating, will be 10%. The current interest rate is coincidentally 10% as well. Interest on the bonds will be paid semi-annually. However, American cannot decide on the maturity of the new issue. The life of the bonds will be 10, 20, or 30 years.

A. Ignoring floatation costs, what will the bonds sell for today if American decides to issue the bonds with a maturity of 10 years? What will the price be if the bonds have a maturity of 20 years? 30 years?

B. If the bonds are issued with 10 years to maturity and the day after they are issued, the market interest rates increase to 12%, what will be the price of American Airline's bonds? What if interest rates drop to 8%?

C. If the bonds are issued with 20 years to maturity and the day after they are issued, the market interest rates increase to 12%, what will be the price of American Airline's bonds? What if interest rates drop to 8%?

D. If the bonds are issued with 30 years to maturity and the day after they are issued, the market interest rates increase to 12%, what will be the price of American Airline's bonds? What if interest rates drop to 8%?

E. Based on your answers to questions (b) through (d), what is the relationship between time to maturity and the price of the bond?

F. Based on your answer to question (a), what is the relationship between current interest rates, the coupon rate, and time to maturity?

Solutions

Expert Solution

a)
Face Value = FV $1,000.00 $1,000.00 $1,000.00
Coupon Rate = 10.00% 10.00% 10.00%
Semiannual Coupon Payment = PMT = 10%/2 x $1000 $50.00 $50.00 $50.00
YTM = Rate/2 5.00% 5.00% 5.00%
Period - Nper x 2 20 40 60
Current Price = PV(rate,period,-PMT,-FV) $1,000.00 $1,000.00 $1,000.00
b)
Face Value = FV $1,000.00 $1,000.00 $1,000.00
Coupon Rate = 10.00% 10.00% 10.00%
Semiannual Coupon Payment = PMT = 10%/2 x $1000 $50.00 $50.00 $50.00
YTM = Rate/2 6.00% 5.00% 4.00%
Period - Nper 20 20 20
Current Price = PV(rate,period,-PMT,-FV) $885.30 $1,000.00 $1,135.90
c)
b)
Face Value = FV $1,000.00 $1,000.00 $1,000.00
Coupon Rate = 10.00% 10.00% 10.00%
Semiannual Coupon Payment = PMT = 10%/2 x $1000 $50.00 $50.00 $50.00
YTM = Rate/2 6.00% 5.00% 4.00%
Period - Nper 40 40 40
Current Price = PV(rate,period,-PMT,-FV) $849.54 $1,000.00 $1,197.93
d)
b)
Face Value = FV $1,000.00 $1,000.00 $1,000.00
Coupon Rate = 10.00% 10.00% 10.00%
Semiannual Coupon Payment = PMT = 10%/2 x $1000 $50.00 $50.00 $50.00
YTM = Rate/2 6.00% 5.00% 4.00%
Period - Nper 60 60 60
Current Price = PV(rate,period,-PMT,-FV) $838.39 $1,000.00 $1,226.23
e)
A bond with a lower coupon rate will be more volatile than a bond with a higher coupon rate. Also, longer-term bonds are more volatile than bonds with a shorter time to maturity
f)
The price of bond remain constant when coupon rate is equal to YTM irrespective of change in years of maturity.

jeff jeffy answered 2 years ago
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