Question

Exodus Limousine Company has $1,000 par value bonds outstanding at 15 percent interest. The bonds will mature in 30 years. Compute the current price of the bonds if the percent yield to maturity is:
a. 4 percent

b. 8 percent

Calculate the final answer up to two decimal places. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. Assume interest is paid annually.

Answer 1

Answer:

if YTM at 4% price :  $2,902.1237

if YTM at 8% price :  $1,788.0448

The bonds are above face value asthey offer a higher coupon payment than the market yield therefore the bond holders are willing to pay above theri face value

Explanation:

the market price of the bond will be the present value of coupo payment and maturity:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 150.000

time 30

rate 0.04

$150 \times \frac{1-(1+0.04)^{-30} }{0.04} = PV$

PV $2,593.8050

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   30.00

rate  0.04

$\frac{1000}{(1 + 0.04)^{30} } = PV$  

PV   308.32

PV c $2,593.8050

PV m  $308.3187

Total $2,902.1237

No we repeat the process with the yield at 8%

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 150.000

time 30

rate 0.08

$150 \times \frac{1-(1+0.08)^{-30} }{0.08} = PV$

PV $1,688.6675

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   30.00

rate  0.08

$\frac{1000}{(1 + 0.08)^{30} } = PV$  

PV   99.38

PV c $1,688.6675

PV m  $99.3773

Total $1,788.0448