Jallouk Corporation has two different bonds currently outstanding. Bond M has a
ID: 2752291 • Letter: J
Question
Jallouk Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $3,000 every six months over the subsequent eight years, and finally pays $3,300 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 10 percent compounded semiannually.
What is the current price of bond M and bond N?
Jallouk Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $3,000 every six months over the subsequent eight years, and finally pays $3,300 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 10 percent compounded semiannually.
Explanation / Answer
Answer: Calculation of the current price of bond M and bond N:
semi-annual discount rate: 0.10 / 2 = 0.05 or 5%
Total "n" = 20 yrs * 2 times per year = 40 years
Bond M:
PV of par paid at maturity: 20,000 / 1.05^40 = 2,840.92
PV of the 16 $3000 pmts
use PVoa and then discount back to "today" by dividing by 1.05^12 because it doesn't START until 6 yrs from today.
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
=3000[(1 - (1 / 1.05^16)) / 0.05]
= 3000[(1-0.45811) / 0.05]
= $32513.4 <PV at t= 6...
PV at t = 0 : 32513.4/1.05^12 = 18104.68
PV of the 12 $3300 pmts
at t = 14
=3300[(1 - (1 / 1.05^12)) / 0.05]
=3300[0.44316 / 0.05]
=29248.56
discount back to today: 29248.56 / 1.05^28 = 7461.12
Add them all together: $28406.72
NOTE: If Bond M never pays the 20k at maturity, subtract the PV of this payment (just use the PVs of the payments)...e.g. 28406.72 - 2840.92 =25565.8(it's not clear from the question)
Bond N: 20,000 / 1.05^40 = 2840.92
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