Jallouk Corporation has two different bonds currently outstanding. Bond M has a
ID: 2775741 • Letter: J
Question
Jallouk Corporation has two different bonds currently outstanding. Bond M has a face value of $50,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2,600 every six months over the subsequent eight years, and finally pays $2,900 every six months over the last six years. Bond N also has a face value of $50,000 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?
Explanation / Answer
Price of N= 50,000 discounted at 10%/2=5% over 2*20=40 semiannual periods.
Price of N= 50,000/(1.05)40 = 7102.28
Price of Bond M= Present Value of $2,600 every six months over the subsequent eight years(7-14)+Present Value of $2,900 every six months over the subsequent six years(15-20)
Discount rate is .1/2=.05 per six months, total periods is double the no of years
Present Value of $2,600 every six months over the subsequent eight years(7-14) at (t=6yrs)
=(2c/y)(1-1/(1+y/2)2T), here y=.1,FV=0,T=8, c=2600
Thus Present Value of $2,600 every six months over the subsequent eight years(7-14) at (t=6yrs)
= (2600/.05)(1-1/(1.05)16)
= 28178.20 discount this back through 12 periods(6yrs) at 10% semiannually to arrive at present value at t=0.
Thus Present Value of $2,600 every six months over the subsequent eight years(7-14) at (t=0 yrs)
=28178.20 /(1.05)12 =15690.676
Similarly, Present Value of $2,900 every six months over the subsequent six years(15-20) at( t=14 yrs)
=(2c/y)(1-1/(1+y/2)2T)+FV/(1+y/2)2T, here y=.1,FV=50000,T=6, c=2900
= (2900/.05)(1-1/(1.05)12)+50000/(1.05)12
= (2900/.05)(1-1/(1.05)12)+50000/(1.05)12
=25703.43 +27841.87 =53545.3
Present Value of $2,900 every six months over the subsequent six years(15-20) at( t=0yrs)
=53545.3/(1.05)28 (discounting back value at t=14 yrs over 14 years semiannually to get present value at t=0)
= 13659.07
Thus price of M= Thus Present Value of $2,600 every six months over the subsequent eight years(7-14) at (t=0 yrs)+Present Value of $2,900 every six months over the subsequent six years(15-20) at( t=0yrs) = 15690.676+ 13659.07= 29349.75
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