Las Paletas Corporation has two different bonds currently outstanding. Bond M ha
ID: 2810257 • Letter: L
Question
Las Paletas 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 $1,300 every six months over the subsequent eight years, and finally pays $1,600 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 8 percent compounded semiannually. What is the current price of bond M and bond N? (Round your answers to 2 decimal places. (e.g., 32.16) Current price Bond M 29834.76 $ 4165.79 Bond NExplanation / Answer
NOTE: As the price of Bond N has been correctly determined the solution for the same is not being provided. The solution provided is only for Bond M
The pricing for Bond M is based on the concept that the current fair value or current price of any financial asset is equal to the total present value of the asset's expected future cash flows discounted at the asset investor's required rate of return.
Bond M has a required return rate of 8 % thereby making this rate the bond cash flow's discounting rate.
The bond has a maturity of 20 years and it does not pay any coupon between Year 0 (current time) to Year 6. The first coupon of $ 1300 comes in at the end of 6 years and 6 months and continues till the end of Year 14 on a semi-annual basis. This is followed by semi-annual coupons of $ 1600 beginning from at the end of 14 years and 6 months and continues till the end of Year 20. Further, the bond also redeems its face value of $ 20000 at the end of Year 20. The total present value of all these cash flows will be equal to the bond's current price.
Applicable discount rate = 0.5 x 8 = 4 % (as compounding is done semi-annually)
PV (at t=0) of first series of coupon payments = 1300 x (1/0.04) x [1-{1/(1.04)^(16)}] x 1/(1.04)^(12) = $ 9461.386 approximately. (where 16 is the number of half-years equivalent to 8 years)
PV (at t=0) of second series of coupon payments = 1600 x (1/0.04) x [1-{1/(1.04)^(12)}] x 1/(1.04)^(28) = $ 5007.537 approximately.
PV (at t=0) of bond face value redeemed = 20000 / (1.04)^(40) = $ 4165.781 approximately.
Current Bond Price = PV of first coupon series payments + PV of second coupon series payments + PV of Bond Face Value = 9461.386 + 5007.537 + 4165.781 = $ 18634.70 approximately.
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